Response of Non-Linear Systems to Renewal Impulses by Path Integration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Iwankiewicz, R.
The cell-to-cell mapping (path integration) technique has been devised for MDOF non-linear and non-hysteretic systems subjected to random trains of impulses driven by an ordinary renewal point process with gamma-distributed integer parameter interarrival times (an Erlang process). Since the renewal...... additional discrete-valued state variables for which the stochastic equations are also formulated....
Smoothing of Piecewise Linear Paths
Directory of Open Access Journals (Sweden)
Michel Waringo
2008-11-01
Full Text Available We present an anytime-capable fast deterministic greedy algorithm for smoothing piecewise linear paths consisting of connected linear segments. With this method, path points with only a small influence on path geometry (i.e. aligned or nearly aligned points are successively removed. Due to the removal of less important path points, the computational and memory requirements of the paths are reduced and traversing the path is accelerated. Our algorithm can be used in many different applications, e.g. sweeping, path finding, programming-by-demonstration in a virtual environment, or 6D CNC milling. The algorithm handles points with positional and orientational coordinates of arbitrary dimension.
Path Integrals and Hamiltonians
Baaquie, Belal E.
2014-03-01
1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.
Discrete Coherent State Path Integrals
Marchioro, Thomas L., II
1990-01-01
The quantum theory provides a fundamental understanding of the physical world; however, as the number of degrees of freedom rises, the information required to specify quantum wavefunctions grows geometrically. Because basis set expansions mirror this geometric growth, a strict practical limit on quantum mechanics as a numerical tool arises, specifically, three degrees of freedom or fewer. Recent progress has been made utilizing Feynman's Path Integral formalism to bypass this geometric growth and instead calculate time -dependent correlation functions directly. The solution of the Schrodinger equation is converted into a large dimensional (formally infinite) integration, which can then be attacked with Monte Carlo techniques. To date, work in this area has concentrated on developing sophisticated mathematical algorithms for evaluating the highly oscillatory integrands occurring in Feynman Path Integrals. In an alternative approach, this work demonstrates two formulations of quantum dynamics for which the number of mathematical operations does not scale geometrically. Both methods utilize the Coherent State basis of quantum mechanics. First, a localized coherent state basis set expansion and an approximate short time propagator are developed. Iterations of the short time propagator lead to the full quantum dynamics if the coherent state basis is sufficiently dense along the classical phase space path of the system. Second, the coherent state path integral is examined in detail. For a common class of Hamiltonians, H = p^2/2 + V( x) the path integral is reformulated from a phase space-like expression into one depending on (q,dot q). It is demonstrated that this new path integral expression contains localized damping terms which can serve as a statistical weight for Monte Carlo evaluation of the integral--a process which scales approximately linearly with the number of degrees of freedom. Corrections to the traditional coherent state path integral, inspired by a
A SCALED CENTRAL PATH FOR LINEAR PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Ya-xiang Yuan
2001-01-01
Interior point methods are very efficient methods for solving large scale linear programming problems. The central path plays a very important role in interior point methods. In this paper we propose a new central path, which scales the variables. Thus it has the advantage of forcing the path to have roughly the same distance from each active constraint boundary near the solution.
Propagators and path integrals
Energy Technology Data Exchange (ETDEWEB)
Holten, J.W. van
1995-08-22
Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role of world-line reparametrization invariance of the classical action and the implementation of the corresponding BRST-symmetry in the quantum theory are discussed. The presence of classical world-line supersymmetry is shown to lead to an unwanted doubling of states for massive spin-1/2 particles. The origin of this phenomenon is traced to a `hidden` topological fermionic excitation. A different formulation of the pseudo-classical mechanics using a bosonic representation of {gamma}{sub 5} is shown to remove these extra states at the expense of losing manifest supersymmetry. (orig.).
Path integrals for awkward actions
Amdahl, David
2016-01-01
Time derivatives of scalar fields occur quadratically in textbook actions. A simple Legendre transformation turns the lagrangian into a hamiltonian that is quadratic in the momenta. The path integral over the momenta is gaussian. Mean values of operators are euclidian path integrals of their classical counterparts with positive weight functions. Monte Carlo simulations can estimate such mean values. This familiar framework falls apart when the time derivatives do not occur quadratically. The Legendre transformation becomes difficult or so intractable that one can't find the hamiltonian. Even if one finds the hamiltonian, it usually is so complicated that one can't path-integrate over the momenta and get a euclidian path integral with a positive weight function. Monte Carlo simulations don't work when the weight function assumes negative or complex values. This paper solves both problems. It shows how to make path integrals without knowing the hamiltonian. It also shows how to estimate complex path integrals b...
Energy Technology Data Exchange (ETDEWEB)
Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Štrajn, R. [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy)
2016-04-29
The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw. - Highlights: • The definition of the path integral in Snyder space is discussed using phase space methods. • The same result is obtained in the first-order formalism of Faddeev and Jackiw. • The path integral formulation of the two-dimensional Snyder harmonic oscillator is outlined.
Path Integrals in Quantum Physics
Rosenfelder, R
2012-01-01
These lectures aim at giving graduate students an introduction to and a working knowledge of path integral methods in a wide variety of fields in physics. Consequently, the lecture notes are organized in three main parts dealing with non-relativistic quantum mechanics, many-body physics and field theory. In the first part the basic concepts of path integrals are developed in the usual heuristic, non-mathematical way followed by standard examples and special applications including numerical evaluation of (euclidean) path integrals by Monte-Carlo methods with a program for the anharmonic oscillator. The second part deals with the application of path integrals in statistical mechanics and many-body problems treating the polaron problem, dissipative quantum systems, path integrals over ordinary and Grassmannian coherent states and perturbation theory for both bosons and fermions. Again a simple Fortran program is included for illustrating the use of strong-coupling methods. Finally, in the third part path integra...
Dressed coordinates: The path-integral approach
Casana, R.; Flores-Hidalgo, G.; Pimentel, B. M.
2007-02-01
The recently introduced dressed coordinates are studied in the path-integral approach. These coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path-integral functional measure. The analysis also generalizes the sum rules established in a previous work.
Path Integration in Conical Space
Inomata, Akira; Junker, Georg
2011-01-01
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of ...
Equivariant Localization of Path Integrals
Szabo, Richard J.
1996-01-01
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing the relations with integrable and topological quantum field theories. Beginning with a detailed review of the relevant mathematical background -- equivariant cohomology and the Duistermaat-Heckman theorem, we demonstrate how the localization ideas are relat...
Path integrals and quantum processes
Swanson, Marc S
1992-01-01
In a clearly written and systematic presentation, Path Integrals and Quantum Processes covers all concepts necessary to understand the path integral approach to calculating transition elements, partition functions, and source functionals. The book, which assumes only a familiarity with quantum mechanics, is ideal for use as a supplemental textbook in quantum mechanics and quantum field theory courses. Graduate and post-graduate students who are unfamiliar with the path integral will also benefit from this contemporary text. Exercise sets are interspersed throughout the text to facilitate self-
Scattering theory with path integrals
Energy Technology Data Exchange (ETDEWEB)
Rosenfelder, R. [Particle Theory Group, Paul Scherrer Institute, CH-5232 Villigen PSI (Switzerland)
2014-03-15
Starting from well-known expressions for the T-matrix and its derivative in standard nonrelativistic potential scattering, I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.
Scattering Theory with Path Integrals
Rosenfelder, R
2013-01-01
Starting from well-known expressions for the $T$-matrix and its derivative in standard nonrelativistic potential scattering I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.
Path Integrals in Quantum Physics
2012-01-01
These lectures aim at giving graduate students an introduction to and a working knowledge of path integral methods in a wide variety of fields in physics. Consequently, the lecture notes are organized in three main parts dealing with non-relativistic quantum mechanics, many-body physics and field theory. In the first part the basic concepts of path integrals are developed in the usual heuristic, non-mathematical way followed by standard examples and special applications including numerical ev...
Spin Observables and Path Integrals
López, J A
2000-01-01
We discuss the formulation of spin observables associated to a non-relativistic spinning particles in terms of grassmanian differential operators. We use as configuration space variables for the pseudo-classical description of this system the positions $x$ and a Grassmanian vector quantum amplitudes as path integrals in this superspace. We compute the quantum action necessary for this description including an explicit expression for the boundary terms. Finally we shown how for simple examples, the path integral may be performed in the semi-classical approximation, leading to the correct quantum propagator.
Path integral for inflationary perturbations
Prokopec, T.; Rigopoulos, G.
2010-01-01
The quantum theory of cosmological perturbations in single-field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well-known gauge-invariant quadratic action for scalar and tensor perturbations, and
Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J
2006-11-01
The Feynman-Kleinert Linearized Path Integral (FK-LPI) representation of quantum correlation functions is extended in applications and algorithms. Diffusion including quantum effects for a flexible simple point charge model of liquid water is explored, including new tests of internal consistency. An ab initio quantum correction factor (QCF) is also obtained to correct the far-infrared spectrum of water. After correction, a spectrum based on a classical simulation is in good agreement with the experiment. The FK-LPI QCF is shown to be superior to the so-called harmonic QCF. New computational algorithms are introduced so that the quantum Boltzmann Wigner phase-space density, the central object in the implementation, can be obtained for arbitrary potentials. One scheme requires only that the standard classical force routine be replaced when turning from one molecular problem to another. The new algorithms are applied to the calculation of the Van Hove spectrum of liquid He(4) at 27 K. The spectrum moments are in very good agreement with the experiment. These observations indicate that the FK-LPI approach can be broadly effective for molecular problems involving the dynamics of light nuclei.
Carr, Joseph
1996-01-01
The linear IC market is large and growing, as is the demand for well trained technicians and engineers who understand how these devices work and how to apply them. Linear Integrated Circuits provides in-depth coverage of the devices and their operation, but not at the expense of practical applications in which linear devices figure prominently. This book is written for a wide readership from FE and first degree students, to hobbyists and professionals.Chapter 1 offers a general introduction that will provide students with the foundations of linear IC technology. From chapter 2 onwa
Integrated assignment and path planning
Murphey, Robert A.
2005-11-01
A surge of interest in unmanned systems has exposed many new and challenging research problems across many fields of engineering and mathematics. These systems have the potential of transforming our society by replacing dangerous and dirty jobs with networks of moving machines. This vision is fundamentally separate from the modern view of robotics in that sophisticated behavior is realizable not by increasing individual vehicle complexity, but instead through collaborative teaming that relies on collective perception, abstraction, decision making, and manipulation. Obvious examples where collective robotics will make an impact include planetary exploration, space structure assembly, remote and undersea mining, hazardous material handling and clean-up, and search and rescue. Nonetheless, the phenomenon driving this technology trend is the increasing reliance of the US military on unmanned vehicles, specifically, aircraft. Only a few years ago, following years of resistance to the use of unmanned systems, the military and civilian leadership in the United States reversed itself and have recently demonstrated surprisingly broad acceptance of increasingly pervasive use of unmanned platforms in defense surveillance, and even attack. However, as rapidly as unmanned systems have gained acceptance, the defense research community has discovered the technical pitfalls that lie ahead, especially for operating collective groups of unmanned platforms. A great deal of talent and energy has been devoted to solving these technical problems, which tend to fall into two categories: resource allocation of vehicles to objectives, and path planning of vehicle trajectories. An extensive amount of research has been conducted in each direction, yet, surprisingly, very little work has considered the integrated problem of assignment and path planning. This dissertation presents a framework for studying integrated assignment and path planning and then moves on to suggest an exact
Continuous-Discrete Path Integral Filtering
Directory of Open Access Journals (Sweden)
Bhashyam Balaji
2009-08-01
Full Text Available A summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering problem is provided in this paper. The practical utility of the path integral formula is demonstrated via some nontrivial examples. Specifically, it is shown that the simplest approximation of the path integral formula for the fundamental solution of the FPKfe can be applied to solve nonlinear continuous-discrete filtering problems quite accurately. The Dirac-Feynman path integral filtering algorithm is quite simple, and is suitable for real-time implementation.
Techniques and applications of path integration
Schulman, L S
2005-01-01
A book of techniques and applications, this text defines the path integral and illustrates its uses by example. It is suitable for advanced undergraduates and graduate students in physics; its sole prerequisite is a first course in quantum mechanics. For applications requiring specialized knowledge, the author supplies background material.The first part of the book develops the techniques of path integration. Topics include probability amplitudes for paths and the correspondence limit for the path integral; vector potentials; the Ito integral and gauge transformations; free particle and quadra
On stability of switched linear systems with perturbed switching paths
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper addresses the stability issue of switched linear systems with perturbed switching paths. First,by introducing thenotions of child-path and parent-path, we are able to define the distance between two switching paths by means of their switching matrices chains. Next, we present the nice properties of the defined distance. Then, a stability criterion is presented for a class of switched linear systems with perturbed switching paths. Finally, an illustrative example is presented to verify the effectiveness of the approach.
Critical Review of Path Integral Formulation
Fujita, Takehisa
2008-01-01
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path integral expression cannot be connected to the dynamics of classical mechanics, even though, superficially, there is some similarity between them. Further, the field theory path integral in terms of many dimensional integrations over fields does not correspond to the field quantization. We clarify the essential difference between Feynman's original formulation of path integral in QED and the modern version of the path integral method prevailing in lattice field theory calculations, and show that the former can make a correct second quantization while the latter cannot quantize fields at all and its physical meaning is unknown.
White Noise Path Integrals in Stochastic Neurodynamics
Carpio-Bernido, M. Victoria; Bernido, Christopher C.
2008-06-01
The white noise path integral approach is used in stochastic modeling of neural activity, where the primary dynamical variables are the relative membrane potentials, while information on transmembrane ionic currents is contained in the drift coefficient. The white noise path integral allows a natural framework and can be evaluated explicitly to yield a closed form for the conditional probability density.
Path integration and the neural basis of the 'cognitive map'.
McNaughton, B.L.; Battaglia, F.P.; Jensen, O.; Moser, E.I.; Moser, M.B
2006-01-01
The hippocampal formation can encode relative spatial location, without reference to external cues, by the integration of linear and angular self-motion (path integration). Theoretical studies, in conjunction with recent empirical discoveries, suggest that the medial entorhinal cortex (MEC) might pe
Langevin equation path integral ground state.
Constable, Steve; Schmidt, Matthew; Ing, Christopher; Zeng, Tao; Roy, Pierre-Nicholas
2013-08-15
We propose a Langevin equation path integral ground state (LePIGS) approach for the calculation of ground state (zero temperature) properties of molecular systems. The approach is based on a modification of the finite temperature path integral Langevin equation (PILE) method (J. Chem. Phys. 2010, 133, 124104) to the case of open Feynman paths. Such open paths are necessary for a ground state formulation. We illustrate the applicability of the method using model systems and the weakly bound water-parahydrogen dimer. We show that the method can lead to converged zero point energies and structural properties.
Feynman Path Integrals Over Entangled States
Green, A G; Keeling, J; Simon, S H
2016-01-01
The saddle points of a conventional Feynman path integral are not entangled, since they comprise a sequence of classical field configurations. We combine insights from field theory and tensor networks by constructing a Feynman path integral over a sequence of matrix product states. The paths that dominate this path integral include some degree of entanglement. This new feature allows several insights and applications: i. A Ginzburg-Landau description of deconfined phase transitions. ii. The emergence of new classical collective variables in states that are not adiabatically continuous with product states. iii. Features that are captured in product-state field theories by proliferation of instantons are encoded in perturbative fluctuations about entangled saddles. We develop a general formalism for such path integrals and a couple of simple examples to illustrate their utility.
Master equations and the theory of stochastic path integrals
Weber, Markus F
2016-01-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on methods that are applicable even when stochastic fluctuations are strong. The reviewed methods include the generating function technique and the Poisson representation, as well as novel ways of mapping the forward and backward master equations onto linear partial differential equations (PDEs). Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE obeyed by the generating function. After outlining these methods, we solve the derived PDEs in terms of two path integrals. The path integrals provide distinct exact representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Furthermore, we review a method for the approxima...
Path integral representations on the complex sphere
Energy Technology Data Exchange (ETDEWEB)
Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2007-08-15
In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S{sub 3C}. The Schroedinger equation, respectively the path integral, separates in exactly 21 orthogonal coordinate systems. We enumerate these coordinate systems and we are able to present the path integral representations explicitly in the majority of the cases. In each solution the expansion into the wave-functions is stated. Also, the kernel and the corresponding Green function can be stated in closed form in terms of the invariant distance on the sphere, respectively on the hyperboloid. (orig.)
Path Integral Approach to Atomic Collisions
Harris, Allison
2016-09-01
The Path Integral technique is an alternative formulation of quantum mechanics that is based on a Lagrangian approach. In its exact form, it is completely equivalent to the Hamiltonian-based Schrödinger equation approach. Developed by Feynman in the 1940's, following inspiration from Dirac, the path integral approach has been widely used in high energy physics, quantum field theory, and statistical mechanics. However, only in limited cases has the path integral approach been applied to quantum mechanical few-body scattering. We present a theoretical and computational development of the path integral method for use in the study of atomic collisions. Preliminary results are presented for some simple systems. Ultimately, this approach will be applied to few-body ion-atom collisions. Work supported by NSF grant PHY-1505217.
Path integration in relativistic quantum mechanics
Redmount, I H; Redmount, Ian H.; Suen, Wai-Mo
1993-01-01
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.
Anomalous paths in quantum mechanical path-integrals
Energy Technology Data Exchange (ETDEWEB)
Grimsmo, Arne L., E-mail: arne.grimsmo@ntnu.no [Department of Physics, The Norwegian University of Science and Technology, N-7491 Trondheim (Norway); Department of Physics, The University of Auckland, Private Bag 92019, Auckland (New Zealand); Klauder, John R., E-mail: klauder@phys.ufl.edu [Departments of Physics and Mathematics, University of Florida, Gainesville, FL 32611 (United States); Skagerstam, Bo-Sture K., E-mail: bo-sture.skagerstam@ntnu.no [Department of Physics, The Norwegian University of Science and Technology, N-7491 Trondheim (Norway); Kavli Institute for Theoretical Physics, Kohn Hall, University of California at Santa Barbara, CA 93106-4030 (United States); CREOL, The College of Optics and Photonics at the University of Central Florida, 4000 Central Florida Boulevard, Orlando, FL 32816 (United States)
2013-11-25
We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the naïve continuum limit but which, nevertheless, induce non-trivial effects due to quantum fluctuations. These effects are seen to modify the geometry of the paths contributing to the path-integral describing the time evolution of the particle, which we investigate through numerical simulations. In particular, we demonstrate the existence of a modified lattice action resulting in paths with any fractal dimension, d{sub f}, between one and two. We argue that d{sub f}=2 is a critical value, and we exhibit a type of lattice modification where the fluctuations in the position of the particle becomes independent of the time step, in which case the paths are interpreted as superdiffusive Lévy flights. We also consider the jaggedness of the paths, and show that this gives an independent classification of lattice theories.
Local-time representation of path integrals.
Jizba, Petr; Zatloukal, Václav
2015-12-01
We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time profiles. The latter quantify the time that the sample paths x(t) in the Feynman path integral spend in the vicinity of an arbitrary point x. Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed.
Analytic central path, sensitivity analysis and parametric linear programming
A.G. Holder; J.F. Sturm; S. Zhang (Shuzhong)
1998-01-01
textabstractIn this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face
Path integral distance for data interpretation
Volchenkov, D
2015-01-01
The process of data interpretation is always based on the implicit introduction of equivalence relations on the set of walks over the database. Every equivalence relation on the set of walks specifies a Markov chain describing the transitions of a discrete time random walk. In order to geometrize and interpret the data, we propose the new distance between data units defined as a "Feynman path integral", in which all possible paths between any two nodes in a graph model of the data are taken into account, although some paths are more preferable than others. Such a path integral distance approach to the analysis of databases has proven its efficiency and success, especially on multivariate strongly correlated data where other methods fail to detect structural components (urban planning, historical language phylogenies, music, street fashion traits analysis, etc. ). We believe that it would become an invaluable tool for the intelligent complexity reduction and big data interpretation.
Noncommutative integrability, paths and quasi-determinants
Di Francesco, Philippe
2010-01-01
In previous work, we showed that the solution of certain systems of discrete integrable equations, notably $Q$ and $T$-systems, is given in terms of partition functions of positively weighted paths, thereby proving the positive Laurent phenomenon of Fomin and Zelevinsky for these cases. This method of solution is amenable to generalization to non-commutative weighted paths. Under certain circumstances, these describe solutions of discrete evolution equations in non-commutative variables: Examples are the corresponding quantum cluster algebras [BZ], the Kontsevich evolution [DFK09b] and the $T$-systems themselves [DFK09a]. In this paper, we formulate certain non-commutative integrable evolutions by considering paths with non-commutative weights, together with an evolution of the weights that reduces to cluster algebra mutations in the commutative limit. The general weights are expressed as Laurent monomials of quasi-determinants of path partition functions, allowing for a non-commutative version of the positiv...
Path Integral Techniques in Conformal Field Theory
Van Tonder, A J
2004-01-01
We present the theory of a two-dimensional conformal scalar field using path integral techniques. We derive the conformal anomaly using an adaptation of the method of Fujikawa, and compare the result with a derivation based on a Pauli-Villars measure, where the anomaly is shifted from the path integral measure to the energy-momentum trace. In the path integral approach the energy-momentum is a true coordinate-invariant tensor quantity, and we explain how it is related to the corresponding non-tensor object arising in the operator approach, obtaining an intuitive explanation within the context of the path integral approach for the anomalous transformation law and anomalous Ward identities of the latter. After carefully calculating nontrivial contact terms arising in certain energy-momentum products, we use these to provide a simple consistency check confirming the change of variables formula for the path integral and to review the relationship between the conformal anomaly and the energy-momentum two-point fun...
Analytic central path, sensitivity analysis and parametric linear programming
A.G. Holder; Sturm, J.F.; Zhang, Shuzhong
1998-01-01
textabstractIn this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face is one-side differentiable with respect to the perturbation parameter. In that case we also show that the whole analytic central path shifts in a uniform fashion. When the objective vector is pertur...
Classical and quantum dynamics from classical paths to path integrals
Dittrich, Walter
2016-01-01
Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name a few. Well-chosen and detailed examples illustrate the perturbation theory, canonical transformations, the action principle and demonstrate the usage of path integrals. This new edition has been revised and enlarged with chapters on quantum electrodynamics, high energy physics, Green’s functions and strong interaction.
Field theory a path integral approach
Das, Ashok
2006-01-01
This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.
Modeling DNA Dynamics by Path Integrals
Zoli, Marco
2013-01-01
Complementary strands in DNA double helix show temporary fluctuational openings which are essential to biological functions such as transcription and replication of the genetic information. Such large amplitude fluctuations, known as the breathing of DNA, are generally localized and, microscopically, are due to the breaking of the hydrogen bonds linking the base pairs (\\emph{bps}). I apply imaginary time path integral techniques to a mesoscopic Hamiltonian which accounts for the helicoidal geometry of a short circular DNA molecule. The \\emph{bps} displacements with respect to the ground state are interpreted as time dependent paths whose amplitudes are consistent with the model potential for the hydrogen bonds. The portion of the paths configuration space contributing to the partition function is determined by selecting the ensemble of paths which fulfill the second law of thermodynamics. Computations of the thermodynamics in the denaturation range show the energetic advantage for the equilibrium helicoidal g...
Current Algebra in the Path Integral framework
Cardenas, V H; Saavedra, J
1998-01-01
In this letter we describe an approach to the current algebra based in the Path Integral formalism. We use this method for abelian and non-abelian quantum field theories in 1+1 and 2+1 dimensions and the correct expressions are obtained. Our results show the independence of the regularization of the current algebras.
Bead-Fourier path integral molecular dynamics
Ivanov, Sergei D.; Lyubartsev, Alexander P.; Laaksonen, Aatto
2003-06-01
Molecular dynamics formulation of Bead-Fourier path integral method for simulation of quantum systems at finite temperatures is presented. Within this scheme, both the bead coordinates and Fourier coefficients, defining the path representing the quantum particle, are treated as generalized coordinates with corresponding generalized momenta and masses. Introduction of the Fourier harmonics together with the center-of-mass thermostating scheme is shown to remove the ergodicity problem, known to pose serious difficulties in standard path integral molecular dynamics simulations. The method is tested for quantum harmonic oscillator and hydrogen atom (Coulombic potential). The simulation results are compared with the exact analytical solutions available for both these systems. Convergence of the results with respect to the number of beads and Fourier harmonics is analyzed. It was shown that addition of a few Fourier harmonics already improves the simulation results substantially, even for a relatively small number of beads. The proposed Bead-Fourier path integral molecular dynamics is a reliable and efficient alternative to simulations of quantum systems.
Path integration in tactile perception of shapes.
Moscatelli, Alessandro; Naceri, Abdeldjallil; Ernst, Marc O
2014-11-01
Whenever we move the hand across a surface, tactile signals provide information about the relative velocity between the skin and the surface. If the system were able to integrate the tactile velocity information over time, cutaneous touch may provide an estimate of the relative displacement between the hand and the surface. Here, we asked whether humans are able to form a reliable representation of the motion path from tactile cues only, integrating motion information over time. In order to address this issue, we conducted three experiments using tactile motion and asked participants (1) to estimate the length of a simulated triangle, (2) to reproduce the shape of a simulated triangular path, and (3) to estimate the angle between two-line segments. Participants were able to accurately indicate the length of the path, whereas the perceived direction was affected by a direction bias (inward bias). The response pattern was thus qualitatively similar to the ones reported in classical path integration studies involving locomotion. However, we explain the directional biases as the result of a tactile motion aftereffect.
Path Integral Bosonization of Massive GNO Fermions
Park, Q H
1997-01-01
We show the quantum equivalence between certain symmetric space sine-Gordon models and the massive free fermions. In the massless limit, these fermions reduce to the free fermions introduced by Goddard, Nahm and Olive (GNO) in association with symmetric spaces $K/G$. A path integral formulation is given in terms of the Wess-Zumino-Witten action where the field variable $g$ takes value in the orthogonal, unitary, and symplectic representations of the group $G$ in the basis of the symmetric space. We show that, for example, such a path integral bosonization is possible when the symmetric spaces $K/G$ are $SU(N) the relation between massive GNO fermions and the nonabelian solitons, and explain the restriction imposed on the fermion mass matrix due to the integrability of the bosonic model.
Computing Resolution-Path Dependencies in Linear Time
Slivovsky, Friedrich
2012-01-01
The alternation of existential and universal quantifiers in a quantified boolean formula (QBF) generates dependencies among variables that must be respected when evaluating the formula. Dependency schemes provide a general framework for representing such dependencies. Since it is generally intractable to determine dependencies exactly, a set of potential dependencies is computed instead, which may include false positives. Among the schemes proposed so far, resolution-path dependencies introduce the fewest spurious dependencies. In this work, we describe an algorithm that detects resolution-path dependencies in linear time, resolving a problem posed by Van Gelder (CP 2011)
Classical and quantum dynamics from classical paths to path integrals
Dittrich, Walter
2017-01-01
Graduate students who wish to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals. The fifth edition has been revised and enlarged to include chapters on quantum electrodynamics, in particular, Schwinger’s proper time method and the treatment of classical and quantum mechanics with Lie brackets and pseudocanonical transformations. It is shown that operator quantum electrodynamics can be equivalently described with c-numbers, as demonstrated by calculating the propagation function for an electron in a prescribed classical electromagnetic field.
Path integrals and symmetry breaking for optimal control theory
Kappen, H J
2005-01-01
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar to the transformation used to relate the classical Hamilton-Jacobi equation to the Schr\\"odinger equation. As a result of the linearity, the usual backward computation can be replaced by a forward diffusion process, that can be computed by stochastic integration or by the evaluation of a path integral. It is shown, how in the deterministic limit the PMP formalism is recovered. The significance of the path integral approach is that it forms the basis for a number of efficient computational methods, such as MC sampling, the Laplace approximation and the variational approximation. We show the effectiveness of the first two methods in number of examples. Examples are given that show the qualitative difference between stochastic and d...
Path integral quantization of parametrised field theory
Varadarajan, M
2004-01-01
Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrised field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary, in general curved, foliations of the flat spacetime. We construct the path integral quantization of parametrised field theory in order to analyse issues at the interface of quantum field theory and general covariance in a path integral context. We show that the measure in the Lorentzian path integral is non-trivial and is the analog of the Fradkin- Vilkovisky measure for quantum gravity. We construct Euclidean functional integrals in the generally covariant setting of parametrised field theory using key ideas of Schleich and show that our constructions imply the existence of non-standard `Wick rotations' of the standard free scalar field 2 point function. We develop a framework to study the problem of time through computations of scalar field 2 point functions. We illustra...
Quantum gravitation the Feynman path integral approach
Hamber, Herbert W
2009-01-01
The book covers the theory of Quantum Gravitation from the point of view of Feynman path integrals. These provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. The path integral method is suitable for both perturbative as well as non-perturbative studies, and is known to already provide a framework of choice for the theoretical investigation of non-abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The ren...
An alternative path integral for quantum gravity
Krishnan, Chethan; Kumar, K. V. Pavan; Raju, Avinash
2016-10-01
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This "Neumann ensemble" perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
An Alternate Path Integral for Quantum Gravity
Krishnan, Chethan; Raju, Avinash
2016-01-01
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in $D$ dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This "Neumann ensemble" perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
An alternative path integral for quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Krishnan, Chethan; Kumar, K.V. Pavan; Raju, Avinash [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)
2016-10-10
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This “Neumann ensemble” perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
Path integral measure for gravitational interactions
Directory of Open Access Journals (Sweden)
Kazuo Fujikawa
1983-10-01
Full Text Available It is pointed out that the path-integral variables as well as the local measure for gravitational interactions are uniquely specified if one imposes the anomaly-free condition on the Becchi-Rouet-Stora supersymmetry associated with general coordinate transformations. This prescription is briefly illustrated for the Einstein gravity and supergravity in four space-time dimensions and the relativistic string theory in two dimensions.
A Path Integral Approach To Noncommutative Superspace
Chepelev, I; Chepelev, Iouri; Ciocarlie, Calin
2003-01-01
A path integral formula for the associative star-product of two superfields is proposed. It is a generalization of the Kontsevich-Cattaneo-Felder's formula for the star-product of functions of bosonic coordinates. The associativity of the star-product imposes certain conditions on the background of our sigma model. For generic background the action is not supersymmetric. The supersymmetry invariance of the action constrains the background and leads to a simple formula for the star-product.
Regularization Paths for Generalized Linear Models via Coordinate Descent
Directory of Open Access Journals (Sweden)
Jerome Friedman
2010-02-01
Full Text Available We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, two-class logistic regression, and multi- nomial regression problems while the penalties include ℓ1 (the lasso, ℓ2 (ridge regression and mixtures of the two (the elastic net. The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.
Master equations and the theory of stochastic path integrals.
Weber, Markus F; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon
Master equations and the theory of stochastic path integrals
Weber, Markus F.; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from
Path integrals for dimerized quantum spin systems
Energy Technology Data Exchange (ETDEWEB)
Foussats, Adriana, E-mail: afoussats@gmail.co [Facultad de Ciencias Exactas, Ingenieria y Agrimensura and Instituto de Fisica Rosario (UNR-CONICET), Av. Pellegrini 250, 2000 Rosario (Argentina); Greco, Andres [Facultad de Ciencias Exactas, Ingenieria y Agrimensura and Instituto de Fisica Rosario (UNR-CONICET), Av. Pellegrini 250, 2000 Rosario (Argentina); Muramatsu, Alejandro [Institut fuer Theoretische Physik III, Universitaet Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart (Germany)
2011-01-11
Dimerized quantum spin systems may appear under several circumstances, e.g. by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase transition to a Neel state as a function of a suitable coupling constant. We present here two path-integral formulations appropriate for spin S=1/2 dimerized systems. The first one deals with a description of the dimers degrees of freedom in an SO(4) manifold, while the second one provides a path-integral for the bond-operators introduced by Sachdev and Bhatt. The path-integral quantization is performed using the Faddeev-Jackiw symplectic formalism for constrained systems, such that the measures and constraints that result from the algebra of the operators is provided in both cases. As an example we consider a spin-Peierls chain, and show how to arrive at the corresponding field-theory, starting with both an SO(4) formulation and bond-operators.
Vehicle path tracking by integrated chassis control
Institute of Scientific and Technical Information of China (English)
Saman Salehpour; Yaghoub Pourasad; Seyyed Hadi Taheri
2015-01-01
The control problem of trajectory based path following for passenger vehicles is studied. Comprehensive nonlinear vehicle model is utilized for simulation vehicle response during various maneuvers in MATLAB/Simulink. In order to follow desired path, a driver model is developed to enhance closed loop driver/vehicle model. Then, linear quadratic regulator (LQR) controller is developed which regulates direct yaw moment and corrective steering angle on wheels. Particle swam optimization (PSO) method is utilized to optimize the LQR controller for various dynamic conditions. Simulation results indicate that, over various maneuvers, side slip angle and lateral acceleration can be reduced by 10%and 15%, respectively, which sustain the vehicle stable. Also, anti-lock brake system is designed for longitudinal dynamics of vehicle to achieve desired slip during braking and accelerating. Proposed comprehensive controller demonstrates that vehicle steerability can increase by about 15% during severe braking by preventing wheel from locking and reducing stopping distance.
Purely geometric path integral for spin foams
Shirazi, Atousa Chaharsough
2013-01-01
Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for a path integral to be at least formally equivalent to the corresponding canonical quantization, at each point in the space of histories it is important that the integrand have not only the correct phase -- a topic of recent focus in spin-foams -- but also the correct modulus, usually referred to as the measure factor. The correct measure factor descends from the Liouville measure on the reduced phase space, and its calculation is a task of canonical analysis. The covariant formulation of gravity from which spin-foams are derived is the Plebanski-Holst formulation, in which the basic variables are a Lorentz connection and a Lorentz-algebra valued two-form, called the Plebanski two-form. However, in the final spin-foam sum, one sums over only spins and intertwiners, which label eigenstates of the Plebanski two-form alone. The spin-foam sum is therefore a discretized version of a Plebanski-Holst path integ...
Quantum Measurement and Extended Feynman Path Integral
Institute of Scientific and Technical Information of China (English)
文伟; 白彦魁
2012-01-01
Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy, but there is still no conclusion and consensus on it. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein-Gordon equation, but also the wave-function-collapse equation. It is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the ＂potential noise＂ of the apparatus or environment and ＂inner correlation＂ of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem.
Path integral for multi-field inflation
Gong, Jinn-Ouk; Shiu, Gary
2016-01-01
We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixing conditions based on the Poisson brackets of the constraints, from which we derive two convenient gauges that are appropriate for multi-field inflation. We then adopt the in-in formalism to derive the most general expression for the power spectrum of the curvature perturbation including the corrections from the interactions of the curvature mode with other light degrees of freedom. We also discuss the contributions of the interactions to the bispectrum.
Path Integral Quantization of Generalized Quantum Electrodynamics
Bufalo, Rodrigo; Zambrano, German Enrique Ramos
2010-01-01
It is shown in this paper a complete covariant quantization of Generalized Electrodynamics by path integral approach. To this goal we first studied the hamiltonian structure of system following Dirac's methodology, and then we follow the Faddeev-Senjanovic procedure to attain the amplitude transition. The complete propagators (Schwinger-Dyson-Fradkin equations) on correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation on one-loop approximation of all Green's functions and a discussion about the obtained results are presented.
An Introduction into the Feynman Path Integral
Grosche, C
1993-01-01
In this lecture a short introduction is given into the theory of the Feynman path integral in quantum mechanics. The general formulation in Riemann spaces will be given based on the Weyl- ordering prescription, respectively product ordering prescription, in the quantum Hamiltonian. Also, the theory of space-time transformations and separation of variables will be outlined. As elementary examples I discuss the usual harmonic oscillator, the radial harmonic oscillator, and the Coulomb potential. Lecture given at the graduate college ''Quantenfeldtheorie und deren Anwendung in der Elementarteilchen- und Festk\\"orperphysik'', Universit\\"at Leipzig, 16-26 November 1992.
Boundary conditions: The path integral approach
Energy Technology Data Exchange (ETDEWEB)
Asorey, M [Departamento de Fisica Teorica, Universidad de Zaragoza 50009 Zaragoza (Spain); Clemente-Gallardo, J [BIFI, Universidad de Zaragoza, 50009 Zaragoza (Spain); Munoz-Castaneda, J M [Departamento de Fisica Teorica, Universidad de Zaragoza 50009 Zaragoza (Spain)
2007-11-15
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Nonlocal boundary conditions can be introduced in Feynman's approach by means of boundary amplitude distributions and complex phases to describe the quantum dynamics in terms of the classical trajectories. The different prescriptions involve only trajectories reaching the boundary and correspond to different choices of boundary conditions of selfadjoint extensions of the Hamiltonian. One dimensional particle dynamics is analysed in detail.
Path integral for multi-field inflation
Gong, Jinn-Ouk; Seo, Min-Seok; Shiu, Gary
2016-07-01
We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixing conditions based on the Poisson brackets of the constraints, from which we derive two convenient gauges that are appropriate for multi-field inflation. We then adopt the in-in formalism to derive the most general expression for the power spectrum of the curvature perturbation including the corrections from the interactions of the curvature mode with other light degrees of freedom. We also discuss the contributions of the interactions to the bispectrum.
High order path integrals made easy
Kapil, Venkat; Behler, Jörg; Ceriotti, Michele
2016-12-01
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the system. Many approaches have been suggested to reduce the required number of replicas. Among these, high-order factorizations of the Boltzmann operator are particularly attractive for high-precision and low-temperature scenarios. Unfortunately, to date, several technical challenges have prevented a widespread use of these approaches to study the nuclear quantum effects in condensed-phase systems. Here we introduce an inexpensive molecular dynamics scheme that overcomes these limitations, thus making it possible to exploit the improved convergence of high-order path integrals without having to sacrifice the stability, convenience, and flexibility of conventional second-order techniques. The capabilities of the method are demonstrated by simulations of liquid water and ice, as described by a neural-network potential fitted to the dispersion-corrected hybrid density functional theory calculations.
Building a cognitive map by assembling multiple path integration systems.
Wang, Ranxiao Frances
2016-06-01
Path integration and cognitive mapping are two of the most important mechanisms for navigation. Path integration is a primitive navigation system which computes a homing vector based on an animal's self-motion estimation, while cognitive map is an advanced spatial representation containing richer spatial information about the environment that is persistent and can be used to guide flexible navigation to multiple locations. Most theories of navigation conceptualize them as two distinctive, independent mechanisms, although the path integration system may provide useful information for the integration of cognitive maps. This paper demonstrates a fundamentally different scenario, where a cognitive map is constructed in three simple steps by assembling multiple path integrators and extending their basic features. The fact that a collection of path integration systems can be turned into a cognitive map suggests the possibility that cognitive maps may have evolved directly from the path integration system.
A Path Integral Approach to Inclusive Processes
Nachtmann, O
2000-01-01
The single-particle inclusive differential cross-section for a reaction$a+b\\to c+X$ is written as the imaginary part of a correlation function in afor ward scattering amplitude for $a+b\\to a+b$ in a modified effective theory.In this modified theory the interaction Hamiltonian $\\tilde H_I$ equals $H_I$in the original theory up to a certain time. Then there is a sign change and$\\tilde H_I$ becomes nonlocal. This is worked out in detail for scalar fieldmodels and for QED plus the abelian gluon model. A suitable path integral fordirect calculations of inclusive cross sections is presented.
Development Path of Urban-rural Integration
Institute of Scientific and Technical Information of China (English)
2012-01-01
The urban and rural areas are regarded as two major components of the regional economic system. Only through joint balanced development of the two can we achieve overall economic optimization and social welfare maximization. But the great social division of labor has separated urban areas from rural areas,which casts the shadow of city-oriented theory on cooperative relations between urban and rural areas. Mutual separation between urban and rural settlements and independent development trigger off a range of social problems. We must undertake guidance through rational development path of urban-rural integration,to eliminate the phenomenon of urban-rural dual structure,and promote the sustainable development of population,resources and environment in urban and rural areas as soon as possible.
Polymer quantum mechanics some examples using path integrals
Energy Technology Data Exchange (ETDEWEB)
Parra, Lorena [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F., México and Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Vergara, J. David [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F. (Mexico)
2014-01-14
In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems.
Path Integral Solution by Sum Over Perturbation Series
Lin, D H
1999-01-01
A method for calculating the relativistic path integral solution via sum over perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov-Bohm-Coulomb system is obtained by the method. Different from the earlier treatment based on the space-time transformation and infinite multiple-valued trasformation of Kustaanheimo-Stiefel in order to perform path integral, the method developed in this contribution involves only the explicit form of a simple Green's function and an explicit path integral is avoided.
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
Path Integrals and Lorentz Violation in Polymer Quantized Scalar Fields
Kajuri, Nirmalya
2014-01-01
We obtain a path integral formulation of polymer quantized scalar field theory, starting from the Hilbert Space framework. This brings the polymer quantized scalar field theory under the ambit of Feynman diagrammatic techniques. The path integral formulation also shows that Lorentz invariance is lost for the Klein-Gordon field.
Towards a Realistic Parsing of the Feynman Path Integral
Directory of Open Access Journals (Sweden)
Ken Wharton
2016-01-01
Full Text Available The Feynman path integral does not allow a one real path interpretation, because the quantum amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, all paths happen, is not a useful or informative account. In this paper it is shown that an intermediate parsing of the path integral, into realistic non-interfering possibilities, is always available. Each realistic possibility formally corresponds to numerous particle paths, but is arguably best interpreted as a spacetime-valued field. Notably, one actual field history can always be said to occur, although it will generally not have an extremized action. The most obvious concerns with this approach are addressed, indicating necessary follow-up research. But without obvious showstoppers, it seems plausible that the path integral might be reinterpreted to explain quantum phenomena in terms of Lorentz covariant field histories.Quanta 2016; 5: 1–11.
Path-integral molecular dynamics simulation of diamond
Ramírez, Rafael; Herrero, Carlos P.; Hernández, Eduardo R.
2006-06-01
Diamond is studied by path-integral molecular dynamics simulations of the atomic nuclei in combination with a tight-binding Hamiltonian to describe its electronic structure and total energy. This approach allows us to quantify the influence of quantum zero-point vibrations and finite temperatures on both the electronic and vibrational properties of diamond. The electron-phonon coupling mediated by the zero-point vibration reduces the direct electronic gap of diamond by 10%. The calculated decrease of the direct gap with temperature shows good agreement with the experimental data available up to 700K . Anharmonic vibrational frequencies of the crystal have been obtained from a linear-response approach based on the path integral formalism. In particular, the temperature dependence of the zone-center optical phonon has been derived from the simulations. The anharmonicity of the interatomic potential produces a red shift of this phonon frequency. At temperatures above 500K , this shift is overestimated in comparison to available experimental data. The predicted temperature shift of the elastic constant c44 displays reasonable agreement with the available experimental results.
Two-path plasmonic interferometer with integrated detector
Energy Technology Data Exchange (ETDEWEB)
Dyer, Gregory Conrad; Shaner, Eric A.; Aizin, Gregory
2016-03-29
An electrically tunable terahertz two-path plasmonic interferometer with an integrated detection element can down convert a terahertz field to a rectified DC signal. The integrated detector utilizes a resonant plasmonic homodyne mixing mechanism that measures the component of the plasma waves in-phase with an excitation field that functions as the local oscillator in the mixer. The plasmonic interferometer comprises two independently tuned electrical paths. The plasmonic interferometer enables a spectrometer-on-a-chip where the tuning of electrical path length plays an analogous role to that of physical path length in macroscopic Fourier transform interferometers.
Path Integrals and the WKB approximation in Loop Quantum Cosmology
Ashtekar, Abhay; Henderson, Adam
2010-01-01
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
Path integrals and the WKB approximation in loop quantum cosmology
Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam
2010-12-01
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
Accelerated nuclear quantum effects sampling with open path integrals
Mazzola, Guglielmo
2016-01-01
We numericaly demonstrate that, in double well models, the autocorrelation time of open path integral Monte Carlo simulations can be much smaller compared to standard ones using ring polymers. We also provide an intuitive explanation based on the role of instantons as transition states of the path integral pseudodynamics. Therefore we propose that, in all cases when the ground state approximation to the finite temperature partition function holds, open path integral simulations can be used to accelerate the sampling in realistic simulations aimed to explore nuclear quantum effects.
Path integrals, hyperbolic spaces and Selberg trace formulae
Grosche, Christian
2013-01-01
In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition.The volume also contains r
Looping probabilities of elastic chains: a path integral approach.
Cotta-Ramusino, Ludovica; Maddocks, John H
2010-11-01
We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end
On the path integral representation of the Wigner function and the Barker-Murray ansatz
Sels, Dries; Brosens, Fons; Magnus, Wim
2012-01-01
The propagator of the Wigner function is constructed from the Wigner-Liouville equation as a phase space path integral over a new effective Lagrangian. In contrast to a paper by Barker and Murray (1983) [1], we show that the path integral can in general not be written as a linear superposition of classical phase space trajectories over a family of non-local forces. Instead, we adopt a saddle point expansion to show that the semiclassical Wigner function is a linear superposition of classical solutions for a different set of non-local time dependent forces. As shown by a simple example the specific form of the path integral makes the formulation ideal for Monte Carlo simulation.
Ab-initio path integral techniques for molecules
Shin, D; Shumway, J; Ho, Ming-Chak; Shin, Daejin
2006-01-01
Path integral Monte Carlo with Green's function analysis allows the sampling of quantum mechanical properties of molecules at finite temperature. While a high-precision computation of the energy of the Born-Oppenheimer surface from path integral Monte Carlo is quite costly, we can extract many properties without explicitly calculating the electronic energies. We demonstrate how physically relevant quantities, such as bond-length, vibrational spectra, and polarizabilities of molecules may be sampled directly from the path integral simulation using Matsubura (temperature) Green's functions (imaginary-time correlation functions). These calculations on the hydrogen molecule are a proof-of-concept, designed to motivate new work on fixed-node path-integral calculations for molecules.
Remembered landmarks enhance the precision of path integration
Directory of Open Access Journals (Sweden)
Shannon O´Leary
2005-01-01
Full Text Available When navigating by path integration, knowledge of ones position becomes increasingly uncertain as one walks from a known location. This uncertainty decreases if one perceives a known landmark location nearby. We hypothesized that remembering landmarks might serve a similar purpose for path integration as directly perceiving them. If this is true, walking near a remembered landmark location should enhance response consistency in path integration tasks. To test this, we asked participants to view a target and then attempt to walk to it without vision. Some participants saw the target plus a landmark during the preview. Compared with no-landmark trials, response consistency nearly doubled when participants passed near the remembered landmark location. Similar results were obtained when participants could audibly perceive the landmark while walking. A control experiment ruled out perceptual context effects during the preview. We conclude that remembered landmarks can enhance path integration even though they are not directly perceived.
Variational path integral molecular dynamics study of a water molecule
Miura, Shinichi
2013-08-01
In the present study, a variational path integral molecular dynamics method developed by the author [Chem. Phys. Lett. 482, 165 (2009)] is applied to a water molecule on the adiabatic potential energy surface. The method numerically generates an exact wavefunction using a trial wavefunction of the target system. It has been shown that even if a poor trial wavefunction is employed, the exact quantum distribution is numerically extracted, demonstrating the robustness of the variational path integral method.
Characterizing regulatory path motifs in integrated networks using perturbational data
Joshi, Anagha Madhusudan; Van Parys, Thomas; de Peer, Yves Van; Michoel, Tom
2010-01-01
We introduce Pathicular http://bioinformatics.psb.ugent.be/software/details/Pathicular, a Cytoscape plugin for studying the cellular response to perturbations of transcription factors by integrating perturbational expression data with transcriptional, protein-protein and phosphorylation networks. Pathicular searches for 'regulatory path motifs', short paths in the integrated physical networks which occur significantly more often than expected between transcription factors and their targets in...
Emergent symmetry in a thermal pure state path integral
Sasa, Shin-ichi; Yokokura, Yuki
2016-01-01
We study a thermally isolated quantum many-body system with an external control represented by a time-dependent parameter. By formulating a thermal pure state path integral, we derive an effective action for trajectories in a thermodynamic state space, where the entropy appears with its conjugate variable. In particular, when operations are quasi-static, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant.
Sensory feedback in a bump attractor model of path integration.
Poll, Daniel B; Nguyen, Khanh; Kilpatrick, Zachary P
2016-04-01
Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.
The perturbative approach to path integrals: A succinct mathematical treatment
Nguyen, Timothy
2016-09-01
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal parameter irrespective of convergence properties. We establish invariance properties of such a Wick expansion under coordinate changes and the action of a Lie group of symmetries, and we use this to study essential features of path integral manipulations, including coordinate changes, Ward identities, Schwinger-Dyson equations, Faddeev-Popov gauge-fixing, and eliminating fields by their equation of motion. We also discuss the asymptotic nature of the Wick expansion and the implications this has for defining path integrals perturbatively and nonperturbatively.
Medial temporal lobe roles in human path integration.
Directory of Open Access Journals (Sweden)
Naohide Yamamoto
Full Text Available Path integration is a process in which observers derive their location by integrating self-motion signals along their locomotion trajectory. Although the medial temporal lobe (MTL is thought to take part in path integration, the scope of its role for path integration remains unclear. To address this issue, we administered a variety of tasks involving path integration and other related processes to a group of neurosurgical patients whose MTL was unilaterally resected as therapy for epilepsy. These patients were unimpaired relative to neurologically intact controls in many tasks that required integration of various kinds of sensory self-motion information. However, the same patients (especially those who had lesions in the right hemisphere walked farther than the controls when attempting to walk without vision to a previewed target. Importantly, this task was unique in our test battery in that it allowed participants to form a mental representation of the target location and anticipate their upcoming walking trajectory before they began moving. Thus, these results put forth a new idea that the role of MTL structures for human path integration may stem from their participation in predicting the consequences of one's locomotor actions. The strengths of this new theoretical viewpoint are discussed.
Lecture notes in topics in path integrals and string representations
Botelho, Luiz C L
2017-01-01
Functional Integrals is a well-established method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and string theory. This book presents a unique, original and modern treatment of strings representations on Bosonic Quantum Chromodynamics and Bosonization theory on 2d Gauge Field Models, besides of rigorous mathematical studies on the analytical regularization scheme on Euclidean quantum field path integrals and stochastic quantum field theory. It follows an analytic approach based on Loop space techniques, functional determinant exact evaluations and exactly solubility of four dimensional QCD loop wave equations through Elfin Botelho fermionic extrinsic self avoiding string path integrals.
INTEGRATED LAYOUT DESIGN OF CELLS AND FLOW PATHS
Institute of Scientific and Technical Information of China (English)
Li Zhihua; Zhong Yifang; Zhou Ji
2003-01-01
The integrated layout problem in manufacturing systems is investigated. An integrated model for concurrent layout design of cells and flow paths is formulated. A hybrid approach combined an enhanced branch-and-bound algorithm with a simulated annealing scheme is proposed to solve this problem. The integrated layout method is applied to re-layout the gear pump shop of a medium-size manufacturer of hydraulic pieces. Results show that the proposed layout method can concurrently provide good solutions of the cell layouts and the flow path layouts.
Mielke, Steven L; Truhlar, Donald G
2016-01-21
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.
The quantum bouncer by the path integral method
Goodings, D. A.; Szeredi, T.
1991-10-01
The path integral formulation of quantum mechanics in the semiclassical or WKB approximation provides a physically intuitive way of relating a classical system to its quantum analog. A fruitful way of studying quantum chaos is based upon applying the Gutzwiller periodic orbit sum rule, a result derived by the path integral method in the WKB approximation. This provides some motivation for learning about path integral techniques. In this paper a pedagogical example of the path integral formalism is presented in the hope of conveying the basic physical and mathematical concepts. The ``quantum bouncer'' is studied—the quantum version of a particle moving in one dimension above a perfectly reflecting surface while subject to a constant force directed toward the surface. The classical counterpart of this system is a ball bouncing on a floor in a constant gravitational field, collisions with the floor being assumed to be elastic. Path integration is used to derive the energy eigenvalues and eigenfunctions of the quantum bouncer in the WKB or semiclassical approximation. The results are shown to be the same as those obtained by solving the Schrödinger equation in the same approximation.
PathSys: integrating molecular interaction graphs for systems biology
Directory of Open Access Journals (Sweden)
Raval Alpan
2006-02-01
Full Text Available Abstract Background The goal of information integration in systems biology is to combine information from a number of databases and data sets, which are obtained from both high and low throughput experiments, under one data management scheme such that the cumulative information provides greater biological insight than is possible with individual information sources considered separately. Results Here we present PathSys, a graph-based system for creating a combined database of networks of interaction for generating integrated view of biological mechanisms. We used PathSys to integrate over 14 curated and publicly contributed data sources for the budding yeast (S. cerevisiae and Gene Ontology. A number of exploratory questions were formulated as a combination of relational and graph-based queries to the integrated database. Thus, PathSys is a general-purpose, scalable, graph-data warehouse of biological information, complete with a graph manipulation and a query language, a storage mechanism and a generic data-importing mechanism through schema-mapping. Conclusion Results from several test studies demonstrate the effectiveness of the approach in retrieving biologically interesting relations between genes and proteins, the networks connecting them, and of the utility of PathSys as a scalable graph-based warehouse for interaction-network integration and a hypothesis generator system. The PathSys's client software, named BiologicalNetworks, developed for navigation and analyses of molecular networks, is available as a Java Web Start application at http://brak.sdsc.edu/pub/BiologicalNetworks.
A Piecewise Linear Fitting Technique for Multivalued Two-dimensional Paths
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V.M. Jimenez-Fernandez
2013-10-01
Full Text Available This paper presents a curve-fitting technique for multivalued two-dimensional piecewise-linear paths. The proposed method is based on a decomposed formulation of the canonical piecewise linear model description of Chua and Kang. The path is treated as a parametric system of two position equations (x(k, y(k, where k is an artificial parameter to map each variable (x and y into an independent k-domain.
Institute of Scientific and Technical Information of China (English)
艾文宝; 张可村
2001-01-01
In this paper, we propose a general path following method, in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap. The algorithm maintains the O ( nL) ineration complexity. It enjoys quadratic convergence if the optimal vertex is nondegenerate.
Polymer density functional approach to efficient evaluation of path integrals
DEFF Research Database (Denmark)
Brukhno, Andrey; Vorontsov-Velyaminov, Pavel N.; Bohr, Henrik
2005-01-01
A polymer density functional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly......, the path integral problem can, in principle, be solved exactly by making use of the two-particle pair correlation function (2p-PCF) for the ends of an open polymer, half of the original. This way the exact data for one-dimensional quantum harmonic oscillator are reproduced in a wide range of temperatures......-consistent iteration so as to correctly account for the interparticle interactions. The algorithm is speeded up by taking convolutions with the aid of fast Fourier transforms. We apply this approximate path integral DFT (PI-DFT) method to systems within spherical symmetry: 3D harmonic oscillator, atoms of hydrogen...
Nearest neighbor interaction in the Path Integral Renormalization Group method
de Silva, Wasanthi; Clay, R. Torsten
2014-03-01
The Path Integral Renormalization Group (PIRG) method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. The many-body ground state wave function is approximated by an optimized linear combination of Slater determinants which satisfies the variational principle. A major advantage of PIRG is that is does not suffer the Fermion sign problem of quantum Monte Carlo. Results are exact in the noninteracting limit and can be enhanced using space and spin symmetries. Many observables can be calculated using Wick's theorem. PIRG has been used predominantly for the Hubbard model with a single on-site Coulomb interaction U. We describe an extension of PIRG to the extended Hubbard model (EHM) including U and a nearest-neighbor interaction V. The EHM is particularly important in models of charge-transfer solids (organic superconductors) and at 1/4-filling drives a charge-ordered state. The presence of lattice frustration also makes studying these systems difficult. We test the method with comparisons to small clusters and long one dimensional chains, and show preliminary results for a coupled-chain model for the (TMTTF)2X materials. This work was supported by DOE grant DE-FG02-06ER46315.
Age differences in virtual environment and real world path integration
Directory of Open Access Journals (Sweden)
Diane E Adamo
2012-09-01
Full Text Available Accurate path integration requires the integration of visual, proprioceptive, and vestibular self-motion cues and age effects associated with alterations in processing information from these systems may contribute to declines in path integration abilities. The present study investigated age-related differences in path integration in conditions that varied as a function of available sources of sensory information. Twenty-two healthy, young (23.8 ± 3.0 yrs. and 16 older (70.1 ± 6.4 yrs. adults participated in distance reproduction and triangle completion tasks performed in a virtual environment and two real world conditions: guided walking and wheelchair propulsion. For walking and wheelchair propulsion conditions, participants wore a blindfold and wore noise-blocking headphones and were guided through the workspace by the experimenter. For the virtual environment (VE condition, participants viewed self-motion information on a computer monitor and used a joystick to navigate through the environment. For triangle completion tasks, older compared to younger individuals showed greater errors in rotation estimations performed in the wheelchair condition; and for rotation and distance estimations in the VE condition. Distance reproduction tasks, in contrast, did not show any age effects. These findings demonstrate that age differences in path integration vary as a function of the available sources of information and by the complexity of outbound pathway.
Path Integrals and the Statistical Thermodynamics of Black Holes.
Martinez, Erik Andres
The path integral is an important element in modern approaches to the quantization of the gravitational field. Path integral representations of partition functions for static and stationary black hole systems as well as path integrals for minisuperspace models of cosmology are presented. The functional integral is defined throughout as a sum over Lorentzian histories. A consistent formulation of Feynman's prescription to construct partition functions in terms of path integrals for general gravitational systems is presented and contrasted with other "Euclideanization" prescriptions. It is shown that the central object in the description of black hole systems is the gravitational action. In particular, the additivity of the entropies of matter and black holes in thermal equilibrium is a consequence of the additivity of their corresponding actions, and thermodynamic potentials like the energy or the pressure are not in general addivite when gravity plays an important role. Partition functions as stationary phase approximations of functional integrals for all the thermodynamic ensembles are then constructed by including gravitation as a part of the thermodynamical system. We show that a complex geometry is required to derive the thermodynamic properties of stationary geometries from the sum over histories. The corresponding real "thermodynamical" action is calculated explicitly and the thermodynamical data that imply thermal equilibrium in the presence of a rotating black hole in interaction with matter fields are presented and related to geometrical data. Some of the consequences for Kerr-Newman black hole systems are also discussed. For minisuperspace cosmologies the Lorentzian path integral is a Green function for the Wheeler-DeWitt operator, and its real part is a solution to the Wheeler -DeWitt equation. It is computed explicitly for the de Sitter minisuperspace model. The resulting Green function is then related to both the Hartle-Hawking and tunneling wave
Path Integral for Lattice Staggered Fermions in the Loop Representation
Aroca, J M; Gambini, R
1998-01-01
The path integral formulation in terms of loop variables is introduced for lattice gauge theories with dynamical fermions. The path integral of lattice compact QED with staggered fermions is expressed as a sum over surfaces with border on self-avoiding fermionic paths. Each surface is weighted with a classical action -- written in terms of integer gauge invariant variables -- which gives via transfer matrix method the Hamiltonian of the loop or P-representation. The surfaces correspond to the world sheets of loop-like pure electric flux excitations and meson-like configurations (open electric flux tubes carrying matter fields at their ends). The gauge non-redundancy and the geometric transparency are two appealing features of this description. From the computational point of view, it involves fewer degrees of freedom than the Kogut-Susskind formulation and offers the possibility of alternative numerical methods for dynamical fermions.
Path Integral Understanding in the Context of the Electromagnetic Theory
Gonzalez, Maria D.
2006-12-01
Introductory electromagnetic courses at the University of Juarez are in general identified by the use of a traditional instruction. The path integral is a fundamental mathematical knowledge to understand the properties of conservative fields such that the electric field. Many students in these courses do not develop the necessary scientific skills and mathematical formalism to understand the fact that the potential difference does not depend on the path followed from one point to another one inside an electric field. It is fundamental to probe the student understanding difficulties to apply the concept of path integral in an electromagnetic context. The use of the software CABRI could become an important didactic choice during the development of the potential difference concept. It was necessary the recollection of data related to the student procedural difficulties in the use of the designed CABRI activities. Sponsor: member Sergio Flores
The path integral formulation of climate dynamics.
Directory of Open Access Journals (Sweden)
Antonio Navarra
Full Text Available The chaotic nature of the atmospheric dynamics has stimulated the applications of methods and ideas derived from statistical dynamics. For instance, ensemble systems are used to make weather predictions recently extensive, which are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts since it allows forecasters to issue probabilistic forecasts. These works have modified the dominant paradigm of the interpretation of the evolution of atmospheric flows (and oceanic motions to some extent attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, which turn out to be the only physical quantity relevant to practice. However, little work has been done on a direct modeling of the probability evolution itself. In this paper it is shown that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows obtaining a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and provides a framework generalizable to red noise, as well as to delaying differential equations, and even field equations, i.e., partial differential equations with noise, for example, general circulation models with noise. These concepts will be applied to an example taken from a simple ENSO model.
The Path Integral Formulation of Climate Dynamics
Navarra, Antonio; Tribbia, Joe; Conti, Giovanni
2013-01-01
The chaotic nature of the atmospheric dynamics has stimulated the applications of methods and ideas derived from statistical dynamics. For instance, ensemble systems are used to make weather predictions recently extensive, which are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts since it allows forecasters to issue probabilistic forecasts. These works have modified the dominant paradigm of the interpretation of the evolution of atmospheric flows (and oceanic motions to some extent) attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, which turn out to be the only physical quantity relevant to practice. However, little work has been done on a direct modeling of the probability evolution itself. In this paper it is shown that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows obtaining a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and provides a framework generalizable to red noise, as well as to delaying differential equations, and even field equations, i.e., partial differential equations with noise, for example, general circulation models with noise. These concepts will be applied to an example taken from a simple ENSO model. PMID:23840577
On Duru-Kleinert Path Integral In Quantum Cosmology
Jafarizadeh, M A; Rastegar, A R
1998-01-01
We show that the Duru-Kleinert fixed energy amplitude leads to the path integral for the propagation amplitude in the closed FRW quantum cosmology with scale factor as one degree of freedom. Then, using the Duru-Kleinert equivalence of corresponding actions, we calculate the tunneling rate, with exact prefactor, through the dilute-instanton approximation to first order in
Path Integration Applied to Structural Systems with Uncertain Properties
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Köylüoglu, H. Ugur
Path integration (cell-to-cell mapping) method is applied to evaluate the joint probability density function (jpdf) of the response of the structural systems, with uncertain properties, subject to white noise excitation. A general methodology to deal with uncertainties is outlined and applied...
Quantum tunneling splittings from path-integral molecular dynamics
Mátyus, Edit; Wales, David J.; Althorpe, Stuart C.
2016-03-01
We illustrate how path-integral molecular dynamics can be used to calculate ground-state tunnelling splittings in molecules or clusters. The method obtains the splittings from ratios of density matrix elements between the degenerate wells connected by the tunnelling. We propose a simple thermodynamic integration scheme for evaluating these elements. Numerical tests on fully dimensional malonaldehyde yield tunnelling splittings in good overall agreement with the results of diffusion Monte Carlo calculations.
Singular path-independent energy integrals for elastic bodies with thin elastic inclusions
Shcherbakov, V. V.
2016-06-01
An equilibrium problem for a two-dimensional homogeneous linear elastic body containing a thin elastic inclusion and an interfacial crack is considered. The thin inclusion is modeled within the framework of Euler-Bernoulli beam theory. An explicit formula for the first derivative of the energy functional with respect to the crack perturbation along the interface is presented. It is shown that the formulas for the derivative associated with translation and self-similar expansion of the crack are represented as path-independent integrals along smooth contour surrounding one or both crack tips. These path-independent integrals consist of regular and singular terms and are analogs of the well-known Eshelby-Cherepanov-Rice J-integral and Knowles-Sternberg M-integral.
Path-integral solution of the one-dimensional Dirac quantum cellular automaton
Energy Technology Data Exchange (ETDEWEB)
D' Ariano, Giacomo Mauro [QUIT group, Dipartimento di Fisica, via Bassi 6, Pavia, 27100 (Italy); INFN Gruppo IV, Sezione di Pavia, via Bassi 6, Pavia, 27100 (Italy); Mosco, Nicola [QUIT group, Dipartimento di Fisica, via Bassi 6, Pavia, 27100 (Italy); Perinotti, Paolo [QUIT group, Dipartimento di Fisica, via Bassi 6, Pavia, 27100 (Italy); INFN Gruppo IV, Sezione di Pavia, via Bassi 6, Pavia, 27100 (Italy); Tosini, Alessandro [QUIT group, Dipartimento di Fisica, via Bassi 6, Pavia, 27100 (Italy)
2014-09-05
Quantum cellular automata, which describe the discrete and exactly causal unitary evolution of a lattice of quantum systems, have been recently considered as a fundamental approach to quantum field theory and a linear automaton for the Dirac equation in one dimension has been derived. In the linear case a quantum cellular automaton is isomorphic to a quantum walk and its evolution is conveniently formulated in terms of transition matrices. The semigroup structure of the matrices leads to a new kind of discrete path-integral, different from the well known Feynman checkerboard one, that is solved analytically in terms of Jacobi polynomials of the arbitrary mass parameter. - Highlights: • Discrete path integral formulation of linear QCAs in terms of transition matrices. • Derivation of the analytical solution for the one dimensional Dirac QCA. • Solution given in terms of Jacobi polynomials versus the arbitrary mass parameter. • The discrete paths and the transition matrices of the Dirac QCA are binary encoded. • Paths are grouped in equivalence classes according to their overall transition matrix.
Mathematical Simulation for Integrated Linear Fresnel Spectrometer Chip
Park, Yeonjoon; Yoon, Hargoon; Lee, Uhn; King, Glen C.; Choi, Sang H.
2012-01-01
A miniaturized solid-state optical spectrometer chip was designed with a linear gradient-gap Fresnel grating which was mounted perpendicularly to a sensor array surface and simulated for its performance and functionality. Unlike common spectrometers which are based on Fraunhoffer diffraction with a regular periodic line grating, the new linear gradient grating Fresnel spectrometer chip can be miniaturized to a much smaller form-factor into the Fresnel regime exceeding the limit of conventional spectrometers. This mathematical calculation shows that building a tiny motionless multi-pixel microspectrometer chip which is smaller than 1 cubic millimter of optical path volume is possible. The new Fresnel spectrometer chip is proportional to the energy scale (hc/lambda), while the conventional spectrometers are proportional to the wavelength scale (lambda). We report the theoretical optical working principle and new data collection algorithm of the new Fresnel spectrometer to build a compact integrated optical chip.
Tackling Higher Derivative Ghosts with the Euclidean Path Integral
Fontanini, Michele
2011-01-01
An alternative to the effective field theory approach to treat ghosts in higher derivative theories is to attempt to integrate them out via the Euclidean path integral formalism. It has been suggested that this method could provide a consistent framework within which we might tolerate the ghost degrees of freedom that plague, among other theories, the higher derivative gravity models that have been proposed to explain cosmic acceleration. We consider the extension of this idea to treating a class of terms with order six derivatives, and find that for a general term the Euclidean path integral approach works in the most trivial background, Minkowski. Moreover we see that even in de Sitter background, despite some difficulties, it is possible to define a probability distribution for tensorial perturbations of the metric.
A linear programming formulation of Mader's edge-disjoint paths problem
Keijsper, J.C.M.; Pendavingh, R.A.; Stougie, L.
2006-01-01
We give a dual pair of linear programs for a minâ€“max result of Mader describing the maximum number of edge-disjoint T-paths in a graph G=(V,E) with TV. We conclude that there exists a polynomial-time algorithm (based on the ellipsoid method) for finding the maximum number of T-paths in a
Renormalization group and linear integral equations
Klein, W.
1983-04-01
We develop a position-space renormalization-group transformation which can be employed to study general linear integral equations. In this Brief Report we employ our method to study one class of such equations pertinent to the equilibrium properties of fluids. The results of applying our method are in excellent agreement with known numerical calculations where they can be compared. We also obtain information about the singular behavior of this type of equation which could not be obtained numerically.
Beam spread functions calculated using Feynman path integrals
Kilgo, Paul; Tessendorf, Jerry
2017-07-01
A method of solving the radiative transfer equation using Feynman path integrals (FPIs) is discussed. The FPI approach is a mathematical framework for computing multiple scattering in participating media. Its numerical behavior is not well known, and techniques are being developed to solve the FPI approach numerically. A missing numerical technique is detailed and used to calculate beam spread functions (BSFs), a commonly studied experimental property of many types of media. The calculations are compared against measured BSFs of sea ice. Analysis shows differently-shaped BSFs, and suggests the width parameter of the calculated BSF's Gaussian fit approaches a value in the limit of the number of path segments. A projection is attempted, but suggests a larger number of path segments would not increase the width of the calculated BSF. The trial suggests the approach is numerically stable, but requires further testing to ensure scientific accuracy.
BOOK REVIEW: Path Integrals in Field Theory: An Introduction
Ryder, Lewis
2004-06-01
In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed
A novel linear tracking integrator with integral compensation and its application.
Shao, Xingling; Liu, Jun; Wang, Honglun; Cao, Zhibin
2017-09-27
A novel linear tracking integrator (LTI) with integral compensation is proposed for efficient integral estimation from a contaminated measurement with a constant or time-varying bias. The limitation of finite-time convergent integral observer (FTCIO) in ruling out the integral drift is firstly revealed via describing function method. Subsequently, by the utilization of integral action in the feedback path, a simple but effective linear tracking integrator is established to provide a practical solution in achieving a drift-free integral estimate. The highlight is that the proposed LTI can simultaneously give the accurate integral and tracking estimates from a noisy measurement without relying on the condition of observability. In addition, frequency-domain analysis of LTI is investigated to give a viable guideline of parameter tuning. Illustrative simulations and comparison with Kalman filter are included to demonstrate the superiority of LTI in accomplishing precise integral tracking in the presence of constant or time-varying bias. Finally, the effectiveness of LTI is also confirmed by an application on autopilot design for aircraft. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Rigorous time slicing approach to Feynman path integrals
Fujiwara, Daisuke
2017-01-01
This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved. The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by...
Misaligned Image Integration With Local Linear Model.
Baba, Tatsuya; Matsuoka, Ryo; Shirai, Keiichiro; Okuda, Masahiro
2016-05-01
We present a new image integration technique for a flash and long-exposure image pair to capture a dark scene without incurring blurring or noisy artifacts. Most existing methods require well-aligned images for the integration, which is often a burdensome restriction in practical use. We address this issue by locally transferring the colors of the flash images using a small fraction of the corresponding pixels in the long-exposure images. We formulate the image integration as a convex optimization problem with the local linear model. The proposed method makes it possible to integrate the color of the long-exposure image with the detail of the flash image without causing any harmful effects to its contrast, where we do not need perfect alignment between the images by virtue of our new integration principle. We show that our method successfully outperforms the state of the art in the image integration and reference-based color transfer for challenging misaligned data sets.
Quantum mechanical path integrals in curved spaces and the type-A trace anomaly
Bastianelli, Fiorenzo; Corradini, Olindo; Vassura, Edoardo
2017-04-01
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in arbitrary coordinates is well understood, and known to require the use of a regularization scheme, in this article we take up an old proposal of constructing the path integral by using Riemann normal coordinates. The method assumes that curvature effects are taken care of by a scalar effective potential, so that the particle lagrangian is reduced to that of a linear sigma model interacting with the effective potential. After fixing the correct effective potential, we test the construction on spaces of maximal symmetry and use it to compute heat kernel coefficients and type-A trace anomalies for a scalar field in arbitrary dimensions up to d = 12. The results agree with expected ones, which are reproduced with great efficiency and extended to higher orders. We prove explicitly the validity of the simplified path integral on maximally symmetric spaces. This simplified path integral might be of further use in worldline applications, though its application on spaces of arbitrary geometry remains unclear.
Mathematical theory of Feynman path integrals an introduction
Albeverio, Sergio A; Mazzucchi, Sonia
2008-01-01
Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
State Space Path Integrals for Electronically Nonadiabatic Reaction Rates
Duke, Jessica Ryan
2016-01-01
We present a state-space-based path integral method to calculate the rate of electron transfer (ET) in multi-state, multi-electron condensed-phase processes. We employ an exact path integral in discrete electronic states and continuous Cartesian nuclear variables to obtain a transition state theory (TST) estimate to the rate. A dynamic recrossing correction to the TST rate is then obtained from real-time dynamics simulations using mean field ring polymer molecular dynamics. We employ two different reaction coordinates in our simulations and show that, despite the use of mean field dynamics, the use of an accurate dividing surface to compute TST rates allows us to achieve remarkable agreement with Fermi's golden rule rates for nonadiabatic ET in the normal regime of Marcus theory. Further, we show that using a reaction coordinate based on electronic state populations allows us to capture the turnover in rates for ET in the Marcus inverted regime.
Path integral quantization of the relativistic Hopfield model
Belgiorno, F; Piazza, F Dalla; Doronzo, M
2016-01-01
The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and dielectric quantum matter, with particular reference to the context of analogue gravity. In order to take into account the constraints occurring in the model, we adopt the Faddeev-Jackiw approach to constrained quantization in the path integral formalism. In particular we demonstrate that the propagator obtained with the Faddeev-Jackiw approach is equivalent to the one which, in the framework of Dirac canonical quantization for constrained systems, can be directly computed as the vacuum expectation value of the time ordered product of the fields. Our analysis also provides an explicit example of quantization of the electromagnetic field in a covariant gauge and coupled with the polarization field, which is a novel contribution to the literature on the Faddeev-Jackiw procedure.
A discrete history of the Lorentzian path integral
Loll, R
2003-01-01
In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features. At the regularized, discrete level this approach solves the problems of (i) having a well-defined Wick rotation, (ii) possessing a coordinate-invariant cutoff, and (iii) leading to_convergent_ sums over geometries. Although little is known as yet about the existence and nature of an underlying continuum theory of quantum gravity in four dimensions, there are already a number of beautiful results in d=2 and d=3 where continuum limits have been found. They include an explicit example of the inequivalence of the Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the cancellation of the conformal factor, and the discovery that causality can act as an effective regulator of quantum geometry.
Remarks on the Origin of Path Integration: Einstein and Feynman
Sauer, Tilman
2008-01-01
I offer some historical comments about the origins of Feynman's path integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's thesis supervisor John Wheeler, it is argued that, contrary to what one might expect, the significance of the interaction between Einstein and Feynman pertained to a critique of classical field theory, rather than to a direct critique of quantum mechanics itself...
A path to integration in an academic health science center.
Panko, W B; Wilson, W
1992-01-01
This article describes a networking and integration strategy in use at the University of Michigan Medical Center. This strategy builds upon the existing technology base and is designed to provide a roadmap that will direct short-term development along a productive, long-term path. It offers a way to permit the short-term development of incremental solutions to current problems while at the same time maximizing the likelihood that these incremental efforts can be recycled into a more comprehensive approach.
Efficient stochastic thermostatting of path integral molecular dynamics
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E.; Manolopoulos, David E.
2010-09-01
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
Path integral approach to the quantum fidelity amplitude.
Vaníček, Jiří; Cohen, Doron
2016-06-13
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called 'dephasing representation,' circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact. © 2016 The Authors.
Spectral integration of linear boundary value problems
Viswanath, Divakar
2012-01-01
Spectral integration is a method for solving linear boundary value problems which uses the Chebyshev series representation of functions to avoid the numerical discretization of derivatives. It is occasionally attributed to Zebib (J. of Computational Physics vol. 53 (1984), p. 443-455) and more often to Greengard (SIAM J. on Numerical Analysis vol. 28 (1991), p. 1071-1080). Its advantage is believed to be its relative immunity to errors that arise when nearby grid points are used to approximate derivatives. In this paper, we reformulate the method of spectral integration by changing it in four different ways. The changes consist of a more convenient integral formulation, a different way to treat and interpret boundary conditions, treatment of higher order problems in factored form, and the use of piecewise Chebyshev grid points. Our formulation of spectral integration is more flexible and powerful as show by its ability to solve a problem that would otherwise take 8192 grid points using only 96 grid points. So...
Moran, B.; Kulkarni, S.S.; Reeves, H.W.
2007-01-01
A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics. ?? Springer Science+Business Media, Inc. 2007.
Energy Technology Data Exchange (ETDEWEB)
Goettert, M.; Neumann, R. [Festo AG und Co.KG, Esslingen (Germany)
2007-02-15
For the design of a continuous path control of servopneumatic drives two design methods are investigated: Non linear controllers based on exact linearization techniques and a linear controller based on linearization along a reference trajectory. With the nonlinear controller better results can be achieved with less realisation effort. (orig.)
Direct path integral estimators for isotope fractionation ratios
Cheng, Bingqing
2014-01-01
Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical and atmospheric phenomena. Accurate evaluation of isotope ratios in atomistic simulations is challenging, because one needs to perform a thermodynamic integration with respect to the isotope mass, along with time-consuming path integral calculations. By re-formulating the problem as a particle exchange in the ring polymer partition function, we derive new estimators giving direct access to the differential partitioning of isotopes, which can simplify the calculations by avoiding thermodynamic integration. We demonstrate the efficiency of these estimators by applying them to investigate the isotope fractionation ratios in the gas-phase Zundel cation, and in a few simple hydrocarbons.
Integral and Multidimensional Linear Distinguishers with Correlation Zero
DEFF Research Database (Denmark)
Bogdanov, Andrey; Leander, Gregor; Nyberg, Kaisa
2012-01-01
Zero-correlation cryptanalysis uses linear approximations holding with probability exactly 1/2. In this paper, we reveal fundamental links of zero-correlation distinguishers to integral distinguishers and multidimensional linear distinguishers. We show that an integral implies zero-correlation li......Zero-correlation cryptanalysis uses linear approximations holding with probability exactly 1/2. In this paper, we reveal fundamental links of zero-correlation distinguishers to integral distinguishers and multidimensional linear distinguishers. We show that an integral implies zero...
Potential theory, path integrals and the Laplacian of the indicator
Lange, Rutger-Jan
2012-11-01
This paper links the field of potential theory — i.e. the Dirichlet and Neumann problems for the heat and Laplace equation — to that of the Feynman path integral, by postulating the following seemingly ill-defined potential: V(x):=∓ {{σ^2}}/2nabla_x^2{1_{{xin D}}} where the volatility is the reciprocal of the mass (i.e. m = 1/ σ 2) and ħ = 1. The Laplacian of the indicator can be interpreted using the theory of distributions: it is the d-dimensional analogue of the Dirac δ'-function, which can formally be defined as partial_x^2{1_{x>0 }} . We show, first, that the path integral's perturbation series (or Born series) matches the classical single and double boundary layer series of potential theory, thereby connecting two hitherto unrelated fields. Second, we show that the perturbation series is valid for all domains D that allow Green's theorem (i.e. with a finite number of corners, edges and cusps), thereby expanding the classical applicability of boundary layers. Third, we show that the minus (plus) in the potential holds for the Dirichlet (Neumann) boundary condition; showing for the first time a particularly close connection between these two classical problems. Fourth, we demonstrate that the perturbation series of the path integral converges as follows:Table Float="No" ID="Taba"> mode of convergence absorbed propagator reflected propagator convex domain alternating monotone concave domain monotone alternating Table> We also discuss the third boundary problem (which poses Robin boundary conditions) and discuss an extension to moving domains.
Path-integral formula for local thermal equilibrium
Hongo, Masaru
2016-01-01
We develop a complete path-integral formulation of relativistic quantum fields in local thermal equilibrium, which brings about the emergence of thermally induced curved spacetime. The resulting action is shown to have full diffeomorphism invariance and gauge invariance in thermal spacetime with imaginary-time independent backgrounds. This leads to the notable symmetry properties of emergent thermal spacetime: Kaluza-Klein gauge symmetry, spatial diffeomorphism symmetry, and gauge symmetry. A thermodynamic potential in local thermal equilibrium, or the so-called Masseiu-Planck functional, is identified as a generating functional for conserved currents such as the energy-momentum tensor and the electric current.
The Path Integral Quantization corresponding to the Deformed Heisenberg Algebra
Pramanik, Souvik; Moussa, Mohamed; Ali, Ahmed Farag
2014-01-01
In this paper, we analyze a deformation of the Heisenberg algebra consistent with both the generalized uncertainty principle and doubly special relativity. We observe that this algebra can give rise to fractional derivatives terms in the corresponding quantum mechanical Hamiltonian. However, a formal meaning can be given to such fractional derivative terms, using the theory of harmonic extensions of functions. Thus we obtain the expression of the propagator of path integral corresponding to this deformed Heisenberg algebra. In fact, we explicitly evaluate this expression for a free particle in one dimension and check its consistency.
Remarks on the Origin of Path Integration: Einstein and Feynman
Sauer, Tilman
2008-01-01
I offer some historical comments about the origins of Feynman's path integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's thesis supervisor John Wheeler, it is argued that, contrary to what one might expect, the significance of the interaction between Einstein and Feynman pertained to a critique of classical field theory, rather than to a direct critique of quantum mechanics itself. Nevertheless, the critical perspective on classical field theory became a motivation and point of departure for Feynman's space-time approach to non-relativistic quantum mechanics.
Remarks on the Origin of Path Integration:. Einstein and Feynman
Sauer, T.
2008-11-01
I offer some historical comments about the origins of Feynman's path-integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's thesis supervisor John Wheeler, it is argued that, contrary to what one might expect, the significance of the interaction between Einstein and Feynman pertained to a critique of classical field theory, rather than to a direct critique of quantum mechanics itself. Nevertheless, the critical perspective on classical field theory became a motivation and point of departure for Feynman's space-time approach to non-relativistic quantum mechanics.
Self-gravitating stellar collapse: explicit geodesics and path integration
Directory of Open Access Journals (Sweden)
Jayashree Balakrishna
2016-11-01
Full Text Available We extend the work of Oppenheimer-Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.
The solution of linear mechanical systems in terms of path superposition
Magrans, Francesc Xavier; Poblet-Puig, Jordi; Rodríguez-Ferran, Antonio
2017-02-01
We prove that the solution of any linear mechanical system can be expressed as a linear combination of signal transmission paths. This is done in the framework of the Global Transfer Direct Transfer (GTDT) formulation for vibroacoustic problems. Transmission paths are expressed as powers of the transfer matrix. The key idea of the proof is to generalise the Neumann series of the transfer matrix - which is convergent only if its spectral radius is smaller than one - into a modified Neumann series that is convergent regardless of the eigenvalues of the transfer matrix. The modification consists in choosing the appropriate combination coefficients for the powers of the transfer matrix in the series. A recursive formula for the computation of these factors is derived. The theoretical results are illustrated by means of numerical examples. Finally, we show that the generalised Neumann series can be understood as an acceleration (i.e. convergence speedup) of the Jacobi iterative method.
Institute of Scientific and Technical Information of China (English)
CHEN Tong; WU Ning; YU Yue
2011-01-01
We have developed a path integral formalism of the quantum mechanics in the rotating frame of reference, and proposed a path integral description of spin degrees of freedom, which is connected to the Schwinger bosons realization of the angular momenta. We
N-slit interference: Path integrals, Bohmian trajectories
Sbitnev, Valeriy I
2010-01-01
Path integrals give a possibility to compute in details routes of particles from particle sources through slit gratings and further to detectors. The path integral for a particle passing through the Gaussian slit results in the Gaussian wavepacket. The wavepackets prepared on N slits and superposed together give rise to interference pattern in the near-field zone. It transforms to diffraction in the far-field zone represented by divergent principal rays, at that all rays are partitioned from each other by (N-2) subsidiary rays. The Bohmian trajectories in the near-field zone of N-slit gratings show wavy behavior. And they become straight in the far-field zone. The trajectories show zigzag behavior on the interference Talbot carpet (ratio of particle wavelength to a distance between slits are much smaller than 1 and N >> 1). Namely, the trajectories prefer to pass through caustics and avoid lacunae, i.e., places with small probability densities. Monochromatic thermal neutrons (wavelength=0.5 nm) simulate radia...
A note on the path integral representation for Majorana fermions
Greco, Andrés
2016-04-01
Majorana fermions are currently of huge interest in the context of nanoscience and condensed matter physics. Different to usual fermions, Majorana fermions have the property that the particle is its own anti-particle thus, they must be described by real fields. Mathematically, this property makes nontrivial the quantization of the problem due, for instance, to the absence of a Wick-like theorem. In view of the present interest on the subject, it is important to develop different theoretical approaches in order to study problems where Majorana fermions are involved. In this note we show that Majorana fermions can be studied in the context of field theories for constrained systems. Using the Faddeev-Jackiw formalism for quantum field theories with constraints, we derived the path integral representation for Majorana fermions. In order to show the validity of the path integral we apply it to an exactly solvable problem. This application also shows that it is rather simple to perform systematic calculations on the basis of the present framework.
An Entropy-Based Approach to Path Analysis of Structural Generalized Linear Models: A Basic Idea
Directory of Open Access Journals (Sweden)
Nobuoki Eshima
2015-07-01
Full Text Available A path analysis method for causal systems based on generalized linear models is proposed by using entropy. A practical example is introduced, and a brief explanation of the entropy coefficient of determination is given. Direct and indirect effects of explanatory variables are discussed as log odds ratios, i.e., relative information, and a method for summarizing the effects is proposed. The example dataset is re-analyzed by using the method.
Reuschel, Johanna; Rösler, Frank; Henriques, Denise Y P; Fiehler, Katja
2011-04-01
Many studies provide evidence that information from different modalities is integrated following the maximum likelihood estimation model (MLE). For instance, we recently found that visual and proprioceptive path trajectories are optimally combined (Reuschel et al. in Exp Brain Res 201:853-862, 2010). However, other studies have failed to reveal optimal integration of such dynamic information. In the present study, we aim to generalize our previous findings to different parts of the workspace (central, ipsilateral, or contralateral) and to different types of judgments (relative vs. absolute). Participants made relative judgments by judging whether an angular path was acute or obtuse, or they made absolute judgments by judging whether a one-segmented straight path was directed to left or right. Trajectories were presented in the visual, proprioceptive, or combined visual-proprioceptive modality. We measured the bias and the variance of these estimates and predicted both parameters using the MLE. In accordance with the MLE model, participants linearly combined and weighted the unimodal angular path information by their reliabilities irrespective of the side of workspace. However, the precision of bimodal estimates was not greater than that for unimodal estimates, which is inconsistent with the MLE. For the absolute judgment task, participants' estimates were highly accurate and did not differ across modalities. Thus, we were unable to test whether the bimodal percept resulted as a weighted average of the visual and proprioceptive input. Additionally, participants were not more precise in the bimodal compared with the unimodal conditions, which is inconsistent with the MLE. Current findings suggest that optimal integration of visual and proprioceptive information of path trajectory only applies in some conditions.
PATH INTEGRAL SOLUTION OF NONLINEAR DYNAMIC BEHAVIOR OF STRUCTURE UNDER WIND EXCITATION
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito' s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted.Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.
Yu, Pengfei; Wang, Hailong; Chen, Jianyong; Shen, Shengping
2017-07-01
In this study, the conservation laws οf dissipative mechanical-diffusion-electrochemical reaction system are systematically obtained based on Noether's theorem. According to linear, irreversible thermodynamics, dissipative phenomena can be described by an irreversible force and an irreversible flow. Additionally, the Lagrange function, L and the generalized Hamilton least-action principle are proposed to be used to obtain the conservation integrals. A group of these integrals, including the J-, M-, and L-integrals, can be then obtained using the classical Noether approach for dissipative processes. The relation between the J-integral and the energy release rate is illustrated. The path-independence of the J-integral is then proven. The J-integral, derived based on Noether's theorem, is a line integral, contrary to the propositions of existing published works that describe it both as a line and an area integral. Herein, we prove that the outcomes are identical, and identify the physical meaning of the area integral, a concept that was not explained previously. To show that the J-integral can dominate the distribution of the corresponding field quantities, an example of a partial, stress-diffusion coupling process is disscussed.
Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Marvin; /SLAC
2009-02-12
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will
Atmospheric Refraction Path Integrals in Ground-Based Interferometry
Mathar, R J
2004-01-01
The basic effect of the earth's atmospheric refraction on telescope operation is the reduction of the true zenith angle to the apparent zenith angle, associated with prismatic aberrations due to the dispersion in air. If one attempts coherent superposition of star images in ground-based interferometry, one is in addition interested in the optical path length associated with the refracted rays. In a model of a flat earth, the optical path difference between these is not concerned as the translational symmetry of the setup means no net effect remains. Here, I evaluate these interferometric integrals in the more realistic arrangement of two telescopes located on the surface of a common earth sphere and point to a star through an atmosphere which also possesses spherical symmetry. Some focus is put on working out series expansions in terms of the small ratio of the baseline over the earth radius, which allows to bypass some numerics which otherwise is challenged by strong cancellation effects in building the opti...
Sesé, Luis M.
This paper addresses several points of interest concerning the computation of the static structure factor of path-integral monatomic quantum fluids. First of all, the connection between the structure factor and the path-integral linear response pair radial correlation function is shown as its defining quantity by assuming a generalized Fermi's potential for the neutron- nuclei interactions, which is to be included in the general expression of the dynamic structure factor. Second, the possibilities of finding Ornstein-Zernike equations for full path-integral fluids, and also for the effective potential models of fluids derived from the path-integral formalism, are explored by working in the grand canonical ensemble. By so doing, the success and features for improvement of the weak-field approach used previously in this context of determining quantum static structure factors [SESE,L.M.,1996, Molec. Phys., 89, 1783; SESE, L.M., and LEDESMA,R., 1997, J. chem. Phys., 106, 1134] can be understood. New numerical applications are performed within this weak-field approach taking as probes the quantum hard-sphere fluid and dense fluid helium-4, the latter being described through LennardJones and Aziz-Slaman underlying interactions. The results show that the structure factors associated with the linear response and instantaneous path-integral pair radial correlation functions differ noticeably from each other with increasing quantum effects. In particular, the linear response description leads to more compressible fluids than the instantaneous one. Besides, the equality between the isothermal compressibilities fixed via the linear response and the quantum particle centre-of-gravity pair radial correlation functions does not hold beyond the situations that can be treated with the Gaussian Feynman-Hibbs effective potential picture. Comparison with experiment in the case of helium-4 (T = 4.2 K) reveals clearly that, under strong quantum conditions, an operative framework more
Spin And Curvature In The Worldline Path Integral
Dilkes, F A
1999-01-01
Several aspects of worldline path-integrals are discussed in the context of quantum field theory. It is shown how “near-diagonal” elements of the Seeley-Gilkey coefficients can be computed both in the presence of an arbitrary Riemann metric, a gauge- potential and a scalar potential. These are connected with derivative expansions and ultraviolet properties of field theories. Recently resolved subtleties connected with curvature and curvilinear coordinate systems are taken into account and non-covariant terms in the worldline action are shown to be a necessary ingredient for a correct expansion. This is contrasted with the success of older formal methods. Rudimentary symbolic algebra is shown to be a practical tool for tracking the combinatorics of higher-order calculations. A significant generalization of the Parker-Toms conjecture and the form of the single-particle effective action in curved space results. Some aspects of spin are also considered and it is shown how the spinning particle...
Thermal momentum distribution from path integrals with shifted boundary conditions
Giusti, Leonardo
2011-01-01
For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction, and (b) the ordinary partition function. In this form the generating function is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.
High-resolution path-integral development of financial options
Ingber, L
2000-01-01
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and also consider multi-factor models including stochastic volatility. Daily Eurodollar futures prices and implied volatilities are fit to determine exponents of functional behavior of diffusions using methods of global optimization, Adaptive Simulated Annealing (ASA), to generate tight fits across moving time windows of Eurodollar contracts. These short-time fitted distributions are then developed into long-time distributions using a robust non-Monte Carlo path-integral algorithm, PATHINT, to generate prices and derivatives commonly used by option traders.
Path integral quantization corresponding to the deformed Heisenberg algebra
Energy Technology Data Exchange (ETDEWEB)
Pramanik, Souvik, E-mail: souvick.in@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108 (India); Moussa, Mohamed, E-mail: mohamed.ibrahim@fsc.bu.edu.eg [Department of Physics, Faculty of Sciences, Benha University, Benha 13518 (Egypt); Faizal, Mir, E-mail: f2mir@uwaterloo.ca [Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Ali, Ahmed Farag, E-mail: ahmed.ali@fsc.bu.edu.eg [Department of Physics, Faculty of Sciences, Benha University, Benha 13518 (Egypt)
2015-11-15
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.
Mathematical methods linear algebra normed spaces distributions integration
Korevaar, Jacob
1968-01-01
Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector
A Modified Linear-Mixing Method for Calculating Atmospheric Path Radiances of Aerosol Mixtures
Abdou, W. A.; Martonchik, J. V.; Kahn, R. A.; West, R. A.; Diner, D. J.
1997-01-01
The top-of-atmosphere (TOA) path radiance generated by an aerosol mixture can be synthesized by linearly adding the contributions of the individual aerosol components, weighted by their fractional optical depths. The method, known as linear mixing, is exact in the single-scattering limit. When multiple scattering is significant, the method reproduces the atmospheric path radiance of the mixture with less than 3% errors for weakly absorbing aerosols up to optical thickness of 0.5. However, when strongly absorbing aerosols are included in the mixture, the errors are much larger. This is due to neglecting the effect of multiple interactions between the aerosol components, especially when the values of the single-scattering albedos of these components are so different that the parameter e = the sum of f(sub i)[(bar)omega(sub i) - (bar)omega(sub mix)]/(bar)omega(sub i) is larger than approximately 0.1, where (bar)omega(sub i)and f(sub i) are the single-scattering albedo and the fractional abundance of the ith component, and (bar)omega(sub mix) is the effective single-scattering albedo of the Mixture. We describe an empirical, modified linear-mixing method which effectively accounts for the multiple interactions between aerosol components. The modified and standard methods are identical when epsilon = 0.0 and give similar results when epsilon is less than or equal to 0.05. For optical depths larger than approximately 0.5, or when epsilon is greater than 0.05, only the modified method can reproduce the radiances within 5% error for common aerosol types up to optical thickness of 2.0. Because this method facilitates efficient and accurate atmospheric path radiance calculations for mixtures of a wide variety of aerosol types, it will be used as part of the aerosol retrieval methodology for the Earth Observing System (EOS) multiangle imaging spectroradiometer (MISR), scheduled for launch into polar orbit in 1998.
Robust integral stabilization of regular linear systems
Institute of Scientific and Technical Information of China (English)
XU Chengzheng; FENG Dexing
2004-01-01
We consider regular systems with control and observation. We prove some necessary and sufficient condition for an exponentially stable regular system to admit an integral stabilizing controller. We propose also some robust integral controllers when they exist.
Quantum Field Theory: From Operators to Path Integrals
Huang, Kerson
1998-07-01
A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained. Quantum Field Theory is an exceptional textbook for graduate students familiar with advanced quantum mechanics as well as physicists with an interest in theoretical physics. It features: * Coverage of quantum electrodynamics with practical calculations and a discussion of perturbative renormalization * A discussion of the Feynman path integrals and a host of current subjects, including the physical approach to renormalization, spontaneous symmetry breaking and superfluidity, and topological excitations * Nineteen self-contained chapters with exercises, supplemented with graphs and charts
Lee, Mi Kyung; Huo, Pengfei; Coker, David F.
2016-05-01
This article reviews recent progress in the theoretical modeling of excitation energy transfer (EET) processes in natural light harvesting complexes. The iterative partial linearized density matrix path-integral propagation approach, which involves both forward and backward propagation of electronic degrees of freedom together with a linearized, short-time approximation for the nuclear degrees of freedom, provides an accurate and efficient way to model the nonadiabatic quantum dynamics at the heart of these EET processes. Combined with a recently developed chromophore-protein interaction model that incorporates both accurate ab initio descriptions of intracomplex vibrations and chromophore-protein interactions treated with atomistic detail, these simulation tools are beginning to unravel the detailed EET pathways and relaxation dynamics in light harvesting complexes.
Theory of extreme correlations using canonical Fermions and path integrals
Energy Technology Data Exchange (ETDEWEB)
Shastry, B. Sriram, E-mail: sriram@physics.ucsc.edu
2014-04-15
The t–J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson–Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitian quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further, a transparent physical interpretation of the previously introduced auxiliary Greens function and the ‘caparison factor’, is obtained. The low energy electron spectral function in this theory, with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale Δ{sub 0} that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying very low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function, related simply to the Fano line shape, has a peculiar energy dependence unlike that of a Lorentzian. The resulting energy dispersion obtained by maximization is a hybrid of a massive and a massless Dirac spectrum E{sub Q}{sup ∗}∼γQ−√(Γ{sub 0}{sup 2}+Q{sup 2}), where the vanishing of Q, a momentum type variable, locates the kink minimum. Therefore the quasiparticle velocity interpolates between (γ∓1) over a width Γ{sub 0} on the two sides of Q=0, implying a kink there that strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations. -- Highlights: •Spectral function of the Extremely Correlated Fermi Liquid theory at low energy.
The most likely voltage path and large deviations approximations for integrate-and-fire neurons.
Paninski, Liam
2006-08-01
We develop theory and numerical methods for computing the most likely subthreshold voltage path of a noisy integrate-and-fire (IF) neuron, given observations of the neuron's superthreshold spiking activity. This optimal voltage path satisfies a second-order ordinary differential (Euler-Lagrange) equation which may be solved analytically in a number of special cases, and which may be solved numerically in general via a simple "shooting" algorithm. Our results are applicable for both linear and nonlinear subthreshold dynamics, and in certain cases may be extended to correlated subthreshold noise sources. We also show how this optimal voltage may be used to obtain approximations to (1) the likelihood that an IF cell with a given set of parameters was responsible for the observed spike train; and (2) the instantaneous firing rate and interspike interval distribution of a given noisy IF cell. The latter probability approximations are based on the classical Freidlin-Wentzell theory of large deviations principles for stochastic differential equations. We close by comparing this most likely voltage path to the true observed subthreshold voltage trace in a case when intracellular voltage recordings are available in vitro.
Path integrals, matter waves, and the double slit
Jones, Eric R.; Bach, Roger A.; Batelaan, Herman
2015-11-01
Basic explanations of the double slit diffraction phenomenon include a description of waves that emanate from two slits and interfere. The locations of the interference minima and maxima are determined by the phase difference of the waves. An optical wave, which has a wavelength λ and propagates a distance L, accumulates a phase of 2π L/λ . A matter wave, also having wavelength λ that propagates the same distance L, accumulates a phase of π L/λ , which is a factor of two different from the optical case. Nevertheless, in most situations, the phase difference, {{Δ }}\\varphi , for interfering matter waves that propagate distances that differ by {{Δ }}L, is approximately 2π {{Δ }}L/λ , which is the same value computed in the optical case. The difference between the matter and optical case hinders conceptual explanations of diffraction from two slits based on the matter-optics analogy. In the following article we provide a path integral description for matter waves with a focus on conceptual explanation. A thought experiment is provided to illustrate the validity range of the approximation {{Δ }}\\varphi ≈ 2π {{Δ }}L/λ .
Theory of Atom Optics: Feynman's Path Integral Approach
Institute of Scientific and Technical Information of China (English)
DENG Lü-bi
2006-01-01
The present theory of atom optics is established mainly on the Schr(o)dinger equations or the matrix mechanics equation.The authors present a new theoretical formulation of atom optics: Feynman's path integral theory.Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating),apertures,and standing wave laser field in Earth's gravitational field by using a type of wave function and calculation is simple.For this reason,we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction),double slit,N slit,rectangular aperture,circular aperture,the Mach-Zehndertype interferometer,the interferometer with the Raman beams,the Sagnac effect,the Aharonov-Casher effect,the Kapitza-Dirac diffraction effect,and the Aharonov-Bohm effect.The authors give a wave function of the state of particles on the screen in abovementioned configurations.Our formulas show good agreement with present experimental measurements.
Quantum effects in graphene monolayers: Path-integral simulations
Herrero, Carlos P.; Ramírez, Rafael
2016-12-01
Path-integral molecular dynamics (PIMD) simulations have been carried out to study the influence of quantum dynamics of carbon atoms on the properties of a single graphene layer. Finite-temperature properties were analyzed in the range from 12 to 2000 K, by using the LCBOPII effective potential. To assess the magnitude of quantum effects in structural and thermodynamic properties of graphene, classical molecular dynamics simulations have been also performed. Particular emphasis has been laid on the atomic vibrations along the out-of-plane direction. Even though quantum effects are present in these vibrational modes, we show that at any finite temperature classical-like motion dominates over quantum delocalization, provided that the system size is large enough. Vibrational modes display an appreciable anharmonicity, as derived from a comparison between kinetic and potential energies of the carbon atoms. Nuclear quantum effects are found to be appreciable in the interatomic distance and layer area at finite temperatures. The thermal expansion coefficient resulting from PIMD simulations vanishes in the zero-temperature limit, in agreement with the third law of thermodynamics.
Path integral approach to two-dimensional QCD in the light-front frame
Energy Technology Data Exchange (ETDEWEB)
Gaete, P. (Instituto de Fisica, Universidade Federal do Rio de Janeiro, C.P. 68528, BR-21945, Rio de Janeiro (Brazil)); Gamboa, J. (Fachbereich 7 Physik, Universitaet Siegen, Siegen, D-57068 (Germany)); Schmidt, I. (Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Casilla 110-V, Valparaiso (Chile))
1994-05-15
Two-dimensional quantum chromodynamics in the light-front frame is studied following Hamiltonian methods. The theory is quantized using the path integral formalism and an effective theory similar to the Nambu--Jona-Lasinio model is obtained. Confinement in two dimensions is derived by analyzing directly the constraints in the path integral.
The path integral representation kernel of evolution operator in Merton-Garman model
Blazhyevskyi, L F; 10.5488/CMP.14.23001
2011-01-01
In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.
Path integral approach to eikonal and next-to-eikonal exponentiation
Laenen, E.; Stavenga, G.; White, C.D.
2009-01-01
We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting wit
Path Integral and Solutions of the Constraint Equations The Case of Reducible Gauge Theories
Ferraro, R; Puchin, M
1994-01-01
It is shown that the BRST path integral for reducible gauge theories, with appropriate boundary conditions on the ghosts, is a solution of the constraint equations. This is done by relating the BRST path integral to the kernel of the evolution operator projected on the physical subspace.
Institute of Scientific and Technical Information of China (English)
CAI Liang; ZHANG Ping; YANG Tao; PAN Xiao-Yin
2011-01-01
By using the path integral approach, we investigate the problem of Hooke's atom (two electrons interacting with Coulomb potential in an external harmonic-oscillator potential) in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.
On the coordinate (in)dependence of the formal path integral
DEFF Research Database (Denmark)
Johnson-Freyd, Theo
. In this short note, aimed primarily at mathematicians, we first briefly recall the notions of Lagrangian classical and quantum field theory and the standard coordinate-full definition of the “formal” or “Feynman-diagrammatic” path integral construction. We then outline a proof of the following claim: the formal......When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber bundle, the independence of the formal path integral on the coordinates becomes much less obvious...... path integral does not depend on the choice of coordinates, but only on a choice of fiberwise volume form. Our outline is an honest proof when the formal path integral is defined without ultraviolet divergences....
Predicting path from undulations for C. elegans using linear and nonlinear resistive force theory
Keaveny, Eric E.; Brown, André E. X.
2017-04-01
A basic issue in the physics of behaviour is the mechanical relationship between an animal and its surroundings. The model nematode C. elegans provides an excellent platform to explore this relationship due to its anatomical simplicity. Nonetheless, the physics of nematode crawling, in which the worm undulates its body to move on a wet surface, is not completely understood and the mathematical models often used to describe this phenomenon are empirical. We confirm that linear resistive force theory, one such empirical model, is effective at predicting a worm’s path from its sequence of body postures for forward crawling, reversing, and turning and for a broad range of different behavioural phenotypes observed in mutant worms. Worms recently isolated from the wild have a higher effective drag anisotropy than the laboratory-adapted strain N2 and most mutant strains. This means the wild isolates crawl with less surface slip, perhaps reflecting more efficient gaits. The drag anisotropies required to fit the observed locomotion data (70 ± 28 for the wild isolates) are significantly larger than the values measured by directly dragging worms along agar surfaces (3–10 in Rabets et al (2014 Biophys. J. 107 1980–7)). A proposed nonlinear extension of the resistive force theory model also provides accurate predictions, but does not resolve the discrepancy between the parameters required to achieve good path prediction and the experimentally measured parameters. We confirm that linear resistive force theory provides a good effective model of worm crawling that can be used in applications such as whole-animal simulations and advanced tracking algorithms, but that the nature of the physical interaction between worms and their most commonly studied laboratory substrate remains unresolved.
Linear integral equations and renormalization group
Klein, W.; Haymet, A. D. J.
1984-08-01
A formulation of the position-space renormalization-group (RG) technique is used to analyze the singular behavior of solutions to a number of integral equations used in the theory of the liquid state. In particular, we examine the truncated Kirkwood-Salsburg equation, the Ornstein-Zernike equation, and a simple nonlinear equation used in the mean-field theory of liquids. We discuss the differences in applying the position-space RG to lattice systems and to fluids, and the need for an explicit free-energy rescaling assumption in our formulation of the RG for integral equations. Our analysis provides one natural way to define a "fractal" dimension at a phase transition.
Hydrogen and muonium in diamond: A path-integral molecular dynamics simulation
Herrero, Carlos P.; Ramírez, Rafael; Hernández, Eduardo R.
2006-06-01
Isolated hydrogen, deuterium, and muonium in diamond have been studied by path-integral molecular dynamics simulations in the canonical ensemble. Finite-temperature properties of these point defects were analyzed in the range from 100 to 800K . Interatomic interactions were modeled by a tight-binding potential fitted to density-functional calculations. The most stable position for these hydrogenic impurities is found at the C-C bond center. Vibrational frequencies have been obtained from a linear-response approach, based on correlations of atom displacements at finite temperatures. The results show a large anharmonic effect in impurity vibrations at the bond center site, which hardens the vibrational modes with respect to a harmonic approximation. Zero-point motion causes an appreciable shift of the defect level in the electronic gap, as a consequence of electron-phonon interaction. This defect level goes down by 70meV when replacing hydrogen by muonium.
Relaxation of two coupled quantum oscillators to quasi-equilibrium states based on path integrals
Dorofeyev, Illarion
2013-01-01
The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths of oscillators. The expression for density matrix was found in the linear regime with respect to the coupling constant between selected oscillators. Time-dependent spatial variances and covariance were investigated analytically and numerically. It was shown that asymptotic variances in the long-time limit are always in accordance with the fluctuation dissipation theorem despite on their initial values. In the weak coupling approach there is good reason to believe that subsystems asymptotically in equilibrium at their own temperatures even despite of the arbitrary difference in temperatures within the whole system.
Path integrals for actions that are not quadratic in their time derivatives
Cahill, Kevin
2015-01-01
The standard way to construct a path integral is to use a Legendre transformation to find the hamiltonian, to repeatedly insert complete sets of states into the time-evolution operator, and then to integrate over the momenta. This procedure is simple when the action is quadratic in its time derivatives, but in most other cases Legendre's transformation is intractable, and the hamiltonian is unknown. This paper shows how to make path integrals without using the hamiltonian.
Error Control of Iterative Linear Solvers for Integrated Groundwater Models
Dixon, Matthew; Brush, Charles; Chung, Francis; Dogrul, Emin; Kadir, Tariq
2010-01-01
An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of 'forward error bound estimation' to show how rescaling the linear system affects the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed using the USGS GSFLOW package and the California State Department of Water Resources' Integrated Water Flow Model (IWFM), we observe that this error bound guides the choice of a prac...
Directory of Open Access Journals (Sweden)
Gülden Gün
2013-01-01
Full Text Available We analyze Noether and -symmetries of the path equation describing the minimum drag work. First, the partial Lagrangian for the governing equation is constructed, and then the determining equations are obtained based on the partial Lagrangian approach. For specific altitude functions, Noether symmetry classification is carried out and the first integrals, conservation laws and group invariant solutions are obtained and classified. Then, secondly, by using the mathematical relationship with Lie point symmetries we investigate -symmetry properties and the corresponding reduction forms, integrating factors, and first integrals for specific altitude functions of the governing equation. Furthermore, we apply the Jacobi last multiplier method as a different approach to determine the new forms of -symmetries. Finally, we compare the results obtained from different classifications.
Power Series Expansion of Propagator for Path Integral and Its Applications
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.
Square-root actions, metric signature, and the path-integral of quantum gravity
Carlini, A; Carlini, A; Greensite, J
1995-01-01
We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand \\exp[ \\sqrt{i} S ] rather than the familiar Feynman expression \\exp[ i S ], and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions.
Square-root actions, metric signature, and the path integral of quantum gravity
Carlini, A.; Greensite, J.
1995-12-01
We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand exp[ √i S] rather than the familiar Feynman expression exp[iS], and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions.
LINEAR SINGULAR INTEGRAL EQUATION ON DOMAINS COMPOSED BY BALLS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
For domains composed by balls in Cn, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain.
Translation and integration of numerical atomic orbitals in linear molecules
Energy Technology Data Exchange (ETDEWEB)
Heinäsmäki, Sami, E-mail: sami.heinasmaki@gmail.com [Department of Physics, University of Oulu, FIN-90014, Oulu (Finland)
2014-02-14
We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.
LINEARIZING THE RESPONSE OF THE NSRL SYNCHRONOUS RECYCLING-INTEGRATORS.
Energy Technology Data Exchange (ETDEWEB)
ODDO, P.; RUSEK, A.; RUSSO, T.
2005-05-16
The Lawrence Berkeley National Laboratory (LBNL) designed recycling-integrators used for the NASA Space Radiation Laboratory (NSRL) dosimetry feature excellent linearity. However, switching transients in the balancing source add a duty-cycle dependence to the response that manifests as a non-linearity near mid-scale and a slope-change above mid-scale. The onset of this non-linearity limits the typical usable dynamic range. Measurements during a recent run showed that at higher intensities the recycling-integrators would operate in the non-linear region enough to exceed the desired tolerance and over count the dose. This report will show how a FPGA, which implements the scalars, was used to compensate the non-linearity allowing higher dose-rates by effectively doubling the dynamic range of the dosimetry system.
Links among impossible differential, integral and zero correlation linear cryptanalysis
DEFF Research Database (Denmark)
Sun, Bing; Liu, Zhiqiang; Rijmen, Vincent
2015-01-01
is to fix this gap and establish links between impossible differential cryptanalysis and integral cryptanalysis. Firstly, by introducing the concept of structure and dual structure, we prove that a → b is an impossible differential of a structure E if and only if it is a zero correlation linear hull...... linear hull always indicates the existence of an integral distinguisher. With this observation we improve the number of rounds of integral distinguishers of Feistel structures, CAST-256, SMS4 and Camellia. Finally, we conclude that an r-round impossible differential of E always leads to an r...
Piloting and Path Integration within and across Boundaries
Mou, Weimin; Wang, Lin
2015-01-01
Three experiments investigated whether navigation is less efficient across boundaries than within boundaries. In an immersive virtual environment, participants learned objects' locations in a large room or a small room. Participants then pointed to the objects' original locations after physically walking a circuitous path without vision.…
Cugliandolo, Leticia F.; Lecomte, Vivien
2017-08-01
The definition and manipulation of Langevin equations with multiplicative white noise require special care (one has to specify the time discretisation and a stochastic chain rule has to be used to perform changes of variables). While discretisation-scheme transformations and non-linear changes of variable can be safely performed on the Langevin equation, these same transformations lead to inconsistencies in its path-integral representation. We identify their origin and we show how to extend the well-known Ito prescription (dB2 = dt ) in a way that defines a modified stochastic calculus to be used inside the path-integral representation of the process, in its Onsager-Machlup form.
Path integrals, SUSY QM and the Atiyah-Singer index theorem for twisted Dirac
Fine, Dana
2016-01-01
Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a path integral. Further, the class of Laplacians includes the square of the twisted Dirac operator, which corresponds to an extension of N=1/2 supersymmetric quantum mechanics. General results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the Atiyah-Singer index theorem.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-01
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-14
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
Shen, Yi; Ren, Gang; Liu, Yang
2016-06-01
In this paper, we propose a biased-shortest path method with minimal congestion. In the method, we use linear-prediction to estimate the queue length of nodes, and propose a dynamic accepting probability function for nodes to decide whether accept or reject the incoming packets. The dynamic accepting probability function is based on the idea of homogeneous network flow and is developed to enable nodes to coordinate their queue length to avoid congestion. A path strategy incorporated with the linear-prediction of the queue length and the dynamic accepting probability function of nodes is designed to allow packets to be automatically delivered on un-congested paths with short traveling time. Our method has the advantage of low computation cost because the optimal paths are dynamically self-organized by nodes in the delivering process of packets with local traffic information. We compare our method with the existing methods such as the efficient path method (EPS) and the optimal path method (OPS) on the BA scale-free networks and a real example. The numerical computations show that our method performs best for low network load and has minimum run time due to its low computational cost and local routing scheme.
A variational path integral molecular dynamics study of a solid helium-4
Miura, Shinichi
2011-01-01
In the present study, a variational path integral molecular dynamics method developed by the author [Chem. Phys. Lett. 482 (2009) 165] is applied to a solid helium-4 in the ground state. The method is a molecular dynamics algorithm for a variational path integral method which can be used to generate the exact ground state numerically. The solid state is shown to successfully be realized by the method, although a poor trial wavefunction that cannot describe the solid state is used.
Which way and how far? Tracking of translation and rotation information for human path integration.
Chrastil, Elizabeth R; Sherrill, Katherine R; Hasselmo, Michael E; Stern, Chantal E
2016-10-01
Path integration, the constant updating of the navigator's knowledge of position and orientation during movement, requires both visuospatial knowledge and memory. This study aimed to develop a systems-level understanding of human path integration by examining the basic building blocks of path integration in humans. To achieve this goal, we used functional imaging to examine the neural mechanisms that support the tracking and memory of translational and rotational components of human path integration. Critically, and in contrast to previous studies, we examined movement in translation and rotation tasks with no defined end-point or goal. Navigators accumulated translational and rotational information during virtual self-motion. Activity in hippocampus, retrosplenial cortex (RSC), and parahippocampal cortex (PHC) increased during both translation and rotation encoding, suggesting that these regions track self-motion information during path integration. These results address current questions regarding distance coding in the human brain. By implementing a modified delayed match to sample paradigm, we also examined the encoding and maintenance of path integration signals in working memory. Hippocampus, PHC, and RSC were recruited during successful encoding and maintenance of path integration information, with RSC selective for tasks that required processing heading rotation changes. These data indicate distinct working memory mechanisms for translation and rotation, which are essential for updating neural representations of current location. The results provide evidence that hippocampus, PHC, and RSC flexibly track task-relevant translation and rotation signals for path integration and could form the hub of a more distributed network supporting spatial navigation. Hum Brain Mapp 37:3636-3655, 2016. © 2016 Wiley Periodicals, Inc.
Path integral methods for the dynamics of stochastic and disordered systems
DEFF Research Database (Denmark)
Hertz, John A.; Roudi, Yasser; Sollich, Peter
2017-01-01
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey...... in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models....
Circular Path and Linear Momentum (CPLM Method for Seismic Response Analysis of Vehicles
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Rishi Ram Parajuli
2016-07-01
Full Text Available We propose a circular path and linear momentum method for the seismic response analysis of vehicles. This method considers the momentum induced by earthquake excitation and applies the concept of centripetal force acting laterally on the vehicle in addition to longitudinal forces. This method is valid for vehicles at rest as well as those moving at a range of speeds. The vertical responses are calculated using a quarter vehicle model. We also calculate the translational motion of the vehicle using a model with six degrees of freedom. Three vehicle types (car, bus, and truck were used in the analysis. We compared the result with analysis of the response of a shaking vehicle from video footage recorded during the Gorkha earthquake. We used the input ground motion from 10 large earthquakes of moment magnitudes 6.7 to 9.0. All three components of the ground motion were used in the analysis. Vehicles at rest and moving at various speeds were analysed. The lateral and longitudinal responses of the vehicles were calculated for different vehicle speeds ranging from 0 to 30.0 m/s, PGA excitations and orientations of the vehicle.
Scalable fiber integrated source for higher-dimensional path-entangled photonic quNits
Schaeff, Christoph; Lapkiewicz, Radek; Fickler, Robert; Ramelow, Sven; Zeilinger, Anton
2012-01-01
Integrated photonic circuits offer the possibility for complex quantum optical experiments in higher-dimensional photonic systems. However, the advantages of integration and scalability can only be fully utilized with the availability of a source for higher-dimensional entangled photons. Here, a novel fiber integrated source for path-entangled photons in the telecom band at 1.55\\mum using only standard fiber technology is presented. Due to the special design the source shows good scalability towards higher-dimensional entangled photonic states (quNits), while path entanglement offers direct compatibility with on-chip path encoding. We present an experimental realization of a path-entangled two-qubit source. A very high quality of entanglement is verified by various measurements, i.a. a tomographic state reconstruction is performed leading to a background corrected fidelity of (99.45+-0.06)%. Moreover, we describe an easy method for extending our source to arbitrarily high dimensions.
Trouvé, Hélène; Couturier, Yves; Etheridge, Francis; Saint-Jean, Olivier; Somme, Dominique
2010-01-01
Background The literature on integration indicates the need for an enhanced theorization of institutional integration. This article proposes path dependence as an analytical framework to study the systems in which integration takes place. Purpose PRISMA proposes a model for integrating health and social care services for older adults. This model was initially tested in Quebec. The PRISMA France study gave us an opportunity to analyze institutional integration in France. Methods A qualitative approach was used. Analyses were based on semi-structured interviews with actors of all levels of decision-making, observations of advisory board meetings, and administrative documents. Results Our analyses revealed the complexity and fragmentation of institutional integration. The path dependency theory, which analyzes the change capacity of institutions by taking into account their historic structures, allows analysis of this situation. The path dependency to the Bismarckian system and the incomplete reforms of gerontological policies generate the coexistence and juxtaposition of institutional systems. In such a context, no institution has sufficient ability to determine gerontology policy and build institutional integration by itself. Conclusion Using path dependence as an analytical framework helps to understand the reasons why institutional integration is critical to organizational and clinical integration, and the complex construction of institutional integration in France. PMID:20689740
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Hélène Trouvé
2010-06-01
Full Text Available Background: The literature on integration indicates the need for an enhanced theorization of institutional integration. This article proposes path dependence as an analytical framework to study the systems in which integration takes place.Purpose: PRISMA proposes a model for integrating health and social care services for older adults. This model was initially tested in Quebec. The PRISMA France study gave us an opportunity to analyze institutional integration in France.Methods: A qualitative approach was used. Analyses were based on semi-structured interviews with actors of all levels of decision-making, observations of advisory board meetings, and administrative documents.Results: Our analyses revealed the complexity and fragmentation of institutional integration. The path dependency theory, which analyzes the change capacity of institutions by taking into account their historic structures, allows analysis of this situation. The path dependency to the Bismarckian system and the incomplete reforms of gerontological policies generate the coexistence and juxtaposition of institutional systems. In such a context, no institution has sufficient ability to determine gerontology policy and build institutional integration by itself.Conclusion: Using path dependence as an analytical framework helps to understand the reasons why institutional integration is critical to organizational and clinical integration, and the complex construction of institutional integration in France.
Directory of Open Access Journals (Sweden)
Hélène Trouvé
2010-06-01
Full Text Available Background: The literature on integration indicates the need for an enhanced theorization of institutional integration. This article proposes path dependence as an analytical framework to study the systems in which integration takes place. Purpose: PRISMA proposes a model for integrating health and social care services for older adults. This model was initially tested in Quebec. The PRISMA France study gave us an opportunity to analyze institutional integration in France. Methods: A qualitative approach was used. Analyses were based on semi-structured interviews with actors of all levels of decision-making, observations of advisory board meetings, and administrative documents. Results: Our analyses revealed the complexity and fragmentation of institutional integration. The path dependency theory, which analyzes the change capacity of institutions by taking into account their historic structures, allows analysis of this situation. The path dependency to the Bismarckian system and the incomplete reforms of gerontological policies generate the coexistence and juxtaposition of institutional systems. In such a context, no institution has sufficient ability to determine gerontology policy and build institutional integration by itself. Conclusion: Using path dependence as an analytical framework helps to understand the reasons why institutional integration is critical to organizational and clinical integration, and the complex construction of institutional integration in France.
Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study
Botelho, Luiz Carlos Lobato
2010-01-01
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent advection, etc. - and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional Lp spaces (the Aubin-Lion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigourous functional integral solutions for the Linear Diffussion equation defined in Infinite-Dimensional Spaces (Separable Hilbert Spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.
The development of path integration: combining estimations of distance and heading.
Smith, Alastair D; McKeith, Laura; Howard, Christina J
2013-12-01
Efficient daily navigation is underpinned by path integration, the mechanism by which we use self-movement information to update our position in space. This process is well understood in adulthood, but there has been relatively little study of path integration in childhood, leading to an underrepresentation in accounts of navigational development. Previous research has shown that calculation of distance and heading both tend to be less accurate in children as they are in adults, although there have been no studies of the combined calculation of distance and heading that typifies naturalistic path integration. In the present study, 5-year-olds and 7-year-olds took part in a triangle-completion task, where they were required to return to the start point of a multi-element path using only idiothetic information. Performance was compared to a sample of adult participants, who were found to be more accurate than children on measures of landing error, heading error, and distance error. Seven-year-olds were significantly more accurate than 5-year-olds on measures of landing error and heading error, although the difference between groups was much smaller for distance error. All measures were reliably correlated with age, demonstrating a clear development of path integration abilities within the age range tested. Taken together, these data make a strong case for the inclusion of path integration within developmental models of spatial navigational processing.
Quantum-classical path integral. I. Classical memory and weak quantum nonlocality.
Lambert, Roberto; Makri, Nancy
2012-12-14
We consider rigorous path integral descriptions of the dynamics of a quantum system coupled to a polyatomic environment, assuming that the latter is well approximated by classical trajectories. Earlier work has derived semiclassical or purely classical expressions for the influence functional from the environment, which should be sufficiently accurate for many situations, but the evaluation of quantum-(semi)classical path integral (QCPI) expressions has not been practical for large-scale simulation because the interaction with the environment introduces couplings nonlocal in time. In this work, we analyze the nature of the effects on a system from its environment in light of the observation [N. Makri, J. Chem. Phys. 109, 2994 (1998)] that true nonlocality in the path integral is a strictly quantum mechanical phenomenon. If the environment is classical, the path integral becomes local and can be evaluated in a stepwise fashion along classical trajectories of the free solvent. This simple "classical path" limit of QCPI captures fully the decoherence of the system via a classical mechanism. Small corrections to the classical path QCPI approximation may be obtained via an inexpensive random hop QCPI model, which accounts for some "back reaction" effects. Exploiting the finite length of nonlocality, we argue that further inclusion of quantum decoherence is possible via an iterative evaluation of the path integral. Finally, we show that the sum of the quantum amplitude factors with respect to the system paths leads to a smooth integrand as a function of trajectory initial conditions, allowing the use of Monte Carlo methods for the multidimensional phase space integral.
National Aeronautics and Space Administration — Develop, integrate and demonstrate a 2-micron pulsed Integrated Path Differential Absorption Lidar (IPDA) instrument CO2 Column Measurement from Airborne platform...
Blondel, Arnaud
2004-05-01
Thermodynamic integration is a widely used method to calculate and analyze the effect of a chemical modification on the free energy of a chemical or biochemical process, for example, the impact of an amino acid substitution on protein association. Numerical fluctuations can introduce large uncertainties, limiting the domain of application of the method. The parametric energy function describing the chemical modification in the thermodynamic integration, the "Alchemical path," determines the amplitudes of the fluctuations. In the present work, I propose a measure of the fluctuations in the thermodynamic integration and an approach to search for a parametric energy path minimizing that measure. The optimal path derived with this approach is very close to the theoretical minimum of the measure, but produces nonergodic sampling. Nevertheless, this path is used to guide the design of a practical and efficient path producing correct sampling. The convergence with this practical path is evaluated on test cases, and compares favorably with that of other methods such as power or polynomial path, soft-core van der Waals, and some other approaches presented in the literature.
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Ting Kuo
2015-05-01
Full Text Available We propose a linear time algorithm, called G2DLP, for generating 2D lattice L(n1, n2 paths, equivalent to two-item multiset permutations, with a given number of turns. The usage of turn has three meanings: in the context of multiset permutations, it means that two consecutive elements of a permutation belong to two different items; in lattice path enumerations, it means that the path changes its direction, either from eastward to northward or from northward to eastward; in open shop scheduling, it means that we transfer a job from one type of machine to another. The strategy of G2DLP is divide-and-combine; the division is based on the enumeration results of a previous study and is achieved by aid of an integer partition algorithm and a multiset permutation algorithm; the combination is accomplished by a concatenation algorithm that constructs the paths we require. The advantage of G2DLP is twofold. First, it is optimal in the sense that it directly generates all feasible paths without visiting an infeasible one. Second, it can generate all paths in any specified order of turns, for example, a decreasing order or an increasing order. In practice, two applications, scheduling and cryptography, are discussed.
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Yunjuan WANG; Detong ZHU
2008-01-01
Based on a differentiable merit function proposed by Taji et al.in "Math.Prog. Stud.,58,1993,369-383",the authors propose an affine scaling interior trust region strategy via optimal path to modify Newton method for the strictly monotone variational inequality problem subject to linear equality and inequality constraints.By using the eigensystem decomposition and affine scaling mapping,the authors form an affine scaling optimal curvilinear path very easily in order to approximately solve the trust region subproblem.Theoretical analysis is given which shows that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.
Bennett, Ilana J; Stark, Craig E L
2016-03-01
Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20-87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network.
Quantum-classical path integral with self-consistent solvent-driven reference propagators.
Banerjee, Tuseeta; Makri, Nancy
2013-10-24
Efficient procedures for evaluating the quantum-classical path integral (QCPI) [J. Chem. Phys. 2013, 137, 22A552] are described. The main idea is to identify a trajectory-specific reference Hamiltonian that captures the dominant effects of the classical "solvent" degrees of freedom on the dynamics of the quantum "system". This time-dependent reference is used to construct a system propagator that is valid for large time increments. Residual "quantum memory" interactions are included via the path integral representation of the density matrix, which converges with large time steps. Two physically motivated reference schemes are considered. The first involves the dynamics of the solvent unperturbed by the system, which forms the basis for the "classical path" approximation. The second is based on solvent trajectories determined self-consistently with the evolution of the system, according to the time-dependent self-consistent field or Ehrenfest model. Application to dissipative two-level systems indicates that both reference schemes allow a substantial increase of the path integral time step, leading to rapid convergence of the path sum. In addition, the time-dependent reference propagators automatically weigh state-to-state coupling against solvent reorganization in the determination of transition probabilities, further enhancing the convergence of the path integral.
Linear energy-preserving integrators for Poisson systems
Cohen, David; Hairer, Ernst
2011-01-01
For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge-Kutta method with infinitely many stages.
Efficient Calculation of Energy Expectation Values in the Path Integral Formalism
Grujic, J
2006-01-01
The path integral formalism, originally introduced by Richard Feynman, represents a powerful general framework for dealing with quantum and statistical theories, as well as an extremely useful tool in many other areas of science. Their numerical integration, however, is notoriously demanding of computer time and it is one of the most challenging computational problems.
Automatic Tool Path Generation for Robot Integrated Surface Sculpturing System
Zhu, Jiang; Suzuki, Ryo; Tanaka, Tomohisa; Saito, Yoshio
In this paper, a surface sculpturing system based on 8-axis robot is proposed, the CAD/CAM software and tool path generation algorithm for this sculpturing system are presented. The 8-axis robot is composed of a 6-axis manipulator and a 2-axis worktable, it carves block of polystyrene foams by heated cutting tools. Multi-DOF (Degree of Freedom) robot benefits from the faster fashion than traditional RP (Rapid Prototyping) methods and more flexibility than CNC machining. With its flexibility driven from an 8-axis configuration, as well as efficient custom-developed software for rough cutting and finish cutting, this surface sculpturing system can carve sculptured surface accurately and efficiently.
A path-integral Langevin equation treatment of low-temperature doped helium clusters.
Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas
2012-06-14
We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)] sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of He(N)-CO(2) clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], an open-source molecular simulation package.
Utama, Briandhika; Purqon, Acep
2016-08-01
Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods.
On linear degeneracy of integrable quasilinear systems in higher dimensions
Ferapontov, E V; Klein, C
2010-01-01
We investigate $(d+1)$-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case $d\\geq 3$ we formulate a conjecture that any such system with an irreducible dispersion relation must be linearly degenerate. We prove this conjecture in the 2-component case, providing a complete classification of multi-dimensional integrable systems in question. In particular, our results imply the non-existence of 2-component integrable systems of hydrodynamic type for $d\\geq 6$. In the second half of the paper we discuss a numerical and analytical evidence for the impossibility of the breakdown of smooth initial data for linearly degenerate systems in 2+1 dimensions.
Semi-classical Locality for the Non-relativistic Path Integral in Configuration Space
Gomes, Henrique
2017-09-01
In an accompanying paper Gomes (arXiv:1504.02818, 2015), we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe M, existing on timeless configuration space Q of some field over M. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. Locality in full can only emerge dynamically, and is not postulated. This new understanding of locality is based solely on the properties of extremal paths in configuration space. I do not demand locality from the start, as it is usually done, but showed conditions under which certain systems exhibit it spontaneously. In this way we recover semi-classical local behavior when regions dynamically decouple from each other, a notion more appropriate for extension into quantum mechanics. The dynamics of a sub-region O within the closed manifold M is independent of its complement, M-O, if the projection of extremal curves on Q onto the space of extremal curves intrinsic to O is a surjective map. This roughly corresponds to e^{i\\hat{H}t}circ prO= prOcirc e^{i\\hat{H}t}, where prO:Q→ Q_O^{partial O} is a linear projection. This criterion for locality can be made approximate—an impossible feat had it been already postulated—and it can be applied for theories which do not have hyperbolic equations of motion, and/or no fixed causal structure. When two regions are mutually independent according to the criterion proposed here, the semi-classical path integral kernel factorizes, showing cluster decomposition which is the ultimate aim of a definition of locality.
Path integral in area tensor Regge calculus and complex connections
Khatsymovsky, V M
2006-01-01
Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection variables. Discrete connection and curvature on classical solutions of the equations of motion are not, strictly speaking, genuine connection and curvature, but more general quantities and, therefore, these do not appear as arguments of a function to be averaged, but are the integration (dummy) variables. We argue that upon integrating out the latter the resulting measure can be well-defined on physical hypersurface (for the area tensors corresponding to certain edge vectors, i.e. to certain metric) as positive and having exponential cutoff at large areas on condition that we confine ourselves to configurations which do not pass through degenerate metrics.
A path integral approach to asset-liability management
Decamps, M.; de Schepper, A.; Goovaerts, M.J.
2006-01-01
Functional integrals constitute a powerful tool in the investigation of financial models. In the recent econophysics literature, this technique was successfully used for the pricing of a number of derivative securities. In the present contribution, we introduce this approach to the field of asset-li
i-PI: A Python interface for ab initio path integral molecular dynamics simulations
Ceriotti, Michele; Manolopoulos, David E
2014-01-01
Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high pressure water.
A Neural Path Integration Mechanism for Adaptive Vector Navigation in Autonomous Agents
DEFF Research Database (Denmark)
Goldschmidt, Dennis; Dasgupta, Sakyasingha; Wörgötter, Florentin
2015-01-01
Animals show remarkable capabilities in navigating their habitat in a fully autonomous and energy-efficient way. In many species, these capabilities rely on a process called path integration, which enables them to estimate their current location and to find their way back home after long-distance......Animals show remarkable capabilities in navigating their habitat in a fully autonomous and energy-efficient way. In many species, these capabilities rely on a process called path integration, which enables them to estimate their current location and to find their way back home after long...... of autonomous agent navigation, but it also reproduces various aspects of animal navigation. Finally, we discuss how the proposed path integration mechanism may be used as a scaffold for spatial learning in terms of vector navigation....
Path integral approach to eikonal and next-to-eikonal exponentiation
Laenen, E; White, C D
2009-01-01
We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.
Path integration in the field of a topological defect: the case of dispiration
Inomata, Akira; Raynolds, James
2011-01-01
The motion of a particle in the field of dispiration (due to a wedge disclination and a screw dislocation) is studied by path integration. By gauging $SO(2) \\otimes T(1)$, first, we derive the metric, curvature, and torsion of the medium of dispiration. Then we carry out explicitly path integration for the propagator of a particle moving in the non-Euclidean medium under the influence of a scalar potential and a vector potential. We obtain also the winding number representation of the propagator by taking the non-trivial topological structure of the medium into account. We extract the energy spectrum and the eigenfunctions from the propagator. Finally we make some remarks for special cases. Particularly, paying attention to the difference between the result of the path integration and the solution of Schr\\"odinger's equation in the case of disclination, we suggest that Schr\\"odinger equation may have to be modified by a curvature term.
On the Structure of QFT in the Particle Picture of the Path Integral Formulation
Jackson, D M; Morales, A
2008-01-01
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately require knowledge of non-perturbative or even Planck scale physics. Alternatively, QFT can be formulated directly in the particle picture, namely as a sum over all multi-particle paths, i.e., over Feynman graphs. This path integral is well-defined, as a map between rings of formal power series. This suggests a program for determining which structures of QFT are provable for this path integral and thus are combinatorial in nature, and which structures are actually sensitive to analytic issues. For a start, we show that the fact that the Legendre transform of the sum of connected graphs yields the effective action is indeed combinatorial in nature and is thus independent of analytic assumptions. Our proof also leads to new methods for the efficient decomposition of Feynman graph...
Robust path integration in the entorhinal grid cell system with hippocampal feed-back.
Samu, Dávid; Eros, Péter; Ujfalussy, Balázs; Kiss, Tamás
2009-07-01
Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code.
Path integral regularization of QED by means of Stueckelberg fields
Jacquot, J L
2005-01-01
With the help of a Stueckelberg field we construct a regularized U(1) gauge invariant action through the introduction of cutoff functions. This action has the property that it converges formally to the unregularized action of QED when the ultraviolet cutoff goes to infinity. Integrating out exactly the Stueckelberg field we obtain a simple effective regularized action, which is fully gauge invariant and gives rise to the same prediction as QED at the tree level and to the one loop order.
Pérez, Alejandro; Tuckerman, Mark E.
2011-08-01
Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems.
Directory of Open Access Journals (Sweden)
Luis M. Sesé
2017-02-01
Full Text Available This work deals with the computation of the structure factors of quantum fluids under complex conditions involving substantial density fluctuations and/or large particle delocalization effects. The method is based on the combination of path-integral Monte Carlo (PIMC simulations and the pair Ornstein-Zernike framework (OZ2. PIMC provides the radial correlation functions (centroid, instantaneous, and thermalized-continuous total linear response, which are used as data input to the OZ2 calculations that lead to their associated structure factors. To undertake this project normal liquid 4He and supercritical 3He are selected, studying conditions in the range (T = 4.2 K; 0.01886 <ρN/Å-3 < 0.02687. Full inter-comparison between the structure factors determined via both OZ2 and direct PIMC calculations is made. In addition, comparison with experimental data, including thermodynamic properties, is made wherever possible. The results establish that, even under severe thermodynamic and/or quantum fluctuation conditions, OZ2 remains in the quantum domain as a highly reliable and cost-effective framework to determine accurate structure factors, also allowing one to understand the related isotopic shifts in fluid He.
Linear Volterra Integral Equations as the Limit of Discrete Systems
Institute of Scientific and Technical Information of China (English)
M. Federson; R.Bianconi; L.Barbanti
2004-01-01
We consider the multidimensional abstract linear integral equation of Volterra typex (t)+(*)∫Rt a (s)x (s)ds =f (t),t∈R,as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions.The functions x,a and f are Banach space-valued de .ned on a compact interval R of R n ,R t is a subinterval of R depending on t∈R and (*)∫denotes either the Bochner-Lebesgue integral or the Henstock integral.The results presented here generalize those in [1]and are in the spirit of [3].As a consequence of our approach,it is possible to study the properties of (1)by transferring the properties of the discrete systems.The Henstock integral setting enables us to consider highly oscillating functions.
Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals
Reuter, M; Schubert, C; Reuter, Martin; Schmidt, Michael G.; Schubert, Christian
1996-01-01
We investigate the usefulness of the ``string-inspired technique'' for gauge theory calculations in a constant external field background. Our approach is based on Strassler's worldline path integral approach to the Bern-Kosower formalism, and on the construction of worldline (super--) Green's functions incorporating external fields as well as internal propagators. The worldline path integral representation of the gluon loop is reexamined in detail. We calculate the two-loop effective actions induced for a constant external field by a scalar and spinor loop, and the corresponding one-loop effective action in the gluon loop case.
Ab initio path integral ring polymer molecular dynamics: Vibrational spectra of molecules
Shiga, Motoyuki; Nakayama, Akira
2008-01-01
The path integral ring polymer molecular dynamics method is combined with 'on-the-fly' ab initio electronic structure calculations and applied to vibrational spectra of small molecules, LiH and H 2O, at the room temperature. The results are compared with those of the numerically exact solution and ab initio path integral centroid molecular dynamics calculation. The peak positions in the calculated spectra are found to be reasonable, showing the red-shift due to potential anharmonicity. This unification enables the investigation of real-time quantum dynamics of chemically complex molecular systems on the ab initio Born-Oppenheimer potential energy surface.
Variational Path-Integral Study on Bound Polarons in Parabolic Quantum Dots and Wires
Institute of Scientific and Technical Information of China (English)
CHEN Qing-Hu; WANG Zhuang-Bing; WU Fu-Li; LUO Meng-Bo; RUAN Yong-Hong; JIAO Zheng-Kuan
2001-01-01
The expression of the ground-state energy of an electron coupled simultaneously with a Coulomb potential and a longitudinal-optical phonon field in parabolic quantum dots and wires is derived within the framework of Feynman variational path-integral theory. We obtain a general result with arbitrary electron-phonon coupling constant,Coulomb binding parameters, and confining potential strength, which could be used for further numerical calculation of polaron properties. Moreover, it is shown that all the previous path-integral formulae for free polarons,bound polarons, and polarons confined in parabolic quantum dots and wires can be recovered in the present formalism.
High-order Path Integral Monte Carlo methods for solving quantum dot problems
Chin, Siu A
2014-01-01
The conventional second-order Path Integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the ground state wave function at large imaginary time. In this work, we show that optimized fourth-order Path Integral Monte Carlo methods, which use no more than 5 free-fermion propagators, can yield accurate quantum dot energies for up to 20 polarized electrons with the use of the Hamiltonian energy estimator.
Quantum field theory from operators to path integrals
Huang, Kerson
1998-01-01
A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained
A path integral approach to asset-liability management
Decamps, Marc; De Schepper, Ann; Goovaerts, Marc
2006-05-01
Functional integrals constitute a powerful tool in the investigation of financial models. In the recent econophysics literature, this technique was successfully used for the pricing of a number of derivative securities. In the present contribution, we introduce this approach to the field of asset-liability management. We work with a representation of cash flows by means of a two-dimensional delta-function perturbation, in the case of a Brownian model and a geometric Brownian model. We derive closed-form solutions for a finite horizon ALM policy. The results are numerically and graphically illustrated.
Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.
Gao, J
2016-01-01
Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects.
A Differential Monolithically Integrated Inductive Linear Displacement Measurement Microsystem
Directory of Open Access Journals (Sweden)
Matija Podhraški
2016-03-01
Full Text Available An inductive linear displacement measurement microsystem realized as a monolithic Application-Specific Integrated Circuit (ASIC is presented. The system comprises integrated microtransformers as sensing elements, and analog front-end electronics for signal processing and demodulation, both jointly fabricated in a conventional commercially available four-metal 350-nm CMOS process. The key novelty of the presented system is its full integration, straightforward fabrication, and ease of application, requiring no external light or magnetic field source. Such systems therefore have the possibility of substituting certain conventional position encoder types. The microtransformers are excited by an AC signal in MHz range. The displacement information is modulated into the AC signal by a metal grating scale placed over the microsystem, employing a differential measurement principle. Homodyne mixing is used for the demodulation of the scale displacement information, returned by the ASIC as a DC signal in two quadrature channels allowing the determination of linear position of the target scale. The microsystem design, simulations, and characterization are presented. Various system operating conditions such as frequency, phase, target scale material and distance have been experimentally evaluated. The best results have been achieved at 4 MHz, demonstrating a linear resolution of 20 µm with steel and copper scale, having respective sensitivities of 0.71 V/mm and 0.99 V/mm.
A Differential Monolithically Integrated Inductive Linear Displacement Measurement Microsystem.
Podhraški, Matija; Trontelj, Janez
2016-03-17
An inductive linear displacement measurement microsystem realized as a monolithic Application-Specific Integrated Circuit (ASIC) is presented. The system comprises integrated microtransformers as sensing elements, and analog front-end electronics for signal processing and demodulation, both jointly fabricated in a conventional commercially available four-metal 350-nm CMOS process. The key novelty of the presented system is its full integration, straightforward fabrication, and ease of application, requiring no external light or magnetic field source. Such systems therefore have the possibility of substituting certain conventional position encoder types. The microtransformers are excited by an AC signal in MHz range. The displacement information is modulated into the AC signal by a metal grating scale placed over the microsystem, employing a differential measurement principle. Homodyne mixing is used for the demodulation of the scale displacement information, returned by the ASIC as a DC signal in two quadrature channels allowing the determination of linear position of the target scale. The microsystem design, simulations, and characterization are presented. Various system operating conditions such as frequency, phase, target scale material and distance have been experimentally evaluated. The best results have been achieved at 4 MHz, demonstrating a linear resolution of 20 µm with steel and copper scale, having respective sensitivities of 0.71 V/mm and 0.99 V/mm.
A Differential Monolithically Integrated Inductive Linear Displacement Measurement Microsystem
Podhraški, Matija; Trontelj, Janez
2016-01-01
An inductive linear displacement measurement microsystem realized as a monolithic Application-Specific Integrated Circuit (ASIC) is presented. The system comprises integrated microtransformers as sensing elements, and analog front-end electronics for signal processing and demodulation, both jointly fabricated in a conventional commercially available four-metal 350-nm CMOS process. The key novelty of the presented system is its full integration, straightforward fabrication, and ease of application, requiring no external light or magnetic field source. Such systems therefore have the possibility of substituting certain conventional position encoder types. The microtransformers are excited by an AC signal in MHz range. The displacement information is modulated into the AC signal by a metal grating scale placed over the microsystem, employing a differential measurement principle. Homodyne mixing is used for the demodulation of the scale displacement information, returned by the ASIC as a DC signal in two quadrature channels allowing the determination of linear position of the target scale. The microsystem design, simulations, and characterization are presented. Various system operating conditions such as frequency, phase, target scale material and distance have been experimentally evaluated. The best results have been achieved at 4 MHz, demonstrating a linear resolution of 20 µm with steel and copper scale, having respective sensitivities of 0.71 V/mm and 0.99 V/mm. PMID:26999146
Accelerated path integral methods for atomistic simulations at ultra-low temperatures.
Uhl, Felix; Marx, Dominik; Ceriotti, Michele
2016-08-07
Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5 (+). We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state.
On the coordinate (in)dependence of the formal path integral
DEFF Research Database (Denmark)
Johnson-Freyd, Theo
. In this short note, aimed primarily at mathematicians, we first briefly recall the notions of Lagrangian classical and quantum field theory and the standard coordinate-full definition of the “formal” or “Feynman-diagrammatic” path integral construction. We then outline a proof of the following claim: the formal...
Integrated Flight Path Planning System and Flight Control System for Unmanned Helicopters
Directory of Open Access Journals (Sweden)
Yu-Hsiang Lin
2011-07-01
Full Text Available This paper focuses on the design of an integrated navigation and guidance system for unmanned helicopters. The integrated navigation system comprises two systems: the Flight Path Planning System (FPPS and the Flight Control System (FCS. The FPPS finds the shortest flight path by the A-Star (A* algorithm in an adaptive manner for different flight conditions, and the FPPS can add a forbidden zone to stop the unmanned helicopter from crossing over into dangerous areas. In this paper, the FPPS computation time is reduced by the multi-resolution scheme, and the flight path quality is improved by the path smoothing methods. Meanwhile, the FCS includes the fuzzy inference systems (FISs based on the fuzzy logic. By using expert knowledge and experience to train the FIS, the controller can operate the unmanned helicopter without dynamic models. The integrated system of the FPPS and the FCS is aimed at providing navigation and guidance to the mission destination and it is implemented by coupling the flight simulation software, X-Plane, and the computing software, MATLAB. Simulations are performed and shown in real time three-dimensional animations. Finally, the integrated system is demonstrated to work successfully in controlling the unmanned helicopter to operate in various terrains of a digital elevation model (DEM.
Path Integral Treatment of Proton Transport Processes in BaZrO3
DEFF Research Database (Denmark)
Zhang, Qianfan; Wahnstrom, Goran; Björketun, Mårten
2008-01-01
Nuclear quantum effects on proton transfer and reorientation in BaZrO3 is investigated theoretically using the ab initio path-integral molecular-dynamics simulation technique. The result demonstrates that adding quantum fluctuations has a large effect on, in particular, the transfer barrier...
Comment on "Dual path integral representation for finite temperature quantum field theory"
Kazinski, P O
2008-01-01
I show that the novel dual path integral representation for finite temperature quantum field theory proposed in [Phys. Rev. D 77, 105030 (2008), arXiv:0803.1667 ] is a well-known representation of quantum mechanics in terms of symbols of operators.
Factors Affecting Technology Integration in K-12 Classrooms: A Path Model
Inan, Fethi A.; Lowther, Deborah L.
2010-01-01
The purpose of this study was to examine the direct and indirect effects of teachers' individual characteristics and perceptions of environmental factors that influence their technology integration in the classroom. A research-based path model was developed to explain causal relationships between these factors and was tested based on data gathered…
Some comments on rigorous quantum field path integrals in the analytical regularization scheme
Energy Technology Data Exchange (ETDEWEB)
Botelho, Luiz C.L. [Universidade Federal Fluminense (UFF), Niteroi, RJ (Brazil). Dept. de Matematica Aplicada]. E-mail: botelho.luiz@superig.com.br
2008-07-01
Through the systematic use of the Minlos theorem on the support of cylindrical measures on R{sup {infinity}}, we produce several mathematically rigorous path integrals in interacting euclidean quantum fields with Gaussian free measures defined by generalized powers of the Laplacian operator. (author)
2012-06-06
...Notice is hereby given that the U.S. International Trade Commission has received a complaint entitled Certain Integrated Circuit Packages Provided With Multiple Heat-Conducting Paths and Products Containing Same, DN 2899; the Commission is soliciting comments on any public interest issues raised by the complaint or complainant's filing under section 210.8(b) of the Commission's Rules of......
Kleinert, H.; Zatloukal, V.
2015-01-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
Accelerated path integral methods for atomistic simulations at ultra-low temperatures
Uhl, Felix; Marx, Dominik; Ceriotti, Michele
2016-08-01
Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5+. We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state.
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo
2012-01-01
This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo
2012-01-01
This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)
Fourier Path Integral Monte Carlo Method for the Calculation of the Microcanonical Density of States
Freeman, D L; Freeman, David L.
1994-01-01
Using a Hubbard-Stratonovich transformation coupled with Fourier path integral methods, expressions are derived for the numerical evaluation of the microcanonical density of states for quantum particles obeying Boltzmann statistics. A numerical algorithmis suggested to evaluate the quantum density of states and illustrated on a one-dimensional model system.
Coherent-state path integrals in the continuum: The SU(2) case
Kordas, G.; Kalantzis, D.; Karanikas, A. I.
2016-09-01
We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
An Integrated Expert System for Linear Scheduling Heavy Earthmoving Operations
Directory of Open Access Journals (Sweden)
Nizar Markiz
2016-01-01
Full Text Available Heavy earthmoving operations are repetitive in nature and vulnerable to time-related restraints and uncertainties. Therefore, at the conceptual stage, scheduling these operations can take a linear form, known as linear schedule or line of balance (LOB. In such type of work, generating a preliminary line of balance for variable sequencing of activities is crucial. In this paper, an integrated expert system for determining preliminary linear schedules for heavy earthmoving operations at the conceptual stage is presented. The proposed system incorporates numerous factors that influence the analysis of earthmoving operations, which include geological and topographical parameters used to determine productivity rates at the conceptual stage. Also, the proposed system is capable of automatically generating a line of balance based on a stochastic scheduling technique via the metaheuristic simulated annealing intelligent approach to incorporate randomness and uncertainties in performing the associated activities. A parametric analysis is conducted in order to quantify the system’s degree of accuracy. An actual case project is then utilized to illustrate its numerical capabilities. Generating accurate linear schedules for heavy earthmoving operations at the conceptual design stage is anticipated to be of major significance to infrastructure project stakeholders, engineers, and construction managers by detecting schedule’s conflicts early in order to enhance overall operational logistics.
Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1
Yang, Danyu
2012-01-01
1.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral is the only possible candidate to enhance a path with vanishing 2-variation into a geometric 2-rough path. 3.Young integral is extended to p^-1+q^-1=1 by assigning a finer scale continuity.
Directory of Open Access Journals (Sweden)
Mihai V. Putz
2009-11-01
Full Text Available The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving many-electronic systems.
Coherent integrated receiver for highly linear microwave photonic links
Klamkin, Jonathan
Phase modulation can be used to improve the signal-to-noise ratio and spurfree dynamic range (SFDR) of microwave photonic links because phase modulation is not limited in input modulation swing and is inherently linear using certain electro-optic devices. Traditional interferometer-based phase demodulators have a sinusoidal response therefore a novel approach is required for achieving linear coherent detection at the receive end of a photonic link employing phase modulation. In this work, a balanced receiver with feedback to a reference tracking phase modulator was developed. With sufficient feedback loop gain, the received signal phase is closely tracked and the phase detection falls within the linear regime of the interferometer response. For stable operation at high frequency the delay of the feedback loop must be kept short, therefore a monolithic approach is required to realize a compact receiver architecture. The monolithic photonic integrated circuit (PIC) developed here consists of a high power balanced uni-traveling-carrier photodiode (UTC-PD), a compact 2x2 multimode interference (MMI) coupler, and multi-quantum well reference phase modulators. This PIC is hybrid integrated with an electronic IC that provides transconductance amplification of the feedback signal for increased loop gain. Novel concepts such as charge compensation, partially depleted absorption, and absorption profile modification were incorporated into the design of the waveguide UTCPDs resulting in record output saturation current and linearity. Both general interference surface ridge (SR) MMI couplers and restricted interference deep ridge (DR) MMI couplers were explored, the latter for reducing the loop delay. Current injection tuning was incorporated into the MMI couplers for fine tuning the output power splitting ratio. The quantum well design of the reference phase modulators was optimized for realizing low Vpi, low insertion loss, low absorption modulation, and improved linearity
Quasi-Linear Algebras and Integrability (the Heisenberg Picture
Directory of Open Access Journals (Sweden)
Alexei Zhedanov
2008-02-01
Full Text Available We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators as functions of ''time'' t. We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, q-Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution interpretation of the corresponding integrable systems.
Hierarchical Non-linear Image Registration Integrating Deformable Segmentation
Institute of Scientific and Technical Information of China (English)
RAN Xin; QI Fei-hu
2005-01-01
A hierarchical non-linear method for image registration was presented, which integrates image segmentation and registration under a variational framework. An improved deformable model is used to simultaneously segment and register feature from multiple images. The objects in the image pair are segmented by evolving a single contour and meanwhile the parameters of affine registration transformation are found out. After that, a contour-constrained elastic registration is applied to register the images correctly. The experimental results indicate that the proposed approach is effective to segment and register medical images.
Exactly solvable path integral for open cavities in terms of quasinormal modes
Maasen van den Brink, A
2000-01-01
We evaluate the finite-temperature Euclidean phase-space path integral for the generating functional of a scalar field inside a leaky cavity. Provided the source is confined to the cavity, one can first of all integrate out the fields on the outside to obtain an effective action for the cavity alone. Subsequently, one uses an expansion of the cavity field in terms of its quasinormal modes (QNMs)-the exact, exponentially damped eigenstates of the classical evolution operator, which previously have been shown to be complete for a large class of models. Dissipation causes the effective cavity action to be nondiagonal in the QNM basis. The inversion of this action matrix inherent in the Gaussian path integral to obtain the generating functional is therefore nontrivial, but can be accomplished by invoking a novel QNM sum rule. The results are consistent with those obtained previously using canonical quantization.
Zhang, Sijie; Schönfeld, Fabian; Wiskott, Laurenz; Manahan-Vaughan, Denise
2014-01-01
Effective spatial navigation is enabled by reliable reference cues that derive from sensory information from the external environment, as well as from internal sources such as the vestibular system. The integration of information from these sources enables dead reckoning in the form of path integration. Navigation in the dark is associated with the accumulation of errors in terms of perception of allocentric position and this may relate to error accumulation in path integration. We assessed this by recording from place cells in the dark under circumstances where spatial sensory cues were suppressed. Spatial information content, spatial coherence, place field size, and peak and infield firing rates decreased whereas sparsity increased following exploration in the dark compared to the light. Nonetheless it was observed that place field stability in darkness was sustained by border information in a subset of place cells. To examine the impact of encountering the environment’s border on navigation, we analyzed the trajectory and spiking data gathered during navigation in the dark. Our data suggest that although error accumulation in path integration drives place field drift in darkness, under circumstances where border contact is possible, this information is integrated to enable retention of spatial representations. PMID:25009477
Bressloff, Paul C
2015-01-01
We consider applications of path-integral methods to the analysis of a stochastic hybrid model representing a network of synaptically coupled spiking neuronal populations. The state of each local population is described in terms of two stochastic variables, a continuous synaptic variable and a discrete activity variable. The synaptic variables evolve according to piecewise-deterministic dynamics describing, at the population level, synapses driven by spiking activity. The dynamical equations for the synaptic currents are only valid between jumps in spiking activity, and the latter are described by a jump Markov process whose transition rates depend on the synaptic variables. We assume a separation of time scales between fast spiking dynamics with time constant [Formula: see text] and slower synaptic dynamics with time constant τ. This naturally introduces a small positive parameter [Formula: see text], which can be used to develop various asymptotic expansions of the corresponding path-integral representation of the stochastic dynamics. First, we derive a variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit [Formula: see text]). We then show how the path integral provides an efficient method for obtaining a diffusion approximation of the hybrid system for small ϵ. The resulting Langevin equation can be used to analyze the effects of fluctuations within the basin of attraction of a metastable state, that is, ignoring the effects of large deviations. We illustrate this by using the Langevin approximation to analyze the effects of intrinsic noise on pattern formation in a spatially structured hybrid network. In particular, we show how noise enlarges the parameter regime over which patterns occur, in an analogous fashion to PDEs. Finally, we carry out a [Formula: see text]-loop expansion of the path integral, and use this to derive corrections to voltage-based mean-field equations, analogous
First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators
Directory of Open Access Journals (Sweden)
R. Naz
2011-01-01
Full Text Available We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations. The difference arises in the gauge terms due to Lagrangians being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian. We have illustrated it here for nonlinear Duffing oscillators.
A linear coherent integrated receiver based on a broadband optical phase-locked loop
Ramaswamy, Anand
Optical Phase-Locked Loops (OPLL) have diverse applications in future communication systems. They can be used in high sensitivity homodyne phase-shift keying receivers for phase noise reduction, provided sufficient loop bandwidth is maintained. Alternative phase-locked loop applications include coherent synchronization of laser arrays and frequency synthesis by offset locking. In this work, a broadband OPLL based coherent receiver is used for linear phase demodulation. Phase modulated (PM) analog optical links have the potential to outperform conventional direct detection links. However, their progress has been stymied by the lack of a linear phase demodulator. We describe how feedback can be used to suppress non-linearities arising from the phase demodulation process. The receiver concept is demonstrated at low frequencies and is found to improve the Spurious Free Dynamic Range (SFDR) of an experimental analog link by over 20dB. In order to extend the operation of the receiver to microwave frequencies, latencies arising from physical delays in the feedback path need to be dramatically reduced. To facilitate this, monolithic and hybrid versions of the receiver based on compact integration of InP photonic integrated circuits (PIC) with InP and SiGe electronic integrated circuits (EIC) have been developed at UCSB. In this work, we develop novel measurement techniques to characterize the linearity of the individual components of the PIC, namely, the semiconductor photodiodes and optical phase modulators. We then demonstrate the operation of the receiver in a high power analog link. The OPLL based receiver has a bandwidth of 1.5GHz. The link gain and shot-noise limited SFDR at 300MHz are -2dB and 125dB-Hz2/3, respectively. Further, optical sampling downconversion is demonstrated as a viable technique to increase the operating frequency of the receiver beyond the baseband range.
Statistical mechanics and field theory. [Path integrals, lattices, pseudofree vertex model
Energy Technology Data Exchange (ETDEWEB)
Samuel, S.A.
1979-05-01
Field theory methods are applied to statistical mechanics. Statistical systems are related to fermionic-like field theories through a path integral representation. Considered are the Ising model, the free-fermion model, and close-packed dimer problems on various lattices. Graphical calculational techniques are developed. They are powerful and yield a simple procedure to compute the vacuum expectation value of an arbitrary product of Ising spin variables. From a field theorist's point of view, this is the simplest most logical derivation of the Ising model partition function and correlation functions. This work promises to open a new area of physics research when the methods are used to approximate unsolved problems. By the above methods a new model named the 128 pseudo-free vertex model is solved. Statistical mechanics intuition is applied to field theories. It is shown that certain relativistic field theories are equivalent to classical interacting gases. Using this analogy many results are obtained, particularly for the Sine-Gordon field theory. Quark confinement is considered. Although not a proof of confinement, a logical, esthetic, and simple picture is presented of how confinement works. A key ingredient is the insight gained by using an analog statistical system consisting of a gas of macromolecules. This analogy allows the computation of Wilson loops in the presence of topological vortices and when symmetry breakdown occurs in the topological quantum number. Topological symmetry breakdown calculations are placed on approximately the same level of rigor as instanton calculations. The picture of confinement that emerges is similar to the dual Meissner type advocated by Mandelstam. Before topological symmetry breakdown, QCD has monopoles bound linearly together by three topological strings. Topological symmetry breakdown corresponds to a new phase where these monopoles are liberated. It is these liberated monopoles that confine quarks. 64 references.
Functional integration of vertical flight path and speed control using energy principles
Lambregts, A. A.
1984-01-01
A generalized automatic flight control system was developed which integrates all longitudinal flight path and speed control functions previously provided by a pitch autopilot and autothrottle. In this design, a net thrust command is computed based on total energy demand arising from both flight path and speed targets. The elevator command is computed based on the energy distribution error between flight path and speed. The engine control is configured to produce the commanded net thrust. The design incorporates control strategies and hierarchy to deal systematically and effectively with all aircraft operational requirements, control nonlinearities, and performance limits. Consistent decoupled maneuver control is achieved for all modes and flight conditions without outer loop gain schedules, control law submodes, or control function duplication.
The Role of Spatial Memory and Frames of Reference in the Precision of Angular Path Integration
Arthur, Joeanna C.; Philbeck, John W.; Kleene, Nicholas J.; Chichka, David
2012-01-01
Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatial memory is particularly likely in spatial updating tasks in which one’s self-location estimate is referenced to external space. To test this idea, we administered passive, nonvisual body rotations (ranging 40° – 140°) about the yaw axis and asked participants to use verbal reports or open-loop manual pointing to indicate the magnitude of the rotation. Prior to some trials, previews of the surrounding environment were given. We found that when participants adopted an egocentric frame of reference, the previously-observed benefit of previews on within-subject response precision was not manifested, regardless of whether remembered spatial frameworks were derived from vision or spatial language. We conclude that the powerful effect of spatial memory is dependent on one’s frame of reference during self-motion updating. PMID:22885073
The role of spatial memory and frames of reference in the precision of angular path integration.
Arthur, Joeanna C; Philbeck, John W; Kleene, Nicholas J; Chichka, David
2012-09-01
Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatial memory is particularly likely in spatial updating tasks in which one's self-location estimate is referenced to external space. To test this idea, we administered passive, non-visual body rotations (ranging 40°-140°) about the yaw axis and asked participants to use verbal reports or open-loop manual pointing to indicate the magnitude of the rotation. Prior to some trials, previews of the surrounding environment were given. We found that when participants adopted an egocentric frame of reference, the previously-observed benefit of previews on within-subject response precision was not manifested, regardless of whether remembered spatial frameworks were derived from vision or spatial language. We conclude that the powerful effect of spatial memory is dependent on one's frame of reference during self-motion updating.
The path-independent M Integral around Röthlisberger channels
Meyer, C. R.; Rice, J. R.
2015-12-01
Röthlisberger channels are essential components of subglacial hydrologic systems. Deviations from the Nye creep closure of the ice around a Röthlisberger channel have been long recognized and enhancement factors or a more complex rheology for ice have been suggested as ameliorations to account for channels closing faster than predicted. Here we use the MM integral, a path-independent integral of the equations of continuum mechanics, with a Glen power-law rheology to unify descriptions of creep closure under a variety of stress states surrounding the Röthlisberger channel. The advantage of this approach is that the MM integral around the Röthlisberger channel is equivalent to the integral around the far field. In this way, the creep closure on the channel wall can be determined as a function of the far-field loading, e.g. antiplane shear as well as overburden pressure. We start by analyzing the case of axisymmetric creep closure and we see that the Nye solution is implied by the path-independence of MM integral. We then examine the effects of antiplane shear in several geometries and derive scalings for the creep closure rate based on the MM integral. The results are compared to observations for tunnel closure measurements in a variety of stress states and it is shown that the additional stress components can account for the deviations from the Nye solution. Furthermore, creep closure can be succinctly written in terms of the path-independent MM integral and the variation with applied shear can be found via scalings, which is useful for subglacial hydrology models.
From path integrals to tensor networks for the AdS /CFT correspondence
Miyaji, Masamichi; Takayanagi, Tadashi; Watanabe, Kento
2017-03-01
In this paper, we discuss tensor network descriptions of AdS /CFT from two different viewpoints. First, we start with a Euclidean path-integral computation of ground state wave functions with a UV cutoff. We consider its efficient optimization by making its UV cutoff position dependent and define a quantum state at each length scale. We conjecture that this path integral corresponds to a time slice of anti-de Sitter (AdS) spacetime. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of AdS3 in terms of the dual two-dimensional conformal field theory (CFT). Both approaches support a correspondence between the hyperbolic time slice H2 in AdS3 and a version of continuous multiscale entanglement renormalization ansatz. We also give a heuristic argument about why we can expect a sub-AdS scale bulk locality for holographic CFTs.
Data Assimilation using a GPU Accelerated Path Integral Monte Carlo Approach
Quinn, John C
2011-01-01
The answers to data assimilation questions can be expressed as path integrals over all possible state and parameter histories. We show how these path integrals can be evaluated numerically using a Markov Chain Monte Carlo method designed to run in parallel on a Graphics Processing Unit (GPU). We demonstrate the application of the method to an example with a transmembrane voltage time series of a simulated neuron as an input, and using a Hodgkin-Huxley neuron model. By taking advantage of GPU computing, we gain a parallel speedup factor of up to about 200 times faster than an equivalent serial computation on a CPU, with performance increasing as the length of the observation time used for data assimilation increases.
Ab Initio Path Integral Molecular Dynamics Simulation of Hydrogen in Silicon
Probert, M. I. J.; Glover, M. J.
2006-05-01
We report results of a first-principles theoretical study of an isolated neutral hydrogen atom in crystalline silicon. Spin-polarised density functional theory is used to treat the electrons, and the path-integral molecular dynamics method is used to describe the quantum properties of the nucleus at finite temperature. This is necessary as the hydrogen atom has sufficiently low mass that it exhibits significant nuclear quantum delocalisation and zero-point motion even at room temperature. Unlike post-hoc treatments, such as calculating a static potential energy surface, the path-integral treatment enables such effects to be included "on-the-fly". This is found to be significant, as a coupling is found between the structure of the host silicon lattice and the quantum delocalisation of the hydrogen defect.
A unified scheme for ab initio molecular orbital theory and path integral molecular dynamics
Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi
2001-11-01
We present a general approach for accurate calculation of chemical substances which treats both nuclei and electrons quantum mechanically, adopting ab initio molecular orbital theory for the electronic structure and path integral molecular dynamics for the nuclei. The present approach enables the evaluation of physical quantities dependent on the nuclear configuration as well as the electronic structure, within the framework of Born-Oppenheimer adiabatic approximation. As an application, we give the path integral formulation of electric response properties—dipole moment and polarizability, which characterize the changes both in electronic structure and nuclear configuration at a given temperature when uniform electrostatic field is present. We also demonstrate the calculation of a water molecule using the present approach and the result of temperature and isotope effects is discussed.
Simulations of one- and two-electron systems by Bead-Fourier path integral molecular dynamics
Ivanov, Sergei D.; Lyubartsev, Alexander P.
2005-07-01
The Bead-Fourier path integral molecular dynamics technique introduced earlier [S. D. Ivanov, A. P. Lyubartsev, and A. Laaksonen, Phys. Rev. E 67 066710 (2003)] is applied for simulation of electrons in the simplest molecules: molecular hydrogen, helium atom, and their ions. Special attention is paid to the correct description of electrons in the core region of a nucleus. In an attempt to smooth the Coulomb potential at small distances, a recipe is suggested. The simulation results are in excellent agreement with the analytical solution for the "harmonic helium atom", as well as with the vibrational potential of the H2 molecule and He ionization energies. It is demonstrated, that the Bead-Fourier path integral molecular dynamics technique is able to provide the accuracy required for the description of electron structure and chemical bonds in cases when electron exchange effects need not be taken into account.
Proton momentum distributions in water: A path integral molecular dynamics study
Srinivasan, Varadharajan; Morrone, Joseph A.; Sebastiani, Daniel; Car, Roberto
2007-03-01
Recent neutron Compton scattering experiments have detected the proton momentum distributions of water. This density in momentum space is a quantum mechanical property of the proton, due to the confining anharmonic potential from covalent and hydrogen bonds. The theoretical calculation of this property can be carried out via ``open'' path integral expressions. In this work, we present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize the SPC/F2 empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.
Proton momentum distribution in water: an open path integral molecular dynamics study
Morrone, Joseph A.; Srinivasan, Varadharajan; Sebastiani, Daniel; Car, Roberto
2007-06-01
Recent neutron Compton scattering experiments have detected the proton momentum distribution in water. The theoretical calculation of this property can be carried out via "open" path integral expressions. In this work, present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize a flexible, single point charge empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.
Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation.
Liang, L Z J; Lemmens, D; Tempere, J
2011-05-01
In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options. These general results allow us to find closed-form pricing formulas for both the perpetual and the finite time-horizon timer options under the 3/2 stochastic volatility model as well as under the Heston stochastic volatility model. For the treatment of timer options under the 3/2 model we will rely on the path integral for the Morse potential, with the Heston model we will rely on the Kratzer potential. © 2011 American Physical Society
From Path Integrals to Tensor Networks for AdS/CFT
Miyaji, Masamichi; Watanabe, Kento
2016-01-01
In this paper, we discuss tensor network descriptions of AdS/CFT from two different viewpoints. First, we start with an Euclidean path-integral computation of ground state wave functions with a UV cut off. We consider its efficient optimization by making its UV cut off position dependent and define a quantum state at each length scale. We conjecture that this path-integral corresponds to a time slice of AdS. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of AdS3 in terms of the dual 2d CFT. Both approaches support a correspondence between the hyperbolic time slice H2 in AdS3 and a version of continuous MERA (cMERA). We also give a heuristic argument why we can expect a sub-AdS scale bulk locality for holographic CFTs.
Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line
Sesé, Luis M.
2016-03-01
Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.
Semi-classical locality for the non-relativistic path integral in configuration space
Gomes, Henrique
2015-01-01
In an accompanying paper, we have put forward an interpretation of quantum mechanics grounded on a non-relativistic Lagrangian 3+1 formalism of a closed Universe, existing on timeless configuration space. However, not much was said there about the role of locality, which was not assumed. In this paper, I describe how subsystems existing in (spatial) regions with fixed boundary conditions can be represented as submanifolds of the complete configuration space. I show that if the action functional can be put in the form of Riemannian distance element, then dynamical independence of the subsystem implies that the respective submanifolds are totally geodesic. When two regions are mutually independent the semi-classical path integral kernel factorizes, showing cluster decomposition. To exemplify these constructions I then construct a specific gravitational system with two propagating physical degrees of freedom and no refoliation-invariance. Finally, considering the path integral in this 3+1 context, I implement an...
Path-integral action of a particle in the noncommutative phase-space
Gangopadhyay, Sunandan
2016-01-01
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum system in the space of Hilbert-Schmidt operators acting on noncommutative configuration space, the path integral action of a particle is derived. It is observed that the action has a similar form to that of a particle in a magnetic field in the noncommutative plane. From this action the energy spectrum is obtained for the free particle and the harmonic oscillator potential. We also show that the nonlocal nature (in time) of the action yields a second class constrained system from which the noncommutative Heisenberg algebra can be recovered.
Calculation rule for Aoyama-Tamra's prescription for path integral with quantum tunneling
Suzuki, H
1995-01-01
We derive a simple calculation rule for Aoyama--Tamra's prescription for path integral with degenerated potential minima. Non-perturbative corrections due to the restricted functional space (fundamental region) can systematically be computed with this rule. It becomes manifest that the prescription might give Borel summable series for finite temperature (or volume) system with quantum tunneling, while the advantage is lost at zero temperature (or infinite volume) limit.
Directory of Open Access Journals (Sweden)
Loredana Teresa Pedata
2012-12-01
Full Text Available The path and the pilot study presented here come from a synergy between a pharmaceutical, universities and institutions in the area. The intervention evaluation wants to establish itself as a means of "re-thinking" youth intervention benefited: the assumption that the integration of knowledge can constitute an enrichment of the whole person, we believe that such enrichment is more likely to occur in group in comparison with others and the development of social skills and human resources.
Gorbenko, Anna; Popov, Vladimir
2017-07-01
Different planning problems for robotic remote laser welding are of considerable interest. In this paper, we consider the problem of integrated task sequencing and path planning for robotic remote laser welding. We propose an efficient approach to solve the problem. In particular, we consider an explicit reduction from the decision version of the problem to the satisfiability problem. We present the results of computational experiments for different satisfiability algorithms.
Polyakov's spin factor for a classical spinning particle via BRST invariant path integral
Cho, J; Lee, H; Jin-Ho Cho; Seungjoon Hyun; Hyuk-Jae Lee
1994-01-01
For the "classical" formulation of a massive spinning particle, the propagator is obtained along with the spin factor. We treat the system with two kinds of constraints that were recently shown to be concerned with the reparametrization invariance and "quasi-supersymmetry". In the path integral, the BRST invariant Lagrangian is used and the same spin factor is obtained as in the pseudo-classical formulation.
Wang, Fei; Chen, Hong; Guo, Konghui; Cao, Dongpu
2017-09-01
The path following and directional stability are two crucial problems when a road vehicle experiences a tire blow-out or sudden tire failure. Considering the requirement of rapid road vehicle motion control during a tire blow-out, this article proposes a novel linearized decoupling control procedure with three design steps for a class of second order multi-input-multi-output non-affine system. The evaluating indicators for controller performance are presented and a performance related control parameter distribution map is obtained based on the stochastic algorithm which is an innovation for non-blind parameter adjustment in engineering implementation. The analysis on the robustness of the proposed integrated controller is also performed. The simulation studies for a range of driving conditions are conducted, to demonstrate the effectiveness of the proposed controller.
Integrating cell on chip—Novel waveguide platform employing ultra-long optical paths
Fohrmann, Lena Simone; Sommer, Gerrit; Pitruzzello, Giampaolo; Krauss, Thomas F.; Petrov, Alexander Yu.; Eich, Manfred
2017-09-01
Optical waveguides are the most fundamental building blocks of integrated optical circuits. They are extremely well understood, yet there is still room for surprises. Here, we introduce a novel 2D waveguide platform which affords a strong interaction of the evanescent tail of a guided optical wave with an external medium while only employing a very small geometrical footprint. The key feature of the platform is its ability to integrate the ultra-long path lengths by combining low propagation losses in a silicon slab with multiple reflections of the guided wave from photonic crystal (PhC) mirrors. With a reflectivity of 99.1% of our tailored PhC-mirrors, we achieve interaction paths of 25 cm within an area of less than 10 mm2. This corresponds to 0.17 dB/cm effective propagation which is much lower than the state-of-the-art loss of approximately 1 dB/cm of single mode silicon channel waveguides. In contrast to conventional waveguides, our 2D-approach leads to a decay of the guided wave power only inversely proportional to the optical path length. This entirely different characteristic is the major advantage of the 2D integrating cell waveguide platform over the conventional channel waveguide concepts that obey the Beer-Lambert law.
Calculation of heat capacities of light and heavy water by path-integral molecular dynamics
Shiga, Motoyuki; Shinoda, Wataru
2005-10-01
As an application of atomistic simulation methods to heat capacities, path-integral molecular dynamics has been used to calculate the constant-volume heat capacities of light and heavy water in the gas, liquid, and solid phases. While the classical simulation based on conventional molecular dynamics has estimated the heat capacities too high, the quantum simulation based on path-integral molecular dynamics has given reasonable results based on the simple point-charge/flexible potential model. The calculated heat capacities (divided by the Boltzmann constant) in the quantum simulation are 3.1 in the vapor H2O at 300 K, 6.9 in the liquid H2O at 300 K, and 4.1 in the ice IhH2O at 250 K, respectively, which are comparable to the experimental data of 3.04, 8.9, and 4.1, respectively. The quantum simulation also reproduces the isotope effect. The heat capacity in the liquid D2O has been calculated to be 10% higher than that of H2O, while it is 13% higher in the experiment. The results demonstrate that the path-integral simulation is a promising approach to quantitatively evaluate the heat capacities for molecular systems, taking account of quantum-mechanical vibrations as well as strongly anharmonic motions.
i-PI: A Python interface for ab initio path integral molecular dynamics simulations
Ceriotti, Michele; More, Joshua; Manolopoulos, David E.
2014-03-01
Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water. Catalogue identifier: AERN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AERN_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 138626 No. of bytes in distributed program, including test data, etc.: 3128618 Distribution format: tar.gz Programming language: Python. Computer: Multiple architectures. Operating system: Linux, Mac OSX, Windows. RAM: Less than 256 Mb Classification: 7.7. External routines: NumPy Nature of problem: Bringing the latest developments in the modelling of nuclear quantum effects with path integral molecular dynamics to ab initio electronic structure programs with minimal implementational effort. Solution method: State-of-the-art path integral molecular dynamics techniques are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic
A linearly and circularly polarized active integrated antenna
Khoshniat, Ali
This thesis work presents a new harmonic suppression technique for microstrip patch antennas. Harmonic suppression in active integrated antennas is known as an effective method to improve the efficiency of amplifiers in transmitter side. In the proposed design, the antenna works as the radiating element and, at the same time, as the tuning load for the amplifier circuit that is directly matched to the antenna. The proposed active antenna architecture is easy to fabricate and is symmetric, so it can be conveniently mass-produced and designed to have circular polarization, which is preferred in many applications such as satellite communications. The antenna simulations were performed using Ansoft High Frequency System Simulator (HFSS) and all amplifier design steps were simulated by Advanced Design System (ADS). The final prototypes of the linearly polarized active integrated antenna and the circularly polarized active integrated antenna were fabricated using a circuit board milling machine. The antenna radiation pattern was measured inside Utah State University's anechoic chamber and the results were satisfactory. Power measurements for the amplifiers' performance were carried out inside the chamber and calculated by using the Friis transmission equation. It is seen that a significant improvement in the efficiency is achieved compared to the reference antenna without harmonic suppression. Based on the success in the single element active antenna design, the thesis also presents a feasibility of applying the active integrated antenna in array configuration, in particular, in scanning array design to yield a low-profile, low-cost alternative to the parabolic antenna transmitter of satellite communication systems.
Linear Quadratic Integral Control for the Active Suspension of Vehicle
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The quarter model of an active suspension is established in the form of controllable autoregressive moving average (CARMA) model. An accelerometer can be mounted on the wheel hub for measuring road disturbance; this signal is used to identify the CARMA model parameters by recursive forgetting factors least square method. The linear quadratic integral (LQI) control method for the active suspension is presented. The LQI control algorithm is fit for vehicle suspension control, for the control performance index can comprise multi controlled variables. The simulation results show that the vertical acceleration and suspension travel both are decreased with the LQI control in the low frequency band, and the suspension travel is increased with the LQI control in the middle or high frequency band. The suspension travel is very small in the middle or high frequency band, the suspension bottoming stop will not happen, so the vehicle ride quality can be improved apparently by the LQI control.
Imaoka, Haruna; Kinugawa, Kenichi
2017-03-01
Thermal conductivity, shear viscosity, and bulk viscosity of normal liquid 4He at 1.7-4.0 K are calculated using path integral centroid molecular dynamics (CMD) simulations. The calculated thermal conductivity and shear viscosity above lambda transition temperature are on the same order of magnitude as experimental values, while the agreement of shear viscosity is better. Above 2.3 K the CMD well reproduces the temperature dependences of isochoric shear viscosity and of the time integral of the energy current and off-diagonal stress tensor correlation functions. The calculated bulk viscosity, not known in experiments, is several times larger than shear viscosity.
NLOS UV Channel Modeling Using Numerical Integration and an Approximate Closed-Form Path Loss Model
Gupta, Ankit; Brandt-Pearce, Maïté
2012-01-01
In this paper we propose a simulation method using numerical integration, and develop a closed-form link loss model for physical layer channel characterization for non-line of sight (NLOS) ultraviolet (UV) communication systems. The impulse response of the channel is calculated by assuming both uniform and Gaussian profiles for transmitted beams and different geometries. The results are compared with previously published results. The accuracy of the integration approach is compared to the Monte Carlo simulation. Then the path loss using the simulation method and the suggested closed-form expression are presented for different link geometries. The accuracies are evaluated and compared to the results obtained using other methods.
Optimal paths for a light-driven engine with a linear phenomenological heat transfer law
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
An irreversible light-driven engine is described in this paper, in which the heat transfer between the working fluid and the environment obeys a linear phenomenological heat transfer law [ q ∝Δ(T -1)], with a working fluid composed of the bimolecular reacting system 2SO 3 F■S 2 O 6 F2. Piston trajectories maximizing work output and minimizing entropy generation are determined for such an engine with rate-dependent loss mechanisms of friction and heat leakage. The optimal control theory is applied to determine the optimal configurations of the piston motion trajectory and the fluid temperature. Numerical examples for the optimal configuration are provided, and the obtained results are compared with those derived with Newtonian heat transfer law [ q ∝Δ(T )].
Neill, A. J.; Tetzlaff, D.; Strachan, N.; Soulsby, C.
2016-12-01
The non-linearities of runoff generation processes are strongly influenced by the connectivity of hillslopes and channel networks, particularly where overland flow is an important runoff mechanism. Despite major advances in understanding hydrological connectivity and runoff generation, the role of connectivity in the contamination of potable water supplies by faecal pathogens from grazing animals remains unclear. This is a water quality issue with serious implications for public health. Here, we sought to understand the dynamics of hydrological connectivity, flow paths and linked faecal pathogen transport in a montane catchment in Scotland with high deer populations. We firstly calibrated, within an uncertainty framework, a parsimonious tracer-aided hydrological model to daily discharge and stream isotope data. The model, developed on the basis of past empirical and tracer studies, conceptualises the catchment as three interacting hydrological source areas (dynamic saturation zone, dynamic hillslope, and groundwater) for which water fluxes, water ages and storage-based connectivity can be simulated. We next coupled several faecal indicator organism (FIO; a common indicator of faecal pathogen contamination) behaviour and transport schemes to the robust hydrological models. A further calibration was then undertaken based on the ability of each coupled model to simulate daily FIO concentrations. This gave us a final set of coupled behavioural models from which we explored how in-stream FIO dynamics could be related to the changing connectivity between the three hydrological source areas, flow paths, water ages and consequent dominant runoff generation processes. We found that high levels of FIOs were transient and episodic, and strongly correlated with periods of high connectivity through overland flow. This non-linearity in connectivity and FIO flux was successfully captured within our dynamic, tracer-aided hydrological model.
The optimal path of piston motion for Otto cycle with linear phenomenological heat transfer law
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
An Otto cycle engine with internal and external irreversibilities of friction and heat leakage, in which the heat transfer between the working fluid and the environment obeys linear phenomenological heat transfer law [q ∝△(T -1)], is studied in this paper. The optimal piston motion trajectory for maximizing the work output per cycle is derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston trajectories for the cases of with and without piston acceleration constraint on each stroke and the optimal distribution of the total cycle time among the strokes. The optimal piston motion with acceleration constraint for each stroke consists of three segments, including initial maximum acceleration and final maximum deceleration boundary segments, respectively. Numerical examples for optimal configuration are provided, and the obtained results are compared with those obtained with Newton’s heat transfer law [q ∝△(T )]. The results also show that optimizing the piston motion can improve power and efficiency of the engine by more than 9%. This is primarily due to the decrease in heat leakage loss on the initial portion of the power stroke.
The optimal path of piston motion for Otto cycle with linear phenomenological heat transfer law
Institute of Scientific and Technical Information of China (English)
XIA ShaoJun; CHEN LinGen; SUN FengRui
2009-01-01
An Otto cycle engine with internal and external irreversibilities of friction and heat leakage, in which the heat transfer between the working fluid and the environment obeys linear phenomenological heat transfer law [q∝△(T-1)], is studied in this paper. The optimal piston motion trajectory for maximizing the work output per cycle is derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston trajectories for the cases of with and without piston acceleration constraint on each stroke and the optimal distribution of the total cycle time among the strokes. The optimal piston motion with acceleration constraint for each stroke consists of three segments, including initial maximum acceleration and final maximum deceleration boundary segments,respectively. Numerical examples for optimal configuration are provided, and the obtained results are compared with those obtained with Newton's heat transfer law [q∝△(T)]. The results also show that optimizing the piston motion can improve power and efficiency of the engine by more than 9%. This is primarily due to the decrease in heat leakage loss on the initial portion of the power stroke.
Energy Technology Data Exchange (ETDEWEB)
Geng, Hua Y., E-mail: huay.geng@gmail.com [National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, CAEP, P.O. Box 919-102, Mianyang, Sichuan, 621900 (China); Department of Chemistry and Chemical Biology, Cornell University, Baker Laboratory, Ithaca, NY 14853 (United States)
2015-02-15
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of r{sub s}=0.912.
Geng, Hua Y.
2015-02-01
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model-the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of rs = 0.912.
Minary, Peter; Martyna, Glenn J.; Tuckerman, Mark E.
2003-02-01
In this paper (Paper I) and a companion paper (Paper II), novel new algorithms and applications of the isokinetic ensemble as generated by Gauss' principle of least constraint, pioneered for use with molecular dynamics 20 years ago, are presented for biophysical, path integral, and Car-Parrinello based ab initio molecular dynamics. In Paper I, a new "extended system" version of the isokinetic equations of motion that overcomes the ergodicity problems inherent in the standard approach, is developed using a new theory of non-Hamiltonian phase space analysis [M. E. Tuckerman et al., Europhys. Lett. 45, 149 (1999); J. Chem. Phys. 115, 1678 (2001)]. Reversible multiple time step integrations schemes for the isokinetic methods, first presented by Zhang [J. Chem. Phys. 106, 6102 (1997)] are reviewed. Next, holonomic constraints are incorporated into the isokinetic methodology for use in fast efficient biomolecular simulation studies. Model and realistic examples are presented in order to evaluate, critically, the performance of the new isokinetic molecular dynamic schemes. Comparisons are made to the, now standard, canonical dynamics method, Nosé-Hoover chain dynamics [G. J. Martyna et al., J. Chem. Phys. 97, 2635 (1992)]. The new isokinetic techniques are found to yield more efficient sampling than the Nosé-Hoover chain method in both path integral molecular dynamics and biophysical molecular dynamics calculations. In Paper II, the use of isokinetic methods in Car-Parrinello based ab initio molecular dynamics calculations is presented.
A path integral formula with applications to quantum random walks in Z{sup d}
Energy Technology Data Exchange (ETDEWEB)
Yang Weishih [Department of Mathematics, Temple University, Philadelphia, PA 19122 (United States); Liu, Chaobin [Department of Mathematics, Bowie State University, Bowie, MD 20715 (United States); Zhang Kai [Department of Mathematics, Temple University, Philadelphia, PA 19122 (United States)
2007-07-20
We consider general quantum random walks in a d-dimensional half-space. We first obtain a path integral formula for general quantum random walks in a d-dimensional space. Our path integral formula is valid for general quantum random walks on Cayley graphs as well. Then the path integral formula is applied to obtain the scaling limit of the exit distribution, the expectation of exit time and the asymptotic behaviour of the exit probabilities, for general quantum random walks in a half-space under some conditions on amplitude functions. The conditions are shown to be satisfied by both the Hadamard and Grover quantum random walks in two-dimensional half-spaces. For the two-dimensional case, we show that the critical exponent for the scaling limit of the hitting distribution is 1 as the lattice spacing tends to zero, i.e. the natural magnitude of the hitting position is of order O(1) if the lattice spacing is set to be 1/n. We also show that the rate of convergence of the total hitting probability has lower bound n{sup -2} and upper bound n{sup -2+{epsilon}} for any {epsilon} > 0. For a quantum random walk with a fixed starting point, we show that the probability of hitting times at the hyperplane decays faster than that of the classical random walk. In both one and two dimensions, given the event of a hit, the conditional expectation of hitting times is finite, in contrast to being infinite for the classical case. In the one-dimensional case, we also obtain an exact order of the probability distribution of the hitting time at 0.
Energy Technology Data Exchange (ETDEWEB)
Liu, Jian, E-mail: jianliupku@pku.edu.cn [Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); State Key Joint Laboratory of Environmental Simulation and Pollution Control, College of Environmental Sciences and Engineering, Peking University, Beijing 100871 (China); Zhang, Zhijun [Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China)
2016-01-21
Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems.
Energy Technology Data Exchange (ETDEWEB)
Garberoglio, Giovanni, E-mail: garberoglio@fbk.eu [Interdisciplinary Laboratory for Computational Science (LISC), FBK-CMM and University of Trento, via Sommarive 18, I-38123 Povo (Italy); Jankowski, Piotr [Department of Quantum Chemistry, Faculty of Chemistry, Nicolaus Copernicus University, Gagarina 7, PL-87-100 Toruń (Poland); Szalewicz, Krzysztof [Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716 (United States); Harvey, Allan H. [Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305-3337 (United States)
2014-07-28
We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H{sub 2}) and deuterium (D{sub 2}) in the temperature range 15–2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H{sub 2} between 100 and 200 K.
Krajewski, Florian R.; Müser, Martin H.
2005-07-01
The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent H=0), there is one regime in which the chain is pinned (large masses m of chain particles) and one in which it is unpinned (small m). If the embedding potential can be classified as a random walk on large length scales ( H=1/2), then the chain is always pinned irrespective of the value of m. For H=1/2, two phonon-like branches appear in the spectra.
Ab initio Path Integral Molecular Dynamics Based on Fragment Molecular Orbital Method
Fujita, Takatoshi; Watanabe, Hirofumi; Tanaka, Shigenori
2009-10-01
We have developed an ab initio path integral molecular dynamics method based on the fragment molecular orbital method. This “FMO-PIMD” method can treat both nuclei and electrons quantum mechanically, and is useful to simulate large hydrogen-bonded systems with high accuracy. After a benchmark calculation for water monomer, water trimer and glycine pentamer have been studied using the FMO-PIMD method to investigate nuclear quantum effects on structure and molecular interactions. The applicability of the present approach is demonstrated through a number of test calculations.
Formation of bound states in expanded metal studied via path integral molecular dynamics
Deymier, P. A.; Oh, Ki-Dong
2004-03-01
The usefulness of the restricted path integral molecular dynamics method for the study of strongly correlated electrons is demonstrated by studying the formation of bound electronic states in a half-filled expanded three-dimensional hydrogenoid body-centred cubic lattice at finite temperature. Starting from a metallic state with one-component plasma character, we find that bound electrons form upon expansion of the lattice. The bound electrons are spatially localized with their centre for the motion of gyration located at ionic positions. The number of bound electrons increases monotonically with decreasing density.
Path Integral Molecular Dynamics for Hydrogen with Orbital-Free Density Functional Theory
Runge, Keith; Karasiev, Valentin; Deymier, Pierre
2014-03-01
The computational bottleneck for performing path-integral molecular dynamics (PIMD) for nuclei on a first principles electronic potential energy surface has been the speed with which forces from the electrons can be generated. Recent advances in orbital-free density functional theory (OF-DFT) not only allow for faster generation of first principles forces but also include the effects of temperature on the electron density. We will present results of calculations on hydrogen in warm dense matter conditions where the protons are described by PIMD and the electrons by OF-DFT. Work supported by U.S. Dept. of Energy, grant DE-SC0002139.
Kapila, Vivek; Deymier, Pierre; Runge, Keith
2011-10-01
Several areas of study including heavy ion beam, large scale laser, and high pressure or Thomson scattering studies necessitate a fundamental understanding of warm dense matter (WDM) i.e. matter at high temperature and high density. The WDM regime, however, lacks any adequate highly developed class of simulation methods. Recent progress to address this deficit has been the development of orbital-free Density Functional Theory (ofDFT). However, scant benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as harmonic necklaces. Quantum exchange takes the form of cross linking between electron necklaces. The fermion sign problem is addressed by restricting the density matrix to positive values. The molecular dynamics algorithm is employed to sample phase space. Here, we focus on the behavior of strongly correlated electron plasmas under WDM conditions. We compute the kinetic and potential energies and compare them to those obtained with the ofDFT method. Several areas of study including heavy ion beam, large scale laser, and high pressure or Thomson scattering studies necessitate a fundamental understanding of warm dense matter (WDM) i.e. matter at high temperature and high density. The WDM regime, however, lacks any adequate highly developed class of simulation methods. Recent progress to address this deficit has been the development of orbital-free Density Functional Theory (ofDFT). However, scant benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as
Path-integral molecular dynamics simulations for water anion clusters (HO)5- and (DO)5-
Takayanagi, Toshiyuki; Yoshikawa, Takehiro; Motegi, Haruki; Shiga, Motoyuki
2009-11-01
Quantum path-integral molecular dynamics simulations have been performed for the (HO)5- and (DO)5- anion clusters on the basis of a semiempirical one-electron pseudopotential-polarization model. Due to larger zero-point vibrational amplitudes for H atoms than that of D atoms, hydrogen-bond lengths in the (HO)5- cluster are slightly larger than those in (DO)5-. The distribution of the vertical detachment energies for (HO)5- also show a broader feature than that for (DO)5-. The present PIMD simulations thus demonstrate the importance of nuclear quantum effects in water anion clusters.
Artoun, Ojenie; David-Rus, Diana; Emmett, Matthew; Fishman, Lou; Fital, Sandra; Hogan, Chad; Lim, Jisun; Lushi, Enkeleida; Marinov, Vesselin
2006-05-01
In this report we summarize an extension of Fourier analysis for the solution of the wave equation with a non-constant coefficient corresponding to an inhomogeneous medium. The underlying physics of the problem is exploited to link pseudodifferential operators and phase space path integrals to obtain a marching algorithm that incorporates the backward scattering into the evolution of the wave. This allows us to successfully apply single-sweep, one-way marching methods in inherently two-way environments, which was not achieved before through other methods for this problem.
Path integral representation of spin foam models of 4d gravity
Conrady, Florian
2008-01-01
We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= gamma < 1, the states can be restricted to SU(2) spin networks.
Quantum Brownian Motions and Navier-Stokes Weakly Turbulence — a Path Integral Study
Botelho, Luiz C. L.
In this paper, we present a new method to solve exactly the Schrödinger Harmonic oscillator wave equation in the presence of time-dependent parameter. We also apply such technique to solve exactly the problem of random frequency averaged quantum propagator of a harmonic oscillator with white-noise statistics frequency. We still apply our technique to solve exactly the Brownian Quantum Oscillator in the presence of an electric field. Finally, we use these quantum mechanic techniques to solve exactly the Statistical-Turbulence of the Navier-Stokes in a region of fluid random stirring weakly (analytical) coupling through time-dependent Euclidean-Quantum oscillators path-integrals.
Unified path integral approach to theories of diffusion-influenced reactions
Prüstel, Thorsten; Meier-Schellersheim, Martin
2017-08-01
Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.
Integrability of Quadratic Non-autonomous Quantum Linear Systems
Lopez, Raquel
The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is
The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator
Govaerts, Jan; Mattelaer, Olivier
2009-01-01
The canonical operator quantisation formulation corresponding to the Klauder-Daubechies construction of the phase space path integral is considered. This formulation is explicitly applied and solved in the case of the harmonic oscillator, thereby illustrating in a manner complementary to Klauder and Daubechies' original work some of the promising features offered by their construction of a quantum dynamics. The Klauder-Daubechies functional integral involves a regularisation parameter eventually taken to vanish, which defines a new physical time scale. When extrapolated to the field theory context, besides providing a new regularisation of short distance divergences, keeping a finite value for that time scale offers some tantalising prospects when it comes to strong gravitational quantum systems.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals
Energy Technology Data Exchange (ETDEWEB)
Sinitskiy, Anton V.; Voth, Gregory A., E-mail: gavoth@uchicago.edu [Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago, 5735 S. Ellis Ave., Chicago, Illinois 60637 (United States)
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
van Zon, Ramses; Hernández de la Peña, Lisandro; Peslherbe, Gilles H; Schofield, Jeremy
2008-10-01
In this paper, the imaginary-time path-integral representation of the canonical partition function of a quantum system and nonequilibrium work fluctuation relations are combined to yield methods for computing free-energy differences in quantum systems using nonequilibrium processes. The path-integral representation is isomorphic to the configurational partition function of a classical field theory, to which a natural but fictitious Hamiltonian dynamics is associated. It is shown that if this system is prepared in an equilibrium state, after which a control parameter in the fictitious Hamiltonian is changed in a finite time, then formally the Jarzynski nonequilibrium work relation and the Crooks fluctuation relation hold, where work is defined as the change in the energy as given by the fictitious Hamiltonian. Since the energy diverges for the classical field theory in canonical equilibrium, two regularization methods are introduced which limit the number of degrees of freedom to be finite. The numerical applicability of the methods is demonstrated for a quartic double-well potential with varying asymmetry. A general parameter-free smoothing procedure for the work distribution functions is useful in this context.
Geng, Hua Y
2014-01-01
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model, the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4 fold for a two-level implementation, and can be increased to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibration...
Transport properties of liquid para-hydrogen: The path integral centroid molecular dynamics approach
Yonetani, Yoshiteru; Kinugawa, Kenichi
2003-11-01
Several fundamental transport properties of a quantum liquid para-hydrogen (p-H2) at 17 K have been numerically evaluated by means of the quantum dynamics simulation called the path integral centroid molecular dynamics (CMD). For comparison, classical molecular dynamics (MD) simulations have also been performed under the same condition. In accordance with the previous path integral simulations, the calculated static properties of the liquid agree well with the experimental results. For the diffusion coefficient, thermal conductivity, and shear viscosity, the CMD predicts the values closer to the experimental ones though the classical MD results are far from the reality. The agreement of the CMD result with the experimental one is especially good for the shear viscosity with the difference less than 5%. The calculated diffusion coefficient and the thermal conductivity agree with the experimental values at least in the same order. We predict that the ratio of bulk viscosity to shear viscosity for liquid p-H2 is much larger than classical van der Waals simple liquids such as rare gas liquids.
Dvornikov, Maxim; Gitman, D. M.
2012-11-01
We study massive 1/2-spin particles in various external backgrounds keeping in mind applications to neutrino physics. We are mainly interested in massive Majorana (Weyl) fields. However, massive neutral Dirac particles are also considered. We formulate classical Lagrangian theory of the massive Weyl field in terms of Grassmann-odd two-component spinors. Then we construct the Hamiltonian formulation of such a theory, which turns out to be a theory with second-class constraints. Using this formulation we canonically quantize the massive free Weyl field. We derive propagators of the Weyl field and relate them to the propagator of a massive Dirac particle. We also study the massive Weyl particles propagating in the background mater. We find the path integral representation for the propagator of such a field, as well as the corresponding pseudoclassical particle action. The massless limit of the Weyl field interacting with the matter is considered and compared with results of other works. Finally, the path integral representation for the propagator of the neutral massive Dirac particle with an anomalous magnetic moment moving in the background matter and external electromagnetic field, as well as the corresponding pseudoclassical particle action are constructed.
Path integral approach for electron transport in disturbed magnetic field lines
Energy Technology Data Exchange (ETDEWEB)
Kanno, Ryutaro; Nakajima, Noriyoshi; Takamaru, Hisanori
2002-05-01
A path integral method is developed to investigate statistical property of an electron transport described as a Langevin equation in a statically disturbed magnetic field line structure; especially a transition probability of electrons strongly tied to field lines is considered. The path integral method has advantages that 1) it does not include intrinsically a growing numerical error of an orbit, which is caused by evolution of the Langevin equation under a finite calculation accuracy in a chaotic field line structure, and 2) it gives a method of understanding the qualitative content of the Langevin equation and assists to expect statistical property of the transport. Monte Carlo calculations of the electron distributions under both effects of chaotic field lines and collisions are demonstrated to comprehend above advantages through some examples. The mathematical techniques are useful to study statistical properties of various phenomena described as Langevin equations in general. By using parallel generators of random numbers, the Monte Carlo scheme to calculate a transition probability can be suitable for a parallel computation. (author)
Barth, A. M.; Vagov, A.; Axt, V. M.
2016-09-01
We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.
Directory of Open Access Journals (Sweden)
Gary Raucher
2013-09-01
Full Text Available This paper examines, from an emic stance, a strand of Western esoteric wisdom that offers a particular perspective on psycho-spiritual development in relation to spiritual emergence, the mutually interdependent evolution of consciousness and substance, and the functional role of human incarnation within our planetary life. The writings of Alice A. Bailey (1880-1949 and Lucille Cedercrans (1921-1984 serve as significant reference points in this effort. These teachings hold an integral view of human development in which a person’s awareness and self-identification progress from polarization in physical matter and sensation through progressively subtler gradients of emotional and mental experience, culminating in “The Path of Initiation,” a phase of psychological and spiritual expansions into deepening levels of transcendent, supramental consciousness and functioning. The esoteric teachings described here portray this path descriptively rather than prescriptively, and have significant parallels to Sri Aurobindo’s Integral vision. Both consider human life in form to be a vital and necessary phase within the larger cosmic evolution of consciousness and matter, and both are frameworks that expansively embrace the significance of the Divine as both immanent and transcendent presence. The important issue of epistemological methodology and the testing of esoteric assertions is also considered.
Path-integrated measurements of carbon dioxide in the urban canopy layer
Büns, Christian; Kuttler, Wilhelm
2012-01-01
Continuous CO 2 concentration measurements have been recorded within the city center of Essen, Germany, using a path-integrated measuring system above a typical urban area over the course of nine months (February-October 2010). Mean monthly urban CO 2 concentrations were 396 and 446 ppm in summer and winter, respectively, which were 8.5 % in average higher than at a nearby suburban measuring site. Urban-suburban differences mainly occur due to increased CO 2 emissions from traffic and industry within the urban area, as well as domestic heating in winter. Among the analyzed meteorological variables, low wind velocities increased CO 2 concentrations as well as high atmospheric stability within the urban boundary layer, respectively. The influence of wind direction reflects the heterogeneous distribution of local CO 2 sources at the recording sites, particularly industrial point sources. Other point sources in the vicinity of the urban site strongly influence the additional point measurements but show no significant effect on the measured CO 2 concentrations by the path-integrated measuring system. Within an eight-day case study, a significant positive correlation between CO 2 concentration and traffic count ( R = 0.26; p system provides CO 2 concentrations on a greater temporal and spatial scale than common point measurements, which can be influenced by strong adjacent local CO 2 sources.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.
Sinitskiy, Anton V; Voth, Gregory A
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
Isotope dependence of the lattice parameter of germanium from path-integral Monte Carlo simulations
Noya, José C.; Herrero, Carlos P.; Ramírez, Rafael
1997-07-01
The dependence of the lattice parameter upon the isotope mass for five isotopically pure Ge crystals was studied by quantum path-integral Monte Carlo simulations. The interatomic interactions in the solid were described by an empirical potential of the Stillinger-Weber type. At 50 K the isotopic effect leads to an increase of 2.3×10-4 Å in the lattice parameter of 70Ge with respect to 76Ge. Comparison of the simulation results with available experimental data for 74Ge shows that the employed model provides a realistic description of this anharmonic effect. The path-integral results were compared to those derived from a quasiharmonic approximation of the crystal. Within this approximation, the calculated fractional change of the lattice parameter of 74Ge with respect to a crystal whose atoms have the average mass of natural Ge amounts to Δa/a=-9.2×10-6 at T=0 K. Some limitations of the quasiharmonic approximation are shown at temperatures above 200 K.
Relations between the EU and Republic of Kosovo - The path of Kosovo integration towards the EU
Directory of Open Access Journals (Sweden)
Arif Riza
2016-07-01
Full Text Available Almost all the European Union member states have surpassed various challenges toward their integration into the European family. Although all these challenges are special cases on their own, Kosovo’s journey differs from the above mentioned cases, because Kosovo has not been recognized as an independent state by some members of the European family. The other key element that differs Kosovo’s journey from other cases is the presence of international institutions such as: EULEX, ICO, UNMIK, KFOR etc. in Kosovo’s territory. These organizations were not present in other member states of the European Union and other countries which aim for European integration. This manuscript aims to analyze the Kosovo challenges in its path towards the European family, which is only possible if Kosovo can create sustainable politics and cause fundamental changes in all fields, whether in public or private institutions, in order to build the rule of law. In general, this article will discuss the presence of international institutions in Kosovo such as: EULEX, ICO, UNMIK, KFOR and other international organizations, their effects on the rule of law, economic development and the sustainability of institutions. Moreover, this paper will particularly analyze the influence of the above mentioned factors to ease Kosovo’s path, as an observed country, compared to other countries in the region.
Tansey, Timothy N; Iwanaga, Kanako; Bezyak, Jill; Ditchman, Nicole
2017-05-04
Individuals with disabilities are more likely to live in poverty, have more health issues, and be less likely to be employed than their same-aged peers. Although these issues may be attenuated by vocational rehabilitation services, amotivation and ambivalence to employment can limit the readiness of persons with disabilities to engage in these services. Drawing on self-efficacy, self-determination, and stages of change theories, the purpose of this study was to develop and test an integrated self-determined work motivation model for people with disabilities. Participants included 277 people with disabilities recruited through vocational rehabilitation agencies across 8 states. Path analysis was used to evaluate the contribution of functional disability, self-determination, and social efficacy variables in a hypothesized integrated self-determined work motivation model. Model estimations used maximum likelihood estimation and model-data fit was examined using several goodness-of-fit indices. The initial path analysis indicated a less than optimal fit between the model and the observed data. Post hoc model modifications were conducted based on examination of the critical ratios and modification indices and theoretical consideration. The respecified integrated self-determined work motivation model fit the data very well, χ2/df = 1.88, CFI = .99, and RMSEA = 0.056. The R2 for the endogenous variables in the model ranged from .19 to .54. Findings from this study support the integrated self-determined work motivation model in vocational rehabilitation as a useful framework for understanding the relationship among functioning levels, self-determination and self-efficacy factors, vocational rehabilitation engagement, and readiness for employment. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Automated Milling Path Tracking and CAM-ROB Integration for Industrial Redundant Manipulators
Directory of Open Access Journals (Sweden)
Luis Gracia
2012-09-01
Full Text Available The present paper explores the industrial capabilities of a CAM‐ROB system implementation based on a commercial CAD/CAM system (NX™ for an industrial robotic workcell of eight joints, committed to the rapid prototyping of 3D CAD‐defined models. The workcell consists of a KUKATM KR15/2 manipulator assembled on a linear track and synchronized with a rotary table. A redundancy resolution scheme is developed to deal with the redundancies due to the additional joints of the robot, plus the one from the symmetry axis of the milling tool. During the path tracking, the use of these redundancies is optimized by adjusting two performance criterion vectors related to singularity avoidance and maintenance of a preferred reference posture, as secondary tasks to be done. In addition, two suitable fuzzy inference engines adjust the weight of each joint in these tasks. The developed system is validated in a real prototyping of a carving.
Energy Technology Data Exchange (ETDEWEB)
Reinhardt, Hugo [Tuebingen Univ. (Germany). Inst. fuer Theoretische Physik
2012-11-01
The first volume of this two-volume textbook gives a modern introduction to the quantum theory, which connects Feynman's path-integral formulation with the traditional operator formalism. In easily understandable form starting from the double-slit experiment the characteristic features and foundations of quantum theory are made accessible by means of the functional-integral approach. Just this approach makes a ''derivation'' of the Schroedinger equation from the principle of the interfering alternatives possible. In the following the author developes the traditional operator formulation of quantum mechanics, which is better suited for practical solution of elementary problems. However he then refers to the functional-integral approach, when this contributes to a better understanding. A further advance of this concept: The functional-integral approach facilitates essentially the later access to quantum field theory. The work is in like manner suited for the self-study as for the deepening accompanying of the course.
Mu, Tingkui; Pacheco, Shaun; Chen, Zeyu; Zhang, Chunmin; Liang, Rongguang
2017-02-13
In this paper, the design and experimental demonstration of a snapshot linear-Stokes imaging spectropolarimeter (SLSIS) is presented. The SLSIS, which is based on division-of-focal-plane polarimetry with four parallel linear polarization channels and integral field spectroscopy with numerous slit dispersive paths, has no moving parts and provides video-rate Stokes-vector hyperspectral datacubes. It does not need any scanning in the spectral, spatial or polarization dimension and offers significant advantages of rapid reconstruction without heavy computation during post-processing. The principle and the experimental setup of the SLSIS are described in detail. The image registration, Stokes spectral reconstruction and calibration procedures are included, and the system is validated using measurements of tungsten light and a static scene. The SLSIS's snapshot ability to resolve polarization spectral signatures is demonstrated using measurements of a dynamic scene.
Zheng, Zewei; Zou, Yao
2016-11-01
This paper investigates the path following control problem for an unmanned airship in the presence of unknown wind and uncertainties. The backstepping technique augmented by a robust adaptive radial basis function neural network (RBFNN) is employed as the main control framework. Based on the horizontal dynamic model of the airship, an improved adaptive integral line-of-sight (LOS) guidance law is first proposed, which suits any parametric paths. The guidance law calculates the desired yaw angle and estimates the wind. Then the controller is extended to cope with the airship yaw tracking and velocity control by resorting to the augmented backstepping technique. The uncertainties of the dynamics are compensated by using the robust RBFNNs. Each robust RBFNN utilizes an nth-order smooth switching function to combine a conventional RBFNN with a robust control. The conventional RBFNN dominates in the neural active region, while the robust control retrieves the transient outside the active region, so that the stability range can be widened. Stability analysis shows that the controlled closed-loop system is globally uniformly ultimately bounded. Simulations are provided to validate the effectiveness of the proposed control approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Aristeidis Antonakis
2017-04-01
Full Text Available In this article, a new multi-objective approach to the aircraft climb path optimization problem, based on the Particle Swarm Optimization algorithm, is introduced to be used for aircraft–engine integration studies. This considers a combination of a simulation with a traditional Energy approach, which incorporates, among others, the use of a proposed path-tracking scheme for guidance in the Altitude–Mach plane. The adoption of population-based solver serves to simplify case setup, allowing for direct interfaces between the optimizer and aircraft/engine performance codes. A two-level optimization scheme is employed and is shown to improve search performance compared to the basic PSO algorithm. The effectiveness of the proposed methodology is demonstrated in a hypothetic engine upgrade scenario for the F-4 aircraft considering the replacement of the aircraft’s J79 engine with the EJ200; a clear advantage of the EJ200-equipped configuration is unveiled, resulting, on average, in 15% faster climbs with 20% less fuel.
Greybody factors for Schwarzschild black holes: Path-ordered exponentials and product integrals
Gray, Finnian
2015-01-01
In recent work concerning the sparsity of the Hawking flux [arXiv:1506.03975v2], we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focussing specifically on Schwarzschild black holes, we re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, (being based on a "transfer matrix" formalism), are closely related to so-called "product integrals", leading to quite straightforward and direct numerical evaluation, while avoiding any need for numerically solving differential equations. Furthermore, while considerable analytic information is already available regarding both the high-frequency and low-frequency asymptotics of these greybody factors, numerical approaches seem better adapted to finding suitable "global mo...
DEFF Research Database (Denmark)
Cook, Gerald; Lin, Ching-Fang
1980-01-01
The local linearization algorithm is presented as a possible numerical integration scheme to be used in real-time simulation. A second-order nonlinear example problem is solved using different methods. The local linearization approach is shown to require less computing time and give significant...... improvement in accuracy over the classical second-order integration methods....
Design of a novel integrated position sensor based on Hall effects for linear oscillating actuator
Wang, Tianyi; Yan, Liang; Jiao, Zongxia
2015-07-01
Linear oscillating actuator provides linear reciprocate motion directly without other auxiliary components, which is suitable for high integration applications in aerospace industry. Accurate position control is essential for linear oscillating motor and relies on concise measurement of mover position. However, most position measurements are dependent on external complicated sensors, which hinders further integration of linear oscillating actuation system. In this paper, a novel position sensing system for linear oscillating actuator based on Hall effects is proposed to achieve accurate and high integration measurement simultaneously. Axial sensing magnetic field with approximately linear relationship with position is created for direct and convenient measurement. Analytical model of sensing magnetic field is set up for optimization and validated by finite element method and experimental results. Finally, sensing magnets are integrated into motor prototype for experiments. Dynamic position results are tested in experiments and prove to be effective and accurate for position sensing with short-stroke.
Path integral evaluation of non-abelian anomaly and Pauli-Villars-Gupta regularization
Okuyama, K; Okuyama, Kiyoshi; Suzuki, Hiroshi
1996-01-01
When the path integral method of anomaly evaluation is applied to chiral gauge theories, two different types of gauge anomaly, i.e., the consistent form and the covariant form, appear depending on the regularization scheme for the Jacobian factor. We clarify the relation between the regularization scheme and the Pauli--Villars--Gupta (PVG) type Lagrangian level regularization. The conventional PVG, being non-gauge invariant for chiral gauge theories, in general corresponds to the consistent regularization scheme. The covariant regularization scheme, on the other hand, is realized by the generalized PVG Lagrangian recently proposed by Frolov and Slavnov. These correspondences are clarified by reformulating the PVG method as a regularization of the composite gauge current operator.
Gaussian white noise analysis and its application to Feynman path integral
Suryawan, Herry Pribawanto
2016-02-01
In applied science, Gaussian white noise (the time derivative of Brownian motion) is often chosen as a mathematical idealization of phenomena involving sudden and extremely large fluctuations. It is also possible to define and study Gaussian white noise in a mathematically rigorous framework. In this survey paper we review the Gaussian white noise as an object in an infinite dimensional topological vector space. A brief construction of Gaussian white noise space and Gaussian white noise distributions will be presented. Gaussian white noise analysis provides a framework which offers various generalization of concept known from finite dimensional analysis to the infinite dimensional case, among them are differential operators, Fourier transform, and distribution theory. We will also present some recent developments and results on the application of Gaussian white noise theory to Feynman's path integral approach for quantum mechanics.
Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
Behtash, Alireza; Schaefer, Thomas; Sulejmanpasic, Tin; Unsal, Mithat
2015-01-01
We show that the semi-classical analysis of generic Euclidean path integrals necessarily requires complexification of the action and measure, and consideration of complex saddle solutions. We demonstrate that complex saddle points have a natural interpretation in terms of the Picard-Lefschetz theory. Motivated in part by the semi-classical expansion of QCD with adjoint matter on ${\\mathbb R}^3\\times S^1$, we study quantum-mechanical systems with bosonic and fermionic (Grassmann) degrees of freedom with harmonic degenerate minima, as well as (related) purely bosonic systems with harmonic non-degenerate minima. We find exact finite action non-BPS bounce and bion solutions to the holomorphic Newton equations. We find not only real solutions, but also complex solution with non-trivial monodromy, and finally complex multi-valued and singular solutions. Complex bions are necessary for obtaining the correct non-perturbative structure of these models. In the supersymmetric limit the complex solutions govern the groun...
Path-integral simulation of ice VII: Pressure and temperature effects
Herrero, Carlos P
2015-01-01
Effects of pressure and temperature on structural and thermodynamic properties of ice VII have been studied by using path-integral molecular dynamics (PIMD) simulations. Temperatures between 25 and 450 K, as well as pressures up to 12 GPa were considered. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. We analyze the pressure dependence of the molar volume, bulk modulus, interatomic distances, kinetic energy, and atomic delocalization at various temperatures. Results of PIMD simulations are compared with those derived from a quasi-harmonic approximation (QHA) of vibrational modes, which helps to assess the importance of anharmonic effects, as well as the influence of the different modes on the properties of ice VII. The accuracy of the QHA for describing this high-pressure phase decreases for rising temperature, but this approximation becomes more reliable as pressure grows, since anharmonicity becomes less relevant. Comparisons with low-pressure cubic ice ...
A New Perspective on Path Integral Quantum Mechanics in Curved Space-Time
Directory of Open Access Journals (Sweden)
Singh Dinesh
2013-09-01
Full Text Available Abstract. A new approach to path integral quantum mechanics in curved space-time is presented for scalar particle propagation, expressed in terms of Lie transport and Fermi or Riemann normal co-ordinates to describe local curvature. While the presence of local curvature results in a strictly non-unitary representation of local time translation, the formalism nevertheless correctly recovers the free-particle Lagrangian in curved space-time, along with new terms that predict a simultaneous breakdown of time-reversal symmetry and a quantum violation of the weak equivalence principle at the particle’s Compton wavelength scale. Furthermore, the formalism reveals the prediction of a gauge-invariant phase factor interpreted as the gravitational Aharonov-Bohm effect and Berry’s phase.
Path integral centroid molecular dynamics simulation of para-hydrogen sandwiched by graphene sheets
Minamino, Yuki; Kinugawa, Kenichi
2016-11-01
The carbon-hydrogen composite systems of para-hydrogen (p-H2) sandwiched by a couple of graphene sheets have been investigated by means of path integral centroid molecular dynamics simulations at 17 K. It has been shown that sandwiched hydrogen is liquid-like but p-H2 molecules are preferably adsorbed onto the graphene sheets because of attractive graphene-hydrogen interaction. The diffusion coefficient of p-H2 molecules in the direction parallel to the graphene sheets is comparable to that in pure liquid p-H2. There exists a characteristic mode of 140 cm-1 of the p-H2 molecules, attributed to adsorption-binding motion perpendicular to the graphene sheets.
Isotope effects in water as investigated by neutron diffraction and path integral molecular dynamics
Energy Technology Data Exchange (ETDEWEB)
Zeidler, Anita [University of Bath; Salmon, Phil [University of Bath; Fischer, Henry E [Institut Laue-Langevin (ILL); Neuefeind, Joerg C [ORNL; Simonson, J Michael {Mike} [ORNL; Markland, Thomas [Columbia University
2012-01-01
The structure of heavy and light water at 300 K was investigated by using a joint approach in which the method of neutron di raction with oxygen isotope substitution was combined with path integral molecular dynamics simulations. The di raction results, which give intra-molecular O-D and O-H bond distances of 0.985(5) and 0.990(5) A, were found to be in best agreement with those obtained by using the exible anharmonic TTM3-F water model. Both techniques show a di erence of '0.5% between the O-D and O-H intra-molecular bond lengths and the results support a competing quantum e ects model for water in which its structural and dynamical properties are governed by an o set between intra-molecular and inter-molecular quantum contributions. Further consideration of the O-O correlations is needed in order to improve agreement with experiment.
Energy Technology Data Exchange (ETDEWEB)
Kinugawa, Kenichi [Nara Women`s Univ., Nara (Japan). Dept. of Chemistry
1998-10-01
It has been unsuccessful to solve a set of time-dependent Schroedinger equations numerically for many-body quantum systems which involve, e.g., a number of hydrogen molecules, protons, and excess electrons at a low temperature, where quantum effect evidently appears. This undesirable situation is fatal for the investigation of real low-temperature chemical systems because they are essentially composed of many quantum degrees of freedom. However, if we use a new technique called `path integral centroid molecular dynamics (CMD) simulation` proposed by Cao and Voth in 1994, the real-time semi-classical dynamics of many degrees of freedom can be computed by utilizing the techniques already developed in the traditional classical molecular dynamics (MD) simulations. Therefore, the CMD simulation is expected to be very powerful tool for the quantum dynamics studies or real substances. (J.P.N.)
Wang, Qi; Suzuki, Kimichi; Nagashima, Umpei; Tachikawa, Masanori; Yan, Shiwei
2013-11-01
The geometric isotope effects on the structures of hydrated chloride ionic hydrogen bonded clusters are explored by carrying out path integral molecular dynamics simulations. First, an outer shell coordinate is selected to display the rearrangement of single and multi hydration shell cluster structures. Next, to show the competition of intramolecular and intermolecular nuclear quantum effects, the intramolecular OH∗ stretching and intermolecular ion-water wagging motions are studied for single and multi shell structures, respectively. The results indicate that the intermolecular nuclear quantum effects stabilize the ionic hydrogen bonds in single shell structures, while they are destabilized through the competition with intramolecular nuclear quantum effects in multi shell structures. In addition, the correlations between ion-water stretching motion and other cluster vibrational coordinates are discussed. The results indicate that the intermolecular nuclear quantum effects on the cluster structures are strongly related to the cooperation of the water-water hydrogen bond interactions.
Reilly, Anthony M.; Habershon, Scott; Morrison, Carole A.; Rankin, David W. H.
2010-03-01
Path-integral molecular dynamics (PIMD) simulations with an empirical interaction potential have been used to determine the experimental equilibrium structure of solid nitromethane at 4.2 and 15 K. By comparing the time-averaged molecular structure determined in a PIMD simulation to the calculated minimum-energy (zero-temperature) molecular structure, we have derived structural corrections that describe the effects of thermal motion. These corrections were subsequently used to determine the equilibrium structure of nitromethane from the experimental time-averaged structure. We find that the corrections to the intramolecular and intermolecular bond distances, as well as to the torsion angles, are quite significant, particularly for those atoms participating in the anharmonic motion of the methyl group. Our results demonstrate that simple harmonic models of thermal motion may not be sufficiently accurate, even at low temperatures, while molecular simulations employing more realistic potential-energy surfaces can provide important insight into the role and magnitude of anharmonic atomic motions.
Low-temperature anharmonicity of barium titanate: A path-integral molecular-dynamics study
Geneste, Grégory; Dammak, Hichem; Hayoun, Marc; Thiercelin, Mickael
2013-01-01
We investigate the influence of quantum effects on the dielectric and piezoelectric properties of barium titanate in its (low-temperature) rhombohedral phase, and show the strongly anharmonic character of this system even at low temperature. For this purpose, we perform path-integral molecular-dynamics simulations under fixed pressure and fixed temperature, using an efficient Langevin thermostat-barostat, and an effective Hamiltonian derived from first-principles calculations. The quantum fluctuations are shown to significantly enhance the static dielectric susceptibility (≈ by a factor of 2) and the piezoelectric constants, reflecting the strong anharmonicity of this ferroelectric system even at very low temperature. The slow temperature-evolution of the dielectric properties observed below ≈100 K is attributed (i) to zero-point energy contributions and (ii) to harmonic behavior if the quantum effects are turned off.
Path Integral Monte Carlo and Density Functional Molecular Dynamics Simulations of Warm Dense Matter
Militzer, Burkhard; Driver, Kevin
2011-10-01
We analyze the applicability of two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), to study the regime of warm dense matter. We discuss the advantages as well as the limitations of each method and propose directions for future development. Results for dense, liquid helium, where both methods have been applied, demonstrate the range of each method's applicability. Comparison of the equations of state from simulations with analytical theories and free energy models show that DFT is useful for temperatures below 100000 K and then PIMC provides accurate results for all higher temperatures. We characterize the structure of the liquid in terms of pair correlation functions and study the closure of the band gap with increasing density and temperature. Finally, we discuss simulations of heavier elements and demonstrate the reliability are both methods in such cases with preliminary results.
Ananth, Nandini
2013-09-01
We introduce mapping-variable ring polymer molecular dynamics (MV-RPMD), a model dynamics for the direct simulation of multi-electron processes. An extension of the RPMD idea, this method is based on an exact, imaginary time path-integral representation of the quantum Boltzmann operator using continuous Cartesian variables for both electronic states and nuclear degrees of freedom. We demonstrate the accuracy of the MV-RPMD approach in calculations of real-time, thermal correlation functions for a range of two-state single-mode model systems with different coupling strengths and asymmetries. Further, we show that the ensemble of classical trajectories employed in these simulations preserves the Boltzmann distribution and provides a direct probe into real-time coupling between electronic state transitions and nuclear dynamics.
Low-temperature metallic liquid hydrogen: an ab-initio path-integral molecular dynamics perspective
Chen, Ji; Li, Xin-Zheng; Zhang, Qianfan; Probert, Matthew; Pickard, Chris; Needs, Richard; Michaelides, Angelos; Wang, Enge
2013-03-01
Experiments and computer simulations have shown that the melting temperature of solid hydrogen drops with pressure above about 65 GPa, suggesting that a low temperature liquid state might exist. It has also been suggested that this liquid state might be non-molecular and metallic, although evidence for such behaviour is lacking. Using a combination of ab initio path-integral molecular dynamics and the two-phase methods, we have simulated the melting of solid hydrogen under finite temperatures. We found an atomic solid phase from 500 to 800 GPa which melts at < 200 K. Beyond this and up to pressures of 1,200 GPa a metallic atomic liquid is stable at temperatures as low as 50 K. The quantum motion of the protons is critical to the low melting temperature in this system as ab initio simulations with classical nuclei lead to a considerably higher melting temperature of ~300 K across the entire pressure range considered.
Witt, Alexander; Ivanov, Sergei D.; Shiga, Motoyuki; Forbert, Harald; Marx, Dominik
2009-05-01
Centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) are two conceptually distinct extensions of path integral molecular dynamics that are able to generate approximate quantum dynamics of complex molecular systems. Both methods can be used to compute quasiclassical time correlation functions which have direct application in molecular spectroscopy; in particular, to infrared spectroscopy via dipole autocorrelation functions. The performance of both methods for computing vibrational spectra of several simple but representative molecular model systems is investigated systematically as a function of temperature and isotopic substitution. In this context both CMD and RPMD feature intrinsic problems which are quantified and investigated in detail. Based on the obtained results guidelines for using CMD and RPMD to compute infrared spectra of molecular systems are provided.
Isotope effects in water as investigated by neutron diffraction and path integral molecular dynamics
Zeidler, Anita; Salmon, Philip S.; Fischer, Henry E.; Neuefeind, Jörg C.; Simonson, J. Mike; Markland, Thomas E.
2012-07-01
The structures of heavy and light water at 300 K were investigated by using a joint approach in which the method of neutron diffraction with oxygen isotope substitution was complemented by path integral molecular dynamics simulations. The diffraction results, which give intra-molecular O-D and O-H bond distances of 0.985(5) and 0.990(5) Å, were found to be in best agreement with those obtained by using the flexible anharmonic TTM3-F water model. Both techniques show a difference of ≃ 0.5% between the O-D and O-H intra-molecular bond lengths, and the results support a competing quantum effects model for water in which its structural and dynamical properties are governed by an offset between intra-molecular and inter-molecular quantum contributions. Further consideration of the O-O correlations is needed in order to improve agreement with experiment.
Yoshikawa, Takehiro; Sugawara, Shuichi; Takayanagi, Toshiyuki; Shiga, Motoyuki; Tachikawa, Masanori
2012-02-01
Path-integral molecular dynamics simulations have been performed for porphycene and its isotopic variants in order to understand the effect of isotopic substitution of inner protons on the double proton transfer mechanism. We have used an on-the-fly direct dynamics technique at the semiempirical PM6 level combined with specific reaction parameterization. Our quantum simulations show that double proton transfer of the unsubstituted porphycene at T = 300 K mainly occurs via a so-called concerted mechanism through the D2h second-order saddle point. In addition, we found that both isotopic substitution and temperature significantly affect the double proton transfer mechanism. For example, the contribution of the stepwise mechanism increases with a temperature increase. We have also carried out hypothetical simulations with the porphycene configurations being completely planar. It has been found that out-of-plane vibrational motions significantly decrease the contribution of the concerted proton transfer mechanism.
The canonical versrus path integral quantization approach to generalized Kodama states (Part I)
Ita, Eyo Eyo
2007-01-01
This is the fifth paper in the series outlining an algorithm to consistently quantize four-dimensional gravity. We derive the pure Kodama state in analogy to the no-boundary proposal for constructing quantum gravitational wavefunctions, checking at each stage of the process the equivalence of the canonical and path integral approaches. A family of additional pure Kodama states is identified via the canonical approach and a criterion for their suitability as a basis of states is examined. We provide an interpretation for the problem of time within the context of the generalized Kodama states and propose a possible method of resolution. We also develop different techniques for solving the Gauss' law constraintsd at the kinematical level, in preparation for future work in this series.
Path integral polymer propagator of relativistic and non-relativistic particles
Morales-Técotl, Hugo A; Ruelas, Juan C
2016-01-01
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The mechanical models we consider are deparametrized and thus the group averaging technique is used to deal with the corresponding constraints. The transition amplitudes are written in a vertex expansion form used in the spin foam models, where here a vertex is actually a jump in position. Polymer Propagators previously obtained by spectral methods for a nonrelativistic polymer particle, both free and in a box, are regained with this method. Remarkably, the approach is also shown to yield the polymer propagator of the relativistic particle. This reduces to the standard form in the continuum limit for which the length scale parameter of the polymer quantization is taken to be small. Some possible future developments are commented upon.
Quantum Mechanical Single Molecule Partition Function from PathIntegral Monte Carlo Simulations
Energy Technology Data Exchange (ETDEWEB)
Chempath, Shaji; Bell, Alexis T.; Predescu, Cristian
2006-10-01
An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.
Topics in mode conversion theory and the group theoretical foundations of path integrals
Richardson, Andrew Stephen
discrete Beisenberg-Wey1 group to construct the symbol of a matrix. We then go on to show how the path integral arises when calculating the symbol of a function of an operator. We also show how the phase space and configuration space path integrals arise when considering reductions of the regular representation of the Heisenberg-Wey1 group to the primary representations and irreducible representations, respectively. We also show how the path integral can be interpreted as a Fourier transform on the space of measures, opening up the possibility of using tools from statistical mechanics (such as maximum entropy techniques) to analyze the path integral. We conclude with a survey of ideas for future research and describe several potential applications of this group theoretical perspective to problems in mode conversion.
Accelerating the convergence of path integral dynamics with a generalized Langevin equation.
Ceriotti, Michele; Manolopoulos, David E; Parrinello, Michele
2011-02-28
The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.
Path integral approach for quantum motion on spaces of non-constant curvature according to Koenigs
Energy Technology Data Exchange (ETDEWEB)
Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2006-08-15
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ''Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat space and divides it by a two-dimensional superintegrable potential. These superintegrable potentials are the isotropic singular oscillator, the Holt-potential, and the Coulomb potential. In all cases a non-trivial space of non-constant curvature is generated. We can study free motion and the motion with an additional superintegrable potential. For possible bound-state solutions we find in all three cases an equation of eighth order in the energy E. The special cases of the Darboux spaces are easily recovered by choosing the parameters accordingly. (orig.)
A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results
Baaquie, Belal E.
1997-12-01
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic volatility is reviewed starting from the first principles of finance. The equation of Merton and Garman is then recast using the path integration technique of theoretical physics. The price of the stock option is shown to be the analogue of the Schrödinger wavefunction of quantum mechanics and the exact Hamiltonian and Lagrangian of the system is obtained. The results of Hull and White are generalized to the case when stock price and volatility have non-zero correlation. Some exact results for pricing stock options for the general correlated case are derived.
Path-integral action of a particle in the noncommutative plane.
Gangopadhyay, Sunandan; Scholtz, Frederik G
2009-06-19
Noncommutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on noncommutative configuration space. Taking this as a departure point, we formulate a coherent state approach to the path-integral representation of the transition amplitude. From this we derive an action for a particle moving in the noncommutative plane and in the presence of an arbitrary potential. We find that this action is nonlocal in time. However, this nonlocality can be removed by introducing an auxilary field, which leads to a second class constrained system that yields the noncommutative Heisenberg algebra upon quantization. Using this action, the propagator of the free particle and harmonic oscillator are computed explicitly.
Path-integral Monte Carlo method for Rényi entanglement entropies.
Herdman, C M; Inglis, Stephen; Roy, P-N; Melko, R G; Del Maestro, A
2014-07-01
We introduce a quantum Monte Carlo algorithm to measure the Rényi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path-integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability, and interactions. We present proof-of-principle calculations and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large-scale many-body systems of interacting bosons.
Correct Path-Integral Formulation of Quantum Thermal Field Theory in Coherent State Representation
Institute of Scientific and Technical Information of China (English)
SU Jun-Chen; ZHENG Fu-Hou
2005-01-01
The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and ψ4 theory as examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and ψ4 theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.
Finite Size Effect in Path Integral Monte Carlo Simulations of 4He Systems
Institute of Scientific and Technical Information of China (English)
ZHAO Xing-Wen; CHENG Xin-Lu
2008-01-01
Path integral Monte Carlo (PIMC) simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of 4He. We determine the energy as a function of temperature at saturated-vapor-pressure (SVP) conditions in the temperature range of T ∈ [1.0 K,4.0 K], and the equation of state (EOS) in the ground state for systems consisted of 32, 64 and 128 4He atoms, respectively. We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T ∈ [2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.
Thermally assisted tunneling of hydrogen in silicon: A path-integral Monte Carlo study
Herrero, Carlos P.
1997-04-01
Quantum transition-state theory, based on the path-integral formalism, has been applied to study the jump rate of atomic hydrogen and deuterium in crystalline silicon. This technique provides a methodology to study the influence of vibrational mode quantization and quantum tunneling on the impurity jump rate. The atomic interactions were modeled by effective potentials, fitted to earlier ab initio pseudopotential calculations. Silicon nuclei were treated as quantum particles up to second-nearest neighbors of the impurity. The hydrogen jump rate follows an Arrhenius law, describable with classical transition-state theory, at temperatures higher than 100 K. At ~80 K, a change in the slope of the Arrhenius plot is obtained for hydrogen, as expected for the onset of a diffusion regime controlled by phonon-assisted tunneling of the impurity. For deuterium, no change of slope is observed in the studied temperature range (down to 40 K).
A PATH INTEGRAL FORMULATION OF THE WRIGHT-FISHER PROCESS WITH GENIC SELECTION
SCHRAIBER, JOSHUA G.
2014-01-01
The Wright-Fisher process with selection is an important tool in population genetics theory. Traditional analysis of this process relies on the diffusion approximation. The diffusion approximation is usually studied in a partial differential equations framework. In this paper, I introduce a path integral formalism to study the Wright-Fisher process with selection and use that formalism to obtain a simple perturbation series to approximate the transition density. The perturbation series can be understood in terms of Feynman diagrams, which have a simple probabilistic interpretation in terms of selective events. The perturbation series proves to be an accurate approximation of the transition density for weak selection and is shown to be arbitrarily accurate for any selection coefficient. PMID:24269333
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer F.; Remus, Ruben G.; Fay, James J.; Reithmaier, Karl
2014-01-01
Double-pulse 2-micron lasers have been demonstrated with energy as high as 600 millijouls and up to 10 Hz repetition rate. The two laser pulses are separated by 200 microseconds and can be tuned and locked separately. Applying double-pulse laser in DIAL system enhances the CO2 measurement capability by increasing the overlap of the sampled volume between the on-line and off-line. To avoid detection complicity, integrated path differential absorption (IPDA) lidar provides higher signal-to-noise ratio measurement compared to conventional range-resolved DIAL. Rather than weak atmospheric scattering returns, IPDA rely on the much stronger hard target returns that is best suited for airborne platforms. In addition, the IPDA technique measures the total integrated column content from the instrument to the hard target but with weighting that can be tuned by the transmitter. Therefore, the transmitter could be tuned to weight the column measurement to the surface for optimum CO2 interaction studies or up to the free troposphere for optimum transport studies. Currently, NASA LaRC is developing and integrating a double-Pulsed 2-micron direct detection IPDA lidar for CO2 column measurement from an airborne platform. The presentation will describe the development of the 2-micron IPDA lidar system and present the airborne measurement of column CO2 and will compare to in-situ measurement for various ground target of different reflectivity.
Maintaining a cognitive map in darkness: the need to fuse boundary knowledge with path integration.
Cheung, Allen; Ball, David; Milford, Michael; Wyeth, Gordon; Wiles, Janet
2012-01-01
Spatial navigation requires the processing of complex, disparate and often ambiguous sensory data. The neurocomputations underpinning this vital ability remain poorly understood. Controversy remains as to whether multimodal sensory information must be combined into a unified representation, consistent with Tolman's "cognitive map", or whether differential activation of independent navigation modules suffice to explain observed navigation behaviour. Here we demonstrate that key neural correlates of spatial navigation in darkness cannot be explained if the path integration system acted independently of boundary (landmark) information. In vivo recordings demonstrate that the rodent head direction (HD) system becomes unstable within three minutes without vision. In contrast, rodents maintain stable place fields and grid fields for over half an hour without vision. Using a simple HD error model, we show analytically that idiothetic path integration (iPI) alone cannot be used to maintain any stable place representation beyond two to three minutes. We then use a measure of place stability based on information theoretic principles to prove that featureless boundaries alone cannot be used to improve localization above chance level. Having shown that neither iPI nor boundaries alone are sufficient, we then address the question of whether their combination is sufficient and--we conjecture--necessary to maintain place stability for prolonged periods without vision. We addressed this question in simulations and robot experiments using a navigation model comprising of a particle filter and boundary map. The model replicates published experimental results on place field and grid field stability without vision, and makes testable predictions including place field splitting and grid field rescaling if the true arena geometry differs from the acquired boundary map. We discuss our findings in light of current theories of animal navigation and neuronal computation, and elaborate on
Maintaining a cognitive map in darkness: the need to fuse boundary knowledge with path integration.
Directory of Open Access Journals (Sweden)
Allen Cheung
Full Text Available Spatial navigation requires the processing of complex, disparate and often ambiguous sensory data. The neurocomputations underpinning this vital ability remain poorly understood. Controversy remains as to whether multimodal sensory information must be combined into a unified representation, consistent with Tolman's "cognitive map", or whether differential activation of independent navigation modules suffice to explain observed navigation behaviour. Here we demonstrate that key neural correlates of spatial navigation in darkness cannot be explained if the path integration system acted independently of boundary (landmark information. In vivo recordings demonstrate that the rodent head direction (HD system becomes unstable within three minutes without vision. In contrast, rodents maintain stable place fields and grid fields for over half an hour without vision. Using a simple HD error model, we show analytically that idiothetic path integration (iPI alone cannot be used to maintain any stable place representation beyond two to three minutes. We then use a measure of place stability based on information theoretic principles to prove that featureless boundaries alone cannot be used to improve localization above chance level. Having shown that neither iPI nor boundaries alone are sufficient, we then address the question of whether their combination is sufficient and--we conjecture--necessary to maintain place stability for prolonged periods without vision. We addressed this question in simulations and robot experiments using a navigation model comprising of a particle filter and boundary map. The model replicates published experimental results on place field and grid field stability without vision, and makes testable predictions including place field splitting and grid field rescaling if the true arena geometry differs from the acquired boundary map. We discuss our findings in light of current theories of animal navigation and neuronal computation
Agarwal, Animesh
2015-01-01
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however computationally this technique is very demanding. The abovementioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One possible solution to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this ...
General Linear Models: An Integrated Approach to Statistics
Directory of Open Access Journals (Sweden)
Andrew Faulkner
2008-09-01
Full Text Available Generally, in psychology, the various statistical analyses are taught independently from each other. As a consequence, students struggle to learn new statistical analyses, in contexts that differ from their textbooks. This paper gives a short introduction to the general linear model (GLM, in which it is showed that ANOVA (one-way, factorial, repeated measure and analysis of covariance is simply a multiple correlation/regression analysis (MCRA. Generalizations to other cases, such as multivariate and nonlinear analysis, are also discussed. It can easily be shown that every popular linear analysis can be derived from understanding MCRA.
Krajewski, Florian R.; Müser, Martin H.
2005-03-01
The commensurate Frenkel Kontorova (FK) model is studied using path-integral molecular dynamics (PIMD). We focus on the highly discrete case, in which the embedding potential has a much greater maximum curvature than the harmonic potential connecting two particles in the FK chain. When efficient sampling methods are used, the dynamical interpretation of adiabatic PIMD appears to represent quite accurately the true time correlation functions of this highly correlated many-body system. We have found that the discrete, quantum FK model shows different behavior than its continuum version. The spectral density does not show the characteristic ω-2Θ(ω-ωc) cusp of the continuum solution in the pinned phase (m>mc). We also identify a dynamical quantum hysteresis in addition to the regular classical hysteresis when an external force is applied to the FK chain. In the unpinned phase (m⩽mc), we find a linear response damping coefficient which is finite and only weakly dependent on temperature T at small values of T.
Abshire, James B.; Riris, Haris; Weaver, Clark J.; Mao, Jianping; Allan, Graham R.; Hasselbrack, William E.; Browell, Edward V.
2013-01-01
We report on airborne CO2 column absorption measurements made in 2009 with a pulsed direct-detection lidar operating at 1572.33 nm and utilizing the integrated path differential absorption technique. We demonstrated these at different altitudes from an aircraft in July and August in flights over four locations in the central and eastern United States. The results show clear CO2 line shape and absorption signals, which follow the expected changes with aircraft altitude from 3 to 13 km. The lidar measurement statistics were also calculated for each flight as a function of altitude. The optical depth varied nearly linearly with altitude, consistent with calculations based on atmospheric models. The scatter in the optical depth measurements varied with aircraft altitude as expected, and the median measurement precisions for the column varied from 0.9 to 1.2 ppm. The altitude range with the lowest scatter was 810 km, and the majority of measurements for the column within it had precisions between 0.2 and 0.9 ppm.
Scattering from the Potential Barrier $V=cosh^{-2} \\omega x$ from the Path Integration over SO(1,2)
Ahmedov, H
1996-01-01
Unitary irreducible representation of the group SO(1,2) is obtained in the mixed basis, i.e. between the compact and noncompact basis and the new addition theorems are derived which are required in path integral applications involving the positively signed potential. The Green function for the potential barrier $V=cosh^{-2}\\omega x$ is evaluated from the path integration over the coset space SO(1,2)/K where K is the compact subgroup.The transition and the reflection coefficients are given.Results for the moving barrier $V=cosh^{-2}\\omega (x-g_0t)$ are also presented.
Song, Linze; Shi, Qiang
2015-05-07
We present a new non-perturbative method to calculate the charge carrier mobility using the imaginary time path integral approach, which is based on the Kubo formula for the conductivity, and a saddle point approximation to perform the analytic continuation. The new method is first tested using a benchmark calculation from the numerical exact hierarchical equations of motion method. Imaginary time path integral Monte Carlo simulations are then performed to explore the temperature dependence of charge carrier delocalization and mobility in organic molecular crystals (OMCs) within the Holstein and Holstein-Peierls models. The effects of nonlocal electron-phonon interaction on mobility in different charge transport regimes are also investigated.
Quantum-dot-based integrated non-linear sources
DEFF Research Database (Denmark)
Bernard, Alice; Mariani, Silvia; Andronico, Alessio
2015-01-01
The authors report on the design and the preliminary characterisation of two active non-linear sources in the terahertz and near-infrared range. The former is associated to difference-frequency generation between whispering gallery modes of an AlGaAs microring resonator, whereas the latter is gra...
The Effect of Learning in Virtual Path Integration%虚拟路径整合的学习效应
Institute of Scientific and Technical Information of China (English)
过继成思; 宛小昂
2015-01-01
Path integration is one type of navigations in which navigators integrate self-motion information to update their current position and orientation relative to the origin of their travel. Human path integration ability is often measured in the path completion task. In this task, participants travel along several segments, make several turns at the intersections of each two segments, and arrive at the end of the outbound path. Then they are asked to directly return to the origin of the outbound path. Previous studies have revealed that athletes showed better path completion performance than general population. The purpose of the present study was to examine whether the path integration ability of general population can be improved if they are repeatedly exposed to outbound paths with the same configurations. In two experiments, we used the Head-Mounted Display Virtual Reality to present hallway mazes, and each outbound path consisted of 5 segments. Participants pressed a button on the gamepad to travel along a segment, so the information about transition was based on optical flow. By contrast, they were asked to actually rotate their bodies at the intersections, so the information about rotation came from both optical flow and body senses. Each participant completed 4 blocks, 6 trials of each. Within each block, they performed the path completion task on 6 different outbound paths. From one block to the next, they performed the path completion task on outbound paths with the same configurations. In Experiment 1, all the 5 segments within each outbound path had the same lengths, and the turning angle at each interaction was always 60 degree, clockwise or counterclockwise. When the participants repeatedly performed the path completion task on these outbound paths with the same configurations, they showed reduced position errors, direction errors, and RTs. By contrast, more complicated path configurations were used in Experiment 2. Specifically, within each outbound
International Organization for Standardization. Geneva
2003-01-01
Information technology - Telecommunications and information exchange between systems - Private integrated services network - Inter-exchange signalling protocol - Path replacement additional network feature
Integration of non-linear cellular mechanisms regulating microvascular perfusion.
Griffith, T M; Edwards, D H
1999-01-01
It is becoming increasingly evident that interactions between the different cell types present in the vessel wall and the physical forces that result from blood flow are highly complex. This short article will review evidence that irregular fluctuations in vascular resistance are generated by non-linearity in the control mechanisms intrinsic to the smooth muscle cell and can be classified as chaotic. Non-linear systems theory has provided insights into the mechanisms involved at the cellular level by allowing the identification of dominant control variables and the construction of one-dimensional iterative maps to model vascular dynamics. Experiments with novel peptide inhibitors of gap junctions have shown that the coordination of aggregate responses depends on direct intercellular communication. The sensitivity of chaotic trajectories to perturbation may nevertheless generate a high degree of variability in the response to pharmacological interventions and altered perfusion conditions.
General Linear Models: An Integrated Approach to Statistics
Andrew Faulkner; Sylvain Chartier
2008-01-01
Generally, in psychology, the various statistical analyses are taught independently from each other. As a consequence, students struggle to learn new statistical analyses, in contexts that differ from their textbooks. This paper gives a short introduction to the general linear model (GLM), in which it is showed that ANOVA (one-way, factorial, repeated measure and analysis of covariance) is simply a multiple correlation/regression analysis (MCRA). Generalizations to other cases, such as multiv...
PathText: a text mining integrator for biological pathway visualizations
Kemper, Brian; Matsuzaki, Takuya; Matsuoka, Yukiko; Tsuruoka, Yoshimasa; Kitano, Hiroaki; Ananiadou, Sophia; Tsujii, Jun'ichi
2010-01-01
Motivation: Metabolic and signaling pathways are an increasingly important part of organizing knowledge in systems biology. They serve to integrate collective interpretations of facts scattered throughout literature. Biologists construct a pathway by reading a large number of articles and interpreting them as a consistent network, but most of the models constructed currently lack direct links to those articles. Biologists who want to check the original articles have to spend substantial amounts of time to collect relevant articles and identify the sections relevant to the pathway. Furthermore, with the scientific literature expanding by several thousand papers per week, keeping a model relevant requires a continuous curation effort. In this article, we present a system designed to integrate a pathway visualizer, text mining systems and annotation tools into a seamless environment. This will enable biologists to freely move between parts of a pathway and relevant sections of articles, as well as identify relevant papers from large text bases. The system, PathText, is developed by Systems Biology Institute, Okinawa Institute of Science and Technology, National Centre for Text Mining (University of Manchester) and the University of Tokyo, and is being used by groups of biologists from these locations. Contact: brian@monrovian.com. PMID:20529930
Ab initio path-integral molecular dynamics and the quantum nature of hydrogen bonds
Yexin, Feng; Ji, Chen; Xin-Zheng, Li; Enge, Wang
2016-01-01
The hydrogen bond (HB) is an important type of intermolecular interaction, which is generally weak, ubiquitous, and essential to life on earth. The small mass of hydrogen means that many properties of HBs are quantum mechanical in nature. In recent years, because of the development of computer simulation methods and computational power, the influence of nuclear quantum effects (NQEs) on the structural and energetic properties of some hydrogen bonded systems has been intensively studied. Here, we present a review of these studies by focussing on the explanation of the principles underlying the simulation methods, i.e., the ab initio path-integral molecular dynamics. Its extension in combination with the thermodynamic integration method for the calculation of free energies will also be introduced. We use two examples to show how this influence of NQEs in realistic systems is simulated in practice. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275008, 91021007, and 10974012) and the China Postdoctoral Science Foundation (Grant No. 2014M550005).
Fishman, Louis
2000-11-01
The role of mathematical modeling in the physical sciences will be briefly addressed. Examples will focus on computational acoustics, with applications to underwater sound propagation, electromagnetic modeling, optics, and seismic inversion. Direct and inverse wave propagation problems in both the time and frequency domains will be considered. Focusing on fixed-frequency (elliptic) wave propagation problems, the usual, two-way, partial differential equation formulation will be exactly reformulated, in a well-posed manner, as a one-way (marching) problem. This is advantageous for both direct and inverse considerations, as well as stochastic modeling problems. The reformulation will require the introduction of pseudodifferential operators and their accompanying phase space analysis (calculus), in addition to path integral representations for the fundamental solutions and their subsequent computational algorithms. Unlike the more traditional, purely numerical applications of, for example, finite-difference and finite-element methods, this approach, in effect, writes the exact, or, more generally, the asymptotically correct, answer as a functional integral and, subsequently, computes it directly. The overall computational philosophy is to combine analysis, asymptotics, and numerical methods to attack complicated, real-world problems. Exact and asymptotic analysis will stress the complementary nature of the direct and inverse formulations, as well as indicating the explicit structural connections between the time- and frequency-domain solutions.
On the Path Integral Loop Representation of (2+1) Lattice Non-Abelian Theory
Aroca, J M; Gambini, R
1998-01-01
A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The corresponding path integral for SU(2) lattice gauge theory is expressed as a sum over colored surfaces, i.e. only involving the $j_p$ attached to the lattice plaquettes. This surfaces may be interpreted as the world sheets of the spin networks In 2+1 dimensions, this can be accomplished by working in a lattice dual to a tetrahedral lattice constructed on a face centered cubic Bravais lattice. On such a lattice, the integral of gauge variables over boundaries or singular lines - which now always bound three coloured surfaces - only contributes when four singular lines intersect at one vertex and can be explicitly computed producing a 6-j or Racah symbol. We performed a strong coupling expansion for the free energy. The convergence of the series expansions is quite different fr...
Wong, Kin-Yiu; Xu, Yuqing; Xu, Liang
2015-11-01
Enzymatic reactions are integral components in many biological functions and malfunctions. The iconic structure of each reaction path for elucidating the reaction mechanism in details is the molecular structure of the rate-limiting transition state (RLTS). But RLTS is very hard to get caught or to get visualized by experimentalists. In spite of the lack of explicit molecular structure of the RLTS in experiment, we still can trace out the RLTS unique "fingerprints" by measuring the isotope effects on the reaction rate. This set of "fingerprints" is considered as a most direct probe of RLTS. By contrast, for computer simulations, oftentimes molecular structures of a number of TS can be precisely visualized on computer screen, however, theoreticians are not sure which TS is the actual rate-limiting one. As a result, this is an excellent stage setting for a perfect "marriage" between experiment and theory for determining the structure of RLTS, along with the reaction mechanism, i.e., experimentalists are responsible for "fingerprinting", whereas theoreticians are responsible for providing candidates that match the "fingerprints". In this Review, the origin of isotope effects on a chemical reaction is discussed from the perspectives of classical and quantum worlds, respectively (e.g., the origins of the inverse kinetic isotope effects and all the equilibrium isotope effects are purely from quantum). The conventional Bigeleisen equation for isotope effect calculations, as well as its refined version in the framework of Feynman's path integral and Kleinert's variational perturbation (KP) theory for systematically incorporating anharmonicity and (non-parabolic) quantum tunneling, are also presented. In addition, the outstanding interplay between theory and experiment for successfully deducing the RLTS structures and the reaction mechanisms is demonstrated by applications on biochemical reactions, namely models of bacterial squalene-to-hopene polycyclization and RNA 2'-O
Planeta, David S
2007-01-01
In this paper I present general outlook on questions relevant to the basic graph algorithms; Finding the Shortest Path with Positive Weights and Minimum Spanning Tree. I will show so far known solution set of basic graph problems and present my own. My solutions to graph problems are characterized by their linear worst-case time complexity. It should be noticed that the algorithms which compute the Shortest Path and Minimum Spanning Tree problems not only analyze the weight of arcs (which is the main and often the only criterion of solution hitherto known algorithms) but also in case of identical path weights they select this path which walks through as few vertices as possible. I have presented algorithms which use priority queue based on multilevel prefix tree -- PTrie. PTrie is a clever combination of the idea of prefix tree -- Trie, the structure of logarithmic time complexity for insert and remove operations, doubly linked list and queues. In C++ I will implement linear worst-case time algorithm computin...
Directory of Open Access Journals (Sweden)
Hector James Ingram Page
2015-02-01
Full Text Available Head direction cells fire to signal the direction in which an animal's head is pointing. They are able to track head direction using only internally-derived information (path integration. In this simulation study we investigate the factors that affect path integration accuracy. Specifically, two major limiting factors are identified: rise time, the time after stimulation it takes for a neuron to start firing, and the presence of symmetric non-offset within-layer recurrent collateral connectivity. On the basis of the latter, the important prediction is made that head direction cell regions directly involved in path integration will not contain this type of connectivity; giving a theoretical explanation for architectural observations. Increased neuronal rise time is found to slow path integration, and the slowing effect for a given rise time is found to be more severe in the context of short conduction delays. Further work is suggested on the basis of our findings, which represent a valuable contribution to understanding of the head direction cell system.
Kleinert, H; Zatloukal, V
2013-11-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
Wiese, Kay Jörg
2016-04-01
We derive and study two different formalisms used for nonequilibrium processes: the coherent-state path integral, and an effective, coarse-grained stochastic equation of motion. We first study the coherent-state path integral and the corresponding field theory, using the annihilation process A+A→A as an example. The field theory contains counterintuitive quartic vertices. We show how they can be interpreted in terms of a first-passage problem. Reformulating the coherent-state path integral as a stochastic equation of motion, the noise generically becomes imaginary. This renders it not only difficult to interpret, but leads to convergence problems at finite times. We then show how alternatively an effective coarse-grained stochastic equation of motion with real noise can be constructed. The procedure is similar in spirit to the derivation of the mean-field approximation for the Ising model, and the ensuing construction of its effective field theory. We finally apply our findings to stochastic Manna sandpiles. We show that the coherent-state path integral is inappropriate, or at least inconvenient. As an alternative, we derive and solve its mean-field approximation, which we then use to construct a coarse-grained stochastic equation of motion with real noise.
Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi
2000-12-01
We present an accurate calculational scheme for many-body systems composed of electrons and nuclei, by path integral molecular dynamics technique combined with the ab initio molecular orbital theory. Based upon the scheme, the simulation of a water molecule at room temperature is demonstrated, applying all-electron calculation at the Hartree-Fock level of theory.
Ould-Lahoucine, H. K.; Chetouani, L.
2012-07-01
Exact Green function for a Dirac particle subject to a couple of orthogonal plane wave fields is obtained throughout a path integral approach. In addition, a suitable representation of the Dirac matrices is deduced so that the initial problem becomes the one of a free particle.
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
KLYNAC: Compact linear accelerator with integrated power supply
Energy Technology Data Exchange (ETDEWEB)
Malyzhenkov, Alexander [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-05-16
Accelerators and accelerator-based light sources have a wide range of applications in science, engineering technology and medicine. Today the scienti c community is working towards improving the quality of the accelerated beam and its parameters while trying to develop technology for reducing accelerator size. This work describes a design of a compact linear accelerator (linac) prototype, resonant Klynac device, which is a combined linear accelerator and its power supply - klystron. The intended purpose of a Klynac device is to provide a compact and inexpensive alternative to a conventional 1 to 6 MeV accelerator, which typically requires a separate RF source, an accelerator itself and all the associated hardware. Because the Klynac is a single structure, it has the potential to be much less sensitive to temperature variations than a system with separate klystron and linac. We start by introducing a simpli ed theoretical model for a Klynac device. We then demonstrate how a prototype is designed step-by-step using particle-in-cell simulation studies for mono- resonant and bi-resonant structures. Finally, we discuss design options from a stability point of view and required input power as well as behavior of competing modes for the actual built device.
High order explicit symplectic integrators for the Discrete Non Linear Schr\\"odinger equation
Boreux, Jehan; Hubaux, Charles
2010-01-01
We propose a family of reliable symplectic integrators adapted to the Discrete Non-Linear Schr\\"odinger equation; based on an idea of Yoshida (H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, 150, 5,6,7, (1990), pp. 262.) we can construct high order numerical schemes, that result to be explicit methods and thus very fast. The performances of the integrators are discussed, studied as functions of the integration time step and compared with some non symplectic methods.
Directory of Open Access Journals (Sweden)
Mireille Bousquet-Mélou
2008-04-01
Full Text Available Let a and b be two positive integers. A culminating path is a path of ℤ 2 that starts from (0,0, consists of steps (1,a and (1,-b, stays above the x-axis and ends at the highest ordinate it ever reaches. These paths were first encountered in bioinformatics, in the analysis of similarity search algorithms. They are also related to certain models of Lorentzian gravity in theoretical physics. We first show that the language on a two letter alphabet that naturally encodes culminating paths is not context-free. Then, we focus on the enumeration of culminating paths. A step by step approach, combined with the kernel method, provides a closed form expression for the generating function of culminating paths ending at a (generic height k. In the case a = b, we derive from this expression the asymptotic behaviour of the number of culminating paths of length n. When a > b, we obtain the asymptotic behaviour by a simpler argument. When a < b, we only determine the exponential growth of the number of culminating paths. Finally, we study the uniform random generation of culminating paths via various methods. The rejection approach, coupled with a symmetry argument, gives an algorithm that is linear when a ≥ b, with no precomputation stage nor non-linear storage required. The choice of the best algorithm is not as clear when a < b. An elementary recursive approach yields a linear algorithm after a precomputation stage involving O (n 3 arithmetic operations, but we also present some alternatives that may be more efficient in practice.
Quantum path-integral study of the phase diagram and isotope effects of neon
Ramirez, R; 10.1063/1.3023036
2011-01-01
The phase diagram of natural neon has been calculated for temperatures in the range 17-50 K and pressures between 0.01 and 2000 bar. The phase coexistence between solid, liquid, and gas phases has been determined by the calculation of the separate free energy of each phase as a function of temperature. Thus, for a given pressure, the coexistence temperature was obtained by the condition of equal free energy of coexisting phases. The free energy was calculated by using non-equilibrium techniques such as adiabatic switching and reversible scaling. The phase diagram obtained by classical Monte Carlo simulations has been compared to that obtained by quantum path-integral simulations. Quantum effects related to the finite mass of neon cause that coexistence lines are shifted towards lower temperatures when compared to the classical limit. The shift found in the triple point amounts to 1.5 K, i.e., about 6 % of the triple-point temperature. The triple-point isotope effect has been determined for 20Ne, 21Ne, 22Ne, a...
Dopieralski, Przemyslaw; Perrin, Charles L; Latajka, Zdzislaw
2011-11-08
The issue of the symmetry of short, low-barrier hydrogen bonds in solution is addressed here with advanced ab initio simulations of a hydrogen maleate anion in different environments, starting with the isolated anion, going through two crystal structures (sodium and potassium salts), then to an aqueous solution, and finally in the presence of counterions. By Car-Parrinello and path integral molecular dynamics simulations, it is demonstrated that the position of the proton in the intramolecular hydrogen bond of an aqueous hydrogen maleate anion is entirely related to the solvation pattern around the oxygen atoms of the intramolecular hydrogen bond. In particular, this anion has an asymmetric hydrogen bond, with the proton always located on the oxygen atom that is less solvated, owing to the instantaneous solvation environment. Simulations of water solutions of hydrogen maleate ion with two different counterions, K(+) and Na(+), surprisingly show that the intramolecular hydrogen-bond potential in the case of the Na(+) salt is always asymmetric, regardless of the hydrogen bonds to water, whereas for the K(+) salt, the potential for H motion depends on the location of the K(+). It is proposed that repulsion by the larger and more hydrated K(+) is weaker than that by Na(+) and competitive with solvation by water.
Neural Network-Based Solutions for Stochastic Optimal Control Using Path Integrals.
Rajagopal, Karthikeyan; Balakrishnan, Sivasubramanya Nadar; Busemeyer, Jerome R
2017-03-01
In this paper, an offline approximate dynamic programming approach using neural networks is proposed for solving a class of finite horizon stochastic optimal control problems. There are two approaches available in the literature, one based on stochastic maximum principle (SMP) formalism and the other based on solving the stochastic Hamilton-Jacobi-Bellman (HJB) equation. However, in the presence of noise, the SMP formalism becomes complex and results in having to solve a couple of backward stochastic differential equations. Hence, current solution methodologies typically ignore the noise effect. On the other hand, the inclusion of noise in the HJB framework is very straightforward. Furthermore, the stochastic HJB equation of a control-affine nonlinear stochastic system with a quadratic control cost function and an arbitrary state cost function can be formulated as a path integral (PI) problem. However, due to curse of dimensionality, it might not be possible to utilize the PI formulation for obtaining comprehensive solutions over the entire operating domain. A neural network structure called the adaptive critic design paradigm is used to effectively handle this difficulty. In this paper, a novel adaptive critic approach using the PI formulation is proposed for solving stochastic optimal control problems. The potential of the algorithm is demonstrated through simulation results from a couple of benchmark problems.
Energy Technology Data Exchange (ETDEWEB)
Heilmann, D.B.
2007-02-15
The two-plane HUBBARD model, which is a model for some electronic properties of undoped YBCO superconductors as well as displays a MOTT metal-to-insulator transition and a metal-to-band insulator transition, is studied within Dynamical Mean-Field Theory using HIRSCH-FYE Monte Carlo. In order to find the different transitions and distinguish the types of insulator, we calculate the single-particle spectral densities, the self-energies and the optical conductivities. We conclude that there is a continuous transition from MOTT to band insulator. In the second part, ground state properties of a diagonally disordered HUBBARD model is studied using a generalisation of Path Integral Renormalisation Group, a variational method which can also determine low-lying excitations. In particular, the distribution of antiferromagnetic properties is investigated. We conclude that antiferromagnetism breaks down in a percolation-type transition at a critical disorder, which is not changed appreciably by the inclusion of correlation effects, when compared to earlier studies. Electronic and excitation properties at the system sizes considered turn out to primarily depend on the geometry. (orig.)
The quantum nature of the hydrogen bond: insight from path-integral molecular dynamics
Walker, Brent; Li, Xin-Zheng; Michaelides, Angelos
2011-03-01
Hydrogen (H) bonds are weak, generally intermolecular bonds, that hold together much of soft matter, the condensed phases of water, network liquids, and many ferroelectric crystals. The small mass of H means H-bonds are inherently quantum mechanical; effects such as zero point motion and tunneling should be considered, although often are not. In particular, a consistent picture of quantum nuclear effects on the strength of H-bonds and consequently the structure of H-bonded systems is still absent. Here, we report ab initio path-integral molecular dynamics studies on the quantum nature of the H-bond. Systematic examination of a range of H-bonded systems shows that quantum nuclei weaken weak H-bonds but strengthen relatively strong ones. This correlation arises from a competition between anharmonic intermolecular bond bending and intramolecular bond stretching. A simple rule of thumb enables predictions to be made for H-bonded bonded materials in general with merely classical knowledge (e.g. H-bond strength or H-bond length). Our work rationalizes the contrasting influence of quantum nuclear dynamics on a wide variety of materials, including liquid water and HF, and highlights the need for flexible molecules in force-field based studies of quantum nuclear dynamics.
Path-integral molecular dynamics simulation of 3C-SiC
Ramírez, Rafael; Herrero, Carlos P.; Hernández, Eduardo R.; Cardona, Manuel
2008-01-01
Molecular dynamics simulations of 3C-SiC have been performed as a function of pressure and temperature. These simulations treat both electrons and atomic nuclei by quantum mechanical methods. While the electronic structure of the solid is described by an efficient tight-binding Hamiltonian, the nuclei dynamics is treated by the path-integral formulation of statistical mechanics. To assess the relevance of nuclear quantum effects, the results of quantum simulations are compared to others where either the Si nuclei, the C nuclei, or both atomic nuclei are treated as classical particles. We find that the experimental thermal expansion of 3C-SiC is realistically reproduced by our simulations. The calculated bulk modulus of 3C-SiC and its pressure derivative at room temperature show also good agreement with the available experimental data. The effect of the electron-phonon interaction on the direct electronic gap of 3C-SiC has been calculated as a function of temperature and related to results obtained for bulk diamond and Si. Comparison to available experimental data shows satisfactory agreement, although we observe that the employed tight-binding model tends to overestimate the magnitude of the electron-phonon interaction. The effect of treating the atomic nuclei as classical particles on the direct gap of 3C-SiC has been assessed. We find that nonlinear quantum effects related to the atomic masses are particularly relevant at temperatures below 250K .
Energy Technology Data Exchange (ETDEWEB)
Wang, Qi [Department of Chemistry, Tsukuba University, 1-1-1 Tennodai, Tsukuba 305-8571 (Japan); Suzuki, Kimichi [Research Institute for Nanosystem, National Institute of Advanced Industrial Science and Technology, Chuo-2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568 (Japan); Nagashima, Umpei, E-mail: u.nagashima@aist.go.jp [Department of Chemistry, Tsukuba University, 1-1-1 Tennodai, Tsukuba 305-8571 (Japan); Research Institute for Nanosystem, National Institute of Advanced Industrial Science and Technology, Chuo-2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568 (Japan); Tachikawa, Masanori [Quantum Chemistry Division, Graduate School of Science, Yokohama-City University, Seto 22-2, Kanazawa-ku, Yokohama 236-0027 (Japan); Yan, Shiwei [College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875 (China)
2013-11-29
Highlights: • PIMD simulations with PM6-DH+ potential are carried out for Cl{sup −}(H{sub 2}O){sub n} clusters. • The geometric isotope effects on the rearrangement of single and multi shell structures are presented. • The competition of intramolecular and intermolecular nuclear quantum effects on the cluster structures is shown. • The correlations between r(Cl…O) and other vibration motions are discussed. - Abstract: The geometric isotope effects on the structures of hydrated chloride ionic hydrogen bonded clusters are explored by carrying out path integral molecular dynamics simulations. First, an outer shell coordinate is selected to display the rearrangement of single and multi hydration shell cluster structures. Next, to show the competition of intramolecular and intermolecular nuclear quantum effects, the intramolecular OH{sup ∗} stretching and intermolecular ion–water wagging motions are studied for single and multi shell structures, respectively. The results indicate that the intermolecular nuclear quantum effects stabilize the ionic hydrogen bonds in single shell structures, while they are destabilized through the competition with intramolecular nuclear quantum effects in multi shell structures. In addition, the correlations between ion–water stretching motion and other cluster vibrational coordinates are discussed. The results indicate that the intermolecular nuclear quantum effects on the cluster structures are strongly related to the cooperation of the water–water hydrogen bond interactions.
Path integral Monte Carlo and density functional molecular dynamics simulations of hot, dense helium
Militzer, B.
2009-04-01
Two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), are applied to study hot, dense helium in the density-temperature range of 0.387-5.35gcm-3 and 500K-1.28×108K . One coherent equation of state is derived by combining DFT-MD data at lower temperatures with PIMC results at higher temperatures. Good agreement between both techniques is found in an intermediate-temperature range. For the highest temperatures, the PIMC results converge to the Debye-Hückel limiting law. In order to derive the entropy, a thermodynamically consistent free-energy fit is used that reproduces the internal energies and pressure derived from the first-principles simulations. The equation of state is presented in the form of a table as well as a fit and is compared with different free-energy models. Pair-correlation functions and the electronic density of states are discussed. Shock Hugoniot curves are compared with recent laser shock-wave experiments.
Mühlbacher, Lothar; Ankerhold, Joachim
2005-05-01
Electron transfer (ET) across molecular chains including an impurity is studied based on a recently improved real-time path-integral Monte Carlo (PIMC) approach [L. Mühlbacher, J. Ankerhold, and C. Escher, J. Chem. Phys. 121 12696 (2004)]. The reduced electronic dynamics is studied for various bridge lengths and defect site energies. By determining intersite hopping rates from PIMC simulations up to moderate times, the relaxation process in the extreme long-time limit is captured within a sequential transfer model. The total transfer rate is extracted and shown to be enhanced for certain defect site energies. Superexchange turns out to be relevant for extreme gap energies only and then gives rise to different dynamical signatures for high- and low-lying defects. Further, it is revealed that the entire bridge compound approaches a steady state on a much shorter time scale than that related to the total transfer. This allows for a simplified description of ET along donor-bridge-acceptor systems in the long-time range.
Energy Technology Data Exchange (ETDEWEB)
Yoshikawa, Takehiro; Sugawara, Shuichi [Department of Chemistry, Saitama University, Shimo-Okubo 255, Sakura-ku, Saitama City, Saitama 338-8570 (Japan); Takayanagi, Toshiyuki, E-mail: tako@mail.saitama-u.ac.jp [Department of Chemistry, Saitama University, Shimo-Okubo 255, Sakura-ku, Saitama City, Saitama 338-8570 (Japan); Shiga, Motoyuki [Center for Computational Science and E-systems, Japan Atomic Energy Agency, University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa City, Chiba 277-8563 (Japan); Tachikawa, Masanori [Quantum Chemistry Division, Graduate School of Nanobioscience, Yokohama-City University, Seto 22-2, Kanazawa-ku, Yokohama 236-0027 (Japan)
2012-02-06
Highlights: Black-Right-Pointing-Pointer Double proton transfer mechanisms in porphycene were studied with quantum simulations. Black-Right-Pointing-Pointer Both isotopic substitution and temperature significantly affect the transfer mechanism. Black-Right-Pointing-Pointer Nuclear quantum effects are playing important roles in the transfer mechanism. - Abstract: Path-integral molecular dynamics simulations have been performed for porphycene and its isotopic variants in order to understand the effect of isotopic substitution of inner protons on the double proton transfer mechanism. We have used an on-the-fly direct dynamics technique at the semiempirical PM6 level combined with specific reaction parameterization. Our quantum simulations show that double proton transfer of the unsubstituted porphycene at T = 300 K mainly occurs via a so-called concerted mechanism through the D{sub 2h} second-order saddle point. In addition, we found that both isotopic substitution and temperature significantly affect the double proton transfer mechanism. For example, the contribution of the stepwise mechanism increases with a temperature increase. We have also carried out hypothetical simulations with the porphycene configurations being completely planar. It has been found that out-of-plane vibrational motions significantly decrease the contribution of the concerted proton transfer mechanism.
Dvornikov, Maxim
2012-01-01
We study massive 1/2-spin particles in various external backgrounds keeping in mind applications to neutrino physics. We are mainly interested in massive Majorana (Weyl) fields. However, massive neutral Dirac particles have been also considered. We have formulated classical Lagrangian theory of the massive Weyl field in terms of Grassmann-odd two component spinors. Then we construct the Hamiltonian formulation of such a theory, which turns out to be a theory with second-class constraints. Using this formulation we canonically quantize the massive free Weyl field. We derive propagators of the Weyl field and relate them to the propagator of a massive Dirac particle. We also study the massive Weyl particles propagating in the background mater. We find the path integral representation for the propagator of such a field as well as the corresponding pseudoclassical particle action. The massless limit of the Weyl field interacting with the matter is considered and compared with results of other works. Finally, the p...
Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom
Ruokosenmäki, Ilkka; Kylänpää, Ilkka; Rantala, Tapio T
2015-01-01
We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We...
Equilibrium fractionation of H and O isotopes in water from path integral molecular dynamics
Pinilla, Carlos; Blanchard, Marc; Balan, Etienne; Ferlat, Guillaume; Vuilleumier, Rodolphe; Mauri, Francesco
2014-06-01
The equilibrium fractionation factor between two phases is of importance for the understanding of many planetary and environmental processes. Although thermodynamic equilibrium can be achieved between minerals at high temperature, many natural processes involve reactions between liquids or aqueous solutions and solids. For crystals, the fractionation factor α can be theoretically determined using a statistical thermodynamic approach based on the vibrational properties of the phases. These calculations are mostly performed in the harmonic approximation, using empirical or ab-initio force fields. In the case of aperiodic and dynamic systems such as liquids or solutions, similar calculations can be done using finite-size molecular clusters or snapshots obtained from molecular dynamics (MD) runs. It is however difficult to assess the effect of these approximate models on the isotopic fractionation properties. In this work we present a systematic study of the calculation of the D/H and 18O/16O equilibrium fractionation factors in water for the liquid/vapour and ice/vapour phases using several levels of theory within the simulations. Namely, we use a thermodynamic integration approach based on Path Integral MD calculations (PIMD) and an empirical potential model of water. Compared with standard MD, PIMD takes into account quantum effects in the thermodynamic modeling of systems and the exact fractionation factor for a given potential can be obtained. We compare these exact results with those of modeling strategies usually used, which involve the mapping of the quantum system on its harmonic counterpart. The results show the importance of including configurational disorder for the estimation of isotope fractionation in liquid phases. In addition, the convergence of the fractionation factor as a function of parameters such as the size of the simulated system and multiple isotope substitution is analyzed, showing that isotope fractionation is essentially a local effect in
Path integration and cognitive mapping in a continuous attractor neural network model.
Samsonovich, A; McNaughton, B L
1997-08-01
A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of self-location from the current representation and from the perceived velocity of motion. In the model, a place-cell assembly called a "chart" contains a two-dimensional attractor set called an "attractor map" that can be used to represent coordinates in any arbitrary environment, once associative binding has occurred between chart locations and sensory inputs. In hippocampus, there are different spatial relations among place fields in different environments and behavioral contexts. Thus, the same units may participate in many charts, and it is shown that the number of uncorrelated charts that can be encoded in the same recurrent network is potentially quite large. According to this theory, the firing of a given place cell is primarily a cooperative effect of the activity of its neighbors on the currently active chart. Therefore, it is not particularly useful to think of place cells as encoding any particular external object or event. Because of its recurrent connections, hippocampal field CA3 is proposed as a possible location for this "multichart" architecture; however, other implementations in anatomy would not invalidate the main concepts. The model is implemented numerically both as a network of integrate-and-fire units and as a "macroscopic" (with respect to the space of states) description of the system, based on a continuous approximation defined by a system of stochastic differential equations. It provides an explanation for a number of hitherto perplexing observations on hippocampal place fields, including doubling, vanishing, reshaping in distorted environments, acquiring directionality in a two-goal shuttling task, rapid formation in a novel environment, and slow rotation after disorientation. The model makes several new predictions about the expected properties of hippocampal place cells and other cells of the
Directory of Open Access Journals (Sweden)
Mohammad Almousa
2013-01-01
Full Text Available The aim of this study is to present the use of a semi analytical method called the optimal homotopy asymptotic method (OHAM for solving the linear Fredholm integral equations of the first kind. Three examples are discussed to show the ability of the method to solve the linear Fredholm integral equations of the first kind. The results indicated that the method is very effective and simple.
On the geometry of classically integrable two-dimensional non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Mohammedi, N., E-mail: nouri@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique (CNRS - UMR 6083), Universite Francois Rabelais de Tours, Faculte des Sciences et Techniques, Parc de Grandmont, F-37200 Tours (France)
2010-11-11
A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.
PALAS: An Integrated WWW Based Laboratory for Supporting the Teaching of Linear Systems.
Jandre, F. C.; Seixas, J. M.
For supporting the teaching activities on linear system theory, a World Wide Web-based laboratory is being developed. It integrates both simulation and implementation aspects in the same framework. Modules covering the main topics of the linear system analysis are developed using a colloquial language approach in order to attract and retain the…
Spectral Properties of Integral Differential Operators Applied in Linear Antenna Modeling
Bekers, D.J.; Eijndhoven, S.J.L. van
2012-01-01
The current on a linear strip or wire solves an equation governed by a linear integro-differential operator that is the composition of the Helmholtz operator and an integral operator with a logarithmically singular displacement kernel. Investigating the spectral behaviour of this classical operator,
Jang, Seogjoo; Voth, Gregory A
2017-05-07
Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.
Finding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo Approach
Kant, Philipp
2013-01-01
The reduction of a large number of scalar integrals to a small set of master integrals via Laporta's algorithm is common practice in multi-loop calculations. It is also a major bottleneck in terms of running time and memory consumption. It involves solving a large set of linear equations where many of the equations are linearly dependent. We propose a simple algorithm that eliminates all linearly dependent equations from a given system, reducing the time and space requirements of a subsequent run of Laporta's algorithm.
DEFF Research Database (Denmark)
Christensen, Bent Jesper; Kruse, Robinson; Sibbertsen, Philipp
We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional...
Institute of Scientific and Technical Information of China (English)
MA Qinghua; YANG Enhao
2000-01-01
An estimation method for solutions to the general linear system of Volterratype integral inequalities containing several iterated integral functionals is obtained. This method is based on a result proved by the present second author in Journ. Math. Anal. Appl.(1984). A certain two-dimensional system of nonlinear ordinary differential equations is also discussed to demonstrate the usefulness of our method.
Singh, Upendra N.; Refaat, Tamer F.; Petros, Mulugeta
2017-01-01
The societal benefits of understanding climate change through identification of global carbon dioxide sources and sinks led to the desired NASA's active sensing of carbon dioxide emissions over nights, days, and seasons (ASCENDS) space-based missions of global carbon dioxide measurements. For more than 15 years, NASA Langley Research Center (LaRC) have developed several carbon dioxide active remote sensors using the differential absorption lidar (DIAL) technique operating at the two-micron wavelength. Currently, an airborne two-micron triple-pulse integrated path differential absorption (IPDA) lidar is under development. This IPDA lidar measures carbon dioxide as well as water vapor, the dominant interfering molecule on carbon dioxide remote sensing. Advancement of this triple-pulse IPDA lidar development is presented.
Mouhat, Félix; Sorella, Sandro; Vuilleumier, Rodolphe; Saitta, Antonino Marco; Casula, Michele
2017-06-13
We introduce a novel approach for a fully quantum description of coupled electron-ion systems from first principles. It combines the variational quantum Monte Carlo solution of the electronic part with the path integral formalism for the quantum nuclear dynamics. On the one hand, the path integral molecular dynamics includes nuclear quantum effects by adding a set of fictitious classical particles (beads) aimed at reproducing nuclear quantum fluctuations via a harmonic kinetic term. On the other hand, variational quantum Monte Carlo can provide Born-Oppenheimer potential energy surfaces with a precision comparable to the most-advanced post-Hartree-Fock approaches, and with a favorable scaling with the system size. In order to cope with the intrinsic noise due to the stochastic nature of quantum Monte Carlo methods, we generalize the path integral molecular dynamics using a Langevin thermostat correlated according to the covariance matrix of quantum Monte Carlo nuclear forces. The variational parameters of the quantum Monte Carlo wave function are evolved during the nuclear dynamics, such that the Born-Oppenheimer potential energy surface is unbiased. Statistical errors on the wave function parameters are reduced by resorting to bead grouping average, which we show to be accurate and well-controlled. Our general algorithm relies on a Trotter breakup between the dynamics driven by ionic forces and the one set by the harmonic interbead couplings. The latter is exactly integrated, even in the presence of the Langevin thermostat, thanks to the mapping onto an Ornstein-Uhlenbeck process. This framework turns out to be also very efficient in the case of noiseless (deterministic) ionic forces. The new implementation is validated on the Zundel ion (H5O2(+)) by direct comparison with standard path integral Langevin dynamics calculations made with a coupled cluster potential energy surface. Nuclear quantum effects are confirmed to be dominant over thermal effects well beyond
Algebraic Properties of First Integrals for Scalar Linear Third-Order ODEs of Maximal Symmetry
Directory of Open Access Journals (Sweden)
K. S. Mahomed
2013-01-01
Full Text Available By use of the Lie symmetry group methods we analyze the relationship between the first integrals of the simplest linear third-order ordinary differential equations (ODEs and their point symmetries. It is well known that there are three classes of linear third-order ODEs for maximal cases of point symmetries which are 4, 5, and 7. The simplest scalar linear third-order equation has seven-point symmetries. We obtain the classifying relation between the symmetry and the first integral for the simplest equation. It is shown that the maximal Lie algebra of a first integral for the simplest equation y′′′=0 is unique and four-dimensional. Moreover, we show that the Lie algebra of the simplest linear third-order equation is generated by the symmetries of the two basic integrals. We also obtain counting theorems of the symmetry properties of the first integrals for such linear third-order ODEs. Furthermore, we provide insights into the manner in which one can generate the full Lie algebra of higher-order ODEs of maximal symmetry from two of their basic integrals.
Koda, Shin-Ichi; Takatsuka, Kazuo
2011-03-01
The coherent path integral is generalized such that the identity operator represented in a complete (actually overcomplete) set of the coherent states with the “time-variable” exponents are inserted between two consecutive short-time propagators. Since such a complete set of any given exponent can constitute the identity operator, the exponent may be varied from time to time without loss of generality as long as it is set common to all the Gaussians. However, a finite truncation of the coherent state expansion should result in different values of the propagator depending on the choice of the exponents. Furthermore, approximation methodology to treat with the exact propagator can also depend on this choice, and thereby many different semiclassical propagators may emerge from these combinations. Indeed, we show that the well-known semiclassical propagators such as those of Van Vleck, Herman-Kluk, Heller’s thawed Gaussian, and many others can be derived in a systematic manner, which enables one to comprehend these semiclassical propagators from a unified point of view. We are particularly interested in our generalized form of the Herman-Kluk propagator, since the relative accuracy of this propagator has been well established by Kay, and since, nevertheless, its derivation was not necessarily clear. Thus our generalized Herman-Kluk propagator replaces the classical Hamiltonian with a Gaussian averaged quantum Hamiltonian, generating non-Newtonian trajectories. We perform a numerical test to assess the quality of such a family of generalized Herman-Kluk propagators and find that the original Herman-Kluk gives an accurate result. The reason why this has come about is also discussed.
Different strategies for spatial updating in yaw and pitch path integration
Directory of Open Access Journals (Sweden)
Caspar Mathias Goeke
2013-02-01
Full Text Available Research in spatial navigation revealed the existence of discrete strategies defined by the use of distinct reference frames during virtual path integration. The present study investigated the distribution of these navigation strategies as a function of gender, video gaming experience, and self-estimates of spatial navigation abilities in a population of 300 subjects. Participants watched videos of virtual passages through a star-field with one turn in either the horizontal (yaw or the vertical (pitch axis. At the end of a passage they selected one out of four homing arrows to indicate the initial starting location. To solve the task, participants could employ two discrete strategies, navigating within either an egocentric or an allocentric reference frame. The majority of valid subjects (232/260 consistently used the same strategy in more than 75% of all trials. With that approach 33.1% of all participants were classified as Turners (using an egocentric reference frame on both axes and 46.5% as Nonturners (using an allocentric reference frame on both axes. 9.2% of all participants consistently used an egocentric reference frame in the yaw plane but an allocentric reference frame in the pitch plane (Switcher. Investigating the influence of gender on navigation strategies revealed that females predominantly used the Nonturner strategy while males used both the Turner and the Nonturner strategy with comparable probabilities. Other than expected, video gaming experience did not influence strategy use. Based on a strong quantitative basis with the sample size about an order of magnitude larger than in typical psychophysical studies these results demonstrate that most people reliably use one out of three possible navigation strategies (Turners, Nonturners, Switchers for spatial updating and provides a sound estimate of how those strategies are distributed within the general population.
Hayes, Robin L; Paddison, Stephen J; Tuckerman, Mark E
2009-12-31
The mono-, di-, and tetrahydrates of trifluoromethanesulfonic acid, which contain characteristic H(3)O(+), H(5)O(2)(+), and H(9)O(4)(+) structures, provide model systems for understanding proton transport in materials with high perfluorosulfonic acid density such as perfluorosulfonic acid membranes commonly employed in hydrogen fuel cells. Ab initio molecular dynamics simulations indicate that protons in these solids are predisposed to transfer to the water most strongly bound to sulfonate groups via a Grotthuss-type mechanism, but quickly return to the most solvated defect structure either due to the lack of a nearby species to stabilize the new defect or a preference for the proton to be maximally hydrated. Path integral molecular dynamics of the mono- and dihydrate reveal significant quantum effects that facilitate proton transfer to the "presolvated" water or SO(3)(-) in the first solvation shell and increase the Zundel character of all the defects. These trends are quantified in free energy profiles for each bonding environment. Hydrogen bonding criteria for HOH-OH(2) and HOH-O(3)S are extracted from the two-dimensional potential of mean force. The quantum radial distribution function, radius of gyration, and root-mean-square displacement position correlation function show that the protonic charge is distributed over two or more water molecules. Metastable structural defects with one excess proton shared between two sulfonate groups and another Zundel or Eigen type cation defect are found for the mono- and dihydrate but not for the tetrahydrate crystal. Results for the tetrahydrate native crystal exhibit minor differences at 210 and 250 K. IR spectra are calculated for all native and stable defect structures. Graph theory techniques are used to characterize the chain lengths and ring sizes in the hydrogen bond network. Low conductivities when limited water is present may be attributable to trapping of protons between SO(3)(-) groups and the increased
Energy Technology Data Exchange (ETDEWEB)
Lagin, L.J. [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550 (United States)], E-mail: lagin1@llnl.gov; Bettenhausen, R.C.; Bowers, G.A.; Carey, R.W.; Edwards, O.D.; Estes, C.M.; Demaret, R.D.; Ferguson, S.W.; Fisher, J.M.; Ho, J.C.; Ludwigsen, A.P.; Mathisen, D.G.; Marshall, C.D.; Matone, J.T.; McGuigan, D.L.; Sanchez, R.J.; Stout, E.A.; Tekle, E.A.; Townsend, S.L.; Van Arsdall, P.J. [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550 (United States)] (and others)
2008-04-15
final optics, target positioners and diagnostics. Additional capabilities to support fusion ignition shots in a National Ignition Campaign (NIC) beginning in 2010 will include a cryogenic target system, target diagnostics, and integrated experimental shot data analysis with tools for data visualization and archiving. This talk discusses the current status of the control system implementation and discusses the plan to complete the control system on the path to ignition.
Directory of Open Access Journals (Sweden)
S. Ishii
2013-05-01
Full Text Available The National Institute of Information and Communications Technology (NICT has made a great deal of effort to develop a coherent 2 μm differential absorption and wind lidar (Co2DiaWiL for measuring CO2 and wind speed. First, coherent Integrated Path Differential Absorption (IPDA lidar experiments were conducted using the Co2DiaWiL and a foothill target (tree and ground surface located about 7.12 km south of NICT on 11, 27, and 28 December 2010. The detection sensitivity of a 2 μm IPDA lidar was examined in detail using the CO2 concentration measured by the foothill reflection. The precisions of CO2 measurements for the foothill target and 900, 4500 and 27 000 shot pairs were 6.5, 2.8, and 1.2%, respectively. The results indicated that a coherent IPDA lidar with a laser operating at a high pulse repetition frequency of a few tens of KHz is necessary for XCO2 (column-averaged dry air mixing ratio of CO2 measurement with a precision of 1–2 ppm in order to observe temporal and spatial variations in the CO2. Statistical comparisons indicated that, although a small amount of in situ data and the fact that they were not co-located with the foothill target made comparison difficult, the CO2 volume mixing ratio obtained by the Co2DiaWiL measurements for the foothill target and atmospheric returns was about −5 ppm lower than the 5 min running averages of the in situ sensor. Not only actual difference of sensing volume or the natural variability of CO2 but also the fluctuations of temperature could cause this difference. The statistical results indicated that there were no biases between the foothill target and atmospheric return measurements. The 2 μm coherent IPDA lidar can detect the CO2 volume mixing ratio change of 3% in the 5 min signal integration. In order to detect the position of the foothill target, to measure a range with a high SNR (signal-to-noise ratio, and to reduce uncertainty due to the presence of aerosols and clouds, it is
Durlak, Piotr; Morrison, Carole A; Middlemiss, Derek S; Latajka, Zdzislaw
2007-08-14
We have studied the double proton transfer (DPT) reaction in the cyclic dimer of chloroacetic acid using both classical and path integral Car-Parrinello molecular dynamics. We also attempt to quantify the errors in the potential energy surface that arise from the use of a pure density functional. In the classical dynamics a clear reaction mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. This mechanism is considerably altered when quantum tunneling is permitted in the simulation. The introduction of path integrals leads to considerable changes in the thermally averaged molecular geometry, leading to shorter and more centered hydrogen bond linkages.
Directory of Open Access Journals (Sweden)
Daniel T. L. Shek
2012-01-01
Full Text Available An integration of the qualitative evaluation findings collected in different cohorts of students who participated in Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes (n=252 students in 29 focus groups was carried out. With specific focus on how the informants described the program, results showed that the descriptions were mainly positive in nature, suggesting that the program was well received by the program participants. When the informants were invited to name three metaphors that could stand for the program, positive metaphors were commonly used. Beneficial effects of the program in different psychosocial domains were also voiced by the program participants. The qualitative findings integrated in this paper provide further support for the effectiveness of the Tier 1 Program of Project P.A.T.H.S. in promoting holistic development in Chinese adolescents in Hong Kong.
Kapil, Venkat; Ceriotti, Michele
2016-01-01
The quantum nature of light nuclei influences the structural and dynamic properties of matter up to room temperature and even above. The precise description of such effects in atomistic mod- elling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the system. Many techniques have been suggested to reduce the required number of replicas, including high-order factorizations of the Boltzmann operator, that are particularly attractive for high-precision and low-temperature scenar- ios. Unfortunately, to date several technical challenges have prevented a widespread use of these approaches to study nuclear quantum effects in condensed-phase systems. Here we introduce an inexpensive molecular dynamics scheme that overcomes these limitations, thus making it possible to exploit the improved convergence of high-order path integrals without having to sacrifice the stability, convenience and flexibility of conventional...
Durlak, Piotr; Morrison, Carole A.; Middlemiss, Derek S.; Latajka, Zdzislaw
2007-08-01
We have studied the double proton transfer (DPT) reaction in the cyclic dimer of chloroacetic acid using both classical and path integral Car-Parrinello molecular dynamics. We also attempt to quantify the errors in the potential energy surface that arise from the use of a pure density functional. In the classical dynamics a clear reaction mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. This mechanism is considerably altered when quantum tunneling is permitted in the simulation. The introduction of path integrals leads to considerable changes in the thermally averaged molecular geometry, leading to shorter and more centered hydrogen bond linkages.
Kamibayashi, Yuki; Miura, Shinichi
2016-08-01
In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction.
Ab initio path integral molecular dynamics simulation study on the dihydrogen bond of NH4+⋯BeH2
Hayashi, Aiko; Shiga, Motoyuki; Tachikawa, Masanori
2005-07-01
An ab initio path integral molecular dynamics simulation has been performed to study the quantum and thermal effects of a dihydrogen bonded cation, NH4+⋯BeH2. In this system, an attractive interaction exists between two neighboring hydrogen atoms as N δ- H δ+ ⋯H δ- Be δ+ involving large-amplitude of vibration. Some properties playing a key role for this dihydrogen bonded system, such as the bond length, bond angle, and distribution of atomic charges, are investigated in detail by comparing the results of path integral and classical molecular dynamics with those of the equilibrium structure. It was found that the atomic charges of H δ+ and H δ- are decreased and the dihydrogen H δ+ ⋯H δ- bond length is expanded as the thermal and zero-point quantum effects.
Gangopadhyay, Sunandan
2014-01-01
The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a particle moving in the noncommutative plane and in the presence of a magnetic field and an arbitrary potential. Using this action, the equation of motion and the energy spectrum for the partcle are obtained explicitly. The Aharonov-Bohm phase is derived using a variety of methods and several dualities between this system and other commutative and noncommutative systems are demonstrated. Finally, the equivalence of the path integral formulation with the noncommutative Schr\\"{o}dinger equation is also established.
Institute of Scientific and Technical Information of China (English)
刘松芬; 胡北来
2003-01-01
The internal energy and pressure of dense hydrogen plasma are calculated by the direct path integral Monte Carlo approach. The Kelbg potential is used as interaction potentials both between electrons and between protons and electrons in the calculation. The complete formulae for internal energy and pressure in dense hydrogen plasma derived for the simulation are presented. The correctness of the derived formulae are validated by the obtained simulation results. The numerical results are discussed in details.
Energy Technology Data Exchange (ETDEWEB)
Agarwal, Animesh, E-mail: animesh@zedat.fu-berlin.de; Delle Site, Luigi, E-mail: dellesite@fu-berlin.de [Institute for Mathematics, Freie Universität Berlin, Berlin (Germany)
2015-09-07
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.
Agarwal, Animesh; Delle Site, Luigi
2015-09-01
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas
2014-06-21
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψT, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas, E-mail: pnroy@uwaterloo.ca [Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
2014-06-21
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
Hayes, Robin L; Paddison, Stephen J; Tuckerman, Mark E
2011-06-16
Trifluoromethanesulfonic acid hydrates provide a well-defined system to study proton dissociation and transport in perfluorosulfonic acid membranes, typically used as the electrolyte in hydrogen fuel cells, in the limit of minimal water. The triflic acid pentahydrate crystal (CF(3)SO(3)H·5H(2)O) is sufficiently aqueous that it contains an extended three-dimensional water network. Despite it being extended, however, long-range proton transport along the network is structurally unfavorable and would require considerable rearrangement. Nevertheless, the triflic acid pentahydrate crystal system can provide a clear picture of the preferred locations of local protonic defects in the water network, which provides insights about related structures in the disordered, low-hydration environment of perfluorosulfonic acid membranes. Ab initio molecular dynamics simulations reveal that the proton defect is most likely to transfer to the closest water that has the expected presolvation and only contains water in its first solvation shell. Unlike the tetrahydrate of triflic acid (CF(3)SO(3)H·4H(2)O), there is no evidence of the proton preferentially transferring to a water molecule bridging two of the sulfonate groups. However, this could be an artifact of the crystal structure since the only such water molecule is separated from the proton by long O-O distances. Hydrogen bonding criteria, using the two-dimensional potential of mean force, are extracted. Radial distribution functions, free energy profiles, radii of gyration, and the root-mean-square displacement computed from ab initio path integral molecular dynamics simulations reveal that quantum effects do significantly extend the size of the protonic defect and increase the frequency of proton transfer events by nearly 15%. The calculated IR spectra confirm that the dominant protonic defect mostly exists as an Eigen cation but contains some Zundel ion characteristics. Chain lengths and ring sizes determined from the
Directory of Open Access Journals (Sweden)
A. Sato
2012-11-01
Full Text Available The National Institute of Information and Communications Technology (NICT have made a great deal of effort to develop a coherent 2-μm differential absorption and wind lidar (Co2DiaWiL for measuring CO2 and wind speed. First, coherent Integrated Path Differential Absorption (IPDA lidar experiments were conducted using the Co2DiaWiL and a hard target (surface return located about 7.12 km south of NICT on 11, 27, and 28 December 2010. The detection sensitivity of a 2-μm IPDA lidar was examined in detail using the CO2 concentration measured by the hard target. The precisions of CO2 measurement for the hard target and 900, 4500 and 27 000 shot pairs were 6.5, 2.8, and 1.2%, respectively. The results indicated that a coherent IPDA lidar with a laser operating at a high pulse repetition frequency of a few tens of KHz is necessary for measuring the CO2 concentration of the hard target with a precision of 1–2 ppm. Statistical comparisons indicated that, although a small amount of in situ data and the fact that they were not co-located with the hard target made comparison difficult, the CO2 volume mixing ratio measured with the Co2DiaWiL was about 5 ppm lower than that measured with the in situ sensor. The statistical results indicated that there were no differences between the hard target and atmospheric return measurements. A precision of 1.5% was achieved from the atmospheric return, which is lower than that obtained from the hard-target returns. Although long-range DIfferential Absorption Lidar (DIAL CO2 measurement with the atmospheric return can result in highly precise measurement, the precision of the atmospheric return measurement was widely distributed comparing to that of the hard target return. Our results indicated that it is important to use a Q-switched laser to measure the range-gated differential absorption optical depth with the atmospheric return and that it is better to simultaneously conduct both hard target and atmospheric return
Directory of Open Access Journals (Sweden)
Etsuji Okamoto
2011-09-01
Full Text Available Introduction: In April 2008, Japan launched a radical reform in regional health planning that emphasized the development of disease-oriented clinical care pathways. These 'inter-provider critical paths' have sought to ensure effective integration of various providers ranging among primary care practitioners, acute care hospitals, rehabilitation hospitals, long-term care facilities and home care. Description of policy practice: All 47 prefectures in Japan developed their Regional Health Plans pursuant to the guideline requiring that these should include at least four diseases: diabetes, acute myocardial infarction, cerebrovascular accident and cancer. To illustrate the care pathways developed, this paper describes the guideline referring to strokes and provides examples of the new Regional Health Plans as well as examples of disease-oriented inter-provider clinical paths. In particular, the paper examines the development of information sharing through electronic health records (EHR to enhance effective integration among providers is discussed.Discussion and conclusion: Japan's reform in 2008 is unique in that the concept of "disease-oriented regional inter-provider critical paths" was adopted as a national policy and all 47 prefectures developed their Regional Health Plans simultaneously. How much the new regional health planning policy has improved the quality and outcome of care remains to be seen and will be evaluated in 2013 after the five year planned period of implementation has concluded. Whilst electronic health records appear to be a useful tool in supporting care integration they do not guarantee success in the application of an inter-provider critical path.
Directory of Open Access Journals (Sweden)
Etsuji Okamoto
2011-09-01
Full Text Available Introduction: In April 2008, Japan launched a radical reform in regional health planning that emphasized the development of disease-oriented clinical care pathways. These 'inter-provider critical paths' have sought to ensure effective integration of various providers ranging among primary care practitioners, acute care hospitals, rehabilitation hospitals, long-term care facilities and home care. Description of policy practice: All 47 prefectures in Japan developed their Regional Health Plans pursuant to the guideline requiring that these should include at least four diseases: diabetes, acute myocardial infarction, cerebrovascular accident and cancer. To illustrate the care pathways developed, this paper describes the guideline referring to strokes and provides examples of the new Regional Health Plans as well as examples of disease-oriented inter-provider clinical paths. In particular, the paper examines the development of information sharing through electronic health records (EHR to enhance effective integration among providers is discussed. Discussion and conclusion: Japan's reform in 2008 is unique in that the concept of "disease-oriented regional inter-provider critical paths" was adopted as a national policy and all 47 prefectures developed their Regional Health Plans simultaneously. How much the new regional health planning policy has improved the quality and outcome of care remains to be seen and will be evaluated in 2013 after the five year planned period of implementation has concluded. Whilst electronic health records appear to be a useful tool in supporting care integration they do not guarantee success in the application of an inter-provider critical path.
Directory of Open Access Journals (Sweden)
Diego Alfredo Núñez-Altamirano
2016-07-01
Full Text Available This article deals with the kinematics and dynamics of a novel leg based on the Peaucellier–Lipkin mechanism, which is better known as the straight path tracer. The basic Peaucellier–Lipkin linkage with 1 degree of freedom was transformed into a more skillful mechanism, through the addition of 4 more degrees of freedom. The resulting 5-degree-of-freedom leg enables the walking machine to move along paths that are straight lines and/or concave or convex curves. Three degrees of freedom transform the leg in relation to a reachable center of rotation that the machine walks around. Once the leg is transformed, the remaining 2 degrees of freedom position the foot at a desirable Cartesian point during the transfer or support phase. We analyzed the direct and inverse kinematics developed for the leg when the foot describes a straight line and found some interesting relationships among the motion parameters. The dynamic model equations of motion for the leg were derived from the Lagrangian dynamic formulation to calculate the required torques during a particular transfer phase.
Wan, Yuhang; Carlson, John A.; Kesler, Benjamin A.; Peng, Wang; Su, Patrick; Al-Mulla, Saoud A.; Lim, Sung Jun; Smith, Andrew M.; Dallesasse, John M.; Cunningham, Brian T.
2016-07-01
A compact analysis platform for detecting liquid absorption and emission spectra using a set of optical linear variable filters atop a CMOS image sensor is presented. The working spectral range of the analysis platform can be extended without a reduction in spectral resolution by utilizing multiple linear variable filters with different wavelength ranges on the same CMOS sensor. With optical setup reconfiguration, its capability to measure both absorption and fluorescence emission is demonstrated. Quantitative detection of fluorescence emission down to 0.28 nM for quantum dot dispersions and 32 ng/mL for near-infrared dyes has been demonstrated on a single platform over a wide spectral range, as well as an absorption-based water quality test, showing the versatility of the system across liquid solutions for different emission and absorption bands. Comparison with a commercially available portable spectrometer and an optical spectrum analyzer shows our system has an improved signal-to-noise ratio and acceptable spectral resolution for discrimination of emission spectra, and characterization of colored liquid’s absorption characteristics generated by common biomolecular assays. This simple, compact, and versatile analysis platform demonstrates a path towards an integrated optical device that can be utilized for a wide variety of applications in point-of-use testing and point-of-care diagnostics.
Montoya-Castillo, Andrés
2016-01-01
We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In additions, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function $\\mathcal{C}_{zz}(t) = \\mathrm{Re}\\langle \\sigma_z(0)\\sigma_...
Montoya-Castillo, Andrés; Reichman, David R.
2017-01-01
We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function Cz z(t ) =Re ⟨σz(0 ) σz(t ) ⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.
Uitdehaag, Joost C.M.; Veen, Bart A. van der; Dijkhuizen, Lubbert; Elber, Ron; Dijkstra, Bauke W.
2001-01-01
Cyclodextrin glycosyltransferase (CGTase) is an enzyme belonging to the ol-amylase family that forms cyclodextrins (circularly linked oligosaccharides) from starch. X-ray work has indicated that this cyclization reaction of CGTase involves a 23-Angstrom movement of the nonreducing end of a linear ma
Fracture prediction using modified mohr coulomb theory for non-linear strain paths using AA3104-H19
Dick, Robert; Yoon, Jeong Whan
2016-08-01
Experiment results from uniaxial tensile tests, bi-axial bulge tests, and disk compression tests for a beverage can AA3104-H19 material are presented. The results from the experimental tests are used to determine material coefficients for both Yld2000 and Yld2004 models. Finite element simulations are developed to study the influence of materials model on the predicted earing profile. It is shown that only the YLD2004 model is capable of accurately predicting the earing profile as the YLD2000 model only predicts 4 ears. Excellent agreement with the experimental data for earing is achieved using the AA3104-H19 material data and the Yld2004 constitutive model. Mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on specimens with a central hole and notched specimens. Torsion of a double bridge specimen is conducted to generate points near pure shear conditions. The Nakajima test is utilized to produce points in bi-axial tension. The data from the experiments is used to develop the fracture locus in the principal strain space. Mapping from principal strain space to stress triaxiality space, principal stress space, and polar effective plastic strain space is accomplished using a generalized mapping technique. Finite element modeling is used to validate the Modified Mohr-Coulomb (MMC) fracture model in the polar space. Models of a hole expansion during cup drawing and a cup draw/reverse redraw/expand forming sequence demonstrate the robustness of the modified PEPS fracture theory for the condition with nonlinear forming paths and accurately predicts the onset of failure. The proposed methods can be widely used for predicting failure for the examples which undergo nonlinear strain path including rigid-packaging and automotive forming.
A NOVEL BOUNDARY INTEGRAL EQUATION METHOD FOR LINEAR ELASTICITY--NATURAL BOUNDARY INTEGRAL EQUATION
Institute of Scientific and Technical Information of China (English)
Niu Zhongrong; Wang Xiuxi; Zhou Huanlin; Zhang Chenli
2001-01-01
The boundary integral equation (BIE) of displacement derivatives is put at a disadvantage for the difficulty involved in the evaluation of the hypersingular integrals. In this paper, the operators δij and εij are used to act on the derivative BIE. The boundary displacements, tractions and displacement derivatives are transformed into a set of new boundary tensors as boundary variables. A new BIE formulation termed natural boundary integral equation (NBIE) is obtained. The NBIE is applied to solving two-dimensional elasticity problems. In the NBIE only the strongly singular integrals are contained. The Cauchy principal value integrals occurring in the NBIE are evaluated. A combination of the NBIE and displacement BIE can be used to directly calculate the boundary stresses. The numerical results of several examples demonstrate the accuracy of the NBIE.
Directory of Open Access Journals (Sweden)
Daniel T. L. Shek
2012-01-01
Full Text Available An integration of the qualitative evaluation findings collected from program implementers conducting the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes in different years (n=177 participants in 36 focus groups was carried out. General qualitative data analyses utilizing intra and interrater reliability techniques were performed. Results showed that the descriptors used to describe the program and the metaphors named by the informants that could stand for the program were generally positive in nature. Program participants also perceived the program to be beneficial to the development of the students in different psychosocial domains. The present study further supports the effectiveness of the Tier 1 Program of the Project P.A.T.H.S. in Hong Kong based on the perspective of the program implementers.
Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs
Agapov, S. V.; Bialy, M.; Mironov, A. E.
2017-05-01
For a magnetic geodesic flow on the 2-torus the only known integrable example is that of a flow integrable for all energy levels. It has an integral linear in momenta and corresponds to a one parameter group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on a single energy level is considered. Then, in addition to the example mentioned above, a few other explicit examples with quadratic in momenta integrals can be constructed by means of the Maupertuis' principle. Recently we proved that such an integrability problem can be reduced to a remarkable semi-Hamiltonian system of quasi-linear PDEs and to the question of the existence of smooth periodic solutions for this system. Our main result of the present paper states that any Liouville metric with the zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with a small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of an integral quadratic in momenta.
Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs
Agapov, S. V.; Bialy, M.; Mironov, A. E.
2017-01-01
For a magnetic geodesic flow on the 2-torus the only known integrable example is that of a flow integrable for all energy levels. It has an integral linear in momenta and corresponds to a one parameter group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on a single energy level is considered. Then, in addition to the example mentioned above, a few other explicit examples with quadratic in momenta integrals can be constructed by means of the Maupertuis' principle. Recently we proved that such an integrability problem can be reduced to a remarkable semi-Hamiltonian system of quasi-linear PDEs and to the question of the existence of smooth periodic solutions for this system. Our main result of the present paper states that any Liouville metric with the zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with a small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of an integral quadratic in momenta.
Design of an aluminium bicycle path integrated in a steel bridge
Maljaars, J.; Soetens, F.; Burggraaf, H.G.
2007-01-01
This paper describes the design of the aluminium structure of a bicycle path which is mounted on an existing steel brige. The benefits of aluminium, being low self weight, freedom in design obtained by extrusion and good corrosion resistance were maximal utilized. One of the main drawbacks of alumin
Integration of Visual and Joint Information to Enable Linear Reaching Motions
Eberle, Henry; Nasuto, Slawomir J.; Hayashi, Yoshikatsu
2017-01-01
A new dynamics-driven control law was developed for a robot arm, based on the feedback control law which uses the linear transformation directly from work space to joint space. This was validated using a simulation of a two-joint planar robot arm and an optimisation algorithm was used to find the optimum matrix to generate straight trajectories of the end-effector in the work space. We found that this linear matrix can be decomposed into the rotation matrix representing the orientation of the goal direction and the joint relation matrix (MJRM) representing the joint response to errors in the Cartesian work space. The decomposition of the linear matrix indicates the separation of path planning in terms of the direction of the reaching motion and the synergies of joint coordination. Once the MJRM is numerically obtained, the feedfoward planning of reaching direction allows us to provide asymptotically stable, linear trajectories in the entire work space through rotational transformation, completely avoiding the use of inverse kinematics. Our dynamics-driven control law suggests an interesting framework for interpreting human reaching motion control alternative to the dominant inverse method based explanations, avoiding expensive computation of the inverse kinematics and the point-to-point control along the desired trajectories.
Fractional order differentiation by integration: An application to fractional linear systems
Liu, Dayan
2013-02-04
In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.
Abnormal gut integrity is associated with reduced linear growth in rural Malawian children.
Weisz, Ariana J; Manary, Micah J; Stephenson, Kevin; Agapova, Sophia; Manary, Faith G; Thakwalakwa, Chrissie; Shulman, Robert J; Manary, Mark J
2012-12-01
The aim of the present study was to investigate the relation of environmental enteropathy, as measured by the dual sugar absorption test, to linear growth faltering in 2- to 5-year-old Malawian children. Dietary quality, food insecurity, anthropometry, and site-specific sugar testing were measured in 418 children, and anthropometry was reassessed 3 months later. A linear regression model predicting linear growth was created. Better growth was associated with less urinary lactulose excretion, more clean water usage, not sleeping with animals, and no previous history of malnutrition. Eighty-seven percent of children studied demonstrated evidence of environmental enteropathy. In conclusion, abnormal gut integrity is associated with reduced linear growth in a population of rural African preschool-age children.
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Kimichi, E-mail: ki-suzuki@aist.go.jp [Research Institute for Nanosystem, National Institute of Advanced Industrial Science and Technology, Chuo-2, 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568 (Japan); Kayanuma, Megumi [Institut de Chimie, UMR 7177 CNRS/Universite de Strasbourg, 4 rue Blaise Pascal 67000, Strasbourg (France); Tachikawa, Masanori [Quantum Chemistry Division, Graduate School of Science, Yokohama-city University, Seto 22-2, Kanazawa-ku, Yokohama 236-0027 (Japan); Ogawa, Hiroshi [Research Institute for Nanosystem, National Institute of Advanced Industrial Science and Technology, Chuo-2, 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568 (Japan); Nishihara, Hirotomo; Kyotani, Takashi [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); Nagashima, Umpei [Research Institute for Nanosystem, National Institute of Advanced Industrial Science and Technology, Chuo-2, 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568 (Japan)
2011-09-15
Research highlights: > The stable hydrogen adsorption sites on C{sub 36}H{sub 12} were evaluated at 300 K using path integral molecular dynamics. > In the static MO calculation and conventional MD simulation, five stable adsorption sites of hydrogen atom were found. > In path integral simulation, only four stable adsorption sites were obtained. > The thermal and nuclear quantum effects are key role to settle the hydrogen adsorption sites on carbon materials. - Abstract: To settle the hydrogen adsorption sites on buckybowl C{sub 36}H{sub 12}, which is picked up from zeolite-templated carbon (ZTC), we have performed path integral molecular dynamics (PIMD) simulation including thermal and nuclear quantum fluctuations under semi-empirical PM3 method. In the static PM3 calculation and classical simulation the five stable adsorption sites of hydrogen atom are optimized inside a buckybowl C{sub 36}H{sub 12}, which are labeled as {alpha}-, {beta}{sub 1}-, {beta}{sub 2}-, {gamma}-, and {delta}-carbons from edge to innermost carbon. In PIMD simulation, meanwhile, stable adsorption site is not appeared on {delta}-carbon, but on only {alpha}-, {beta}{sub 1}-, {beta}{sub 2}-, and {gamma}-carbons. This result is due to the fact that the adsorbed hydrogen atom can easily go over the barrier for hydrogen transferring from {delta}- to {beta}{sub 1}-carbons by thermal and nuclear quantum fluctuations. The thermal and nuclear quantum effects are key role to settle the hydrogen adsorption sites on carbon materials.
A comparison of NH{sub 3} point monitoring and diode laser based path integrated measurements
Energy Technology Data Exchange (ETDEWEB)
Goldstein, N.; Richtsmeier, S.C.; Lee, J.; Bien, F. [Spectral Sciences, Inc., Burlington, MA (United States); Fetzer, G.J.; Groff, K.W. [Monitor Labs., Inc., Englewood, CO (United States)
1994-12-31
Measurements made using two different types of ammonia monitors during a two-month field study in the summer of 1994 are discussed. The first was a diode-laser based open path monitor designed for automated operation in an industrial environment. The second is a monitoring analyzer based on thermal decomposition of ammonia to NO and subsequent analysis by O{sub 3}-NO chemiluminescence. The two monitors provided consistent measurements of ammonia concentration during weeks of continuous unattended operation.
Meija, Juris; Pagliano, Enea; Mester, Zoltán
2014-09-02
Uncertainty of the result from the method of standard addition is often underestimated due to neglect of the covariance between the intercept and the slope. In order to simplify the data analysis from standard addition experiments, we propose x-y coordinate swapping in conventional linear regression. Unlike the ratio of the intercept and slope, which is the result of the traditional method of standard addition, the result of the inverse standard addition is obtained directly from the intercept of the swapped calibration line. Consequently, the uncertainty evaluation becomes markedly simpler. The method is also applicable to nonlinear curves, such as the quadratic model, without incurring any additional complexity.
Path Integral Monte Carlo Approach to the U(1) Lattice Gauge Theory in (2+1) Dimensions
Loan, M; Sloggett, C; Hamer, C; Loan, Mushtaq; Brunner, Michael; Sloggett, Clare; Hamer, Chris
2003-01-01
Path Integral Monte Carlo simulations have been performed for U(1) lattice gauge theory in (2+1) dimensions on anisotropic lattices. We extract the static quark potential, the string tension and the low-lying "glueball" spectrum. The Euclidean string tension and mass gap decrease exponentially at weak coupling in excellent agreement with the predictions of Polyakov and G{\\" o}pfert and Mack, but their magnitudes are five times bigger than predicted. Extrapolations are made to the extreme anisotropic or Hamiltonian limit, and comparisons are made with previous estimates obtained in the Hamiltonian formulation.
Müser, Martin H.
2001-04-01
Classical and path integral molecular dynamics (PIMD) simulations are used to study α and β quartz in a large range of temperatures at zero external stress. PIMD account for quantum fluctuations of atomic vibrations, which can modify material properties at temperatures below the Debye temperature. The difference between classical and quantum mechanical results for bond lengths, bond angles, elastic moduli, and some dynamical properties is calculated and comparison to experimental data is done. Only quantum mechanical simulations are able to reproduce the correct thermomechanical properties below room temperature. It is discussed in how far classical and PIMD simulations can be helpful in constructing improved potential energy surfaces for silica.
Kakizaki, Akira; Takayanagi, Toshiyuki; Shiga, Motoyuki
2007-11-01
Path integral molecular dynamics simulations for the H6+ and D6+ cluster cations have been carried out in order to understand the floppy nature of their molecular structure due to quantum-mechanical fluctuation. A full-dimensional analytical potential energy surface for the ground electronic state of H6+ has been developed on the basis of accurate ab initio electronic structure calculations at the CCSD(T)/cc-pVTZ level. It is found that the outer H 2(D 2) nuclei rotate almost freely and that the probability density distributions of the central H 2(D 2) nuclei show strong spatial delocalization.
Kawashima, Yukio; Tachikawa, Masanori
2013-05-01
Ab initio path integral molecular dynamics simulation was performed to understand the nuclear quantum effect on the hydrogen bond of hydrogen malonate anion. Static calculation predicted the proton transfer barrier as 0.12 kcal/mol. Conventional ab initio molecular dynamics simulation at 300 K found proton distribution with a double peak on the proton transfer coordinate. Inclusion of thermal effect alone elongates the hydrogen bond length, which increases the barrier height. Inclusion of nuclear quantum effect washes out this barrier, and distributes a single broad peak in the center. H/D isotope effect on the proton transfer is also discussed.
Yoshikawa, Takehiro; Sugawara, Shuichi; Takayanagi, Toshiyuki; Shiga, Motoyuki; Tachikawa, Masanori
2010-08-01
Full-dimensional path-integral molecular dynamics simulations were performed to determine whether the double proton transfer tautomerization of porphycene is a concerted or a stepwise process. We employed an on-the-fly direct dynamics technique at the semiempirical PM6 method whose parameters were determined so as that the relative energies of the stationary points approximately reproduce previously reported electronic structure calculations. It was found that double proton transfer occurs dominantly through the concerted pathway via the second-order saddle point structure and that contribution of the stepwise mechanism increases with a temperature increase. Nuclear quantum effects play essential roles in determining the proton transfer mechanism.
Wosiek, Jacek
2015-01-01
Recently found positive representation for an arbitrary complex, gaussian weight is used to construct a statistical formulation of gaussian path integrals directly in the Minkowski time. The positivity of Minkowski weights is achieved by doubling the number of real variables. The continuum limit of the new representation exists only if some of the additional couplings tend to infinity and are tuned in a specific way. The construction is then successfully applied to three quantum mechanical examples including a particle in a constant magnetic field -- a simplest prototype of a Wilson line. Further generalizations are shortly discussed and an intriguing interpretation of new variables is alluded to.
Miura, Shinichi; Okazaki, Susumu
2001-09-01
In this paper, the path integral molecular dynamics (PIMD) method has been extended to employ an efficient approximation of the path action referred to as the pair density matrix approximation. Configurations of the isomorphic classical systems were dynamically sampled by introducing fictitious momenta as in the PIMD based on the standard primitive approximation. The indistinguishability of the particles was handled by a pseudopotential of particle permutation that is an extension of our previous one [J. Chem. Phys. 112, 10 116 (2000)]. As a test of our methodology for Boltzmann statistics, calculations have been performed for liquid helium-4 at 4 K. We found that the PIMD with the pair density matrix approximation dramatically reduced the computational cost to obtain the structural as well as dynamical (using the centroid molecular dynamics approximation) properties at the same level of accuracy as that with the primitive approximation. With respect to the identical particles, we performed the calculation of a bosonic triatomic cluster. Unlike the primitive approximation, the pseudopotential scheme based on the pair density matrix approximation described well the bosonic correlation among the interacting atoms. Convergence with a small number of discretization of the path achieved by this approximation enables us to construct a method of avoiding the problem of the vanishing pseudopotential encountered in the calculations by the primitive approximation.
Liu, Xuan; Meisne, Eric; Han, Jae-Ho; Zhang, Kang; Gehlbach, Peter; Taylor, Russell; Kang, Jin U.
2010-02-01
Contemporary retinal microsurgery is performed by skilled surgeons through operating microscopes, utilizing free hand techniques and manually operated micro-instruments. One technically challenging procedure is the incising and peeling of the internal limiting membrane (ILM) while minimizing damage to the underlying retina. One strategy for minimizing damage is to improve visualization of the ILM layer. Here we present a preliminary evaluation of a prototype tool that integrates an ultra high resolution Fourier domain common path Optical Coherence Tomography (OCT) with an intelligent microsurgical instrument. The tool provides OCT guided visualization of the ILM layer at the point of tissue contact by the surgical tool. We have evaluated the imaging properties of the common path OCT system. The common path OCT system used in this study has a maximum imaging depth of 1.3mm and a sensitivity of 91dB. We have achieved an experimental axial resolution of 3μm in air and this appears to be sufficient to both identify the ILM and to perform surgical maneuvers. We scanned the single mode fiber probe using an intelligent microsurgical instrument to form B-Mode images. We imaged a porcine eye with both anterior eye segment and the vitreous removed. The image obtained show distinct functional layers of retina.
Institute of Scientific and Technical Information of China (English)
Mei CAO; Qingyu ZHANG
2008-01-01
To cope with an increasingly turbulent environment, manufacturing firms increasingly implement integration practices to enhance flexibility in the production process. This research develops a framework to explore the relationships among organizational integration practices, manufacturing flexibility, and competitive advantage. The study develops valid and reliable instruments to measure these constructs, and it applies structural equation modeling to test relationships among these variables using a large sample. The results indicate strong, positive, and direct relationships between organizational integration practices and manufacturing flexibility, and between manufacturing flexibility and competitive advantage. The results also indicate that organizational integration practices enhance competitive advantage directly as well as indirectly by facilitating manufacturing flexibility.
Mühlbacher, L; Escher, C M
2004-01-01
An improved real-time quantum Monte Carlo procedure is presented and applied to describe the electronic transfer dynamics along molecular chains. The model consists of discrete electronic sites coupled to a thermal environment which is integrated out exactly within the path integral formulation. The approach is numerically exact and its results reduce to known analytical findings (Marcus theory, golden rule) in proper limits. Special attention is paid to the role of superexchange and sequential hopping at lower temperatures in symmetric donor-bridge-acceptor systems. In contrast to previous approximate studies, superexchange turns out to play a significant role only for extremely high lying bridges where the transfer is basically frozen or for extremely low temperatures where for weaker dissipation a description in terms of rate constants is no longer feasible. For bridges with increasing length an algebraic decrease of the yield is found for short as well as for longer bridges. The approach can be extended t...
Directory of Open Access Journals (Sweden)
Bousserhane I.K.
2006-01-01
Full Text Available In this paper the position control of a linear induction motor using adaptive fuzzy back stepping design with integral action is proposed. First, the indirect field oriented control for LIM is derived. Then, an integral back stepping design for indirect field oriented control of LIM is proposed to compensate the uncertainties which occur in the control. Finally, the fuzzy integral-back stepping controller is investigated, where a simple fuzzy inference mechanism is used to achieve a position tracking objective under the mechanical parameters uncertainties. The effectiveness of the proposed control scheme is verified by numerical simulation. The numerical validation results of the proposed scheme have presented good performances compared to the conventional integral back stepping control.
Li, Xiaobo; Hu, Haofeng; Liu, Tiegen; Huang, Bingjing; Song, Zhanjie
2016-04-04
We consider the degree of linear polarization (DOLP) polarimetry system, which performs two intensity measurements at orthogonal polarization states to estimate DOLP. We show that if the total integration time of intensity measurements is fixed, the variance of the DOLP estimator depends on the distribution of integration time for two intensity measurements. Therefore, by optimizing the distribution of integration time, the variance of the DOLP estimator can be decreased. In this paper, we obtain the closed-form solution of the optimal distribution of integration time in an approximate way by employing Delta method and Lagrange multiplier method. According to the theoretical analyses and real-world experiments, it is shown that the variance of the DOLP estimator can be decreased for any value of DOLP. The method proposed in this paper can effectively decrease the measurement variance and thus statistically improve the measurement accuracy of the polarimetry system.
Kapila, Vivek; Deymier, Pierre; Runge, Keith
2012-02-01
Warm dense matter (WDM) can be characterized by electron temperatures of a few eV and densities an order of magnitude or more beyond ambient. This regime currently lacks any adequate highly developed class of simulation methods. Recent developments in orbital-free Density Functional Theory (ofDFT) aim to provide such a simulation method, however, little benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as harmonic necklaces, while, quantum exchange takes the form of cross linking between electron necklaces. The fermion sign problem is addressed by restricting the density matrix to positive values and a molecular dynamics algorithm is employed to sample phase space. Here, we focus on the behavior of strongly correlated electron plasmas under WDM conditions. We compute the kinetic and potential energies and compare them to those obtained with the ofDFT method.
Runge, Keith; Deymier, Pierre
2013-03-01
Recent progress in orbital-free Density Functional Theory (OF-DFT), particularly with regard to temperature dependent functionals, has promise for the simulation of warm dense matter (WDM) systems. WDM includes systems with densities of an order of magnitude beyond ambient or more and temperatures measured in kilokelvin. A challenge for the development of temperature dependent OF-DFT functionals is the lack of benchmark information with temperature and pressure dependence on simple models under WDM conditions. We present an approach to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Electrons are described as harmonic necklaces within the discrete path integral representation while quantum exchange takes the form of cross linking between electron necklaces. A molecular dynamics algorithm is used to sample phase space and the fermion sign problem is addressed by restricting the density matrix to positive values. The temperature dependence of kinetic energies for the strongly coupled electron plasma is presented for a number of Wigner-Seitz radii in terms of a fourth order Sommerfeld expansion. Supported by US DoE Grant DE-SC0002139
Bernstein, D. R.; Dashen, R.; Flatte, S. M.
1983-01-01
A theory is developed which describes intensity moments for wave propagation through random media. It is shown using the path integral technique that these moments are significantly different from those of a Rayleigh distribution in certain asymptotic regions. The path integral approach is extended to inhomogeneous, anisotropic media possessing a strong deterministic velocity profile. The behavior of the corrections to Rayleigh statistics is examined, and it is shown that the important characteristics can be attributed to a local micropath focusing function. The correction factor gamma is a micropath focusing parameter defined in terms of medium fluctuations. The value of gamma is calculated for three ocean acoustic experiments, using internal waves as the medium fluctuations. It is found that all three experiments show excellent agreement as to the relative values of the intensity moments. The full curved ray is found to yield results that are significantly different from the straight-line approximations. It is noted that these methods are applicable to a variety of experimental situations, including atmospheric optics and radio waves through plasmas.
Wong, Kin-Yiu; Xu, Yuqing; York, Darrin M
2014-06-30
Detailed understandings of the reaction mechanisms of RNA catalysis in various environments can have profound importance for many applications, ranging from the design of new biotechnologies to the unraveling of the evolutionary origin of life. An integral step in the nucleolytic RNA catalysis is self-cleavage of RNA strands by 2'-O-transphosphorylation. Key to elucidating a reaction mechanism is determining the molecular structure and bonding characteristics of transition state. A direct and powerful probe of transition state is measuring isotope effects on biochemical reactions, particularly if we can reproduce isotope effect values from quantum calculations. This article significantly extends the scope of our previous joint experimental and theoretical work in examining isotope effects on enzymatic and nonenzymatic 2'-O-transphosphorylation reaction models that mimic reactions catalyzed by RNA enzymes (ribozymes), and protein enzymes such as ribonuclease A (RNase A). Native reactions are studied, as well as reactions with thio substitutions representing chemical modifications often used in experiments to probe mechanism. Here, we report and compare results from eight levels of electronic-structure calculations for constructing the potential energy surfaces in kinetic and equilibrium isotope effects (KIE and EIE) computations, including a "gold-standard" coupled-cluster level of theory [CCSD(T)]. In addition to the widely used Bigeleisen equation for estimating KIE and EIE values, internuclear anharmonicity and quantum tunneling effects were also computed using our recently developed ab initio path-integral method, that is, automated integration-free path-integral method. The results of this work establish an important set of benchmarks that serve to guide calculations of KIE and EIE for RNA catalysis. Copyright © 2014 Wiley Periodicals, Inc.
Test-Taker Characteristics and Integrated Speaking Test Performance: A Path-Analytic Study
Huang, Heng-Tsung Danny; Hung, Shao-Ting Alan; Hong, He-Ting Vivian
2016-01-01
This study explored the relationships among language proficiency, two selected test-taker characteristics (i.e., topical knowledge and anxiety), and integrated speaking test performance. Data collection capitalized on three sets of instruments: three integrated tasks derived from TOEFL-iBT preparation materials, the state anxiety inventory created…
Test-Taker Characteristics and Integrated Speaking Test Performance: A Path-Analytic Study
Huang, Heng-Tsung Danny; Hung, Shao-Ting Alan; Hong, He-Ting Vivian
2016-01-01
This study explored the relationships among language proficiency, two selected test-taker characteristics (i.e., topical knowledge and anxiety), and integrated speaking test performance. Data collection capitalized on three sets of instruments: three integrated tasks derived from TOEFL-iBT preparation materials, the state anxiety inventory created…
Institute of Scientific and Technical Information of China (English)
J. CABALLERO; B. L(ó)PEZ; K. SADARANGANI
2007-01-01
We use a technique associated with measures of noncompactness to prove the existence of nondecreasing solutions to an integral equation with linear modification of the argument in the space C[0,1]. In the last thirty years there has been a great deal of work in the field of differential equations with a modified argument. A special class is represented by the differential equation with affine modification of the argument which can be delay differential equations or differential equations with linear modifications of the argument. In this case we study the following integral equation x(t) = a(t) + (Tx)(t)∫σ(t)o u(t,s,x(s),x(λs))ds 0λ1 which can be considered in connection with the following Cauchy problem x'(t) = u(t,s,x(t),x(λt)), t∈[0,1], 0 λ 1 x(0) = uo.
2014-01-09
nanoparticles (NPs) were added to luminescent porous silicon by drop casting. These NPs interact with this system by modifying its optical properties ...response by Au NPs in sapphire: Nonlinear optical response of Au metallic NPs, synthesized and embedded in sapphire by using ion implantation, as a...Linear and nonlinear plasmonics from isotropic and anisotropic integrated nanocomposites for quantum information applications. Jorge-Alejandro Reyes
Van der Veken, Frederik F
2014-01-01
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in calculations for constructing or modelling parton density functions. We develop an algorithm to express piecewise path ordered exponentials as path ordered integrals over the separate segments, and apply it on linear segments, reducing the number of diagrams needed to be calculated. We show how different linear path topologies can be related using their colour structure. This framework allows one to easily switch results between different Wilson line structures, which is especially useful when testing different structures against each other, e.g. when checking universality properties of non-perturbative objects.
Displaced path integral formulation for the momentum distribution of quantum particles
Lin, Lin; Car, Roberto; Parrinello, Michele
2010-01-01
The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end to end distribution of the Feynman paths, i.e. the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to one-dimensional model systems and to an empirical water model.
Institute of Scientific and Technical Information of China (English)
LIU An-guo; YANG Kai-zhong
2004-01-01
This paper meant to analyze the spatial evolution of a large country in its process of integration with the world economy in general, and, to look into the possible effect of China's accession into WTO on the future development of its spatial economy in particular. Through an approach of increasing returns, external economy, product differentiation and path-dependence, with foreign trade costs incurred by different regions within the large country discriminated, a model of investment and employment flow is developed as a simulation of a large country's process of integration with the world economy. The modeling indicates that in the process of integration, as there exist differences in foreign trade costs among different regions within the large country, either the spatial economy of the country deviates from its symmetric structure in autarky and falls into a core-periphery relationship, or the effect of industrial agglomeration is reinforced, amplified and locked in, if the agglomeration had been started. The economic gap on either the aggregate or structural basis between different regions within the large country will increase rapidly as the integration proceeds.
Implicit objective integration for sensitivity analysis in non-linear solid mechanics
Leu, Liang-Jeno; Mukherjee, Subrata
1994-11-01
Incrementally objective integration schemes are proposed for the accurate and efficient determination of design sensitivity coefficients (DSCs) for solid mechanics problems with both material and geometrical non-linearities. The derivation of these schemes are based on the direct differentiation of objective schemes that are used in stress analysis for problems of this class. Two widely used objective stress rates, the Jaumann rate and the Green-Naghdi rate, are considered here within the only minor changes of the integration scheme. Numerical results are presented for a simple shear problem with different material consititutive laws, including a hypoelastic model and a isotropic viscoplastic model, for these two objective rates. The num0rical results are compared with analytical solutions or direct integration solutions. The close agreement among these solutions demonstrates the accuracy and efficiency of the proposed scheme.
Distasio, Robert A., Jr.; Santra, Biswajit; Ko, Hsin-Yu; Car, Roberto
2014-03-01
In this work, we report highly accurate ab initio path-integral molecular dynamics (AI-PIMD) simulations on liquid water at ambient conditions utilizing the recently developed PBE0+vdW(SC) exchange-correlation functional, which accounts for exact exchange and a self-consistent pairwise treatment of van der Waals (vdW) or dispersion interactions, combined with nuclear quantum effects (via the colored-noise generalized Langevin equation). The importance of each of these effects in the theoretical prediction of the structure of liquid water will be demonstrated by a detailed comparative analysis of the predicted and experimental oxygen-oxygen (O-O), oxygen-hydrogen (O-H), and hydrogen-hydrogen (H-H) radial distribution functions as well as other structural properties. In addition, we will discuss the theoretically obtained proton momentum distribution, computed using the recently developed Feynman path formulation, in light of the experimental deep inelastic neutron scattering (DINS) measurements. DOE: DE-SC0008626, DOE: DE-SC0005180.
A path to better healthcare simulation systems: leveraging the integrated systems design approach.
Scerbo, M.W.; Murray, W.B.; Antonius, T.A.J.; Alinier, G.; Caird, J.; Stricker, E.; Rice, J.; Kyle, R.
2011-01-01
This article addresses the necessary steps in the design of simulation-based instructional systems. A model for designing instructional systems is presented which stipulates that the outcome metrics be defined before the simulation system is designed. This ensures integration of educational objectiv
Identification of shear buildings using an instrumental variable method and linear integral filters
Concha, Antonio; Garrido, Rubén; Alvarez-Icaza, Luis
2016-12-01
This paper develops a method for estimating the parameters of a seismically excited building. Acceleration measurements of the ground and of the building floors, containing offsets and noise, are used for identification purposes. The proposed scheme estimates the complete model of the building if all the floors are equipped with accelerometers. Moreover, it also estimates a reduced model of the structure if only some floors are instrumented. The methodology is based on the combined use of the Instrumental Variable method and Linear Integral Filters. The Instrumental Variable method employs as instrument an auxiliary model of the structure, and it is able to directly identify the continuous-time structure model using discrete-time data without resorting on model transformations from continuous-time to discrete-time, and vice-versa. Using Linear Integral Filters allows obtaining a linear in the parameters expression that depends only on acceleration measurements suitable for parameter identification purposes. These filters eliminate measurement offsets and attenuate high-frequency measurement noise. The above features together with the use of the Instrumental variable method reduce the likelihood of biased parameter estimates. Experiments on a testbed employing a reduced-scale five-story structure allow comparing the results obtained using the Instrumental Variable method and those produced by the standard Least Squares method.
Blaschke, D.; Ebert, D.
2017-08-01
For the investigation of back-reactions of composite mesons in the NJL model, a variational path-integral treatment is formulated which yields an effective action Aeff [Dσ ,Dπ ; S ], depending on the propagators Dσ, Dπ of σ- and π-mesons and on the full quark propagator S. The stationarity conditions δAeff / δS = 0, δAeff / δDσ = 0, δAeff / δDπ = 0, then lead to coupled Schwinger-Dyson (SD) equations for the quark self-energy and the meson polarization functions. These results reproduce and extend results of the so-called ;Φ-derivable; approach and provide a functional formulation for diagrammatic resummations of 1 /Nc -corrections in the NJL model. Finally, we perform a low-momentum estimate of the quark and meson loop contributions to the polarization function of the pion and on this basis discuss the Goldstone theorem.
Curotto, E; Freeman, David L; Doll, J D
2008-05-28
A Monte Carlo path integral method to study the coupling between the rotation and bending degrees of freedom for water is developed. It is demonstrated that soft internal degrees of freedom that are not stretching in nature can be mapped with stereographic projection coordinates. For water, the bending coordinate is orthogonal to the stereographic projection coordinates used to map its orientation. Methods are developed to compute the classical and quantum Jacobian terms so that the proper infinitely stiff spring constant limit is recovered in the classical limit, and so that the nonconstant nature of the Riemann Cartan curvature scalar is properly accounted in the quantum simulations. The theory is used to investigate the effects of the geometric coupling between the bending and the rotating degrees of freedom for the water monomer in an external field in the 250 to 500 K range. We detect no evidence of geometric coupling between the bending degree of freedom and the orientations.
Gratton, Steven
2010-01-01
In this paper we present a path integral formulation of stochastic inflation, in which volume weighting can easily be implemented. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow-roll. The slow-roll end of inflation mitigates certain "Youngness Paradox"-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper time volume weighting as a viable measure for answering at least some interesting cosmological questions.
Yolcu, Cem; Şimşek, Kadir; Westin, Carl-Fredrik; Özarslan, Evren
2016-01-01
We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field, and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multi-dimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike for the case of traditional methods that employ a diffusion tensor, aniso...
Shiga, Motoyuki; Takayanagi, Toshiyuki
2003-09-01
The equilibrium structure of the negatively charged water dimer (H 2O) 2- has been studied using the path-integral molecular dynamics simulation. All the atomic motions as well as the excess electron were treated quantum mechanically, employing a semi-empirical model combining a water-water interatomic potential with an electron-water pseudopotential. It is demonstrated that the molecular structure of (H 2O) 2- is more flexible than that of (H 2O) 2; both the donor switching and donor-acceptor interchange can more effectively occur in (H 2O) 2- than in (H 2O) 2. We conclude that this floppy character is a result of the breakdown of the adiabatic Born-Oppenheimer picture.
Torrent, Marc; Geneste, Gregory
2012-02-01
The low-temperature phases of dense hydrogen and deuterium have been investigated using first-principles path-integral molecular dynamics, a technique that we have recently implemented in the ABINIT code and that allows to account for the quantum fluctuations of atomic nuclei. A massively parallelized scheme is applied to produce trajectories of several tens of thousands steps using a 64-atom supercell and a Trotter number of 64. The so-called phases I, II and III are studied and compared to the structures proposed in the literature. The quantum fluctuations produce configurational disorder and are shown to systematically enhance the symmetry of the system: a continuous gain of symmetry in the angular density of probability of the molecules is found from classical particles to quantum D2 and finally to quantum H2. Particular emphasis is made on the ``broken-symmetry'' phase (phase II).
Suzuki, Kimichi; Shiga, Motoyuki; Tachikawa, Masanori
2008-10-01
Path integral molecular dynamics simulation based on the fourth order Trotter expansion has been performed to elucidate the geometrical isotope effect of water dimer anions, H3O2-, D3O2-, and T3O2-, at different temperatures from 50 to 600 K. At low temperatures below 200 K the hydrogen-bonded hydrogen nucleus is near the center of two oxygen atoms with mostly O⋯X⋯O geometry (where X =H, D, or T), while at high temperatures above 400 K, hydrogen becomes more delocalized, showing the coexistence between O⋯X-O and O-X⋯O. The OO distance tends to be shorter as the isotopomer is heavier at low temperatures, while this ordering becomes opposite at high temperatures. It is concluded that the coupling between the OO stretching mode and proton transfer modes is a key to understand such a temperature dependence of a hydrogen-bonded structure.
Energy Technology Data Exchange (ETDEWEB)
Filinov, V.S.; Fortov, V.E. [Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13, bd. 2, 125412 Moscow (Russian Federation); Bonitz, M. [Institute for Theoretical Physics and Astrophysics, Christian Albrechts University Kiel, Leibnizstrasse 15, D-24098 Kiel (Germany); Ivanov, Y.B. [National Research Center ' ' Kurchatov Institute' ' , Kurchatov Sq. 1, 123182 Moscow, Russia, National Research Nuclear University ' ' MEPhI' ' , Kashirskoe sh. 31, 115409 Moscow (Russian Federation); Ilgenfritz, E.M. [Joint Institute for Nuclear Reseach, Joliot-Curie str. 6, Dubna, 141980, Moscow Region (Russian Federation)
2015-02-01
Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), color quantum path-integral Monte-Carlo (PIMC) calculations of the thermodynamic properties of the QGP are performed. We extend our previous zero chemical potential simulations to the QGP at finite baryon chemical potential. The results indicate that color PIMC can be applied not only above the QCD critical temperature T{sub c} but also below T{sub c}. Besides reproducing the lattice equation of state our approach yields also valuable additional insight into the internal structure of the QGP, via the pair distribution functions of the various quasiparticles. In particular, the pair distribution function of gluons reflects the existence of gluon-gluon bound states at low temperatures and μ = 175 MeV, i.e. glueballs, while meson-like bound states are not found. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Energy Technology Data Exchange (ETDEWEB)
Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2007-08-15
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short''Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional flat space and divides it by a three-dimensional superintegrable potential. Such superintegrable potentials will be the isotropic singular oscillator, the Holt-potential, the Coulomb potential, or two centrifugal potentials, respectively. In all cases a non-trivial space of non-constant curvature is generated. In order to obtain a proper quantum theory a curvature term has to be incorporated into the quantum Hamiltonian. For possible bound-state solutions we find equations up to twelfth order in the energy E. (orig.)
The inefficiency of re-weighted sampling and the curse of system size in high order path integration
Ceriotti, Michele; Riordan, Oliver; Manolopoulos, David E
2011-01-01
Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we present a very general analysis of the accuracy and efficiency of this approach, highlighting some of its weaknesses. We then give an example of how our results can be used, specifically to assess the feasibility of high-order path integral methods. We demonstrate that the most promising of these techniques -- which is based on re-weighted sampling -- is bound to fail as the size of the system is increased, because of the exponential growth of the statistical uncertainty in the re-weighted average.
DEFF Research Database (Denmark)
Karnøe, Peter; Garud, Raghu
2012-01-01
This paper employs path creation as a lens to follow the emergence of the Danish wind turbine cluster. Supplier competencies, regulations, user preferences and a market for wind power did not pre-exist; all had to emerge in a tranformative manner involving multiple actors and artefacts. Competenc......This paper employs path creation as a lens to follow the emergence of the Danish wind turbine cluster. Supplier competencies, regulations, user preferences and a market for wind power did not pre-exist; all had to emerge in a tranformative manner involving multiple actors and artefacts....... Competencies emerged through processes and mechanisms such as co-creation that implicated multiple learning processes. The process was not an orderly linear one as emergent contingencies influenced the learning processes. An implication is that public policy to catalyse clusters cannot be based...
Institute of Scientific and Technical Information of China (English)
A. Diaf
2015-01-01
We obtain analytical expressions for the energy eigenvalues of both the Schi ¨oberg and Eckart potentials using an approximation of the centrifugal term. In order to determine the ℓ-states solutions, we use the Feynman path integral approach to quantum mechanics. We show that by performing nonlinear space–time transformations in the radial path integral, we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system. The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions. We show that the Eckart potential can be derived from the Schi ¨oberg potential. The obtained results are compared to those by other methods and found to be consistent.
Uthirajoo, Eswaran; Ramiah, Harikrishnan; Kanesan, Jeevan; Reza, Ahmed Wasif
2014-01-01
For the first time, a new circuit to extend the linear operation bandwidth of a LTE (Long Term Evolution) power amplifier, while delivering a high efficiency is implemented in less than 1 mm2 chip area. The 950 µm × 900 µm monolithic microwave integrated circuit (MMIC) power amplifier (PA) is fabricated in a 2 µm InGaP/GaAs process. An on-chip analog pre-distorter (APD) is designed to improve the linearity of the PA, up to 20 MHz channel bandwidth. Intended for 1.95 GHz Band 1 LTE application, the PA satisfies adjacent channel leakage ratio (ACLR) and error vector magnitude (EVM) specifications for a wide LTE channel bandwidth of 20 MHz at a linear output power of 28 dBm with corresponding power added efficiency (PAE) of 52.3%. With a respective input and output return loss of 30 dB and 14 dB, the PA's power gain is measured to be 32.5 dB while exhibiting an unconditional stability characteristic from DC up to 5 GHz. The proposed APD technique serves to be a good solution to improve linearity of a PA without sacrificing other critical performance metrics.