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.
Accurate free energy calculation along optimized paths.
Chen, Changjun; Xiao, Yi
2010-05-01
The path-based methods of free energy calculation, such as thermodynamic integration and free energy perturbation, are simple in theory, but difficult in practice because in most cases smooth paths do not exist, especially for large molecules. In this article, we present a novel method to build the transition path of a peptide. We use harmonic potentials to restrain its nonhydrogen atom dihedrals in the initial state and set the equilibrium angles of the potentials as those in the final state. Through a series of steps of geometrical optimization, we can construct a smooth and short path from the initial state to the final state. This path can be used to calculate free energy difference. To validate this method, we apply it to a small 10-ALA peptide and find that the calculated free energy changes in helix-helix and helix-hairpin transitions are both self-convergent and cross-convergent. We also calculate the free energy differences between different stable states of beta-hairpin trpzip2, and the results show that this method is more efficient than the conventional molecular dynamics method in accurate free energy calculation.
Lloyd, Seth; Dreyer, Olaf
2013-01-01
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete...
International Nuclear Information System (INIS)
These notes form a fairly standard introduction to Wiener integration on Rsup(n) and on Riemannian manifolds. Feynman path integrals for non-relativistic quantum mechanics are also considered and compared to Wiener integrals. The basic approach is via cylinder set measures, Gaussian measures, and abstract Wiener spaces. (Auth.)
Vanícek, Jirí
2011-01-01
Nuclear tunneling and other nuclear quantum effects have been shown to play a significant role in molecules as large as enzymes even at physiological temperatures. I discuss how these quantum phenomena can be accounted for rigorously using Feynman path integrals in calculations of the equilibrium and kinetic isotope effects as well as of the temperature dependence of the rate constant. Because these calculations are extremely computationally demanding, special attention is devoted to increasing the computational efficiency by orders of magnitude by employing efficient path integral estimators.
Continuous-Discrete Path Integral Filtering
Balaji, Bhashyam
2008-01-01
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.
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.
Path Integral for Quantum Operations
Tarasov, Vasily E.
2007-01-01
In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation). We consider the path integral for quantum operation with a simple infinitesimal generator.
Thermoalgebras and path integral
Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.
2009-09-01
Using a representation for Lie groups closely associated with thermal problems, we derive the algebraic rules of the real-time formalism for thermal quantum field theories, the so-called thermo-field dynamics (TFD), including the tilde conjugation rules for interacting fields. These thermo-group representations provide a unified view of different approaches for finite-temperature quantum fields in terms of a symmetry group. On these grounds, a path integral formalism is constructed, using Bogoliubov transformations, for bosons, fermions and non-abelian gauge fields. The generalization of the results for quantum fields in (S1)d×R topology is addressed.
Yamada, Kenta; Kawashima, Yukio; Tachikawa, Masanori
2014-05-13
We performed ab initio path integral molecular dynamics (PIMD) simulations with a density functional theory (DFT) method to accurately predict hyperfine coupling constants (HFCCs) in the ethyl radical (CβH3-CαH2) and its Mu-substituted (muoniated) compound (CβH2Mu-CαH2). The substitution of a Mu atom, an ultralight isotope of the H atom, with larger nuclear quantum effect is expected to strongly affect the nature of the ethyl radical. The static conventional DFT calculations of CβH3-CαH2 find that the elongation of one Cβ-H bond causes a change in the shape of potential energy curve along the rotational angle via the imbalance of attractive and repulsive interactions between the methyl and methylene groups. Investigation of the methyl-group behavior including the nuclear quantum and thermal effects shows that an unbalanced CβH2Mu group with the elongated Cβ-Mu bond rotates around the Cβ-Cα bond in a muoniated ethyl radical, quite differently from the CβH3 group with the three equivalent Cβ-H bonds in the ethyl radical. These rotations couple with other molecular motions such as the methylene-group rocking motion (inversion), leading to difficulties in reproducing the corresponding barrier heights. Our PIMD simulations successfully predict the barrier heights to be close to the experimental values and provide a significant improvement in muon and proton HFCCs given by the static conventional DFT method. Further investigation reveals that the Cβ-Mu/H stretching motion, methyl-group rotation, methylene-group rocking motion, and HFCC values deeply intertwine with each other. Because these motions are different between the radicals, a proper description of the structural fluctuations reflecting the nuclear quantum and thermal effects is vital to evaluate HFCC values in theory to be comparable to the experimental ones. Accordingly, a fundamental difference in HFCC between the radicals arises from their intrinsic molecular motions at a finite temperature, in
Path Integral and Asian Options
Peng Zhang
2010-01-01
In this paper we analytically study the problem of pricing an arithmetically averaged Asian option in the path integral formalism. By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action functional whose potential term is an exponential function. This path integral is evaluated by use of the Feynman-Kac theorem. After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion for t...
Risk Sensitive Path Integral Control
Broek, L.J. van den; Wiegerinck, W.A.J.J.; Kappen, H. J.
2012-01-01
Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dynamics in continuous space-time. Path integral methods find the control that minimizes the expected cost-to-go. In this paper we show that under the same assumptions, path integral methods generalize directly to risk sensitive stochastic optimal control. Here the method minimizes in expectation an exponentially weighted cost-to-go. Depending on the exponential weight,...
Path Integral and Asset Pricing
Zura Kakushadze
2014-01-01
We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White model, we can apply the same techniques to "less-tractable" models such as the Black-Karasinski model. We give explicit formulas for computing the bond pricing function in such models in the analog of quantum mechanical "semiclassical" approximation. We al...
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...
Chaichian, M.; Demichev, A. P.
1993-01-01
Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of q-oscillator.
Thomas, EGF
1996-01-01
We construct an analogue of the Feynman path integral for the case of -1/i partial derivative/partial derivative t phi t = H-o phi t in which H-o is a self-adjoint operator in the space L(2)(M) = C-M, where M is a finite set, the paths being functions of R with values in M. The path integral is a fa
Path Integral Simulations of Graphene
Yousif, Hosam
2007-10-01
Some properties of graphene are explored using a path integral approach. The path integral method allows us to simulate relatively large systems using monte carlo techniques and extract thermodynamic quantities. We simulate the effects of screening a large external charge potential, as well as conductivity and charge distributions in graphene sheets.
Simple and accurate analytical calculation of shortest path lengths
Melnik, Sergey
2016-01-01
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for synthetic random networks with specified degree distribution (the so-called configuration model networks). Our method allows us to accurately predict the distribution of shortest path lengths on real-world networks using their degree distribution, or joint degree-degree distribution. Compared to some other methods, our approach is simpler and yields more accurate results. In order to obtain the analytical results, we use the analogy between an infection reaching a node in $n$ discrete time steps (i.e., as in the susceptible-infected epidemic model) and that node being at a distance $n$ from the source of the infection.
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
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.
Quantitative Molecular Thermochemistry Based on Path Integrals
Energy Technology Data Exchange (ETDEWEB)
Glaesemann, K R; Fried, L E
2005-03-14
The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal mode analysis to calculate the vibrational and rotational contributions. We utilize path integral Monte Carlo (PIMC) for going beyond the harmonic analysis, to calculate the vibrational and rotational contributions to ab initio energies. This is an application and extension of a method previously developed in our group.
Path-integral evolution of multivariate systems with moderate noise
Ingber, L.
2000-01-01
A non Monte Carlo path-integral algorithm that is particularly adept at handling nonlinear Lagrangians is extended to multivariate systems. This algorithm is particularly accurate for systems with moderate noise.
A New Path Generation Algorithm Based on Accurate NURBS Curves
Directory of Open Access Journals (Sweden)
Sawssen Jalel
2016-04-01
Full Text Available The process of finding an optimum, smooth and feasible global path for mobile robot navigation usually involves determining the shortest polyline path, which will be subsequently smoothed to satisfy the requirements. Within this context, this paper deals with a novel roadmap algorithm for generating an optimal path in terms of Non-Uniform Rational B-Splines (NURBS curves. The generated path is well constrained within the curvature limit by exploiting the influence of the weight parameter of NURBS and/or the control points’ locations. The novelty of this paper lies in the fact that NURBS curves are not used only as a means of smoothing, but they are also involved in meeting the system’s constraints via a suitable parameterization of the weights and locations of control points. The accurate parameterization of weights allows for a greater benefit to be derived from the influence and geometrical effect of this factor, which has not been well investigated in previous works. The effectiveness of the proposed algorithm is demonstrated through extensive MATLAB computer simulations.
International Nuclear Information System (INIS)
In this paper we study path integral for a single spinless particle on a star graph with N edges, whose vertex is known to be described by U(N) family of boundary conditions. After carefully studying the free particle case, both at the critical and off-critical levels, we propose a new path integral formulation that correctly captures all the scale-invariant subfamily of boundary conditions realized at fixed points of boundary renormalization group flow. Our proposal is based on the folding trick, which maps a scalar-valued wave function on star graph to an N-component vector-valued wave function on half-line. All the parameters of scale-invariant subfamily of boundary conditions are encoded into the momentum independent weight factors, which appear to be associated with the two distinct path classes on half-line that form the cyclic group Z2. We show that, when bulk interactions are edge-independent, these weight factors are generally given by an N-dimensional unitary representation of Z2. Generalization to momentum dependent weight factors and applications to worldline formalism are briefly discussed. - Highlights: ► We propose the new path integral formulation on star graph with N edges. ►U(N) family of boundary conditions is well-described by weight factors. ► The scale-invariant weight factor is given by N-dimensional unitary representation of Z2. ► Generalization to momentum dependent weight factors is briefly discussed.
Dragovich, Branko
2000-01-01
Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum mechanics.
Path Integral and the Induction Law
Barone, F. A.; Farina, C.
2005-01-01
We show how the induction law is correctly used in the path integral computation of the free particle propagator. The way this primary path integral example is treated in most textbooks is a little bit missleading.
Path integral measure factorization in path integrals for diffusion of Yang--Mills fields
Storchak, S. N.
2007-01-01
Factorization of the (formal) path integral measure in a Wiener path integrals for Yang--Mills diffusion is studied. Using the nonlinear filtering stochastic differential equation, we perform the transformation of the path integral defined on a total space of the Yang--Mills principal fiber bundle and come to the reduced path integral on a Coulomb gauge surface. Integral relation between the path integral representing the "quantum" evolution given on the original manifold of Yang--Mills field...
Perturbative Methods in Path Integration
Johnson-Freyd, Theodore Paul
This dissertation addresses a number of related questions concerning perturbative "path" integrals. Perturbative methods are one of the few successful ways physicists have worked with (or even defined) these infinite-dimensional integrals, and it is important as mathematicians to check that they are correct. Chapter 0 provides a detailed introduction. We take a classical approach to path integrals in Chapter 1. Following standard arguments, we posit a Feynman-diagrammatic description of the asymptotics of the time-evolution operator for the quantum mechanics of a charged particle moving nonrelativistically through a curved manifold under the influence of an external electromagnetic field. We check that our sum of Feynman diagrams has all desired properties: it is coordinate-independent and well-defined without ultraviolet divergences, it satisfies the correct composition law, and it satisfies Schrodinger's equation thought of as a boundary-value problem in PDE. Path integrals in quantum mechanics and elsewhere in quantum field theory are almost always of the shape ∫ f es for some functions f (the "observable") and s (the "action"). In Chapter 2 we step back to analyze integrals of this type more generally. Integration by parts provides algebraic relations between the values of ∫ (-) es for different inputs, which can be packaged into a Batalin--Vilkovisky-type chain complex. Using some simple homological perturbation theory, we study the version of this complex that arises when f and s are taken to be polynomial functions, and power series are banished. We find that in such cases, the entire scheme-theoretic critical locus (complex points included) of s plays an important role, and that one can uniformly (but noncanonically) integrate out in a purely algebraic way the contributions to the integral from all "higher modes," reducing ∫ f es to an integral over the critical locus. This may help explain the presence of analytic continuation in questions like the
Timeless path integral for relativistic quantum mechanics
Chiou, Dah-Wei
2010-01-01
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all possible paths in the constraint surface specified by the (relativistic) Hamiltonian constraint, and each path contributes with a phase identical to the classical action divided by $\\hbar$. The timeless path integral manifests the timeless feature as it is compl...
Feynman Path Integrals Over Entangled States
Green, A.G.; Hooley, C. A.; 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 e...
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 correspo...
Path Integral Quantization of Spinning Superparticle
ELEGLA, H. A.; FARAHAT, N. I.
2008-01-01
The Hamilton-Jacobi formalism is used to discuss the path integral quantization of a spinning superparticle model. The equations of motion are obtained as total differential equations in many variables. The equations of motion are integrable, and the path integral is obtained as an integration over the canonical phase space coordinates.
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
Differential neural network configuration during human path integration
Directory of Open Access Journals (Sweden)
Aiden EGF Arnold
2014-04-01
Full Text Available Path integration is a fundamental skill for navigation in both humans and animals. Despite recent advances in unravelling the neural basis of path integration in animal models, relatively little is known about how path integration operates at a neural level in humans. Previous attempts to characterize the neural mechanisms used by humans to visually path integrate have suggested a central role of the hippocampus in allowing accurate performance, broadly resembling results from animal data. However, in recent years both the central role of the hippocampus and the perspective that animals and humans share similar neural mechanisms for path integration has come into question. The present study uses a data driven analysis to investigate the neural systems engaged during visual path integration in humans, allowing for an unbiased estimate of neural activity across the entire brain. Our results suggest that humans employ common task control, attention and spatial working memory systems across a frontoparietal network during path integration. However, individuals differed in how these systems are configured into functional networks. High performing individuals were found to more broadly express spatial working memory systems in prefrontal cortex, while low performing individuals engaged an allocentric memory system based primarily in the medial occipito-temporal region. These findings suggest that visual path integration in humans over short distances can operate through a spatial working memory system engaging primarily the prefrontal cortex and that the differential configuration of memory systems recruited by task control networks may help explain individual biases in spatial learning strategies.
Path integral evaluation of Dbrane amplitudes
Chaudhuri, Shyamoli
1999-01-01
We extend Polchinski's evaluation of the measure for the one-loop closed string path integral to open string tree amplitudes with boundaries and crosscaps embedded in Dbranes. We explain how the nonabelian limit of near-coincident Dbranes emerges in the path integral formalism. We give a careful path integral derivation of the cylinder amplitude including the modulus dependence of the volume of the conformal Killing group.
Continuous-Discrete Path Integral Filtering
Bhashyam Balaji
2008-01-01
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 F...
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
Path integral for inflationary perturbations
Prokopec, Tomislav; Rigopoulos, Gerasimos
2010-07-01
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 determine the interactions to arbitrary order. This approach does not require the explicit solution of the energy and momentum constraints, a novel feature which simplifies the determination of the interaction vertices. The constraints and the necessary imposition of gauge conditions is reflected in the appearance of various commuting and anticommuting auxiliary fields in the action. These auxiliary fields are not propagating physical degrees of freedom but need to be included in internal lines and loops in a diagrammatic expansion. To illustrate the formalism we discuss the tree-level three-point and four-point functions of the inflaton perturbations, reproducing the results already obtained by the methods used in the current literature. Loop calculations are left for future work.
Path Dependent Option Pricing: the path integral partial averaging method
Andrew Matacz
2000-01-01
In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computational burden placed on the subsequent numerical evaluation. For short-medium term options it leads to a general approximation formula that only requires the evaluation of a one d...
Path integrals with generalized Grassmann variables
Energy Technology Data Exchange (ETDEWEB)
Chaichian, M. [Helsinki Univ. (Finland). Dept. of Physics; Demichev, A.P.
1995-04-01
The path integral representations the evolution of q-oscillators with root of unity values of q-parameter is constructed using Bargmann-Fock representations with commuting and non-commuting variables, the differential calculi being q-deformed in both cases. For q{sup 2} = -1 a new form of Grassmann-like path integral is obtained. (author). 14 refs.
't Hooft's quantum determinism -- path integral viewpoint
Blasone, Massimo; Jizba, Petr; Kleinert, Hagen
2005-01-01
We present a path integral formulation of 't Hooft's derivation of quantum from classical physics. Our approach is based on two concepts: Faddeev-Jackiw's treatment of constrained systems and Gozzi's path integral formulation of classical mechanics. This treatment is compared with our earlier one [quant-ph/0409021] based on Dirac-Bergmann's method.
Path Integral for Relativistic Equations of Motion
Gosselin, Pierre; Polonyi, Janos
1997-01-01
A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic limit is briefly discussed from the point of view of the renormalization group.
Path integral representation for spin systens
Karchev, Naoum
2012-01-01
The present paper is a short review of different path integral representations of the partition function of quantum spin systems. To begin with, I consider coherent states for SU(2) algebra. Different parameterizations of the coherent states lead to different path integral representations. They all are unified within an U(1) gauge theory of quantum spin systems.
Path Integrals over Velocities in Quantum Mechanics
Gitman, D. M.; Shvartsman, Sh. M.
1993-01-01
Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals over velocities of space-time coordinates. In the representations the integration over velocities is not restricted by any boundary conditions; matrices, which have to be inverted in course of doing Gaussian integrals, do not contain any derivatives in time, ...
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.
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.)
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. PMID:26754972
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.
Covariant path integrals and black holes
Vendrell, F
1997-01-01
The thermal nature of the propagator in a collapsed black-hole spacetime is shown to follow from the non-trivial topology of the configuration space in tortoise coordinates by using the path integral formalism.
Numerical path integration with Coulomb potential
Myrheim, Jan
2003-01-01
A simple and efficient method for quantum Monte Carlo simulation is presented, based on discretization of the action in the path integral, and a Gaussian averaging of the potential, which works well e.g. with the Coulomb potential.
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.
Path Integral Formulation of Noncommutative Quantum Mechanics
Acatrinei, C S
2001-01-01
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic oscillator is calculated.
Path Integral Control and State Dependent Feedback
Thijssen, Sep; Kappen, H. J.
2014-01-01
In this paper we address the problem to compute state dependent feedback controls for path integral control problems. To this end we generalize the path integral control formula and utilize this to construct parameterized state dependent feedback controllers. In addition, we show a novel relation between control and importance sampling: better control, in terms of control cost, yields more efficient importance sampling, in terms of effective sample size. The optimal control provides a zero-va...
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.
Transformation of variables and integration measures in path integrals
International Nuclear Information System (INIS)
A specific transformation of variables in path integrals is studied in contrast with the so-called Nicolai mapping in the supersymmetry theory. Full bosonic and fermionic actions are reduced to free actions by this transformation. We derive some formulas, which are useful in evaluating path integrals. (author)
Path Integral for the Dirac Equation
Polonyi, Janos
1998-01-01
A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the spin and the chirality flips.
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.
Path Integrals in Noncommutative Quantum Mechanics
Dragovich, B; Dragovich, Branko; Rakic, Zoran
2003-01-01
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated. Our approach is based on the fact that a quantum-mechanical system with a noncommutative configuration space may be regarded as another effective system with commuting spatial coordinates. Since path integral for quadratic Lagrangians is exactly solvable and a general formula for probability amplitude exists, we restricted our research to this class of Lagrangians. We found general relation between quadratic Lagrangians in their commutative and noncommutative regimes. The corresponding noncommutative path integral is presented. This method is illustrated by two quantum-mechanical systems in the noncommutative plane: a particle in a constant field and a harmonic oscillator.
Path Integral Approach to Noncommutative Quantum Mechanics
Dragovich, B; Dragovich, Branko; Rakic, Zoran
2004-01-01
We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the another one with usual commutative coordinates and momenta. We found connection between quadratic classical Hamiltonians, as well as Lagrangians, in their commutative and noncommutative regimes. The general procedure to compute Feynman's path integral on this noncommutative phase space with quadratic Lagrangians (Hamiltonians) is presented. Using this approach, a particle in a constant field, ordinary and inverted harmonic oscillators are elaborated in detail.
Accurate pattern registration for integrated circuit tomography
Energy Technology Data Exchange (ETDEWEB)
Levine, Zachary H.; Grantham, Steven; Neogi, Suneeta; Frigo, Sean P.; McNulty, Ian; Retsch, Cornelia C.; Wang, Yuxin; Lucatorto, Thomas B.
2001-07-15
As part of an effort to develop high resolution microtomography for engineered structures, a two-level copper integrated circuit interconnect was imaged using 1.83 keV x rays at 14 angles employing a full-field Fresnel zone plate microscope. A major requirement for high resolution microtomography is the accurate registration of the reference axes in each of the many views needed for a reconstruction. A reconstruction with 100 nm resolution would require registration accuracy of 30 nm or better. This work demonstrates that even images that have strong interference fringes can be used to obtain accurate fiducials through the use of Radon transforms. We show that we are able to locate the coordinates of the rectilinear circuit patterns to 28 nm. The procedure is validated by agreement between an x-ray parallax measurement of 1.41{+-}0.17 {mu}m and a measurement of 1.58{+-}0.08 {mu}m from a scanning electron microscope image of a cross section.
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...
Transport path optimization algorithm based on fuzzy integrated weights
Hou, Yuan-Da; Xu, Xiao-Hao
2014-11-01
Natural disasters cause significant damage to roads, making route selection a complicated logistical problem. To overcome this complexity, we present a method of using a trapezoidal fuzzy number to select the optimal transport path. Using the given trapezoidal fuzzy edge coefficients, we calculate a fuzzy integrated matrix, and incorporate the fuzzy multi-weights into fuzzy integrated weights. The optimal path is determined by taking two sets of vertices and transforming undiscovered vertices into discoverable ones. Our experimental results show that the model is highly accurate, and requires only a few measurement data to confirm the optimal path. The model provides an effective, feasible, and convenient method to obtain weights for different road sections, and can be applied to road planning in intelligent transportation systems.
Path Integral Methods for Stochastic Differential Equations
Chow, Carson C.; Buice, Michael A.
2015-01-01
Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic and path integral methods to calculate moments of the probability density function of SDEs. The methods can be extended to high dimensional systems such as networks of coupled neurons and even deterministic systems with quenched disorder.
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.
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. PMID:26764662
Path integral evaluation of equilibrium isotope effects
Zimmermann, Tomas
2009-01-01
A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic approximation for vibrations or rigid rotor approximation for the rotations. In particular, zero point energy and anharmonicity effects are described correctly quantum mechanically. The approach is based on the thermodynamic integration with respect to the mass of isotopes and on the Feynman path integral representation of the partition function. An efficient estimator for the derivative of free energy is used whose statistical error is independent of the number of imaginary time slices in the path integral, speeding up calculations by a factor of 60 at 500 K. We describe the implementation of the methodology in the molecular dynamics package Amber 10. The method is tested on three [1,5] sigmatropic hydrogen shift reactions. Because of the computational expense, we use ab initio pote...
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.
Path integral Monte Carlo and the electron gas
Brown, Ethan W.
Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational
A taxonomy of integral reaction path analysis
Energy Technology Data Exchange (ETDEWEB)
Grcar, Joseph F.; Day, Marcus S.; Bell, John B.
2004-12-23
W. C. Gardiner observed that achieving understanding through combustion modeling is limited by the ability to recognize the implications of what has been computed and to draw conclusions about the elementary steps underlying the reaction mechanism. This difficulty can be overcome in part by making better use of reaction path analysis in the context of multidimensional flame simulations. Following a survey of current practice, an integral reaction flux is formulated in terms of conserved scalars that can be calculated in a fully automated way. Conditional analyses are then introduced, and a taxonomy for bidirectional path analysis is explored. Many examples illustrate the resulting path analysis and uncover some new results about nonpremixed methane-air laminar jets.
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...
Real-time accurate hand path tracking and joint trajectory planning for industrial robots(Ⅱ)
Institute of Scientific and Technical Information of China (English)
谭冠政; 胡生员
2002-01-01
Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Cartesian space mainly through increasing the number of knots on the path and the segments of the path. But, this method resulted in the heavier on-line computational burden for the robot controller. In this paper, aiming at this drawback, the authors propose a new kind of real-time accurate hand path tracking and joint trajectory planning method for robots. Through selecting some extra knots on the specified hand path by a certain rule, which enables the number of knots on each segment to increase from two to four, and through introducing a sinusoidal function and a cosinoidal function to the joint displacement equation of each segment, this method can raise the path tracking accuracy of robot′s hand greatly but does not increase the computational burden of robot controller markedly.
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
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.
Path-integral simulation of solids
Herrero, Carlos P.; Ramirez, Rafael
2014-01-01
The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practicaltechniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-...
Path Integral Quantization of Generalized Quantum Electrodynamics
Bufalo, Rodrigo; Pimentel, Bruto Max; Zambrano, German Enrique Ramos
2010-01-01
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the hamiltonian structure of system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an expl...
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.
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 in Holomorphic Representation without Gauge Fixation
Shabanov, Sergei V.
1996-01-01
A method of path integral construction without gauge fixing in the holomorphic representation is proposed for finite-dimensional gauge models. This path integral determines a manifestly gauge-invariant kernel of the evolution operator.
Real-Time Feynman Path Integral Realization of Instantons
Cherman, Aleksey
2014-01-01
In Euclidean path integrals, quantum mechanical tunneling amplitudes are associated with instanton configurations. We explain how tunneling amplitudes are encoded in real-time Feynman path integrals. The essential steps are borrowed from Picard-Lefschetz theory and resurgence theory.
Real-time accurate hand path tracking and joint trajectory planning for industrial robots(Ⅰ)
Institute of Scientific and Technical Information of China (English)
谭冠政; 梁丰; 王越超
2002-01-01
Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Car-tesian space mainly through increasing the number of knots on the path and the number of the path′s segments, which results in the heavier online computational burden for the robot controller. Aiming at overcoming this drawback, the authors propose a new kind of real-time accurate hand path tracking and joint trajectory planning method. Through selecting some extra knots on the specified hand path by a certain rule and introducing a sinusoidal function to the joint displacement equation of each segment, this method can greatly raise the path tracking accuracy of robot′s hand and does not change the number of the path′s segments. It also does not increase markedly the computational burden of robot controller. The result of simulation indicates that this method is very effective, and has important value in increasing the application of industrial robots.
Breakdown of the coherent state path integral: two simple examples
Wilson, Justin H.; Galitski, Victor
2010-01-01
We show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. As suggested by previous authors, we note that the problems do not arise in the time-discretized version of the path integral.
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 measure for first order and metric gravities
Aros, Rodrigo; Contreras, Mauricio; Zanelli, Jorge
2003-01-01
The equivalence between the path integrals for first order gravity and the standard torsion-free, metric gravity in 3+1 dimensions is analyzed. Starting with the path integral for first order gravity, the correct measure for the path integral of the metric theory is obtained.
Path integral quantization of Yang-Mills theory
Muslih, Sami I.
2000-01-01
Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's and Popov's method is not necessary if the canonical path integral formulation is used.
Path integration on the upper half-plane
International Nuclear Information System (INIS)
Feynman's path integral is considered on the Poincare upper half-plane. It is shown that the fundamental solution to the heat equation δf/δt = ΔHf can be expressed in terms of a path integral. A simple relation between the path integral and the Selberg trace formula is discussed briefly. (author)
A Key Event Path Analysis Approach for Integrated Systems
Jingjing Liao
2012-01-01
By studying the key event paths of probabilistic event structure graphs (PESGs), a key event path analysis approach for integrated system models is proposed. According to translation rules concluded from integrated system architecture descriptions, the corresponding PESGs are constructed from the colored Petri Net (CPN) models. Then the definitions of cycle event paths, sequence event paths, and key event paths are given. Whereafter based on the statistic results after the simulation of CPN m...
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.
Noncommutative Quantum Mechanics with Path Integral
Dragovich, B; Dragovich, Branko; Rakic, Zoran
2005-01-01
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment of the usual formalism. In particular, we found explicit connections between quadratic Hamiltonians and Lagrangians, in their commutative and noncommutative regimes. In the quantum case we give general procedure how to compute Feynman's path integral in this noncommutative phase space with quadratic Lagrangians (Hamiltonians). This approach is applied to a charged particle in the noncommutative plane exposed to constant homogeneous electric and magnetic fields.
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.
Path integral quantization of generalized quantum electrodynamics
International Nuclear Information System (INIS)
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green's functions and a discussion about the obtained results are presented.
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.
Path integral discussion for Smorodinsky-Winternitz potentials. Pt. 1
International Nuclear Information System (INIS)
Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimensional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integralformulation is not possible, we list in all soluble cases the path integral evaluations explicity in terms of the propagators and the spectral expansions into the wave-functions. (orig.)
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. PMID:27140973
Path integral approach to the quantum fidelity amplitude
2016-01-01
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. PMID:27140973
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.
Accurate Electromagnetic Modeling Methods for Integrated Circuits
Sheng, Z.
2010-01-01
The present development of modern integrated circuits (IC’s) is characterized by a number of critical factors that make their design and verification considerably more difficult than before. This dissertation addresses the important questions of modeling all electromagnetic behavior of features on t
Canonical formulation and path integral for local vacuum energy sequestering
Bufalo, R.; Klusoň, J.; Oksanen, M.
2016-01-01
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity...
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.
Multiloop string vertices from the path integral
Bochicchio, M.; Lerda, A.
1989-02-01
We derive the multiloop vertices for the bosonic string using path integral methods and establish a precise equivalence between the functional approach to string perturbation theory and the operator formalism on Riemann surfaces recently developed by various authors. One of us (A.L.) would like to thank P. Di Vecchia and S. Sciuto for helpful discussions and INFN, Sezione di Torino, for the kind hospitality extended to him during the completion of this work. The work of M.B. was partially supported by the National Science Foundation under Grant NSF-PHY85-07627. The work of A.L. was partially supported by the US Department of Energy under grant DE-AC02-76ER03069.
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.
Complexified Path Integrals, Exact Saddles, and Supersymmetry.
Behtash, Alireza; Dunne, Gerald V; Schäfer, Thomas; Sulejmanpasic, Tin; Ünsal, Mithat
2016-01-01
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular. This is in contrast to instanton solutions, which are real, smooth, and single valued. The multivaluedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to nonsupersymmetric theories. PMID:26799010
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.
Soft Modes Contribution into Path Integral
Belyaev, V M
1993-01-01
A method for nonperturbative path integral calculation is proposed. Quantum mechanics as a simplest example of a quantum field theory is considered. All modes are decomposed into hard (with frequencies $\\omega^2 >\\omega^2_0$) and soft (with frequencies $\\omega^2 <\\omega^2_0$) ones, $\\omega_0$ is a some parameter. Hard modes contribution is considered by weak coupling expansion. A low energy effective Lagrangian for soft modes is used. In the case of soft modes we apply a strong coupling expansion. To realize this expansion a special basis in functional space of trajectories is considered. A good convergency of proposed procedure in the case of potential $V(x)=\\lambda x^4$ is demonstrated. Ground state energy of the unharmonic oscillator is calculated.
Canonical path integral quantization of Einstein's gravitational field
Muslih, Sami I.
2000-01-01
The connection between the canonical and the path integral formulations of Einstein's gravitational field is discussed using the Hamilton - Jacobi method. Unlike conventional methods, it is shown that our path integral method leads to obtain the measure of integration with no $\\delta$- functions, no need to fix any gauge and so no ambiguous deteminants will appear.
Path Integral and Effective Hamiltonian in Loop Quantum Cosmology
Huang, Haiyun; Ma, Yongge; Qin, Li
2011-01-01
We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $k=0,+1,-1$ are considered. To construct the path integrals in the timeless framework, a multiple group-averaging approach is proposed. Meanwhile, since the transition amplitude in the deparameterized framework can be expressed in terms of group-averaging, the path integrals can be formulated for both deparameterized and timeless frameworks. T...
Path Integral Solution by Sum Over Perturbation Series
Lin, De-Hone
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 simpl...
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.
Path-integral simulation of solids.
Herrero, C P; Ramírez, R
2014-06-11
The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity. PMID:24810944
Path Integral Quantization for a Toroidal Phase Space
Bodmann, Bernhard G.; Klauder, John R.
1999-01-01
A Wiener-regularized path integral is presented as an alternative way to formulate Berezin-Toeplitz quantization on a toroidal phase space. Essential to the result is that this quantization prescription for the torus can be constructed as an induced representation from anti-Wick quantization on its covering space, the plane. When this construction is expressed in the form of a Wiener-regularized path integral, symmetrization prescriptions for the propagator emerge similar to earlier path-inte...
Path-Integration Computation of the Transport Properties of Nanoparticles
Douglas, Jack
2014-03-01
There is need for effective computational methods for calculating the transport properties of polymers and complex-shaped particle aggregates arising in materials science and biology as a foundation for rational material design and the design of well-defined measurements assessing the environmental impact of nanoparticles. We focus on the problem of calculating basic solution transport properties (translational diffusion coefficient, intrinsic viscosity) of isolated particles having essentially any geometry using a novel computational method involving path integration developed by Mansfield and Douglas. The basic concepts behind the method are described and the method is validated in cases where exact analytic, or at least highly accurate numerical estimates, are known for comparison. After defining and validating our method, some applications of the program are given to some non-trivial problems illustrating the use of the program for charactering such as nanoparticles with grafted DNA brush layers, DNA orgami, carbon nanotubes, etc. The path-integration method is evidently a powerful tool for computing basic transport properties of complex-shaped objects and should find wide application in polymer science, nanotechnological applications and biology.
On a path integral with a topological constraint
Khandekar, D.C.; Bhagwat, K.V.; Wiegel, F.W.
1988-01-01
We discuss a new method to evaluate a path integral with a topological constraint involving a point singularity in a plane. The path integration is performed explicitly in the universal covering space. Our method is an alternative to an earlier method of Inomata.
Space-time transformations in radial path integrals
International Nuclear Information System (INIS)
Nonlinear space-time transformations in the radial path integral are discussed. A transformation formula is derived, which relates the original path integral to the Green's function of a new quantum system with an effective potential containing an observable quantum correction proportional(h/2π)2. As an example the formula is applied to spherical Brownian motion. (orig.)
Yang-Mills theory and fermionic path integrals
Fujikawa, Kazuo
2016-01-01
The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In this brief review I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this review are mostly pedagogical except for a recent analysis of path integral bosonization.
Accurate stepping on a narrow path: mechanics, EMG, and motor cortex activity in the cat.
Farrell, Brad J; Bulgakova, Margarita A; Sirota, Mikhail G; Prilutsky, Boris I; Beloozerova, Irina N
2015-11-01
How do cats manage to walk so graciously on top of narrow fences or windowsills high above the ground while apparently exerting little effort? In this study we investigated cat full-body mechanics and the activity of limb muscles and motor cortex during walking along a narrow 5-cm path on the ground. We tested the hypotheses that during narrow walking 1) lateral stability would be lower because of the decreased base-of-support area and 2) the motor cortex activity would increase stride-related modulation because of imposed demands on lateral stability and paw placement accuracy. We measured medio-lateral and rostro-caudal dynamic stability derived from the extrapolated center of mass position with respect to the boundaries of the support area. We found that cats were statically stable in the frontal plane during both unconstrained and narrow-path walking. During narrow-path walking, cats walked slightly slower with more adducted limbs, produced smaller lateral forces by hindlimbs, and had elevated muscle activities. Of 174 neurons recorded in cortical layer V, 87% of forelimb-related neurons (from 114) and 90% of hindlimb-related neurons (from 60) had activities during narrow-path walking distinct from unconstrained walking: more often they had a higher mean discharge rate, lower depth of stride-related modulation, and/or longer period of activation during the stride. These activity changes appeared to contribute to control of accurate paw placement in the medio-lateral direction, the width of the stride, rather than to lateral stability control, as the stability demands on narrow-path and unconstrained walking were similar.
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.
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, 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
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, black holes and configuration space topology
Ortiz, M E
1999-01-01
A path integral derivation is given of a thermal propagator in a collapsing black-hole spacetime. The thermal nature of the propagator as seen by an inertial observer far from the black hole is understood in terms of homotopically non-trivial paths in the configuration space appropriate to tortoise coordinates.
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...
Complex Path Integrals and the Space of Theories
Ferrante, D D; Guralnik, Z; Pehlevan, C
2013-01-01
The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is related to certain Dp-branes and their properties, which can be further understood in terms of the "physical states" of another theory. We also look into representations of the Feynman Path Integral in terms of a Mellin-Barnes transform, bringing the singularity structure of the theory to the foreground. This implies that, as a sum over paths, we should consider more generic paths than just Brownian ones. Finally, we are able to study the Space of Theories through our examples in terms of their Quantum Phases and associated Stokes' Phenomena (wall-crossing).
Geometric Phase and Chiral Anomaly in Path Integral Formulation
Fujikawa, Kazuo
2007-01-01
All the geometric phases, adiabatic and non-adiabatic, are formulated in a unified manner in the second quantized path integral formulation. The exact hidden local symmetry inherent in the Schr\\"{o}dinger equation defines the holonomy. All the geometric phases are shown to be topologically trivial. The geometric phases are briefly compared to the chiral anomaly which is naturally formulated in the path integral.
Ab-initio path integral techniques for molecules
Shin, Daejin; Ho, Ming-Chak; Shumway, J.
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 s...
Canonical and path integral quantization of string cosmology models
Cavaglia, M; Ungarelli, C.
1999-01-01
We discuss the quantisation of a class of string cosmology models that are characterized by scale factor duality invariance. We compute the amplitudes for the full set of classically allowed and forbidden transitions by applying the reduce phase space and the path integral methods. We show that these approaches are consistent. The path integral calculation clarifies the meaning of the instanton-like behaviour of the transition amplitudes that has been first pointed out in previous investigati...
Efficient stochastic thermostatting of path integral molecular dynamics
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E.; Manolopoulos, David E.
2010-01-01
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...
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.
Path Integrals and Exotic Options:. Methods and Numerical Results
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
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.
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.
Path integration and the neural basis of the 'cognitive map'.
B.L. McNaughton; F.P. Battaglia; O. Jensen; E.I. Moser; M.B Moser
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
Canonical formulation and path integral for local vacuum energy sequestering
Bufalo, R; Oksanen, M
2016-01-01
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a BRST-exact formulation of the theory, which can be considered as a topological field theory.
Canonical formulation and path integral for local vacuum energy sequestering
Bufalo, R.; KlusoÅ, J.; Oksanen, M.
2016-08-01
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the Universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a Becchi-Rouet-Stora-Tyutin-exact formulation of the theory, which can be considered as a topological field theory.
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. PMID:26801023
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.
Transition probabilities for diffusion equations by means of path integrals
Goovaerts, Marc; DE SCHEPPER, Ann; Decamps, Marc
2002-01-01
In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible, leading to analytical expressions for the transition probabilities and for the maximum probability paths. A second part consists of the derivation of an analytical approximation for the transition probab...
Transition probabilities for diffusion equations by means of path integrals.
Goovaerts, Marc; De Schepper, A; Decamps, M.
2002-01-01
In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible, leading to analytical expressions for the transition probabilities and for the maximum probability paths. A second part consists of the derivation of an analytical approximation for the transition probab...
Converged Nuclear Quantum Statistics from Semi-Classical Path Integrals
Poltavskyi, Igor; Tkatchenko, Alexandre
2015-03-01
The quantum nature of nuclear motions plays a vital role in the structure, stability, and thermodynamics of molecular systems. The standard approach to take nuclear quantum effects (NQE) into account is the Feynman-Kac imaginary-time path-integral molecular dynamics (PIMD). Conventional PIMD simulations require exceedingly large number of classical subsystems (beads) to accurately capture NQE, resulting in considerable computational cost even at room temperature due to the rather high internal vibrational frequencies of many molecules of interest. We propose a novel parameter-free form for the PI partition function and estimators to calculate converged thermodynamic averages. Our approach requires the same ingredients as the conventional PIMD simulations, but decreases the number of required beads by roughly an order of magnitude. This greatly extends the applicability of ab initio PIMD for realistic molecular systems. The developed method has been applied to study the thermodynamics of N2, H2O, CO2, and C6H6 molecules. For all of the considered systems at room temperature, 4 to 8 beads are enough to recover the NQE contribution to the total energy within 2% of the fully converged quantum result.
High accurate interpolation of NURBS tool path for CNC machine tools
Liu, Qiang; Liu, Huan; Yuan, Songmei
2016-06-01
Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation. Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency.
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 to ...... the friction controlled slip of a structure on a foundation where the friction coefficient is modelled as a random variable. Exact results derived using the total probability theorem are compared to the ones obtained via path integration.......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 to...
Path integrals, BRST identities, and regularization schemes in nonstandard gauges
International Nuclear Information System (INIS)
The path integral of a gauge theory is studied in Coulomb-like gauges. The Christ-Lee terms of operator ordering are reproduced within the path integration framework. In the presence of fermions, a new operator term, in addition to that of Christ and Lee, is discovered. Such terms are found to be instrumental in restoring the invariance of the effective Lagrangian under a field-dependent gauge transformation, which underlies the BRST symmetry. A unitary regularization scheme which maintains manifest BRST symmetry and is free from energy divergences is proposed for a nonabelian gauge field
Recent developments in the path integral approach to anomalies
International Nuclear Information System (INIS)
After a brief summary of the path integral approach to anomalous identities, some of the recent developments in this approach are discussed. The topics discussed include (i) Construction of the effective action by means of the covariant current, (ii) Gauss law constraint in anomalous gauge theories, (iii) Path integral approach to anomalies in superconformal transformations, (iv) Conformal and ghost number anomalies in string theory in analogy with the instanton calculation, (v) Covariant local Lorentz anomaly and its connection with the mathematical construction of the consistent anomaly. (author)
Regularized path integrals and anomalies -- U(1) chiral gauge theory
Kopper, Christoph; Lévêque, Benjamin
2011-01-01
We analyse the origin of the Adler anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [1]. Here we analyse U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-p...
Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology
Institute of Scientific and Technical Information of China (English)
秦立; 邓果; 马永革
2012-01-01
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantizations inherit more features from full loop quantum gravity. The path integrals can be formulated in both timeless and deparameterized frameworks. It turns out that the effective Hamiltonians derived from the two different viewpoints are equivalent to each other. Moreover, the first-order modified Friedmann equations are derived and predict quantum bounces for contracting universe, which coincide with those obtained in canonical theory.
Path integral approach to non-relativistic electron charge transfer
International Nuclear Information System (INIS)
A path integral approach has been generalized for the non-relativistic electron charge transfer processes. The charge transfer - the capture of an electron by an ion passing another atom, or more generally the problem of rearrangement collisions - is formulated in terms of influence functionals. It has been shown that the electron charge transfer process can be treated either as an electron transition problem or as ion and atom elastic scattering in the effective potential field. The first-order Born approximation for the electron charge transfer reaction cross section has been reproduced to prove the adequacy of the path integral approach for this problem. (author)
Belof, Jonathan; Dubois, Jonathan
2013-06-01
Warm dense matter (WDM), the regime of degenerate and strongly coupled Coulomb systems, is of great interest due to it's importance in understanding astrophysical processes and high energy density laboratory experiments. Path Integral Monte Carlo (PIMC) presents a particularly attractive formalism for tackling outstanding questions in WDM, in that electron correlation can be calculated exactly, with the nuclear and electronic degrees of freedom on equal footing. Here we present an efficient means of solving the Feynman path integral numerically by variational optimization of a trial density matrix, a method originally proposed for simple potentials by Feynman and Kleinert, and we show that this formalism provides an accurate description of warm dense matter with a number of unique advantages over other PIMC approaches. An exchange interaction term is derived for the variationally optimized path, as well as a numerically efficient scheme for dealing with long-range electrostatics. Finally, we present results for the pair correlation functions and thermodynamic observables of the spin polarized electron gas, warm dense hydrogen and all-electron warm dense carbon within the presented VPT-PIMC formalism. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344.
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
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 invariants in abelian Chern–Simons theory
International Nuclear Information System (INIS)
We consider the U(1) Chern–Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin–Turaev surgery invariants
A discrete history of the Lorentzian path integral
Loll, R.
2006-01-01
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 solv
Closed form apporximations for diffusion densities: a path integral approach
M.J. Goovaerts; A. De Schepper; M. Decamps
2004-01-01
In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible, leadin
The Path-Integral Approach to Spontaneous Symmetry Breaking
Kessel, Marcel Theodorus Maria van
2008-01-01
We will investigate two models which exhibit SSB in the canonical approach: the N=1 and N=2 linear sigma model. In both models the Green's functions and the effective potential will be computed in the path-integral approach. We will demonstrate how we get different results than in the canonical approach.
Pricing Derivatives by Path Integral and Neural Networks
Montagna, G.; Morelli, M.; Nicrosini, O.; Amato, P; Farina, M
2002-01-01
Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, while a second algorithm makes use of a neural network parameterization of option prices. The accuracy of the two methods is established from comparisons with the results of the standard procedures used in quantitative finance.
A non-perturbative Lorentzian path integral for gravity
Ambjørn, J.; Jurkiewicz, J.; Loll, R.
2006-01-01
A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated action have a unique Wick rotation to the Euclidean sector. All s
Neural network learning dynamics in a path integral framework
Balakrishnan, J.
2003-01-01
A path-integral formalism is proposed for studying the dynamical evolution in time of patterns in an artificial neural network in the presence of noise. An effective cost function is constructed which determines the unique global minimum of the neural network system. The perturbative method discussed also provides a way for determining the storage capacity of the network.
Closed form approximations for diffusion densities: a path integral approach
M. Goovaerts; A. De Schepper; M. Decamps
2004-01-01
In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible, leadin
Numerical calculation of path integrals : The small-polaron model
Raedt, Hans De; Lagendijk, Ad
1983-01-01
The thermodynamic properties of the small-polaron model are studied by means of a discrete version of the Feynman path-integral representation of the partition function. This lattice model describes a fermion interacting with a boson field. The bosons are treated analytically, the fermion contributi
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...
Quantum tunneling splittings from path-integral molecular dynamics.
Mátyus, Edit; Wales, David J; Althorpe, Stuart C
2016-03-21
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. PMID:27004863
Path Integral Quantization of Landau-Ginzburg Theory
Eshraim, Walaa I
2013-01-01
Hamilton-Jacobi approach for a constrained system is discussed. The equation of motion for a singular systems are obtained as total differential equations in many variables. The integrability conditions are investigated without using any gauge fixing condition. The path integral quantization for systems with finite degrees of freedom is applied to the field theories with constraints. The Landau-Ginzburg theory is investigated in details.
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. PMID:27498645
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.
Accurate object tracking system by integrating texture and depth cues
Chen, Ju-Chin; Lin, Yu-Hang
2016-03-01
A robust object tracking system that is invariant to object appearance variations and background clutter is proposed. Multiple instance learning with a boosting algorithm is applied to select discriminant texture information between the object and background data. Additionally, depth information, which is important to distinguish the object from a complicated background, is integrated. We propose two depth-based models that can compensate texture information to cope with both appearance variants and background clutter. Moreover, in order to reduce the risk of drifting problem increased for the textureless depth templates, an update mechanism is proposed to select more precise tracking results to avoid incorrect model updates. In the experiments, the robustness of the proposed system is evaluated and quantitative results are provided for performance analysis. Experimental results show that the proposed system can provide the best success rate and has more accurate tracking results than other well-known algorithms.
Kapania, Nitin R.; Gerdes, J. Christian
2015-12-01
This paper presents a feedback-feedforward steering controller that simultaneously maintains vehicle stability at the limits of handling while minimising lateral path tracking deviation. The design begins by considering the performance of a baseline controller with a lookahead feedback scheme and a feedforward algorithm based on a nonlinear vehicle handling diagram. While this initial design exhibits desirable stability properties at the limits of handling, the steady-state path deviation increases significantly at highway speeds. Results from both linear and nonlinear analyses indicate that lateral path tracking deviations are minimised when vehicle sideslip is held tangent to the desired path at all times. Analytical results show that directly incorporating this sideslip tangency condition into the steering feedback dramatically improves lateral path tracking, but at the expense of poor closed-loop stability margins. However, incorporating the desired sideslip behaviour into the feedforward loop creates a robust steering controller capable of accurate path tracking and oversteer correction at the physical limits of tyre friction. Experimental data collected from an Audi TTS test vehicle driving at the handling limits on a full length race circuit demonstrates the improved performance of the final controller design.
Gauge invariance of parametrized systems and path integral quantization
De Cicco, H; Cicco, Hernan De; Simeone, Claudio
1999-01-01
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The procedure is applied to the relativistic particle and toy universes, which are quantized by imposing canonical gauge conditions in the path integral; in the case of empty models, we first quantize the parametrized system called ``ideal clock'', and then we examine the possibility of obtaining the amplitude for the minisuperspaces by matching them with the ideal clock. The relation existing between the geometrical properties of the constraint surface and the variables identifying the quantum states in the path integral is discussed.
Gauge Invariance of Parametrized Systems and Path Integral Quantization
de Cicco, Hernán; Simeone, Claudio
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action functional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The procedure is applied to the relativistic particle and toy universes, which are quantized by imposing canonical gauge conditions in the path integral; in the case of empty models, we first quantize the parametrized system called "ideal clock," and then we examine the possibility of obtaining the amplitude for the minisuperspaces by matching them with the ideal clock. The relation existing between the geometrical properties of the constraint surface and the variables identifying the quantum states in the path integral is discussed.
Path integral Liouville dynamics for thermal equilibrium systems
International Nuclear Information System (INIS)
We show a new imaginary time path integral based method—path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics [J. Liu and W. H. Miller, J. Chem. Phys. 134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits
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.
Path Integral Monte Carlo Calculation of the Deuterium Hugoniot
International Nuclear Information System (INIS)
Restricted path integral Monte Carlo simulations have been used to calculate the equilibrium properties of deuterium for two densities: 0.674 and 0.838 g cm -3 (rs=2.00 and 1.86) in the temperature range of 105≤T≤106 K . We carefully assess size effects and dependence on the time step of the path integral. Further, we compare the results obtained with a free particle nodal restriction with those from a self-consistent variational principle, which includes interactions and bound states. By using the calculated internal energies and pressures, we determine the shock Hugoniot and compare with recent laser shock wave experiments as well as other theories. (c) 2000 The American Physical Society
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.
Regularized path integrals and anomalies -- U(1) axial gauge theory
Kopper, Christoph
2011-01-01
We analyse the origin of the Adler anomaly of axial U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [1]. Here we analyse U(1) axial gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor-Identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.
Regularized path integrals and anomalies: U(1) chiral gauge theory
International Nuclear Information System (INIS)
We analyze the origin of the Adler-Bell-Jackiw anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [Kopper, C. and Mueller, V. F., 'Renormalization of spontaneously broken SU(2) Yang-Mills theory with flow equations', Rev. Math. Phys. 21, 781 (2009)]. Here we analyze U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.
Formulation of fields in terms of path-integrals
Vatsya, S R
2014-01-01
Path-integral formulation of quantum mechanics defines the amplitude, or wavefunction, as a sum of the phase-factors over trajectories in a base manifold, which is taken here to be a general Riemannian space with trajectories parameterized by their arclengths. Generalized Klein-Gordon equation, deducible from the path-integral representation, provides the quantum mechanical description of a particle. Phase-factors are periodic functions of the classical action. Periodicity of the phase-factors with respect to action is shown in this article to impart corresponding periodicity to one parameter family of amplitudes generated by the translations of arclength. The translation parameter is also identified with arclength that can be adjoined to the base space to obtain an extended manifold, which is endowed with a Riemannian structure induced in it by trajectories in the base. Further, periodicity of the family of amplitudes with respect to the translation parameter together with the solutions of the Klein-Gordon e...
Dynamical Model and Path Integral Formalism for Hubbard Operators
Foussats, A.; Greco, A. (Anna); Zandron, O. S.
1998-01-01
In this paper, the possibility to construct a path integral formalism by using the Hubbard operators as field dynamical variables is investigated. By means of arguments coming from the Faddeev-Jackiw symplectic Lagrangian formalism as well as from the Hamiltonian Dirac method, it can be shown that it is not possible to define a classical dynamics consistent with the full algebra of the Hubbard $X$-operators. Moreover, from the Faddeev-Jackiw symplectic algorithm, and in order to satisfy the H...
Path Integral Solution for an Angle-Dependent Anharmonic Oscillator
Institute of Scientific and Technical Information of China (English)
S.Haouat
2012-01-01
We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we are able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.
Majorana and the path-integral approach to Quantum Mechanics
Esposito, S
2006-01-01
We give, for the first time, the English translation of a manuscript by Ettore Majorana, which probably corresponds to the text for a seminar delivered at the University of Naples in 1938, where he lectured on Theoretical Physics. Some passages reveal a physical interpretation of the Quantum Mechanics which anticipates of several years the Feynman approach in terms of path integrals, independently of the underlying mathematical formulation.
A Rigorous Path Integral Construction in any Dimension
Dynin, Alexander
1998-01-01
We propose a new rigorous time-slicing construction of the phase space Path Integrals for propagators both in Quantum Mechanics and Quantum Field Theory for a fairly general class of quantum observables (e.g. the Schroedinger hamiltonians with smooth scalar potentials of any power growth). Moreover we allow time-dependent hamiltonians and a great variety of discretizations, in particular, the standard, Weyl, and normal ones.
Quantum Brans-Dicke Gravity in Euclidean Path Integral Formulation
Kim, Hongsu
1997-01-01
The conformal structure of Brans-Dicke gravity action is carefully studied. It is discussed that Brans-Dicke gravity action has definitely no conformal invariance. It is shown, however, that this lack of conformal invariance enables us to demonstrate that Brans-Dicke theory appears to have a better short-distance behavior than Einstein gravity as far as Euclidean path integral formulation for quantum gravity is concerned.
Path-Integral Bosonization of Massive Gauged Thirring Model
Bufalo, R
2011-01-01
In this work the bosonization of two-dimensional massive gauged Thirring model in the path-integral framework is presented. After completing the bosonization prescription, by the fermionic mass expansion, we perform an analysis of the strong coupling regime of the model through the transition amplitude, regarding the intention of extending the previous result about the isomorphisms, at quantum level, of the massless gauged Thirring model to the massive case.
Path Integral Confined Dirac Fermions in a Constant Magnetic Field
Merdaci, Abdeldjalil; Jellal, Ahmed; CHETOUANI, Lyazid
2014-01-01
We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a symmetric global projection, which provides a symmetric form for the Green function. Based on this, we show that it is possible to end up with the propagator of the harmonic oscillator for one charged particle. After some transformations, we derive the nor...
A mathematical theory of the Feynman path integral for the generalized Pauli equations
Ichinose, Wataru
2007-01-01
The definitions of the Feynman path integral for the Pauli equation and more general equations in configuration space and in phase space are proposed, probably for the first time. Then it is proved rigorously that the Feynman path integrals are well-defined and are the solutions to the corresponding equations. These Feynman path integrals are defined by the time-slicing method through broken line paths, which is familiar in physics. Our definitions of these Feynman path integra...
Accurate Complex Systems Design: Integrating Serious Games with Petri Nets
Directory of Open Access Journals (Sweden)
Kirsten Sinclair
2016-03-01
Full Text Available Difficulty understanding the large number of interactions involved in complex systems makes their successful engineering a problem. Petri Nets are one graphical modelling technique used to describe and check proposed designs of complex systems thoroughly. While automatic analysis capabilities of Petri Nets are useful, their visual form is less so, particularly for communicating the design they represent. In engineering projects, this can lead to a gap in communications between people with different areas of expertise, negatively impacting achieving accurate designs.In contrast, although capable of representing a variety of real and imaginary objects effectively, behaviour of serious games can only be analysed manually through interactive simulation. This paper examines combining the complementary strengths of Petri Nets and serious games. The novel contribution of this work is a serious game prototype of a complex system design that has been checked thoroughly. Underpinned by Petri Net analysis, the serious game can be used as a high-level interface to communicate and refine the design.Improvement of a complex system design is demonstrated by applying the integration to a proof-of-concept case study.
A note on the path integral for systems with primary and secondary second class constraints
Henneaux, M.; Slavnov, S.
1994-01-01
It is shown that the phase space path integral for a system with arbitrary second class constraints (primary, secondary ...) can be rewritten as a configuration space path integral of the exponent of the Lagrangian action with some local measure.
On the Accurate Identification of Network Paths Having a Common Bottleneck
Directory of Open Access Journals (Sweden)
Muhammad Murtaza Yousaf
2013-01-01
Full Text Available We present a new mechanism for detecting shared bottlenecks between end-to-end paths in a network. Our mechanism, which only needs one-way delays from endpoints as an input, is based on the well-known linear algebraic approach: singular value decomposition (SVD. Clusters of flows which share a bottleneck are extracted from SVD results by applying an outlier detection method. Simulations with varying topologies and different network conditions show the high accuracy of our technique.
Grosche, C.; Pogosyan, G. S.; Sissakian, A. N.
1994-01-01
Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimen\\-sional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into t...
Path integral representation of the evolution operator for the Dirac equation
Lukyanenko, Alexander S.; Lukyanenko, Inna A.
2006-01-01
A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase space. This regularization allows to obtain a representation of the path integral over trajectories in the configuration space, i.e. in the Minkowsky space. This form of the path integral is useful for the formulation of perturbation theory in an external electr...
Path Integral by Space-time Slicing Approximation In Open Bosonic String Field
Ri, Am-Gil; Kim, Tae-Song; Ri, Chol-Man; Im, Song-Jin
2016-01-01
In our paper, we considered how to apply the traditional Feynman path integral to string field. By constructing the complete set in Fock space of non-relativistic and relativistic open bosonic string fields, we extended Feynman path integral to path integral on functional field and use it to quantize open bosonic string 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...
Neural dynamics for landmark orientation and angular path integration.
Seelig, Johannes D; Jayaraman, Vivek
2015-05-14
Many animals navigate using a combination of visual landmarks and path integration. In mammalian brains, head direction cells integrate these two streams of information by representing an animal's heading relative to landmarks, yet maintaining their directional tuning in darkness based on self-motion cues. Here we use two-photon calcium imaging in head-fixed Drosophila melanogaster walking on a ball in a virtual reality arena to demonstrate that landmark-based orientation and angular path integration are combined in the population responses of neurons whose dendrites tile the ellipsoid body, a toroidal structure in the centre of the fly brain. The neural population encodes the fly's azimuth relative to its environment, tracking visual landmarks when available and relying on self-motion cues in darkness. When both visual and self-motion cues are absent, a representation of the animal's orientation is maintained in this network through persistent activity, a potential substrate for short-term memory. Several features of the population dynamics of these neurons and their circular anatomical arrangement are suggestive of ring attractors, network structures that have been proposed to support the function of navigational brain circuits. PMID:25971509
A path-integral approach to the problem of time
Amaral, M M
2016-01-01
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing canonical treatments. In particular, a successful transition through a turning point is provided in the model system, together with a new definition of such a transition in general terms. Some of the results rely on a fruitful relation between the problem of time and general Gribov problems.
Quantum-classical interactions through the path integral
Metaxas, D
2006-01-01
I consider the case of two interacting scalar fields, \\phi and \\psi, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of motion for the classical field, which should be an improvement of the usual semi-classical procedure. As an application, I use this method in order to enforce Gauss's law as a classical equation in a non-abelian gauge theory, and derive the corresponding Feynman rules.
Quantum-classical interactions through the path integral
Metaxas, Dimitrios
2006-01-01
I consider the case of two interacting scalar fields, \\phi and \\psi, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of motion for the classical field, which should be an improvement of the usual semi-classical procedure. As an application I use this method in order to enforce Gauss's law as a classical equation in a non-abelian gauge theory. I argue that the theory is renorm...
International Nuclear Information System (INIS)
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
Liu, Jian; Zhang, Zhijun
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. PMID:26801034
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.
Dornheim, Tobias; Schoof, Tim; Groth, Simon; Filinov, Alexey; Bonitz, Michael
2015-11-28
The uniform electron gas (UEG) at finite temperature is of high current interest due to its key relevance for many applications including dense plasmas and laser excited solids. In particular, density functional theory heavily relies on accurate thermodynamic data for the UEG. Until recently, the only existing first-principle results had been obtained for N = 33 electrons with restricted path integral Monte Carlo (RPIMC), for low to moderate density, rs=r¯/aB≳1. These data have been complemented by configuration path integral Monte Carlo (CPIMC) simulations for rs ≤ 1 that substantially deviate from RPIMC towards smaller rs and low temperature. In this work, we present results from an independent third method-the recently developed permutation blocking path integral Monte Carlo (PB-PIMC) approach [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] which we extend to the UEG. Interestingly, PB-PIMC allows us to perform simulations over the entire density range down to half the Fermi temperature (θ = kBT/EF = 0.5) and, therefore, to compare our results to both aforementioned methods. While we find excellent agreement with CPIMC, where results are available, we observe deviations from RPIMC that are beyond the statistical errors and increase with density. PMID:26627944
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...
Regularized path integrals and anomalies: U(1) chiral gauge theory
Kopper, Christoph; Lévêque, Benjamin
2012-02-01
We analyze the origin of the Adler-Bell-Jackiw anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [Kopper, C. and Müller, V. F., "Renormalization of spontaneously broken SU(2) Yang-Mills theory with flow equations," Rev. Math. Phys. 21, 781 (2009)], 10.1142/S0129055X0900375X. Here we analyze U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.
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.
Path integrals for the Green-Schwarz superstring
International Nuclear Information System (INIS)
The goal of this dissertation is to develop path integral techniques for the evaluation of amplitudes for the Green-Schwarz superstring. The Green-Schwarz Lagrangian provides a manifestly supersymmetric alternative to the more widely used Neveu-Schwarz-Ramond Lagrangian. Until now, however, path integrals for the Green-Schwarz model have rarely been considered, primarily because of difficulties in gauge-fixing the local fermionic symmetry of the action. It is shown that these difficulties can be overcome for the heterotic string. As a consequence, the standard light cone gauge condition may be applied to the fermions, without necessarily imposing (singular) light cone gauge on the bosons. The resulting theory has no conformal or local Lorentz anomalies. The formalism is applied to the calculation of a number of amplitudes. Although fermionic light cone gauge is not Lorentz invariant, the three level propagator is shown to be invariant up to physically irrelevant phases, and to have the correct pole structure. A number of loop amplitudes are then calculated. It is demonstrated that as long as supersymmetry is unbroken, the vacuum energy vanishes to all orders in perturbation theory, and one- and two-particle S-matrix elements for massless particles receive no higher loop corrections. The one loop amplitude at finite temperature is also investigated; it gives the correct sum of free energies of string modes
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
Investigation of a ten-path ultrasonic flow meter for accurate feedwater measurements
Tawackolian, K.; Büker, O.; Hogendoorn, J.; Lederer, T.
2014-07-01
The flow instruments used in thermal power plants cannot be calibrated directly for the actual process conditions, since no traceable calibration facility with known uncertainty is available. A systematic investigation of the relevant influence parameters is therefore needed. It was found in earlier investigations that the dominant influences on the measurement uncertainty are the flow velocity profile and the temperature. In the present work, we report on our experimental study of the temperature and Reynolds number dependence of a new ten-path ultrasonic flow meter prototype. An improved measuring program is developed that allows for a systematic characterization. Special emphasis was placed on producing and validating well defined velocity profiles on a precision calibration flow rig. It was also for the first time intended and validated to generate fully developed Reynolds-similar velocity profiles for different temperatures so that the two main influence parameters, namely temperature and Reynolds number, can be clearly characterized separately. Since such ideal measurement conditions are not found in practical applications, the approach is also tested for a disturbed flow condition. A well defined disturbance is generated with a new flow disturber.
Keyword search over data service integration for accurate results
International Nuclear Information System (INIS)
Virtual Data Integration provides a coherent interface for querying heterogeneous data sources (e.g., web services, proprietary systems) with minimum upfront effort. Still, this requires its users to learn a new query language and to get acquainted with data organization which may pose problems even to proficient users. We present a keyword search system, which proposes a ranked list of structured queries along with their explanations. It operates mainly on the metadata, such as the constraints on inputs accepted by services. It was developed as an integral part of the CMS data discovery service, and is currently available as open source.
Keyword Search over Data Service Integration for Accurate Results
Zemleris, Vidmantas; Robert Gwadera
2013-01-01
Virtual data integration provides a coherent interface for querying heterogeneous data sources (e.g., web services, proprietary systems) with minimum upfront effort. Still, this requires its users to learn the query language and to get acquainted with data organization, which may pose problems even to proficient users. We present a keyword search system, which proposes a ranked list of structured queries along with their explanations. It operates mainly on the metadata, such as the constraints on inputs accepted by services. It was developed as an integral part of the CMS data discovery service, and is currently available as open source.
Keyword Search over Data Service Integration for Accurate Results
Zemleris, Vidmantas; Kuznetsov, Valentin; Gwadera, Robert
2014-06-01
Virtual Data Integration provides a coherent interface for querying heterogeneous data sources (e.g., web services, proprietary systems) with minimum upfront effort. Still, this requires its users to learn a new query language and to get acquainted with data organization which may pose problems even to proficient users. We present a keyword search system, which proposes a ranked list of structured queries along with their explanations. It operates mainly on the metadata, such as the constraints on inputs accepted by services. It was developed as an integral part of the CMS data discovery service, and is currently available as open source.
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...
Lee, Mi Kyung; Huo, Pengfei; Coker, David F
2016-05-27
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. PMID:27090842
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.
Accurate Kirkwood-Buff Integrals from Molecular Dynamics Simulations
DEFF Research Database (Denmark)
Wedberg, Nils Hejle Rasmus Ingemar; O'Connell, John P.; Peters, Günther H.J.;
2010-01-01
theoretical limiting behaviour on the corresponding direct correlation function. The method is evaluated for the pure Lennard-Jones and Stockmayer fluids. The results are verified by comparing pure fluid isothermal compressibilities obtained from the KB integrals with values from derivatives of equations of...
Spinor path integral Quantum Monte Carlo for fermions
Shin, Daejin; Yousif, Hosam; Shumway, John
2007-03-01
We have developed a continuous-space path integral method for spin 1/2 fermions with fixed-phase approximation. The internal spin degrees of freedom of each particle is represented by four extra dimensions. This effectively maps each spinor onto two of the excited states of a four dimensional harmonic oscillator. The phases that appear in the problem can be treated within the fixed-phase approximation. This mapping preserves rotational invariance and allows us to treat spin interactions and fermionic exchange on equal footing, which may lead to new theoretical insights. The technique is illustrated for a few simple models, including a spin in a magnetic field and interacting electrons in a quantum dot in a magnetic field at finite temperature. We will discuss possible extensions of the method to molecules and solids using variational and diffusion Quantum Monte Carlo.
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.
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 integral approach to electron scattering in classical electromagnetic potential
Chuang, Xu; Feng, Feng; Ying-Jun, Li
2016-05-01
As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374360, 11405266, and 11505285) and the National Basic Research Program of China (Grant No. 2013CBA01504).
Quantum-classical interactions through the path integral
Metaxas, Dimitrios
2007-03-01
I consider the case of two interacting scalar fields, ϕ and ψ, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of motion for the classical field which should be an improvement of the usual semiclassical procedure. As an application I use this method in order to enforce Gauss’s law as a classical equation in a non-Abelian gauge theory. I argue that the theory is renormalizable and equivalent to the usual Yang-Mills theory as far as the gauge field terms are concerned. There are additional terms in the effective action that depend on the Lagrange multiplier field λ that is used to enforce the constraint. These terms and their relation to the confining properties of the theory are discussed.
Path integral formalism for a simple interacting nucleon model
International Nuclear Information System (INIS)
The early onset of the baryon density in QCD simulations can be explained by the high flavour degeneracy when using staggered fermions. A simple interacting nucleon gas model had already shown that the gas condenses at very low chemical potential as in the lattice simulations at four flavours. In order to study more carefully the nucleon gas model in the condensation region we have developed the path integral formalism to treat the first quantization non perturbatively, describing the partition function for the interacting system of nucleons. First Monte Carlo results show good agreement with the lattice QCD simulations for the onset chemical potentials and saturation densities. The extrapolation to nature gives reasonable results. (orig.)
Path Integral Confined Dirac Fermions in a Constant Magnetic Field
Merdaci, Abdeldjalil; Chetouani, Lyazid
2014-01-01
We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a symmetric global projection, which provides a symmetric form for the Green function. Based on this, we show that it is possible to end up with the propagator of the harmonic oscillator for one charged particle. After some transformations, we derive the normalized wave functions and the eigenvalues in terms of different physical parameters and quantum numbers. By interchanging quantum numbers, we show that our solutions possed interesting properties. The density of current and the non-relativistic limit are analyzed where different conclusions are obtained.
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.
A Rigorous Path Integral for Supersymmetric Quantum Mechanics and the Heat Kernel
Fine, Dana; Sawin, Stephen
2007-01-01
In a rigorous construction of the path integral for supersymmetric quantum mechanics on a Riemann manifold, based on B\\"ar and Pf\\"affle's use of piecewise geodesic paths, the kernel of the time evolution operator is the heat kernel for the Laplacian on forms. The path integral is approximated by the integral of a form on the space of piecewise geodesic paths which is the pullback by a natural section of Mathai and Quillen's Thom form of a bundle over this space. In the case of closed paths, ...
An Integrative Approach to Accurate Vehicle Logo Detection
Directory of Open Access Journals (Sweden)
Hao Pan
2013-01-01
required for many applications in intelligent transportation systems and automatic surveillance. The task is challenging considering the small target of logos and the wide range of variability in shape, color, and illumination. A fast and reliable vehicle logo detection approach is proposed following visual attention mechanism from the human vision. Two prelogo detection steps, that is, vehicle region detection and a small RoI segmentation, rapidly focalize a small logo target. An enhanced Adaboost algorithm, together with two types of features of Haar and HOG, is proposed to detect vehicles. An RoI that covers logos is segmented based on our prior knowledge about the logos’ position relative to license plates, which can be accurately localized from frontal vehicle images. A two-stage cascade classier proceeds with the segmented RoI, using a hybrid of Gentle Adaboost and Support Vector Machine (SVM, resulting in precise logo positioning. Extensive experiments were conducted to verify the efficiency of the proposed scheme.
Gauge Independence of the Lagrangian Path Integral in a Higher-Order Formalism
Batalin, I. A.; Bering, K.; Damgaard, P. H.
1996-01-01
We propose a Lagrangian path integral based on gauge symmetries generated by a symmetric higher-order $\\Delta$-operator, and demonstrate that this path integral is independent of the chosen gauge-fixing function. No explicit change of variables in the functional integral is required to show this.
Path Integration Working Memory for Multi Task Dead Reckoning and Visual Navigation
Hasson, Cyril; Gaussier, Philippe
2010-01-01
International audience Biologically inspired models for navigation use mechanisms like path integration or sensori-motor learning. This paper describes the use of a proprioceptive working memory to give path integration the potential to store several goals. Then we coupled the path integration working memory to place cell sensori-motor learning to test the potential autonomy this gives to the robot. This navigation architecture intends to combine the benefits of both strategies in order to...
Fresneda, R.; Gitman, D.
2007-01-01
Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman 1993 of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for ...
Spin in the path integral: anti-commuting versus commuting variables
Scholtz, F. G.; Theron, A. N.; Geyer, H. B.
1994-01-01
We discuss the equivalence between the path integral representations of spin dynamics for anti-commuting (Grassmann) and commuting variables and establish a bosonization dictionary for both generators of spin and single fermion operators. The content of this construction in terms of the representations of the spin algebra is discussed in the path integral setting. Finally it is shown how a `free field realization' (Dyson mapping) can be constructed in the path integral.
Path Integral Quantization of the Symplectic Leaves of the SU(2)* Poisson-Lie Group
Morariu, Bogdan
1997-01-01
The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_q(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parametrizations and also compare the results with the path integral quantization of spin.
Path integrals of spin- J systems in the holomorphic representation
Vieira, V. R.; Sacramento, P. D.
1995-02-01
A path integral expression for the matrix element and the diagonal representative of the spin- J evolution operator or Boltzmann factor is obtained using Bloch coherent states in the holomorphic representation, yielding the appropriate boundary conditions. Quantum Dyson-Schwinger equations of motion are derived and used as criteria to select the appropriate action. In the case of the diagonal representative the equations of motion satisfy the commutation relations of the spin operators and are the classical limit of the Dyson-Schwinger equations, if we redefine the Lagrangian together with the integration measure. It is shown that in the case of a spin in a time-independent magnetic field the saddle-point approximation for both representatives gives the exact results. We present analytical algorithms to obtain the exponential factor and the prefactor in the saddle-point expansion, without an ad hoc reduction to an effective one-dimensional problem, but keeping instead a 2 × 2 matrix structure. We apply our results to several models.
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.
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 .
Quantum Thermal Bath for Path Integral Molecular Dynamics Simulation.
Brieuc, Fabien; Dammak, Hichem; Hayoun, Marc
2016-03-01
The quantum thermal bath (QTB) method has been recently developed to account for the quantum nature of the nuclei by using standard molecular dynamics (MD) simulation. QTB-MD is an efficient but approximate method when dealing with strongly anharmonic systems, while path integral molecular dynamics (PIMD) gives exact results but in a huge amount of computation time. The QTB and PIMD methods have been combined in order to improve the PIMD convergence or correct the failures of the QTB-MD technique. Therefore, a new power spectral density of the random force within the QTB has been developed. A modified centroid-virial estimator of the kinetic energy, especially adapted to QTB-PIMD, has also been proposed. The method is applied to selected systems: a one-dimensional double-well system, a ferroelectric phase transition, and the position distribution of an hydrogen atom in a fuel cell material. The advantage of the QTB-PIMD method is its ability to give exact results with a more reasonable computation time for strongly anharmonic systems. PMID:26799437
Thermal dissociation of dipositronium: path integral Monte Carlo approach
Kylänpää, Ilkka
2009-01-01
Path integral Monte Carlo simulation of the dipositronium "molecule" Ps$_2$ reveals its surprising thermal instability. Although, the binding energy is $\\sim 0.4$ eV, due to the strong temperature dependence of its free energy Ps$_2$ dissociates, or does not form, above $\\sim 1000$ K, except for high densities where a small fraction of molecules are in equilibrium with Ps atoms. This prediction is consistent with the recently reported first observation of stable Ps$_2$ molecules by Cassidy & Mills Jr., Nature {\\bf 449}, 195 (07), and Phys.Rev.Lett. {\\bf 100}, 013401 (08); at temperatures below 1000 K. The relatively sharp transition from molecular to atomic equilibrium, that we find, remains to be experimentally verified. To shed light on the origin of the large entropy factor in free energy we analyze the nature of interatomic interactions of these strongly correlated quantum particles. The conventional diatomic potential curve is given by the van der Waals interaction at large distances, but due to the ...
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.
The path integral representation kernel of evolution operator in Merton-Garman model
Directory of Open Access Journals (Sweden)
V.S. Yanishevsky
2011-06-01
Full Text Available 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 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.
Spin Path Integral And Quantum Mechanics In Rotating Reference of Frame
Chern, Tong; Ning, Wu; Yue, YU
2011-01-01
We developed a path integral formalism for the quantum mechanics in a rotating reference of frame, and proposed a spin path integral description for the spin degrees of freedom in it. We have also give some examples for the applications of our foramlism.
The Brown-Henneaux's central charge from the path-integral boundary condition
Terashima, Hiroaki
2000-01-01
We derive Brown-Henneaux's commutation relation and central charge in the framework of the path integral. If we use the leading part of the asymptotic symmetry to derive the Ward-Takahashi identity, we can see the central charge arises from the fact that the boundary condition of the path integral is not invariant under the transformation.
A Phase Space Path Integral for (2+1)-Dimensional Gravity
Carlip, Steven
1995-01-01
I investigate the relationship between the phase space path integral in (2+1)-dimensional gravity and the canonical quantization of the corresponding reduced phase space in the York time slicing. I demonstrate the equivalence of these two approaches, and discuss some subtleties in the definition of the path integral necessary to prove this equivalence.
Path Integral Evaluation of a Time-Dependent Oscillator in an External Field
Ikot, Akpan Ndem; ITUEN, Eno Etim; ESSIEN, Ime. E.
2008-01-01
The Lagrangian of a system describing the dynamical behaviour of a time-dependent harmonic oscillator is modified and then used to evaluate the Feynman path integral of the oscillator. The path integral of the time-dependent oscillator is shown to reduce to the time-independent within certain limits.
Poisson-Lie T-Duality: the Path-Integral Derivation
Tyurin, Eugene; von Unge, Rikard
1995-01-01
We formulate Poisson-Lie T-duality in a path-integral manner that allows us to analyze the quantum corrections. Using the path-integral, we rederive the most general form of a Poisson-Lie dualizeable background and the generalized Buscher transformation rules it has to satisfy.
The path integral representation kernel of evolution operator in Merton-Garman model
V. S. Yanishevsky; L. F. Blazhyevskyi
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 Solution of PT-/non-PT-Symmetric and non-Hermitian Hulthen Potential
N. Kandirmaz; Sever, R.
2011-01-01
The wave functions and the energy spectrum of PT-/non-PT-Symmetric and non-Hermitian Hulthen potential are of an exponential type and are obtained via the path integral. The path integral is constructed using parametric time and point transformation.
Path Integral Approach to 't Hooft's Derivation of Quantum from Classical Physics
Blasone, Massimo; Jizba, Petr; Kleinert, Hagen
2004-01-01
We present a path-integral formulation of 't Hooft's derivation of quantum from classical physics. The crucial ingredient of this formulation is Gozzi et al.'s supersymmetric path integral of classical mechanics. We quantize explicitly two simple classical systems: the planar mathematical pendulum and the Roessler dynamical system.
Path Integral and Solutions of the Constraint Equations: The Case of Reducible Gauge Theories
Ferraro, R.; Henneaux, M.; 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.
Path integral approach to eikonal and next-to-eikonal exponentiation
Laenen, E.L.M.P.; Stavenga, G.C.; 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
Coherent-state path-integral approach for constrained fermion systems
Junker, Georg; Klauder, John R.
1998-01-01
The coherent-state path-integral representation for the propagator of fermionic systems subjected to first-class constraints is constructed. As in the bosonic case the importance of path-integral measures for Lagrange multipliers is emphasized. One example is discussed in some detail.
A Hamiltonian Path Integral for a Degenerate Parabolic Pseudo-Differential Operator
KUMANO-GO, Naoto
1996-01-01
The symbol of the fundamental solution for a degenerate parabolic pseudo-differential operator of order $m\\,(>0)$ can be described in terms of a Hamiltonian path integral. This Hamiltonian path integral converges in the topology of the symbol class $\\Sn$ and in the weak topology of the symbol class $\\So$.
Path Integral Approach to Two-Dimensional QCD in the Light-Front
Gaete, P.; Gamboa, J.; Schmidt, I
1993-01-01
Two-dimensional quantum cromodynamics 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 analyzing directly the constraints in the path integral.
Two-Dimensional Bosonization from Variable Shifts in the Path Integral
Thomassen, Jan B.
1998-01-01
A method to perform bosonization of a fermionic theory in (1+1) dimensions in a path integral framework is developed. The method relies exclusively on the path integral property of allowing variable shifts, and does not depend on the explicit form of Greens functions. Two examples, the Schwinger model and the massless Thirring model, are worked out.
Numerical evaluation of coherent-state path integrals with applications to time-dependent problems
Burghardt, Bernd; Stolze, Joachim
1999-01-01
We study the application of the coherent-state path integral as a numerical tool for wave-packet propagation. The numerical evaluation of path integrals is reduced to a matrix-vector multiplication scheme. Together with a split-operator technique we apply our method to a time-dependent double-well potential.
An Abelian Model of Gravity and Canonical Quantization by Means of Path Integrals
Bracken, Paul
An Abelian model of gravity is introduced and its constraint structure is obtained. The main task is to show that the model with constraints can be canonically quantized by means of the canonical path integral formalism using the Faddeev-Popov approach. It is shown how the path integral can be simplified by carrying out the integrals over those variables for which the integrals can be computed.
On the coordinate (in)dependence of the formal path integral
Johnson-Freyd, Theo
2010-01-01
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. 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 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.
Institute of Scientific and Technical Information of China (English)
Ting-gui JIA; Shu-gang WANG; Guo-na QU; Jian LIU
2013-01-01
Ventilation characteristic parameters are the base of ventilation network solution; however,they are apt to be affected by operating errors,reading errors,airflow stability,and other factors,and it is difficult to obtain accurate results.In order to check the ventilation characteristic parameters of mines more accurately,the integrated method of circuit and path is adopted to overcome the drawbacks caused by the traditional path method or circuit method in the digital debugging process of ventilation system,which can improve the large local error or the inconsistency between the airflow direction and the actual situation caused by inaccuracy of the ventilation characteristic parameters or checking in the ventilation network solution.The results show that this method can effectively reduce the local error and prevent the pseudo-airflow reversal phenomenon; in addition,the solution results are consistent with the actual situation of mines,and the effect is obvious.
Atmospheric Refraction Path Integrals in Ground-Based Interferometry
Mathar, Richard 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 transl...
Feynman path integrals - from the prodistribution definition to the calculation of glory scattering
International Nuclear Information System (INIS)
In these lectures I present a path integral calculation, starting from a global definition of Feynman path integrals and ending at a scattering cross section formula. Along the way I discuss some basic issues which had to be resolved to exploit the computational power of the proposed definition of Feynman integrals. I propose to compute the glory scattering of gravitational waves by black holes. (orig./HSI)
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 construct path integrals when one can't find the hamiltonian because t...
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.
Wong, Kin-Yiu; Xu, Yuqing; Xu, Liang
2015-11-01
-transphosphorylation. For all these applications, we used our recently-developed path-integral method based on the KP theory, called automated integration-free path-integral (AIF-PI) method, to perform ab initio path-integral calculations of isotope effects. As opposed to the conventional path-integral molecular dynamics (PIMD) and Monte Carlo (PIMC) simulations, values calculated from our AIF-PI path-integral method can be as precise as (not as accurate as) the numerical precision of the computing machine. Lastly, comments are made on the general challenges in theoretical modeling of candidates matching the experimental "fingerprints" of RLTS. This article is part of a Special Issue entitled: Enzyme Transition States from Theory and Experiment.
Fresneda, R
2007-01-01
Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman 1993 of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.
Path integrals in quantum mechanics, statistics, polymer physics, and financial markets
Kleinert, Hagen
2009-01-01
This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying p
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.
A path integral for the master constraint of loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Han Muxin, E-mail: mhan@aei.mpg.d [MPI fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Potsdam (Germany); Institut fuer Theoretische Physik III, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, 91058 Erlangen (Germany)
2010-11-07
In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint program. The physical inner product is expressed by using the group averaging technique for a single self-adjoint master constraint operator. By the standard technique of skeletonization and the coherent state path integral, we derive a path-integral formula from the group averaging for the master constraint operator. Our derivation in this paper suggests there exists a direct link connecting the canonical loop quantum gravity with a path-integral quantization or a spin-foam model of general relativity.
Liu, Meilin
2011-07-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.
M.E. Ortiz; Vendrell, F.
1997-01-01
A quantum mechanical path integral derivation is given of a thermal propagator in non-static Gui spacetime. The thermal nature of the propagator is understood in terms of homotopically non-trivial paths in the configuration space appropriate to tortoise coordinates. The connection to thermal emission from collapsing black holes is discussed.
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.…
Establishing path integral in the entangled state representation for Hamiltonians in quantum optics
Institute of Scientific and Technical Information of China (English)
Wang Ji-Suo; Meng Xiang-Guo; Feng Jian; Gao Yun-Feng
2007-01-01
Based on two mutually conjugate entangled state representations, we establish the path integral formalism for some Hamiltonians of quantum optics in entangled state representations. The Wigner operator in the entangled state representation is presented. Its advantages are explained.
A brief view of known landmarks reorientates path integration in hamsters
Etienne, A. S.; Boulens, V.; Maurer, R.; Rowe, T.; Siegrist, C.
In darkness, hamsters commute between their nest and a feeding site through path integration only, and therefore show cumulative errors in the return direction to the nest. We examined whether a brief presentation of familiar room cues could reset the path integrator. The hamsters could see the room cues either during, or at the end of, the outward journey to the food place, in a conflict situation where motion cues and visual information were set at variance. In both conditions, the animals used mainly visual information to return home. Thus, hamsters can determine their azimuth, and possibly their location, through a visual fix, and can reset their path integrator through the fix. This allows them to update their position during further locomotion in the dark and thus to compute a correct homing vector with respect to a visually induced reference frame. Taking episodic positional fixes may greatly enhance the functional value of path integration.
Path Integral Quantization of the Chiral Schwinger Model in Bosonized Form
Bracken, Paul
The development of the Wess-Zumino action or one-cycle is reviewed from the path integral approach. This is related to the occurrence of anomalies in the theory, and generally signifies a breakdown of gauge invariance. The Jackiw-Rajaraman version of the chiral Schwinger model is studied by means of path integrals. It is shown how the model can be made gauge invariant by using a Wess-Zumino term to write a gauge invariant Lagrangian. The model is considered only in bosonized form without any reference to fermions. The constraints are determined. These components are then used to write a path integral quantization for the bosonized form of the model. Some physical quantities and information, in particular, propagators are derived from the path integral.
Deciphering the hippocampal polyglot: the hippocampus as a path integration system.
McNaughton, B L; Barnes, C A; Gerrard, J L; Gothard, K; Jung, M W; Knierim, J J; Kudrimoti, H; Qin, Y; Skaggs, W E; Suster, M; Weaver, K L
1996-01-01
Hippocampal 'place' cells and the head-direction cells of the dorsal presubiculum and related neocortical and thalamic areas appear to be part of a preconfigured network that generates an abstract internal representation of two-dimensional space whose metric is self-motion. It appears that viewpoint-specific visual information (e.g. landmarks) becomes secondarily bound to this structure by associative learning. These associations between landmarks and the preconfigured path integrator serve to set the origin for path integration and to correct for cumulative error. In the absence of familiar landmarks, or in darkness without a prior spatial reference, the system appears to adopt an initial reference for path integration independently of external cues. A hypothesis of how the path integration system may operate at the neuronal level is proposed. PMID:8576689
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.
Path Integral Evaluation of the Free Propagator on the (D-1)-dimensional Pseudosphere
Wospakrik, Hans J.
1999-01-01
We present an explicit path integral evaluation of the free Hamiltonian propagator on the (D-1)-dimensional pseudosphere, in the horicyclic coordinates, using the integral equation method. This method consists in deriving an integral equation for the propagator that turns out to be of Abel's type.
LaChapelle, J.
2004-01-01
A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schr\\"{o}dinger/diffusion equation in unbounded space. ...
On the coordinate (in)dependence of the formal path integral
Johnson-Freyd, Theo
2010-01-01
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. 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" o...
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. PMID:27238897
International Nuclear Information System (INIS)
A common practical problem in applied science is the nonlinear filtering problem, i.e., the estimation of the state that evolves according to a Langevin equation, given the samples of a related Langevin equation. In this paper, this problem is formulated and solved using statistical mechanics methods and Feynman path integrals. The proposed path integral solution makes it possible to solve challenging higher-dimensional nonlinear filtering problems in real time
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.
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
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.
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.
Comment on 'Path integral solution for a Mie-type potential'
International Nuclear Information System (INIS)
We comment on several incorrect results given in a recent paper by Erkoc and Sever (ES). In particular, it is pointed out that their path integral formula for the one-dimensional Mie-Lennard-Jones potential is wrong, since a quantum correction proportional to (h/2π)2 - which is a consequence of the stochastic nature of the Feynman paths - has been overlooked. The correct expression can be obtained from a general path integral formula, which we have derived in a previous paper. For the particular potential discussed in detail by ES, we give a complete path integral treatment, which allows us to derive the energies and normalized wave functions of the discrete spectrum. (orig.)
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.
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.
International Nuclear Information System (INIS)
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
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...
Barnett-Cowan, Michael; Meilinger, Tobias; Vidal, Manuel; Teufel, Harald; Bülthoff, Heinrich H
2012-01-01
Path integration is a process in which self-motion is integrated over time to obtain an estimate of one's current position relative to a starting point (1). Humans can do path integration based exclusively on visual (2-3), auditory (4), or inertial cues (5). However, with multiple cues present, inertial cues - particularly kinaesthetic - seem to dominate (6-7). In the absence of vision, humans tend to overestimate short distances (physical space therefore does not seem to be accurately represented by the brain. Extensive work has been done on evaluating path integration in the horizontal plane, but little is known about vertical movement (see (3) for virtual movement from vision alone). One reason for this is that traditional motion simulators have a small range of motion restricted mainly to the horizontal plane. Here we take advantage of a motion simulator (8-9) with a large range of motion to assess whether path integration is similar between horizontal and vertical planes. The relative contributions of inertial and visual cues for path navigation were also assessed. 16 observers sat upright in a seat mounted to the flange of a modified KUKA anthropomorphic robot arm. Sensory information was manipulated by providing visual (optic flow, limited lifetime star field), vestibular-kinaesthetic (passive self motion with eyes closed), or visual and vestibular-kinaesthetic motion cues. Movement trajectories in the horizontal, sagittal and frontal planes consisted of two segment lengths (1st: 0.4 m, 2nd: 1 m; ±0.24 m/s(2) peak acceleration). The angle of the two segments was either 45° or 90°. Observers pointed back to their origin by moving an arrow that was superimposed on an avatar presented on the screen. Observers were more likely to underestimate angle size for movement in the horizontal plane compared to the vertical planes. In the frontal plane observers were more likely to overestimate angle size while there was no such bias in the sagittal plane. Finally
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.
Lunev, F. A.
1996-01-01
Simple bosonic path integral representation for path ordered exponent is derived. This representation is used, at first, to obtain new variant of non-Abelian Stokes theorem. Then new pure bosonic worldline path integral representations for fermionic determinant and Green functions are presented. Finally, applying stationary phase method, we get quasiclassical equations of motion in QCD.
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.
Multigrid solution of a path integral formulation for the hydrogen atom
Bai, D
2004-01-01
An efficient multigrid Monte-Carlo algorithm for calculating the ground state of the hydrogen atom using path integral is presented. The algorithm uses a unigrid approach. The action integral near r=0 is modified so that the correct values of observables are obtained. It is demonstrated that the critical slow down (CSD) is eliminated. Finally, the algorithm is compared to the staging algorithm.
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.
Wang, Yi
2016-07-21
Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.
Generation of accurate integral surfaces in time-dependent vector fields.
Garth, Christoph; Krishnan, Han; Tricoche, Xavier; Bobach, Tom; Joy, Kenneth I
2008-01-01
We present a novel approach for the direct computation of integral surfaces in time-dependent vector fields. As opposed to previous work, which we analyze in detail, our approach is based on a separation of integral surface computation into two stages: surface approximation and generation of a graphical representation. This allows us to overcome several limitations of existing techniques. We first describe an algorithm for surface integration that approximates a series of time lines using iterative refinement and computes a skeleton of the integral surface. In a second step, we generate a well-conditioned triangulation. Our approach allows a highly accurate treatment of very large time-varying vector fields in an efficient, streaming fashion. We examine the properties of the presented methods on several example datasets and perform a numerical study of its correctness and accuracy. Finally, we investigate some visualization aspects of integral surfaces. PMID:18988990
Pitfalls of Path Integrals: Amplitudes for Spacetime Regions and the Quantum Zeno Effect
Halliwell, J J
2012-01-01
Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time. We argue that there is, however, under very general conditions, a significant complication in such constructions. This is the fact that the concrete implementation of the restrictions on paths over an interval of time corresponds, in an operator language, to sharp monitoring at every moment of time in the given time interval. Such processes suffer from the quantum Zeno effect -- the continual monitoring of a quantum system in a Hilbert subspace prevents its state from leaving that subspace. As a consequence, path integral amplitudes defined in this seemingly obvious way have physically and intuitively unreasonable properties...
Path integral in area tensor Regge calculus and complex connections
International Nuclear Information System (INIS)
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
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.
Path integral approach to Asian options in the Black-Scholes model
Devreese, Jeroen P. A.; Damiaan Lemmens; Jacques Tempere
2009-01-01
We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is app...
Path integral approach to Asian options in the Black-Scholes model
Devreese, J. P. A.; Lemmens, D.; Tempere, J.
2010-02-01
We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.
Zheng, Chang-Jun; Gao, Hai-Feng; Du, Lei; Chen, Hai-Bo; Zhang, Chuanzeng
2016-01-01
An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR (s) solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton-Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton-Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as α = i / k is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method.
Directory of Open Access Journals (Sweden)
M.L.Mansfield
2002-01-01
Full Text Available Although the calculation of transport properties of complex-shaped particles (Smoluchowski rate constants for diffusion-limited reactions, Stokes friction coefficient, virial coefficients for conductivity, viscosity and other transport properties is straightforward in principle, the accurate evaluation of these quantities for objects of general shape is a problem of classic difficulty. In the present paper, we illustrate a recently developed numerical path-integration method to estimate basic transport properties of representative complex-shaped objects having scientific and technological interest (i.e., star polymers and diffusion-limited aggregates without excluded volume interactions. The methodology applies to objects of essentially arbitrary shape and its validation for special geometries, where exact results are known, is described in a previous paper. Here we calculate the electrostatic capacity and electrical polarizability tensor of these model branched polymers and then exploit exact and approximate electrostatic-hydrodynamic property interrelations to estimate the Stokes translational friction coefficient and the virial coefficients for conductivity and shear viscosity (intrinsic conductivity and viscosity, respectively. Dimensionless ratios of these transport properties and equilibrium measures of particle size (radius of gyration are considered since these ratios are important experimentally in determining macromolecular topological structure and universality class. We also discuss and illustrate the influence of the branching architecture on the equilibrium charge distribution ("equilibrium measure" of these branched polymers where they are treated as conductors. An unexpected qualitative change in the charge distribution is found with increasing arm number in star polymers that may have important physical consequences.
PathPPI: an integrated dataset of human pathways and protein-protein interactions.
Tang, HaiLin; Zhong, Fan; Liu, Wei; He, FuChu; Xie, HongWei
2015-06-01
Integration of pathway and protein-protein interaction (PPI) data can provide more information that could lead to new biological insights. PPIs are usually represented by a simple binary model, whereas pathways are represented by more complicated models. We developed a series of rules for transforming protein interactions from pathway to binary model, and the protein interactions from seven pathway databases, including PID, BioCarta, Reactome, NetPath, INOH, SPIKE and KEGG, were transformed based on these rules. These pathway-derived binary protein interactions were integrated with PPIs from other five PPI databases including HPRD, IntAct, BioGRID, MINT and DIP, to develop integrated dataset (named PathPPI). More detailed interaction type and modification information on protein interactions can be preserved in PathPPI than other existing datasets. Comparison analysis results indicate that most of the interaction overlaps values (O AB) among these pathway databases were less than 5%, and these databases must be used conjunctively. The PathPPI data was provided at http://proteomeview.hupo.org.cn/PathPPI/PathPPI.html. PMID:25591449
Shu, Jian-Jun
2014-01-01
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method, it solves the problem of systems of differential equations involving integral operators not previously considered by the Keller Box method. Two main preparatory stages are required: (i) a merging procedure for differential equations and conditions without integral operators and; (ii) a reduction procedure for differential equations and conditions with integral operators. The differencing processes are effectively simplified by means of the unit-step function. The nonlinear difference equations are solved by Newton method using an efficient block arrow-like matrix factorization technique. As an example of the application of this method, the systems of equations for combined gravity body force and forced convection in laminar film condensation can be solved for prescribed valu...
COMMUNITY ACTION, A PATH FOR SOCIAL INTEGRATION AND INTERCULTURALITY
Carlos Vecina Merchante
2013-01-01
Last years there have taken place demographic important changes in Spain, the increase in the entryof immigrant population has propitiated a more diverse social daily reality. The accession has beenconcrete ways, in which special relevancy has had the residential segregation and the concentrationof immigrant population in concrete places, being of special interest those who traditionally weresuffering social problems and major vulnerability. The result has been an unequal integration andprobl...
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.
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.
Classical Mechanics in Hilbert Space: Path Integral Formulation, and a Quantum Correction
Shee, James
2015-01-01
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory, which recasts classical mechanics in terms of a Hilbert space wherein the Liouville operator acts as the generator of motion, we derive a path integral representation of the classical propagator and suggest an efficient numerical implementation using fast fourier transform techniques. We then include a first quantum correction to derive a revealing expression for the semi-classical path integral, which augments the classical picture of a single trajectory through phase space with additional wave-like spreading.
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...
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.
Path integral measure, constraints and ghosts for massive gravitons with a cosmological constant
Metaxas, Dimitrios
2009-12-01
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.
The path integral measure, constraints and ghosts for massive gravitons with a cosmological constant
Metaxas, Dimitrios
2009-01-01
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.
Wakeful rest promotes the integration of spatial memories into accurate cognitive maps.
Craig, Michael; Dewar, Michaela; Harris, Mathew A; Della Sala, Sergio; Wolbers, Thomas
2016-02-01
Flexible spatial navigation, e.g. the ability to take novel shortcuts, is contingent upon accurate mental representations of environments-cognitive maps. These cognitive maps critically depend on hippocampal place cells. In rodents, place cells replay recently travelled routes, especially during periods of behavioural inactivity (sleep/wakeful rest). This neural replay is hypothesised to promote not only the consolidation of specific experiences, but also their wider integration, e.g. into accurate cognitive maps. In humans, rest promotes the consolidation of specific experiences, but the effect of rest on the wider integration of memories remained unknown. In the present study, we examined the hypothesis that cognitive map formation is supported by rest-related integration of new spatial memories. We predicted that if wakeful rest supports cognitive map formation, then rest should enhance knowledge of overarching spatial relations that were never experienced directly during recent navigation. Forty young participants learned a route through a virtual environment before either resting wakefully or engaging in an unrelated perceptual task for 10 min. Participants in the wakeful rest condition performed more accurately in a delayed cognitive map test, requiring the pointing to landmarks from a range of locations. Importantly, the benefit of rest could not be explained by active rehearsal, but can be attributed to the promotion of consolidation-related activity. These findings (i) resonate with the demonstration of hippocampal replay in rodents, and (ii) provide the first evidence that wakeful rest can improve the integration of new spatial memories in humans, a function that has, hitherto, been associated with sleep.
Wakeful rest promotes the integration of spatial memories into accurate cognitive maps.
Craig, Michael; Dewar, Michaela; Harris, Mathew A; Della Sala, Sergio; Wolbers, Thomas
2016-02-01
Flexible spatial navigation, e.g. the ability to take novel shortcuts, is contingent upon accurate mental representations of environments-cognitive maps. These cognitive maps critically depend on hippocampal place cells. In rodents, place cells replay recently travelled routes, especially during periods of behavioural inactivity (sleep/wakeful rest). This neural replay is hypothesised to promote not only the consolidation of specific experiences, but also their wider integration, e.g. into accurate cognitive maps. In humans, rest promotes the consolidation of specific experiences, but the effect of rest on the wider integration of memories remained unknown. In the present study, we examined the hypothesis that cognitive map formation is supported by rest-related integration of new spatial memories. We predicted that if wakeful rest supports cognitive map formation, then rest should enhance knowledge of overarching spatial relations that were never experienced directly during recent navigation. Forty young participants learned a route through a virtual environment before either resting wakefully or engaging in an unrelated perceptual task for 10 min. Participants in the wakeful rest condition performed more accurately in a delayed cognitive map test, requiring the pointing to landmarks from a range of locations. Importantly, the benefit of rest could not be explained by active rehearsal, but can be attributed to the promotion of consolidation-related activity. These findings (i) resonate with the demonstration of hippocampal replay in rodents, and (ii) provide the first evidence that wakeful rest can improve the integration of new spatial memories in humans, a function that has, hitherto, been associated with sleep. PMID:26235141
An Accurate Integral Method for Vibration Signal Based on Feature Information Extraction
Directory of Open Access Journals (Sweden)
Yong Zhu
2015-01-01
Full Text Available After summarizing the advantages and disadvantages of current integral methods, a novel vibration signal integral method based on feature information extraction was proposed. This method took full advantage of the self-adaptive filter characteristic and waveform correction feature of ensemble empirical mode decomposition in dealing with nonlinear and nonstationary signals. This research merged the superiorities of kurtosis, mean square error, energy, and singular value decomposition on signal feature extraction. The values of the four indexes aforementioned were combined into a feature vector. Then, the connotative characteristic components in vibration signal were accurately extracted by Euclidean distance search, and the desired integral signals were precisely reconstructed. With this method, the interference problem of invalid signal such as trend item and noise which plague traditional methods is commendably solved. The great cumulative error from the traditional time-domain integral is effectively overcome. Moreover, the large low-frequency error from the traditional frequency-domain integral is successfully avoided. Comparing with the traditional integral methods, this method is outstanding at removing noise and retaining useful feature information and shows higher accuracy and superiority.
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.
Stoyanovsky, A. V.
2008-01-01
We define the notion of distribution on an infinite dimensional space motivated by the notion of Feynman path integral and by construction of probability measures for generalized random fields. This notion of distribution turns out to be mathematically equivalent to the notion of generating functional of Green functions.
Making the gravitational path integral more Lorentzian, or: Life beyond Liouville gravity
Loll, R.; Ambjørn, J.; Anagnostopoulos, K.N.
2006-01-01
In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigor- ous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a number of appealing features: i) its quantum geometry is
Walters, Peter L; Makri, Nancy
2015-12-17
We employ the quantum-classical path integral methodology to simulate the outer sphere charge-transfer process of the ferrocene-ferrocenium pair in liquid hexane with unprecedented accuracy. Comparison of the simulation results to those obtained by mapping the solvent on an effective harmonic bath demonstrates the accuracy of linear response theory in this system. PMID:26673195
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. PMID:27497533
Two-Level System Coupled to Phonons : A Discrete Path-Integral Method
Raedt, Bart De; Raedt, Hans De
1983-01-01
A discrete path-integral representation for the partition function of a two-level tunneling system coupled to acoustic phonons is derived. This representation allows calculation of properties in the whole coupling range. As a function of the coupling there is an abrupt (ground-state) transition from
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.
Route-segment odometry and its interactions with global path-integration.
Collett, Thomas S; Collett, Matthew
2015-06-01
Insects such as desert ants and honeybees use visual memories to travel along familiar routes between their nest and a food-site. We trained Cataglyphis fortis foragers along a two-segment route to investigate whether they encode the lengths of route segments over which visual cues remain approximately constant. Our results support earlier studies suggesting that such route-segment odometry exists, and allows an individual to stop using a visual route memory at an appropriate point, even in the absence of any change in the visual surroundings. But we find that the behavioural effects of route-segment odometry are often complicated by interactions with guidance from the global path-integration system. If route-segment odometry and path-integration agree, they act together to produce a precise signal for search. If the endpoint of route-segment odometry arrives first, it does not trigger search but its effect can persist and cause guidance by path-integration to end early. Conversely, if ants start with their path-integration state at zero, they follow a route memory for no more than 3 m, irrespective of the route-segment length. A possible explanation for these results is that if one guidance system is made to overshoot its endpoint, it can cause the other to be cut short. PMID:25904159
Quantum mechanical path integrals with Wiener measures for all polynomial Hamiltonians
International Nuclear Information System (INIS)
We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well-defined path integrals involving Wiener measure on phase space, as a diffusion constant diverges. A related construction achieves a similar result for an arbitrary spin Hamiltonian. (orig.)
Path-integral measure for Chern-Simons theory within the stochastic quantization approach
International Nuclear Information System (INIS)
We discuss how the dependence of the path-integral measure on the metric affects the generating functional for the d=3 Chern-Simons theory. Using the stochastic quantization, we show that the choice of an invariant measure preserves the topological character of the theory. (author). 18 refs
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.
Path-dependent J-integral evaluations around an elliptical hole for large deformation theory
Unger, David J.
2016-08-01
An exact expression is obtained for a path-dependent J-integral for finite strains of an elliptical hole subject to remote tensile tractions under the Tresca deformation theory for a thin plate composed of non-work hardening material. Possible applications include an analytical resistance curve for the initial stage of crack propagation due to crack tip blunting.
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.
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......
International Nuclear Information System (INIS)
In this paper the problem of quantization of the free gravitational field on classical background (the exact solutions of Einstein equations) is considered. The Bogoliubov group coordinates method in path integral formalism is developed. This approach makes it possible to take carefully into account the conservation laws alongside with the perturbation theory expansion
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.
Path integral treatment of a Dirac particle in a weak gravitational plane wave
Energy Technology Data Exchange (ETDEWEB)
Zabat, Sana; Chetouani, Lyazid [Dept. de Physique, Univ. Mentouri, Constantine (Algeria)
2010-05-15
The Green functions for Klein-Gordon and Dirac particles in a weak gravitational field are determined exactly by the path integral formalism. By using simple changes, it is shown that the classical trajectories play an important role in determining these Green functions. (orig.)
Path integral measure and the fermion-boson equivalence in the Schwinger model
International Nuclear Information System (INIS)
I perform a change of field variables in the Schwinger model using the non-invariance of path integral measure under γ5 transformations. The known equivalence of the model with a bosonic field theory and the Kogut-Susskind dipole mechanism is then derived. (author)
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.)
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...
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.
The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator
Govaerts, Jan; Bwayi, Calvin Matondo; 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...
一种快速准确控制复杂路径延时的方法%Accurate complicated path delay control method
Institute of Scientific and Technical Information of China (English)
文鼎童; 陈岚
2009-01-01
在深亚微米超大规模集成电路的物理设计中,为达到时序收敛经常遇到复杂路径延时的准确控制问题,提出了一种新的准确控制复杂路径延时方法,并使用布局布线工具Synopsys Astro实现.实验结果表明,该方法比传统的ECO(Engineer ChangeOrder)精度高,收敛速度快.可广泛应用于超大规模集成电路物理设计.%In submicron VLSI physical design,how to control complicated path delay accurately in order to meet timing is always a great challenge.In this paper,a new complicated path control method is proposed,which works accurately and quickly by using placement & routing tool Synopsys Astro.The experimental results indicate that this method can achieve better accuracy and faster convergence than traditional ECO(Engineer Change Order) method,and can be widely used in VLSI physical design.
An accurate spline polynomial cubature formula for double integration with logarithmic singularity
Bichi, Sirajo Lawan; Eshkuvatov, Z. K.; Long, N. M. A. Nik; Bello, M. Y.
2016-06-01
The paper studied the integration of logarithmic singularity problem J (y ¯)= ∬ ∇ζ (y ¯)l o g |y ¯-y¯0*|d A , where y ¯=(α ,β ), y¯0=(α0,β0) the domain ∇ is rectangle ∇ = [r1, r2] × [r3, r4], the arbitrary point y ¯∈∇ and the fixed point y¯0∈∇. The given density function ζ(y ¯), is smooth on the rectangular domain ∇ and is in the functions class C2,τ (∇). Cubature formula (CF) for double integration with logarithmic singularities (LS) on a rectangle ∇ is constructed by applying type (0, 2) modified spline function DΓ(P). The results obtained by testing the density functions ζ(y ¯) as linear and absolute value functions shows that the constructed CF is highly accurate.
He, Wantao; Li, Zhongwei; Zhong, Kai; Shi, Yusheng; Zhao, Can; Cheng, Xu
2014-11-01
Fast and precise 3D inspection system is in great demand in modern manufacturing processes. At present, the available sensors have their own pros and cons, and hardly exist an omnipotent sensor to handle the complex inspection task in an accurate and effective way. The prevailing solution is integrating multiple sensors and taking advantages of their strengths. For obtaining a holistic 3D profile, the data from different sensors should be registrated into a coherent coordinate system. However, some complex shape objects own thin wall feather such as blades, the ICP registration method would become unstable. Therefore, it is very important to calibrate the extrinsic parameters of each sensor in the integrated measurement system. This paper proposed an accurate and automatic extrinsic parameter calibration method for blade measurement system integrated by different optical sensors. In this system, fringe projection sensor (FPS) and conoscopic holography sensor (CHS) is integrated into a multi-axis motion platform, and the sensors can be optimally move to any desired position at the object's surface. In order to simple the calibration process, a special calibration artifact is designed according to the characteristics of the two sensors. An automatic registration procedure based on correlation and segmentation is used to realize the artifact datasets obtaining by FPS and CHS rough alignment without any manual operation and data pro-processing, and then the Generalized Gauss-Markoff model is used to estimate the optimization transformation parameters. The experiments show the measurement result of a blade, where several sampled patches are merged into one point cloud, and it verifies the performance of the proposed method.
Path integral pricing of Wasabi option in the Black-Scholes model
Cassagnes, Aurelien; Chen, Yu; Ohashi, Hirotada
2014-11-01
In this paper, using path integral techniques, we derive a formula for a propagator arising in the study of occupation time derivatives. Using this result we derive a fair price for the case of the cumulative Parisian option. After confirming the validity of the derived result using Monte Carlo simulation, a new type of heavily path dependent derivative product is investigated. We derive an approximation for our so-called Wasabi option fair price and check the accuracy of our result with a Monte Carlo simulation.
Path-integral theory of an axially confined worm-like chain
Energy Technology Data Exchange (ETDEWEB)
Smith, D.A. [Randall Centre for Molecular Mechanisms of Cell Function, King' s College London, London (United Kingdom)
2001-06-01
A path-integral formulation is developed for the thermodynamic properties of a worm-like chain moving on a surface and laterally confined by a harmonic potential. The free energy of the chain is calculated as a function of its length and boundary conditions at each end. Distribution functions for chain displacements can be constructed by utilizing the Markov property as a function of displacement {phi}(s) and its derivative d{phi}(s)/ds along the path. These quantities are also calculated in the presence of pinning sites which impose fixed positive or negative displacements, foreshadowing their application to a model for the regulation of striated muscle. (author)
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....... The corresponding rates and diffusion coefficient are evaluated using the path-centroid transition state theory. In contrast with what is found assuming classical mechanics for the nuclear motion, the reorientation step becomes rate limiting below 600 K....
path integral approach to closed form pricing formulas in the Heston framework.
Lemmens, Damiaan; Wouters, Michiel; Tempere, Jacques; Foulon, Sven
2008-03-01
We present a path integral approach for finding closed form formulas for option prices in the framework of the Heston model. The first model for determining option prices was the Black-Scholes model, which assumed that the logreturn followed a Wiener process with a given drift and constant volatility. To provide a realistic description of the market, the Black-Scholes results must be extended to include stochastic volatility. This is achieved by the Heston model, which assumes that the volatility follows a mean reverting square root process. Current applications of the Heston model are hampered by the unavailability of fast numerical methods, due to a lack of closed-form formulae. Therefore the search for closed form solutions is an essential step before the qualitatively better stochastic volatility models will be used in practice. To attain this goal we outline a simplified path integral approach yielding straightforward results for vanilla Heston options with correlation. Extensions to barrier options and other path-dependent option are discussed, and the new derivation is compared to existing results obtained from alternative path-integral approaches (Dragulescu, Kleinert).
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.
The use of a path independent integral in non-linear fracture mechanics
International Nuclear Information System (INIS)
The use of the Rice J-intergral to assess conditions at a crack tip in an elastic or non-linear elastic body is well known. The integral equals the energy release rate and is path independent for any contour surrounding the crack tip provided no other singularities are encompassed. The path independence propertiy breaks down, however, in more general situations such as in three dimensional stress systems, plasticity unloading, thermal or creep states. Hence the required crack tip characteristics represented by the value of the integral round a contour whose radius about the tip tends to zero, is not reproduced along contours away from the tip. Consequently, an alternative integral, designated J*, has been proposed which equals J for elastic cases and in the other cases cited above remains path independent. A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. (Auth. )
Eab, C. H.; Lim, S. C.
2014-01-01
This paper considers the Fokker-Planck equation and path integral formulation of the fractional Ornstein-Uhlenbeck process parametrized by two indices. The effective Fokker-Planck equation of this process is derived from the associated fractional Langevin equation. Path integral representation of the process is constructed and the basic quantities are evaluated.
Zhang, Shunli; Zhang, Dinghua; Gong, Hao; Ghasemalizadeh, Omid; Wang, Ge; Cao, Guohua
2014-11-01
Iterative algorithms, such as the algebraic reconstruction technique (ART), are popular for image reconstruction. For iterative reconstruction, the area integral model (AIM) is more accurate for better reconstruction quality than the line integral model (LIM). However, the computation of the system matrix for AIM is more complex and time-consuming than that for LIM. Here, we propose a fast and accurate method to compute the system matrix for AIM. First, we calculate the intersection of each boundary line of a narrow fan-beam with pixels in a recursive and efficient manner. Then, by grouping the beam-pixel intersection area into six types according to the slopes of the two boundary lines, we analytically compute the intersection area of the narrow fan-beam with the pixels in a simple algebraic fashion. Overall, experimental results show that our method is about three times faster than the Siddon algorithm and about two times faster than the distance-driven model (DDM) in computation of the system matrix. The reconstruction speed of our AIM-based ART is also faster than the LIM-based ART that uses the Siddon algorithm and DDM-based ART, for one iteration. The fast reconstruction speed of our method was accomplished without compromising the image quality.
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.
Boninsegni, M; Svistunov, B V
2006-01-01
A detailed description is provided of a new Worm Algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general Path Integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correla...
Development of highly accurate approximate scheme for computing the charge transfer integral.
Pershin, Anton; Szalay, Péter G
2015-08-21
The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the "exact" scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the "exact" calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature. PMID:26298117
Development of highly accurate approximate scheme for computing the charge transfer integral
Energy Technology Data Exchange (ETDEWEB)
Pershin, Anton; Szalay, Péter G. [Laboratory for Theoretical Chemistry, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest (Hungary)
2015-08-21
The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the “exact” scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the “exact” calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature.
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. PMID:26957169
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.
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...
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.
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.
The use of a path independent integral in non-linear fracture mechanics
International Nuclear Information System (INIS)
A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. Numerical examples are presented comparing the J and J* integrals for a number of cracked plates under thermal, plastic and creep environments. To demonstrate the accuracy for a simple thermo-elastic case, a centre cracked plate subject to a symmetric quadratic gradient is included. Here, the J integral is shown to be path dependent whereas good independence is seen for the J* integral. The case of an elastic-plastic plate is invetigated to demonstrate path independence for both integrals in non-linear elasticity, and the effects of unloading are discussed. An alternative method for obtaining the change of potential energy over a small crack extension is briefly mentioned and compared to the J and J* results in this case. An axisymmetric bar with an internal penny-shaped crack subjected to tension is discussed under elastic-plastic materials behavior
Fix, Andreas; Matthey, Renaud; Amediek, Axel; Ehret, Gerhard; Gruet, Florian; Kiemle, Christoph; Klein, Volker; Mileti, Gaetano; Pereira do Carmo, Joao; Quatrevalet, Mathieu
2014-01-01
The Integrated Path Differential Absorption Lidar (IPDA) technique using hard target reflection the near IR has the potential to deliver CO2 column measurements from space with unprecedented accuracy which is a prerequisite to understand the sources and sinks of this dominant anthropogenic greenhouse gas. The observational needs, however, demand for very stringent system requirements, of which two were thoroughly investigated. The first is the online frequency accuracy. With a sub-100-kHz ...
Quasiclassical Limit in q-Deformed Systems, Noncommutativity and the q-Path Integral
Chaichian, Masud; Kulish, P P
1997-01-01
Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms of variables on the quantum planes. We consider the Hamiltonian made of special combination of operators (the analog of even operators in Grassmann algebra) and discuss q-path integrals constructed with the help of contracted ``classical'' algebras.
Path-Integral Approach to Scaling And Anomalies at Finite Temperature
Lin, Chris L
2015-01-01
We derive the relativistic thermodynamic scale equation using imaginary-time path integrals, with complex scalar field theory taken as a concrete example. We use Fujikawa's method to derive the scaling anomaly for this system using a matrix regulator. We make a general scaling argument to show how for anomalous systems, the $\\beta$ function of the vacuum theory can be derived from measurement of macroscopic thermodynamic parameters.
Zheng, Jian
2016-01-01
Visible Cherenkov radiation can offers a method of the measurement of the velocity of a charged particles. The angular width of the radiation is important since it determines the resolution of the velocity measurement. In this article, the angular width of Cherenkov radiation with inclusion of multiple scattering is calculated through the path-integral method, and and the analytical expressions are presented. The condition that multiple scattering process dominates the angular distribution is obtained.
Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator
Institute of Scientific and Technical Information of China (English)
GAO Cheng-Yuan; S.M. Nagiyev; LIU Jin-Ming; E.I. Jafarov; MA Lei; M.Y. Efendiyev
2008-01-01
The SU(1,1) coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between S U(1,1) coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the vse of quasiclassical Bohr-Sommerfeld quantization rule yields the exact expression for the energy spectrum.
Path integral calculation of shock Hugoniot curves of precompressed liquid deuterium
Militzer, B
2003-01-01
Path integral Monte Carlo simulations have been used to study deuterium at high pressure and temperature. The equation of state has been derived in the temperature and density regions of 10 000 <= T <= 1 000 000 K and 0.6 <= rho <= 2.5 g cm sup - sup 3. A series of shock Hugoniot curves is computed for different initial compressions in order to compare with current and future shock wave experiments using liquid deuterium samples precompressed in diamond anvil cells.
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.
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.
Yu, Jirong; Petros, Mulugeta; Reithmaier, Karl; Bai, Yingxin; Trieu, Bo C.; Refaat, Tamer F.; Kavaya, Michael J.; Singh, Upendra N.
2012-01-01
A 2-micron pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This instrument will provide an alternate approach to measure atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement.
Position Measurement for a Relativistic Particle: Restricted-Path-Integral Analysis
Mensky, Michael B.; von Borzeszkowski, Horst
2000-01-01
Measurements of the position of a relativistic particle is considered in the framework of the Restricted-Path-Integral (RPI) approach. The amplitude describing such a measurement is shown to be exponentially small outside the light cone of the space-time point corresponding to the measurement output, in a qualitative agreement with the Hellwig and Kraus' postulate of relativistic state reduction. Theory of the measurement including the probability distribution for different measurement output...
Chern-Simons Path Integrals in S2 × S1
Directory of Open Access Journals (Sweden)
Adrian P. C. Lim
2015-08-01
Full Text Available Using torus gauge fixing, Hahn in 2008 wrote down an expression for a Chern-Simons path integral to compute the Wilson Loop observable, using the Chern-Simons action \\(S_{CS}^\\kappa\\, \\(\\kappa\\ is some parameter. Instead of making sense of the path integral over the space of \\(\\mathfrak{g}\\-valued smooth 1-forms on \\(S^2 \\times S^1\\, we use the Segal Bargmann transform to define the path integral over \\(B_i\\, the space of \\(\\mathfrak{g}\\-valued holomorphic functions over \\(\\mathbb{C}^2 \\times \\mathbb{C}^{i-1}\\. This approach was first used by us in 2011. The main tool used is Abstract Wiener measure and applying analytic continuation to the Wiener integral. Using the above approach, we will show that the Chern-Simons path integral can be written as a linear functional defined on \\(C(B_1^{\\times^4} \\times B_2^{\\times^2}, \\mathbb{C}\\ and this linear functional is similar to the Chern-Simons linear functional defined by us in 2011, for the Chern-Simons path integral in the case of \\(\\mathbb{R}^3\\. We will define the Wilson Loop observable using this linear functional and explicitly compute it, and the expression is dependent on the parameter \\(\\kappa\\. The second half of the article concentrates on taking \\(\\kappa\\ goes to infinity for the Wilson Loop observable, to obtain link invariants. As an application, we will compute the Wilson Loop observable in the case of \\(SU(N\\ and \\(SO(N\\. In these cases, the Wilson Loop observable reduces to a state model. We will show that the state models satisfy a Jones type skein relation in the case of \\(SU(N\\ and a Conway type skein relation in the case of \\(SO(N\\. By imposing quantization condition on the charge of the link \\(L\\, we will show that the state models are invariant under the Reidemeister Moves and hence the Wilson Loop observables indeed define a framed link invariant. This approach follows that used in an article written by us in 2012, for the case of
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
Barnett-Cowan, Michael; Meilinger, Tobias; Vidal, Manuel; Teufel, Harald; Heinrich H Bülthoff
2012-01-01
Path integration is a process in which self-motion is integrated over time to obtain an estimate of one's current position relative to a starting point 1. Humans can do path integration based exclusively on visual 2-3, auditory 4, or inertial cues 5. However, with multiple cues present, inertial cues - particularly kinaesthetic - seem to dominate 6-7. In the absence of vision, humans tend to overestimate short distances (
Perturbative Computation of the Gluonic Effective Action via Polyaokov's World-Line Path Integral
Avramis, S D; Ktorides, C N
2002-01-01
The Polyakov world-line path integral describing the propagation of gluon field quanta is constructed by employing the background gauge fixing method and is subsequently applied to analytically compute the divergent terms of the one (gluonic) loop effective action to fourth order in perturbation theory. The merits of the proposed approach is that, to a given order, it reduces to performing two integrations, one over a set of Grassmann and one over a set of Feynman-type parameters through which one manages to accomodate all Feynman diagrams entering the computation at once.
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
Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach
Boudieb, Sami; CHETOUANI, Lyazid
2013-01-01
The Green function for a Dirac particle moving in a non-Abelian field and having a particular form is exactly determined by the path integral approach. The wave functions were deduced from the residues of Green’s function. It is shown that the classical paths contributed mainly to the determination of the Green function.
Tanizaki, Yuya
2014-01-01
Picard--Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem.
Mieck, Bernhard
2010-01-01
A coherent state path integral is considered for bosons with an ensemble average of a random potential and with an additional, repulsive interaction in the context of BEC under inclusion of specially prepared disorder. The essential normalization of the coherent state path integral, as a generating function of observables, is obtained from the non-equilibrium time contour for 'forward' and 'backward' propagation so that a time contour metric has to be taken into account in the ensemble averag...
Gangopadhyay, Sunandan
2014-01-01
We employ the path integral approach developed in [29] to discuss the (generalized) harmonic oscillator in a noncommutative plane. The action for this system is derived in the coherent state basis with additional degrees of freedom. From this the action in the coherent state basis without any additional degrees of freedom is obtained. This gives the ground state spectrum of the system. We then employ the exact renormalization group approach to show that a duality can be constructed between this (noncommutative) system and a commutative system.
Option pricing formulas and nonlinear filtering: a Feynman path integral perspective
Balaji, Bhashyam
2013-05-01
Many areas of engineering and applied science require the solution of certain parabolic partial differential equa tions, such as the Fokker-Planck and Kolmogorov equations. The fundamental solution, or the Green's function, for such PDEs can be written in terms of the Feynman path integral (FPI). The partial differential equation arising in the valuing of options is the Kolmogorov backward equation that is referred to as the Black-Scholes equation. The utility of this is demonstrated and numerical examples that illustrate the high accuracy of option price calculation even when using a fairly coarse grid.
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.
Calculating splittings between energy levels of different symmetry using path-integral methods.
Mátyus, Edit; Althorpe, Stuart C
2016-03-21
It is well known that path-integral methods can be used to calculate the energy splitting between the ground and the first excited state. Here we show that this approach can be generalized to give the splitting patterns between all the lowest energy levels from different symmetry blocks that lie below the first-excited totally symmetric state. We demonstrate this property numerically for some two-dimensional models. The approach is likely to be useful for computing rovibrational energy levels and tunnelling splittings in floppy molecules and gas-phase clusters. PMID:27004864
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...... point process has not independent increments the state vector of the system, consisting of the generalized displacements and velocities, is not a Markov process. Initially it is shown how the indicated systems can be converted to an equivalent Poisson driven system at the expense of introducing...
A Deformation of Quantum Dynamics through the Phase Space Path Integral
Govaerts, Jan
2008-01-01
Using a regularised construction of the phase space path integral due to Ingrid Daubechies and John Klauder which involves a time scale ultimately taken to vanish, and motivated by the general programme towards a noncommutative space(time) geometry, physical consequences of assuming this time parameter to provide rather a new fundamental time scale are explored in the context of the one dimensional harmonic oscillator. Some tantalising results are achieved, which raise intriguing prospects when extrapolated to the quantum field theory and gravitational contexts.
Cartan-Calculus and its Generalizations via a Path-Integral Approach to Classical Mechanics
Gozzi, E
1997-01-01
In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and show that they are essentially a basis of the cotangent bundle to the tangent bundle to phase-space. In this space we introduce an extended Poisson brackets structure which allows us to re-do all the usual Cartan calculus on symplectic manifolds via these brackets. We also briefly sketch how the Schouten-Nijenhuis, the Frölicher- Nijenhuis and the Nijenhuis-Richardson brackets look in our formalism.
Development of a Pulsed 2-Micron Integrated Path Differential Absorption Lidar for CO2 Measurement
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer; Refaat, Tamer
2013-01-01
Atmospheric carbon dioxide (CO2) is an important greenhouse gas that significantly contributes to the carbon cycle and global radiation budget on Earth. Active remote sensing of CO2 is important to address several limitations that contend with passive sensors. A 2-micron double-pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This active remote sensing instrument will provide an alternate approach of measuring atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise ratio level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement. Commercial, on the shelf, components are implemented for the detection system. Instrument integration will be presented in this paper as well as a background for CO2 measurement at NASA Langley research Center
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
to a simulated sixlegged artificial agent. Input signals from an allothetic compass and odometry are sustained through leaky neural integrator circuits, which are then used to compute the home vector by local excitation-global inhibition interactions. The home vector is computed and represented in circular...... arrays of neurons, where compass directions are population-coded and linear displacements are rate-coded. The mechanism allows for robust homing behavior in the presence of external sensory noise. The emergent behavior of the controlled agent does not only show a robust solution for the problem......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...
Accelerating Ab Initio Path Integral Simulations via Imaginary Multiple-Timestepping.
Cheng, Xiaolu; Herr, Jonathan D; Steele, Ryan P
2016-04-12
This work investigates the use of multiple-timestep schemes in imaginary time for computationally efficient ab initio equilibrium path integral simulations of quantum molecular motion. In the simplest formulation, only every n(th) path integral replica is computed at the target level of electronic structure theory, whereas the remaining low-level replicas still account for nuclear motion quantum effects with a more computationally economical theory. Motivated by recent developments for multiple-timestep techniques in real-time classical molecular dynamics, both 1-electron (atomic-orbital basis set) and 2-electron (electron correlation) truncations are shown to be effective. Structural distributions and thermodynamic averages are tested for representative analytic potentials and ab initio molecular examples. Target quantum chemistry methods include density functional theory and second-order Møller-Plesset perturbation theory, although any level of theory is formally amenable to this framework. For a standard two-level splitting, computational speedups of 1.6-4.0x are observed when using a 4-fold reduction in time slices; an 8-fold reduction is feasible in some cases. Multitiered options further reduce computational requirements and suggest that quantum mechanical motion could potentially be obtained at a cost not significantly different from the cost of classical simulations. PMID:26966920
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...
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.
Two-scale large deviations for chemical reaction kinetics through second quantization path integral
International Nuclear Information System (INIS)
Motivated by the study of rare events for a typical genetic switching model in systems biology, in this paper we aim to establish the general two-scale large deviations for chemical reaction systems. We build a formal approach to explicitly obtain the large deviation rate functionals for the considered two-scale processes based upon the second quantization path integral technique. We get three important types of large deviation results when the underlying two timescales are in three different regimes. This is realized by singular perturbation analysis to the rate functionals obtained by the path integral. We find that the three regimes possess the same deterministic mean-field limit but completely different chemical Langevin approximations. The obtained results are natural extensions of the classical large volume limit for chemical reactions. We also discuss its implication on the single-molecule Michaelis–Menten kinetics. Our framework and results can be applied to understand general multi-scale systems including diffusion processes. (paper)
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.
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.
Symmetries of the Classical Path-Integral on a Generalized Phase-Space, 2
Gozzi, E
2000-01-01
In this paper we continue the study of the path-integral formulation of classical mechanics and in particular we better clarify, with respect to previous papers, the geometrical meaning of the variables entering this formulation.With respect to the first paper with the same title, we correct here the set of transformations for the auxiliary variables $\\lambda_{a}$. We prove that under this new set of transformations the Hamiltonian the same for the Lagrangian. Despite this different transformation, the variables $\\lambda_{a}$ maintain the same operatorial meaning as before but on a different functional space. Cleared up this point we then show that the space spanned by the whole set of variables ($\\phi, c, \\lambda,\\bar c$) of our path-integral is the cotangent bundle to the reversed-parity tangent bundle of the phase space ${\\cal M}$ of our system and it is indicated as $T^{\\star}(\\Pi T{\\cal M})$. In case the reader feel uneasy with this strange Grassmannian double bundle, we show in this paper that it is pos...
Rapid Design Methodology of Layout Euler Path for Integrated Circuits%集成电路版图欧拉路径的快速判寻方法
Institute of Scientific and Technical Information of China (English)
王健; 陈海洋; 蓝海萌
2011-01-01
Euler path of layout is a common methodology used to minimize layout area of integrated circuits. Relationship between Euler path of layout and Boolean expression was discussed, and a fast design methodology to decide if there is an Euler path of layout and search for it was proposed. Using this method, Euler path of layout for a number of typical circuits were designed, one of which was designed with IC design software. The optimized layout area was greatly reduced. The proposed methodology is rapid, accurate, convenient, and has broad potential applications.%版图欧拉路径法是实现集成电路版图面积最小化的常用方法.讨论了版图欧拉路径与布尔表达式的关系,提出一种版图欧拉路径快速判寻方法.利用该方法,设计了几种典型电路的版图欧拉路径,并运用集成电路设计软件设计其中一种电路,经过优化后的版图面积明显减小.该方法快速、准确、方便,具有广阔的应用前景.
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.
Mielke, Steven L; Truhlar, Donald G
2015-01-28
We present an improved version of our "path-by-path" enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P(-6)) to O(P(-12)), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational-rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan-Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300-3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
An area-saving dual-path loop filter for low-voltage integrated phase-locked loops
Institute of Scientific and Technical Information of China (English)
Pan Jie; Yang Haigang; Yang Liwu
2009-01-01
This paper proposes an area-saving dual-path loop filter (LPF) for low-voltage integrated phase-locked loops (PLLs). With this LPF, output current of the lowpass-path charge-pump (CP) is B times (B>1) as great as that of the integration-path CP. By adding voltages across these two paths, the zero-capacitance is magnified B times equivalently. As a result, the chip size is greatly reduced. Based on this LPF, a 1.2 V 3.5 GHz-band PLL is fabricated in SMIC 0.18 μm RFCMOS technology. Its zero-capacitance is only 1/30 of that in conventional second-order LPFs. Measured data show that, at a frequency of 3.20 GHz, phase noise is -120.2 dBc/Hz at 1 MHz offset, reference spur is -72 dBc, and power is 24 mW.
Energy Technology Data Exchange (ETDEWEB)
Tanizaki, Yuya, E-mail: yuya.tanizaki@riken.jp [Department of Physics, The University of Tokyo, Tokyo 113-0033 (Japan); Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 (Japan); Koike, Takayuki, E-mail: tkoike@ms.u-tokyo.ac.jp [Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo 153-8914 (Japan)
2014-12-15
Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. - Highlights: • Real-time path integral is studied based on Picard–Lefschetz theory. • Lucid demonstration is given through simple examples of quantum mechanics. • This technique is applied to quantum mechanics of the double-well potential. • Difficulty for practical applications is revealed, and we discuss its generality. • Quantum tunneling is shown to be closely related to complex classical solutions.
Boninsegni, M.; Prokof'Ev, N. V.; Svistunov, B. V.
2006-09-01
A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general path integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid He4 in two and three dimensions, as well as the calculation of the chemical potential of hcp He4 .
International Nuclear Information System (INIS)
A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general path integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid 4He in two and three dimensions, as well as the calculation of the chemical potential of hcp 4He
Chen, Duan; Cai, Wei; Zinser, Brian; Cho, Min Hyung
2016-09-01
In this paper, we develop an accurate and efficient Nyström volume integral equation (VIE) method for the Maxwell equations for a large number of 3-D scatterers. The Cauchy Principal Values that arise from the VIE are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities. Also, the hyper-singular integrals are computed using interpolated quadrature formulae with tensor-product quadrature nodes for cubes, spheres and cylinders, that are frequently encountered in the design of meta-materials. The resulting Nyström VIE method is shown to have high accuracy with a small number of collocation points and demonstrates p-convergence for computing the electromagnetic scattering of these objects. Numerical calculations of multiple scatterers of cubic, spherical, and cylindrical shapes validate the efficiency and accuracy of the proposed method.
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...
Path integral approach to the full Dicke model with dipole-dipole interaction
Alcalde, M Aparicio; Svaiter, N F
2011-01-01
We consider the full Dicke spin-boson model composed by a single bosonic mode and an ensemble of $N$ identical two-level atoms with different couplings for the resonant and anti-resonant interaction terms, and incorporate a dipole-dipole interaction between the atoms. Assuming that the system is in thermal equilibrium with a reservoir at temperature $\\beta^{-1}$, we compute the free energy in the thermodynamic limit $N\\rightarrow\\infty$ in the saddle-point approximation to the path integral and determine the critical temperature for the superradiant phase transition. In the zero temperature limit, we recover the critical coupling of the quantum phase transition, presented in the literature.
Quantum mechanical path integrals and thermal radiation in static curved spacetimes
Vendrell, F
2000-01-01
The propagator of a spinless particle is calculated from the quantum mechanical path integral formalism in static curved spacetimes endowed with event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild black holes are considered. The role of the topology of the coordinates configuration space is emphasised in this framework. To cover entirely the above spacetimes with a single set of coordinates, tortoise coordinates are extended to complex values. It is shown that the homotopic properties of the complex tortoise configuration space imply the thermal behaviour of the propagator in these spacetimes. The propagator is calculated when end points are located in identical or distinct spacetime regions separated by one or several event-horizons. Quantum evolution through the event-horizons is shown to be unitary in the fifth variable.
Path-independent integrals to identify localized plastic events in two dimensions.
Talamali, Mehdi; Petäjä, Viljo; Vandembroucq, Damien; Roux, Stéphane
2008-07-01
We use a power expansion representation of plane-elasticity complex potentials due to Kolossov and Muskhelishvili to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant contributions correspond to first-order singularities of quadrupolar and dipolar symmetry which can be associated, respectively, with pure deviatoric and pure volumetric plastic strain of an equivalent circular inclusion. By construction of holomorphic functions from the displacement field and its derivatives, it is possible to define path-independent Cauchy integrals which capture the amplitudes of these singularities. Analytical expressions and numerical tests on simple finite-element data are presented. The development of such numerical tools is of direct interest for the identification of local structural reorganizations, which are believed to be the key mechanisms for plasticity of amorphous materials. PMID:18764022
A path integral approach to the full Dicke model with dipole-dipole interaction
Energy Technology Data Exchange (ETDEWEB)
Alcalde, M Aparicio [Instituto de Fisica Teorica, UNESP, Sao Paulo State University, Caixa Postal 70532-2, 01156-970 Sao Paulo, SP (Brazil); Stephany, J [Departamento de Fisica, Seccion de Fenomenos Opticos, Universidad Simon Bolivar, Apartado Postal 89000, Caracas 1080-A (Venezuela, Bolivarian Republic of); Svaiter, N F, E-mail: aparicio@ift.unesp.br, E-mail: stephany@usb.ve, E-mail: nfuxsvai@cbpf.br [Centro Brasileiro de Pesquisas Fisicas, Rua Dr Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ (Brazil)
2011-12-16
We consider the full Dicke spin-boson model composed by a single bosonic mode and an ensemble of N identical two-level atoms with different couplings for the resonant and anti-resonant interaction terms, and incorporate a dipole-dipole interaction between the atoms. Assuming that the system is in thermal equilibrium with a reservoir at temperature {beta}{sup -1}, we compute the free energy in the thermodynamic limit N {yields} {infinity} in the saddle-point approximation to the path integral and determine the critical temperature for the super-radiant phase transition. In the zero temperature limit, we recover the critical coupling of the quantum phase transition, presented in the literature. (paper)
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 ...
Dračínský, Martin; Bouř, Petr; Hodgkinson, Paul
2016-03-01
The influence of temperature on NMR chemical shifts and quadrupolar couplings in model molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory (DFT) calculations of shielding and electric field gradient (EFG) tensors. An approach based on convoluting calculated shielding or EFG tensor components with probability distributions of selected bond distances and valence angles obtained from DFT-PIMD simulations at several temperatures is used to calculate the temperature effects. The probability distributions obtained from the quantum PIMD simulations, which includes nuclear quantum effects, are significantly broader and less temperature dependent than those obtained with conventional DFT molecular dynamics or with 1D scans through the potential energy surface. Predicted NMR observables for the model systems were in excellent agreement with experimental data. PMID:26857802
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.
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.)
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.
Bose–Einstein condensate in a double-well potential: Feynman path integral variational approach
International Nuclear Information System (INIS)
A Bose–Einstein condensate in a double-well potential is considered by using the Feynman path integral theory combined with a variational approach. The system consists of N interacting bosons confined in the double well which is taken as a harmonic potential with a Gaussian barrier. The calculation is carried out within the first cumulant approximation measured with respect to the harmonic action containing variational parameters. Assuming a separable expression for the trial action corresponds to the usual mean field approximation. Performing the variational calculations, we obtain analytical results for the ground state energy and its condensate wavefunction. Using a projection onto the odd contributions, the first excited state energy and condensate wavefunction are determined, too. We find very good agreement with a full numerical solution of the Gross–Pitaevskii equation over the full range of potential parameters. (paper)
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 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.
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.
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.
Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics
Everett, Allen
2004-06-01
We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves. In a model similar to Politzer’s, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events become certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the “many worlds interpretation.” We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments.
Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics
Everett, A
2004-01-01
We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves (CTCs). In a model similar to Politzer's, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events bewcome certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the "many worlds interpretation". We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments.
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).
Accurate computation of Galerkin double surface integrals in the 3-D boundary element method
Adelman, Ross; Duraiswami, Ramani
2015-01-01
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations. Integral equation formulations lead to more compact, but dense linear systems. These dense systems are often solved iteratively via Krylov subspace methods, which may be accelerated via the fast multipole method. There are advantages to Galerkin formulations for such integral equations, as they treat problems associated with kernel singularity, and lead to symmetric and better conditioned matrices. However, the Galerkin method requires each entry in the system matrix to be created via the computation of a double surface integral over one or more pairs of triangles. There are a number of semi-analytical methods to treat these integrals, which all have some issues, and are discussed in this paper. We present novel methods to compute all the integrals that arise in Galerkin fo...
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.
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
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
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 ...
Data Integrity: Why Aren't the Data Accurate? AIR 1989 Annual Forum Paper.
Gose, Frank J.
The accuracy and reliability aspects of data integrity are discussed, with an emphasis on the need for consistency in responsibility and authority. A variety of ways in which data integrity can be compromised are discussed. The following sources of data corruption are described, and the ease or difficulty of identification and suggested actions…
Miralles, Juan Antonio; Van Riper, Kenneth A.
1995-01-01
The equation of state of an ideal Fermi gas is expressed in terms of Fermi-Dirac integrals. We give formulae for evaluation the Fermi-Dirac integrals of orders 1/2, 3/2, and 5/2 and their derivatives in various limits of non- and extreme degeneracy and relativity. We provide tables and a Fortran subroutine for numerical evaluation of the integrals and derivatives when a limit does not apply. The functions can be evaluated to better than 1% accuracy for any temperature and density using these ...
Digital Integrator for Fast Accurate Measurement of Magnetic Flux by Rotating Coils
Arpaia, P; Spiezia, G
2007-01-01
A fast digital integrator (FDI) with dynamic accuracy and a trigger frequency higher than those of a portable digital integrator (PDI), which is a state-of-the-art instrument for magnetic measurements based on rotating coils, was developed for analyzing superconducting magnets in particle accelerators. Results of static and dynamic metrological characterization show how the FDI prototype is already capable of overcoming the dynamic performance of PDI as well as covering operating regions that used to be inaccessible
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...
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
Singh, Upendra N.; Refaat, Tamer F.; Petros, Mulugeta; Yu, Jirong
2016-06-01
The two-micron wavelength is suitable for monitoring atmospheric water vapor and carbon dioxide, the two most dominant greenhouse gases. Recent advances in 2-μm laser technology paved the way for constructing state-of-the-art lidar transmitters for active remote sensing applications. In this paper, a new triple-pulsed 2-μm integrated path differential absorption lidar is presented. This lidar is capable of measuring either two species or single specie with two different weighting functions, simultaneously and independently. Development of this instrument is conducted at NASA Langley Research Center. Instrument scaling for projected future space missions will be discussed.
Directory of Open Access Journals (Sweden)
Singh Upendra N.
2016-01-01
Full Text Available The two-micron wavelength is suitable for monitoring atmospheric water vapor and carbon dioxide, the two most dominant greenhouse gases. Recent advances in 2-μm laser technology paved the way for constructing state-of-the-art lidar transmitters for active remote sensing applications. In this paper, a new triple-pulsed 2-μm integrated path differential absorption lidar is presented. This lidar is capable of measuring either two species or single specie with two different weighting functions, simultaneously and independently. Development of this instrument is conducted at NASA Langley Research Center. Instrument scaling for projected future space missions will be discussed.
Singh Upendra N.; Refaat Tamer F.; Petros Mulugeta; Yu Jirong
2016-01-01
The two-micron wavelength is suitable for monitoring atmospheric water vapor and carbon dioxide, the two most dominant greenhouse gases. Recent advances in 2-μm laser technology paved the way for constructing state-of-the-art lidar transmitters for active remote sensing applications. In this paper, a new triple-pulsed 2-μm integrated path differential absorption lidar is presented. This lidar is capable of measuring either two species or single specie with two different weighting functions, s...
Accurate integration of segmented x-ray optics using interfacing ribs
Civitani, Marta Maria; Basso, Stefano; Citterio, Oberto; Conconi, Paolo; Ghigo, Mauro; Pareschi, Giovanni; Proserpio, Laura; Salmaso, Bianca; Sironi, Giorgia; Spiga, Daniele; Tagliaferri, Gianpiero; Zambra, Alberto; Martelli, Francesco; Parodi, Giancarlo; Fumi, Pierluigi; Gallieni, Daniele; Tintori, Matteo; Bavdaz, Marcos; Wille, Eric
2013-09-01
Future lightweight and long-focal-length x-ray telescopes must guarantee a good angular resolution (e.g., 5 arc sec HEW) and reach an unprecedented large effective area. This goal can be reached with the slumping of borosilicate glass sheets that allow the fabrication of lightweight and low-cost x-ray optical units (XOU). These XOUs, based on mirror segments, have to be assembled together to form complete multishell Wolter-I optics. The technology for the fabrication and the integration of these XOUs is under development in Europe, funded by European Space Agency, and led by the Brera Observatory (INAF-OAB). While the achievement of the required surface accuracy on the glass segments by means of a hot slumping technique is a challenging aspect, adequate attention must be given to the correct integration and coalignment of the mirror segments into the XOUs. To this aim, an innovative assembly concept has been investigated, based on glass reinforcing ribs. The ribs connect pairs of consecutive foils, stacked into a XOU, with both structural and functional roles, providing robust monolithic stacks of mirror plates. Moreover, this integration concept allows the correction of residual low-frequency errors still present on the mirror foil profile after slumping. We present the integration concept, the related error budget, and the results achieved so far with a semi-robotic integration machine especially designed and realized to assemble slumped glass foils into XOUs.
Multidimensional Genome-wide Analyses Show Accurate FVIII Integration by ZFN in Primary Human Cells
Sivalingam, Jaichandran; Kenanov, Dimitar; Han, Hao; Nirmal, Ajit Johnson; Ng, Wai Har; Lee, Sze Sing; Masilamani, Jeyakumar; Phan, Toan Thang; Maurer-Stroh, Sebastian; Kon, Oi Lian
2016-01-01
Costly coagulation factor VIII (FVIII) replacement therapy is a barrier to optimal clinical management of hemophilia A. Therapy using FVIII-secreting autologous primary cells is potentially efficacious and more affordable. Zinc finger nucleases (ZFN) mediate transgene integration into the AAVS1 locus but comprehensive evaluation of off-target genome effects is currently lacking. In light of serious adverse effects in clinical trials which employed genome-integrating viral vectors, this study evaluated potential genotoxicity of ZFN-mediated transgenesis using different techniques. We employed deep sequencing of predicted off-target sites, copy number analysis, whole-genome sequencing, and RNA-seq in primary human umbilical cord-lining epithelial cells (CLECs) with AAVS1 ZFN-mediated FVIII transgene integration. We combined molecular features to enhance the accuracy and activity of ZFN-mediated transgenesis. Our data showed a low frequency of ZFN-associated indels, no detectable off-target transgene integrations or chromosomal rearrangements. ZFN-modified CLECs had very few dysregulated transcripts and no evidence of activated oncogenic pathways. We also showed AAVS1 ZFN activity and durable FVIII transgene secretion in primary human dermal fibroblasts, bone marrow- and adipose tissue-derived stromal cells. Our study suggests that, with close attention to the molecular design of genome-modifying constructs, AAVS1 ZFN-mediated FVIII integration in several primary human cell types may be safe and efficacious. PMID:26689265
Park, Seongchong; Hong, Kee-Suk; Kim, Wan-Seop
2016-03-20
This work introduces a switched integration amplifier (SIA)-based photocurrent meter for femtoampere (fA)-level current measurement, which enables us to measure a 107 dynamic range of spectral responsivity of photometers even with a common lamp-based monochromatic light source. We described design considerations and practices about operational amplifiers (op-amps), switches, readout methods, etc., to compose a stable SIA of low offset current in terms of leakage current and gain peaking in detail. According to the design, we made six SIAs of different integration capacitance and different op-amps and evaluated their offset currents. They showed an offset current of (1.5-85) fA with a slow variation of (0.5-10) fA for an hour under opened input. Applying a detector to the SIA input, the offset current and its variation were increased and the SIA readout became noisier due to finite shunt resistance and nonzero shunt capacitance of the detector. One of the SIAs with 10 pF nominal capacitance was calibrated using a calibrated current source at the current level of 10 nA to 1 fA and at the integration time of 2 to 65,536 ms. As a result, we obtained a calibration formula for integration capacitance as a function of integration time rather than a single capacitance value because the SIA readout showed a distinct dependence on integration time at a given current level. Finally, we applied it to spectral responsivity measurement of a photometer. It is demonstrated that the home-made SIA of 10 pF was capable of measuring a 107 dynamic range of spectral responsivity of a photometer. PMID:27140564
Basuki, T.M.; Skidmore, A.K.; Hussin, Y.A.; Duren, van I.C.
2013-01-01
Integration of multisensor data provides the opportunity to explore benefits emanating from different data sources. A fusion between fraction images derived from spectral mixture analysis of Landsat-7 ETM+ and phased array L-band synthetic aperture radar (PALSAR) is introduced. The aim of this fusio
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.
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…
Multi Sensor Data Integration for AN Accurate 3d Model Generation
Chhatkuli, S.; Satoh, T.; Tachibana, K.
2015-05-01
The aim of this paper is to introduce a novel technique of data integration between two different data sets, i.e. laser scanned RGB point cloud and oblique imageries derived 3D model, to create a 3D model with more details and better accuracy. In general, aerial imageries are used to create a 3D city model. Aerial imageries produce an overall decent 3D city models and generally suit to generate 3D model of building roof and some non-complex terrain. However, the automatically generated 3D model, from aerial imageries, generally suffers from the lack of accuracy in deriving the 3D model of road under the bridges, details under tree canopy, isolated trees, etc. Moreover, the automatically generated 3D model from aerial imageries also suffers from undulated road surfaces, non-conforming building shapes, loss of minute details like street furniture, etc. in many cases. On the other hand, laser scanned data and images taken from mobile vehicle platform can produce more detailed 3D road model, street furniture model, 3D model of details under bridge, etc. However, laser scanned data and images from mobile vehicle are not suitable to acquire detailed 3D model of tall buildings, roof tops, and so forth. Our proposed approach to integrate multi sensor data compensated each other's weakness and helped to create a very detailed 3D model with better accuracy. Moreover, the additional details like isolated trees, street furniture, etc. which were missing in the original 3D model derived from aerial imageries could also be integrated in the final model automatically. During the process, the noise in the laser scanned data for example people, vehicles etc. on the road were also automatically removed. Hence, even though the two dataset were acquired in different time period the integrated data set or the final 3D model was generally noise free and without unnecessary details.
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
Moving to a Soft Path for Water: Integrated Research and Management Needs
Gleick, P. H.
2011-12-01
Water on Earth in its three fundamental phases is integral to the functioning, dynamics, and variability of the global climatological and biological support systems. From a purely scientific point of view, understanding the complexity of the hydrological cycle is of paramount interest and central to our understanding of other planetary geological, atmospheric, chemical, and physical processes. But water is more than that: water is key to economic, social, and political issues as well, including some of the core challenges of our time such central to issues of poverty, health, environmental sustainability, conflict, and economic prosperity. The more society seeks to solve these challenges, the more obvious it becomes that we must improve more than just our understanding of the fundamental science of the hydrological cycle and its links with related global processes; we must also improve our understanding of the complex social, economic, and structural challenges facing water managers and users. We must move to a different paradigm where water is managed in a far more integrated way - what I call the "soft path for water." Central to our basic science needs are (1) an expansion of the frequency and nature of the data we collect, (2) the development of systems for managing, sharing, and analyzing those data, and (3) improvements in our ability to model and forecast the hydrological cycle together with other climatological, geophysical, and biochemical systems. These improvements would lead to a far better understanding of the local, regional, and global details of the water balance on timescales from minutes to millennia. These needs are increasingly well understood in the research community and extensive efforts in these areas are underway under the auspices of national research centers, universities, and international scientific collaborations. But it is also becoming increasingly apparent that many of the current water challenges facing society are not going to be
International Nuclear Information System (INIS)
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.)
International Nuclear Information System (INIS)
Highlights: ► Double proton transfer mechanisms in porphycene were studied with quantum simulations. ► Both isotopic substitution and temperature significantly affect the transfer mechanism. ► 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 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.
A coherent-state-based path integral for quantum mechanics on the Moyal plane
Tan, H S
2006-01-01
Inspired by a recent work that proposes using coherent states to evaluate the Feynman kernel in noncommutative space, we provide an independent formulation of the path-integral approach for quantum mechanics on the Moyal plane, with the transition amplitude defined between two coherent states of mean position coordinates. In our approach, we invoke solely a representation of the of the noncommutative algebra in terms of commutative variables. The kernel expression for a general Hamiltonian was found to contain gaussian-like damping terms, and it is non-perturbative in the sense that it does not reduce to the commutative theory in the limit of vanishing $\\theta$ - the noncommutative parameter. As an example, we studied the free particle's propagator which turned out to be oscillating with period being the product of its mass and $\\theta$. Further, it satisfies the Pauli equation for a charged particle with its spin aligned to a constant, orthogonal $B$ field in the ordinary Landau problem, thus providing an in...
A coherent-state-based path integral for quantum mechanics on the Moyal plane
Energy Technology Data Exchange (ETDEWEB)
Tan, H S [Raffles Junior College, Department of Physics, 10 Bishan Street 21, Singapore 574013 (Singapore)
2006-12-08
Inspired by a recent work that proposes using coherent states to evaluate the Feynman kernel in noncommutative space, we provide an independent formulation of the path-integral approach for quantum mechanics on the Moyal plane, with the transition amplitude defined between two coherent states of mean position coordinates. In our approach, we invoke solely a representation of the noncommutative algebra in terms of commutative variables. The kernel expression for a general Hamiltonian was found to contain Gaussian-like damping terms, and it is non-perturbative in the sense that it does not reduce to the commutative theory in the limit of vanishing {theta}-the noncommutative parameter. As an example, we studied the free particle's propagator which turned out to be oscillating with period being the product of its mass and {theta}. Further, it satisfies the Pauli equation for a charged particle with its spin aligned to a constant, orthogonal B field in the ordinary Landau problem, thus providing an interesting evidence of how noncommutativity can induce spin-like effects at the quantum mechanical level.
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.)
Iterative quantum-classical path integral with dynamically consistent state hopping.
Walters, Peter L; Makri, Nancy
2016-01-28
We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort. PMID:26827203
Iterative quantum-classical path integral with dynamically consistent state hopping
Energy Technology Data Exchange (ETDEWEB)
Walters, Peter L.; Makri, Nancy [Department of Chemistry, University of Illinois, Urbana, Illinois 61801 (United States)
2016-01-28
We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.
MULTI SENSOR DATA INTEGRATION FOR AN ACCURATE 3D MODEL GENERATION
S. Chhatkuli; Satoh, T; Tachibana, K
2015-01-01
The aim of this paper is to introduce a novel technique of data integration between two different data sets, i.e. laser scanned RGB point cloud and oblique imageries derived 3D model, to create a 3D model with more details and better accuracy. In general, aerial imageries are used to create a 3D city model. Aerial imageries produce an overall decent 3D city models and generally suit to generate 3D model of building roof and some non-complex terrain. However, the automatically generated 3D mod...
Wang, Zhongyi; Gao, Qi; Wang, Chengyue; Wei, Runjie; Wang, Jinjun
2016-06-01
Particle image velocimetry (PIV)-based pressure reconstruction has become a popular technique in experimental fluid mechanics. Noise or errors in raw velocity field would significantly affect the quality of pressure reconstruction in PIV measurement. To reduce experimental errors in pressure gradient and improve the precision of reconstructed pressure field, a minimal 2-norm criteria-based new technique called irrotation correction (IC) with orthogonal decomposition is developed. The pressure reconstruction is therefore composed of three steps: calculation of pressure gradient from time-resolved velocity fields of PIV, an irrotation correction on the pressure gradient field, and finally a simple orthogonal-path integration (OPI) for pressure. Systematic assessments of IC algorithm are performed on synthetic solid-body rotation flow, direct numerical simulations of a channel flow and an isotropic turbulent flow. The results show that IC is a robust algorithm which can significantly improve the accuracy of pressure reconstruction primarily in the low wave number domain. After irrotation correction, noisy pressure gradient field ideally becomes an irrotational field on which the pressure integration is independent of integrating paths. Therefore, an OPI algorithm is proposed to perform the pressure integration in an efficient way with very few integration paths. This makes the new technique to be a doable method on three-dimensional pressure reconstruction with acceptable computational cost.
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.
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.
Jiang, Shidong; Luo, Li-Shi
2016-07-01
The integral equation for the flow velocity u (x ; k) in the steady Couette flow derived from the linearized Bhatnagar-Gross-Krook-Welander kinetic equation is studied in detail both theoretically and numerically in a wide range of the Knudsen number k between 0.003 and 100.0. First, it is shown that the integral equation is a Fredholm equation of the second kind in which the norm of the compact integral operator is less than 1 on Lp for any 1 ≤ p ≤ ∞ and thus there exists a unique solution to the integral equation via the Neumann series. Second, it is shown that the solution is logarithmically singular at the endpoints. More precisely, if x = 0 is an endpoint, then the solution can be expanded as a double power series of the form ∑n=0∞∑m=0∞cn,mxn(xln x)m about x = 0 on a small interval x ∈ (0 , a) for some a > 0. And third, a high-order adaptive numerical algorithm is designed to compute the solution numerically to high precision. The solutions for the flow velocity u (x ; k), the stress Pxy (k), and the half-channel mass flow rate Q (k) are obtained in a wide range of the Knudsen number 0.003 ≤ k ≤ 100.0; and these solutions are accurate for at least twelve significant digits or better, thus they can be used as benchmark solutions.
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.
Song, Linze; Shi, Qiang
2015-05-01
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. PMID:25956086
Anderson, Brandon M.; Boyack, Rufus; Wu, Chien-Te; Levin, K.
2016-05-01
In this Rapid Communication we derive the full gauge-invariant electromagnetic response beyond the BCS level using the fermionic superfluid path integral. In the process we identify and redress a failure to satisfy the compressibility sum rule; this shortcoming is associated with the conventional path-integral formulation of BCS-level electrodynamics. The approach in this paper builds on an alternative saddle point scheme. At the mean field level, this leads to the well known gauge-invariant electrodynamics of BCS theory and to the satisfaction of the compressibility sum rule. Moreover, this scheme can be readily extended to address arbitrary higher order fluctuation theories (for example, at the Gaussian level.) At any level this approach will lead to a gauge invariant and compressibility sum rule consistent treatment of electrodynamics and thermodynamics.
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...
Wagner, Gerd; Maxwell, Stephen; Plusquellic, David
2016-06-01
Integrated path concentrations of ambient levels of carbon dioxide and methane have been measured during nighttime periods at NIST, Boulder (CO, USA), using a ground-based, eyesafe laser system. In this contribution, we describe the transmitter and receiver system, demonstrate measurements of CO2 and CH4 in comparison with an in situ point sensor measurement using a commercial cavity ring-down instrument, and demonstrate a speckle noise reduction method.
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.
Lemmens, D.; Wouters, M.; Tempere, J.; S. Foulon
2008-01-01
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our new analytical formulas are tested with numerical ...
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.
Fix, Andreas; Quatrevalet, Mathieu; Witschas, Benjamin; Wirth, Martin; Büdenbender, Christian; Amediek, Axel; Ehret, Gerhard
2016-06-01
The stringent requirements for both the frequency stability and power reference represent a challenging task for Integrated Path Differential Absorption Lidars (IPDA) to measure greenhouse gas columns from satellite or aircraft. Currently, the German-French methane mission MERLIN (Methan Remote Lidar Mission) is prepared. At the same time CHARM-F, an aircraft installed system has been developed at DLR as an airborne demonstrator for a spaceborne greenhouse gas mission. The concepts and realization of these important sub-systems are discussed.
Biryukov, Alexander; Shleenkov, Mark
2014-01-01
The amplitude and probability of quantum transitions are represented as a path integrals in energy state space of the investigated multi-level quantum system. Using this approach we consider rotational dynamics of nitrogen molecules $^{14}N_{2}$ and $^{15}N_{2}$ which interact with a sequence of ultrashort laser pulses. Our computer simulations indicate the complex dependency of the high rotation states excitation probability upon ultrashort laser pulses sequence periods. We observe pronounce...
Directory of Open Access Journals (Sweden)
Wagner Gerd
2016-01-01
Full Text Available Integrated path concentrations of ambient levels of carbon dioxide and methane have been measured during nighttime periods at NIST, Boulder (CO, USA, using a ground-based, eyesafe laser system. In this contribution, we describe the transmitter and receiver system, demonstrate measurements of CO2 and CH4 in comparison with an in situ point sensor measurement using a commercial cavity ring-down instrument, and demonstrate a speckle noise reduction method.
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.
Loo, K E
1998-01-01
We will extend Nonrelativistic Quantum Mechanics as a theory in $L\\sp2$ to a theory in the space of distributions. We will provide 3 major theories of Nonrelativist Quantum Mechanics. First, we will extend the concept of an integral kernel for the evolution operator to a distribution kernel for the $L\\sp2$ transition probability amplitude. Second, we will extend the $L\\sp2$ Schrodinger's equation to a distributions Schrodinger's equation. Lastly, we will rigorously prove that; Feynman's original formulation of the real time, time- sliced path integral is well defined when formulated on the $L\\sp2$ transition probability amplitude.
Mielke, Steven L; Truhlar, Donald G
2009-04-23
We present two enhancements to our methods for calculating vibrational-rotational free energies by Feynman path integrals, namely, a sequential sectioning scheme for efficiently generating random free-particle paths and a stratified sampling scheme that uses the energy of the path centroids. These improved methods are used with three interaction potentials to calculate equilibrium constants for the fractionation behavior of Cl(-) hydration in the presence of a gas-phase mixture of H(2)O, D(2)O, and HDO. Ion cyclotron resonance experiments indicate that the equilibrium constant, K(eq), for the reaction Cl(H(2)O)(-) + D(2)O right harpoon over left harpoon Cl(D(2)O)(-) + H(2)O is 0.76, whereas the three theoretical predictions are 0.946, 0.979, and 1.20. Similarly, the experimental K(eq) for the Cl(H(2)O)(-) + HDO right harpoon over left harpoon Cl(HDO)(-) + H(2)O reaction is 0.64 as compared to theoretical values of 0.972, 0.998, and 1.10. Although Cl(H(2)O)(-) has a large degree of anharmonicity, K(eq) values calculated with the harmonic oscillator rigid rotator (HORR) approximation agree with the accurate treatment to within better than 2% in all cases. Results of a variety of electronic structure calculations, including coupled cluster and multireference configuration interaction calculations, with either the HORR approximation or with anharmonicity estimated via second-order vibrational perturbation theory, all agree well with the equilibrium constants obtained from the analytical surfaces.
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_...
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
The U.S. EPA recently demonstrated the open-path optical remote sensing technology to identify hot spots and estimate mass flux of fugitive gases from closed landfill. The objective of this research is to validate this technology for estimating ammonia and methane emission from concentrated animal f...
Kim, Ellen S; Satter, Martin; Reed, Marilyn; Fadell, Ronald; Kardan, Arash
2016-06-01
Glioblastoma multiforme (GBM) is the most common and lethal malignant glioma in adults. Currently, the modality of choice for diagnosing brain tumor is high-resolution magnetic resonance imaging (MRI) with contrast, which provides anatomic detail and localization. Studies have demonstrated, however, that MRI may have limited utility in delineating the full tumor extent precisely. Studies suggest that MR spectroscopy (MRS) can also be used to distinguish high-grade from low-grade gliomas. However, due to operator dependent variables and the heterogeneous nature of gliomas, the potential for error in diagnostic accuracy with MRS is a concern. Positron emission tomography (PET) imaging with (11)C-methionine (MET) and (18)F-fluorodeoxyglucose (FDG) has been shown to add additional information with respect to tumor grade, extent, and prognosis based on the premise of biochemical changes preceding anatomic changes. Combined PET/MRS is a technique that integrates information from PET in guiding the location for the most accurate metabolic characterization of a lesion via MRS. We describe a case of glioblastoma multiforme in which MRS was initially non-diagnostic for malignancy, but when MRS was repeated with PET guidance, demonstrated elevated choline/N-acetylaspartate (Cho/NAA) ratio in the right parietal mass consistent with a high-grade malignancy. Stereotactic biopsy, followed by PET image-guided resection, confirmed the diagnosis of grade IV GBM. To our knowledge, this is the first reported case of an integrated PET/MRS technique for the voxel placement of MRS. Our findings suggest that integrated PET/MRS may potentially improve diagnostic accuracy in high-grade gliomas.
International Nuclear Information System (INIS)
We present a consistent and comprehensive treatise on the foundations of the extended Hamilton–Lagrange formalism — where the dynamical system is parametrized along a general system evolution parameter s, and the time t is treated as a dependent variable t(s) on equal footing with all other configuration space variables qi(s). In the action principle, the conventional classical action L1dt is then replaced by the generalized action L1ds, with L and L1 denoting the conventional and the extended Lagrangian, respectively. It is shown that a unique correlation of L1 and L exists if we refrain from performing simultaneously a transformation of the dynamical variables. With the appropriate correlation of L1 and L in place, the extension of the formalism preserves its canonical form. In the extended formalism, the dynamical system is described as a constrained motion within an extended space. We show that the value of the constraint and the parameter s constitutes an additional pair of canonically conjugate variables. In the corresponding quantum system, we thus encounter an additional uncertainty relation. As a consequence of the formal similarity of conventional and extended Hamilton–Lagrange formalisms, Feynman's nonrelativistic path integral approach can be converted on a general level into a form appropriate for relativistic quantum physics. In the emerging parametrized quantum description, the additional uncertainty relation serves as the means to incorporate the constraint and hence to finally eliminate the parametrization. We derive the extended Lagrangian L1 of a classical relativistic point particle in an external electromagnetic field and show that the generalized path integral approach yields the Klein–Gordon equation as the corresponding quantum description. We furthermore derive the space–time propagator for a free relativistic particle from its extended Lagrangian L1. These results can be regarded as the proof of principle of the relativistic
Energy Technology Data Exchange (ETDEWEB)
Schnitzer, H.J. (Brandeis Univ., Waltham, MA (USA). Dept. of Physics)
1989-09-25
A path integral construction of superconformal field theories is presented based on gauged supersymmetric Wess-Zumino-Witten actions. The conformal charge of the model is identical to that of a GKO construction. Ghost modes appear in the formalism as a result of gauge fixing. As a consequence, the holomorphic stress-tensor T(z) and superconformal generator G(z) obtained in the construction have ghost contributions. Weak operator first-class constraints restrict the theory to physical states which satisfy the constraints. The superconformal algebra closes when evaluated between ghost-free physical states. (orig.).
Directory of Open Access Journals (Sweden)
Fix Andreas
2016-01-01
Full Text Available The stringent requirements for both the frequency stability and power reference represent a challenging task for Integrated Path Differential Absorption Lidars (IPDA to measure greenhouse gas columns from satellite or aircraft. Currently, the German-French methane mission MERLIN (Methan Remote Lidar Mission is prepared. At the same time CHARM-F, an aircraft installed system has been developed at DLR as an airborne demonstrator for a spaceborne greenhouse gas mission. The concepts and realization of these important sub-systems are discussed.
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.
Dilaton transformation under abelian and non-abelian T-duality in the path-integral approach
International Nuclear Information System (INIS)
We present a convenient method for deriving the transformation of the dilaton under T-duality in the path-integral approach. Subtleties arising in performing the integral over the gauge fields are carefully analysed using Pauli-Villars regularization, thereby clarifying existing ambiguities in the literature. The formalism can not only be applied to the abelian case, but, and this for the first time, to the non-abelian case as well. Furthermore, by choosing a particular gauge, we directly obtain the target-space covariant expression for the dual geometry in the abelian case. Finally it is shown that the conditions for gauging non-abelian isometries are weaker than those generally found in the literature
Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models
Tanizaki, Yuya
2014-01-01
Zero-dimensional $O(n)$-symmetric sigma models are studied by using Picard--Lefschetz integration method in the presence of small symmetry-breaking perturbations. Due to approximate symmetry, downward flows turn out to show significant structures: They slowly travel along the set of pseudo classical points, and branch into other directions so as to span middle-dimensional integration cycles. We propose an efficient way to find such slow motions for computing Lefschetz thimbles. In the limit of symmetry restoration, we figure out that only special combinations of Lefschetz thimbles can survive as convergent integration cycles: Other integrations become divergent due to non-compactness of the complexified group of symmetry. We also compute downward flows of $O(2)$-symmetric fermionic systems, and confirm that all of these properties are true also with fermions.
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.
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
Yoo-Kong, Sikarin; Liewrian, Watchara
2015-12-01
We report on a theoretical investigation concerning the polaronic effect on the transport properties of a charge carrier in a one-dimensional molecular chain. Our technique is based on the Feynman's path integral approach. Analytical expressions for the frequency-dependent mobility and effective mass of the carrier are obtained as functions of electron-phonon coupling. The result exhibits the crossover from a nearly free particle to a heavily trapped particle. We find that the mobility depends on temperature and decreases exponentially with increasing temperature at low temperature. It exhibits large polaronic-like behaviour in the case of weak electron-phonon coupling. These results agree with the phase transition (A.S. Mishchenko et al., Phys. Rev. Lett. 114, 146401 (2015)) of transport phenomena related to polaron motion in the molecular chain. PMID:26701710
Saito, Hiroki
2016-05-01
Motivated by recent experiments [H. Kadau et al., ext-link ext-link-type="uri" xlink:href="http://doi.org/10.1038/nature16485" xlink:type="simple">Nature (London) 530, 194 (2016)ext-link>; I. Ferrier-Barbut et al., ext-link ext-link-type="uri" xlink:href="http://arxiv.org/abs/1601.03318" xlink:type="simple">arXiv:1601.03318ext-link>] and theoretical prediction (F. Wächtler and L. Santos, ext-link ext-link-type="uri" xlink:href="http://arxiv.org/abs/1601.04501" xlink:type="simple">arXiv:1601.04501ext-link>), the ground state of a dysprosium Bose-Einstein condensate with strong dipole-dipole interaction is studied by the path-integral Monte Carlo method. It is shown that quantum fluctuation can stabilize the condensate against dipolar collapse.
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...
Kreis, Karsten; Tuckerman, Mark E; Donadio, Davide; Kremer, Kurt; Potestio, Raffaello
2016-07-12
Quantum delocalization of atomic nuclei affects the physical properties of many hydrogen-rich liquids and biological systems even at room temperature. In computer simulations, quantum nuclei can be modeled via the path-integral formulation of quantum statistical mechanics, which implies a substantial increase in computational overhead. By restricting the quantum description to a small spatial region, this cost can be significantly reduced. Herein, we derive a bottom-up, rigorous, Hamiltonian-based scheme that allows molecules to change from quantum to classical and vice versa on the fly as they diffuse through the system, both reducing overhead and making quantum grand-canonical simulations possible. The method is validated via simulations of low-temperature parahydrogen. Our adaptive resolution approach paves the way to efficient quantum simulations of biomolecules, membranes, and interfaces. PMID:27214610
An Integrative Sales Growth Model for Small Enterprises in Sri Lanka : Path Analysis Approach
B, NISHANTHA
2011-01-01
Small enterprises are increasingly playing an important role in Sri Lanka. However, little is known about the determinants of small enterprise growth in this context. The purpose of this study is to gain an understanding of the factors in different dimensions influencing small enterprise growth in Sri Lanka. Based on an analysis of data from 97 owner-managers of small manufacturing enterprises located in Colombo district, the researcher developed an integrative sales growth model that suggest...
Charting a Path for Health Sciences Librarians in an Integrated Information Environment
1994-01-01
Changes in the health information environment present a major challenge to health sciences librarians. To successfully meet this challenge, librarians must apply the concepts of informal, self-directed, lifelong learning to their own carers. The Joint Commission on Accreditation of Healthcare Organizations is creating an integrated information environment in health care organizations. The health sciences librarian brings unique knowledge and skills to this environment. The reference technique...
Relations between the EU and Republic of Kosovo - The path of Kosovo integration towards the EU
Arif Riza
2016-01-01
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, KFO...
Guided growth of horizontal nanowires: A new path to self-integrated nanosystems
Joselevich, Ernesto
2014-03-01
The large-scale assembly of nanowires with controlled orientation on surfaces remains one of the most critical challenges toward their integration into practical devices. We report the vapor-liquid-solid growth of perfectly aligned, millimeter-long, horizontal GaN and ZnO nanowires with controlled crystallographic orientations on different planes of sapphire and other substrates. The growth directions, crystallographic orientation and faceting of the nanowires vary with each surface orientation, as determined by their epitaxial relationship with the substrate, as well as by a graphoepitaxial effect that guides their growth along surface steps and grooves. Despite their interaction with the surface, these horizontally grown nanowires display few structural defects, exhibiting optical and electronic properties comparable to those of vertically grown nanowires. Guided GaN nanowires and ZnO nanowires present general similarities and a few interesting differences, which shed light into the guided growth mechanism. The controlled horizontal growth of nanowires of different materials on different substrates proves the generality of the guided growth approach. Recently, we demonstrated the feasibility of massively parallel ``self-integration'' of NWs into functional systems based on guided growth, including hundreds of sing-NW based field-effect transistors made all at once, and complex logic circuits, such as a 3-bit address decoder. These examples highlight the potential of guided growth for the large-scale integration of nanowires into practical devices.
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.
Calculation of the equation of state of a dense hydrogen plasma by the Feynman path integral method
International Nuclear Information System (INIS)
A method is developed for calculating the equation of state of a system of quantum particles at a finite temperature, based on the Feynman formulation of quantum statistics. A general analytical expression is found for the virial estimator for the kinetic energy of a system with rigid boundaries at a finite pressure. An effective method is developed for eliminating the unphysical singularity in the electrostatic potential between a discretized Feynman path of an electron and a proton. It is shown that the 'refinement' of an expansion of a quantum-mechanical propagator by addition of high powers of time exacerbates, rather than eliminates, the divergence of a Feynman path integral. A brief summary of the current status of the problem is presented. The proposed new approaches are presented in relation to progress made in this field. Path integral Monte Carlo simulations are performed for nonideal hydrogen plasmas in which both indistinguishability and spin of electrons are taken into account under conditions preceding the formation of the electron shells of atoms. The electron permutation symmetry is represented in terms of Young operators. It is shown that, owing to the singularity of the Coulomb potential, quantum effects on the behavior of the electron component cannot be reduced to small corrections even if the system must be treated as a classical system according to the formal de Broglie criterion. Quantum-mechanical delocalization of electrons substantially weakens the repulsion between electrons as compared to protons. In relatively cold plasmas, many-body correlations lead to complex behavior of the potential of the average force between particles and give rise to repulsive forces acting between protons and electrons at distances of about 5 angstroms. Plasma pressure drops with decreasing plasma temperature as the electron shells of atoms begin to form, and the electron kinetic energy reaches a minimum at a temperature of about 31,000 K. The minimum point
Butko, Yana A.; Grothaus, Martin; Smolyanov, Oleg G.
2016-02-01
Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin's problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.
International Nuclear Information System (INIS)
Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures
Energy Technology Data Exchange (ETDEWEB)
Butko, Yana A., E-mail: yanabutko@yandex.ru, E-mail: kinderknecht@math.uni-sb.de [Bauman Moscow State Technical University, 2nd Baumanskaya street, 5, Moscow 105005, Russia and University of Saarland, Postfach 151150, D-66041 Saarbrücken (Germany); Grothaus, Martin, E-mail: grothaus@mathematik.uni-kl.de [University of Kaiserslautern, 67653 Kaiserslautern (Germany); Smolyanov, Oleg G., E-mail: Smolyanov@yandex.ru [Lomonosov Moscow State University, Vorob’evy gory 1, Moscow 119992 (Russian Federation)
2016-02-15
Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.
A Path to Successful Energy Retrofits: Early Collaboration through Integrated Project Delivery Teams
Energy Technology Data Exchange (ETDEWEB)
Parrish, Kristen
2012-10-31
This document guides you through a process for the early design phases of retrofit projects to help you mitigate frustrations commonly experienced by building owners and designers. It outlines the value of forming an integrated project delivery team and developing a communication and information-sharing infrastructure that fosters collaboration. This guide does not present a complete process for designing an energy retrofit for a building. Instead, it focuses on the early design phase tasks related to developing and selecting energy efficiency measures (EEMs) that benefit from collaboration, and highlights the resulting advantages.
Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
Tanizaki, Yuya; Nishimura, Hiromichi; Kashiwa, Kouji
2015-05-01
The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.
Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
Tanizaki, Yuya; Kashiwa, Kouji
2015-01-01
The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.
Energy Technology Data Exchange (ETDEWEB)
Geng, Yijia; Xu, Shuping; Xu, Weiqing, E-mail: xuwq@jlu.edu.cn [State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130012 (China); Chen, Lei [State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130012 (China); College of Physics, Jilin University, Changchun 130012 (China); Chen, Gang [State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130012 (China); College of Chemistry, Jilin University, Changchun 130012 (China); Bi, Wenbin [State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130012 (China); School of Chemistry and Environmental Engineering, Changchun University of Science and Technology, Changchun 130022 (China); Cui, Haining [College of Physics, Jilin University, Changchun 130012 (China)
2015-05-15
An integrated and portable Raman analyzer featuring an inverted probe fixed on a motor-driving adjustable optical module was designed for the combination of a microfluidic system. It possesses a micro-imaging function. The inverted configuration is advantageous to locate and focus microfluidic channels. Different from commercial micro-imaging Raman spectrometers using manual switchable light path, this analyzer adopts a dichroic beam splitter for both imaging and signal collection light paths, which avoids movable parts and improves the integration and stability of optics. Combined with surface-enhanced Raman scattering technique, this portable Raman micro-analyzer is promising as a powerful tool for microfluidic analytics.
Review of posttraumatic stress disorder and chronic pain: The path to integrated care
Directory of Open Access Journals (Sweden)
Carri-Ann Gibson, MD, DAAPM
2012-06-01
Full Text Available With the large number of Veterans experiencing posttraumatic stress disorder (PTSD and chronic pain, the purpose of this article is to review the prevalence of PTSD and chronic pain, the theoretical models that explain the maintenance of both conditions, and the challenges faced by providers and families who care for these patients. The Department of Veterans Affairs (VA/Department of Defense (DOD VA/DOD Clinical Practice Guideline for Management of Post-Traumatic Stress with special attention to chronic pain is presented. Limited scientific evidence supports specific care and treatment of PTSD and chronic pain, and this challenges providers to investigate and research potential treatment options. Integrated care models designed for working with these patients are reviewed, including a focus on the techniques and strategies to address not only PTSD and chronic pain, but other conditions, including substance dependence and depression. A specific focus on headaches, back pain, and neuropathic pain follows, including treatment recommendations such as pharmacological, psychotherapeutic, and complementary approaches, given the high rates of these pain complaints for Veterans in PTSD clinical programs. Integrated care is presented as a viable solution and approach that challenges clinicians and researchers to develop innovative, scientifically based therapeutics and treatments to enhance the recovery and quality of life for Veterans with PTSD and chronic pain.
TPP: Is the best path to regional integration of Asia Pacific?
Directory of Open Access Journals (Sweden)
Jason Carlos Martínez Jurado
2012-10-01
Full Text Available Asia-Pacific has distinguished itself for its high levels of interdependence and its fast economic growth, however, it lacks of a strong regional institutional framework. Despite the existence of APEC as a forum which includes the region’s diversity of economic development levels and cultural differences, its voluntary approach which relays on open regionalism has not allowed member economies to advance towards its ambitious goals of trade and investment liberalization. Therefore, several of its members have decided to embrace binding schemes, at a bilateral and multilateral basis, among them the TPP, which due to its comprehensive approach, for many represents the better route to achieve regional integration. However, there are questions raised regarding the convenience for Asia-Pacific to transit from a flexible model towards a reciprocal one, and the possible costs involved in such process.
The hidden curriculum in radiology residency programs: A path to isolation or integration?
Energy Technology Data Exchange (ETDEWEB)
Van Deven, T. [Department of Medical Imaging, Schulich School of Medicine and Dentistry (Canada); Hibbert, K., E-mail: khibbert@uwo.ca [Faculty of Education, Schulich School of Medicine and Dentistry (Canada); Faden, L. [Faculty of Education, The University of Western Ontario (Canada); Chhem, R.K. [Institute of History, Philosophy and Ethics of Medicine, Ulm University, Ulm (Germany)
2013-05-15
Purpose: In this qualitative case study involving five academic Radiology centres across Canada, the authors seek to identify the hidden curriculum. Methods: A qualitative case study methodology was used for its potential to explore and provide rich descriptions and allow for the in-depth analysis of multiple data sources that include official institutional documents, surveys, observations and interviews (including undergraduate students, postgraduate, radiologists, imaging scientists, residents, faculty and administrators). This study relied on 48 interviews and involved primary data analysis by the core research team, and a secondary analysis by external examiners. Results: The results revealed that in four of the five major centres studied, a hidden curriculum of isolation prevailed, reinforcing an image of the radiologist as an independent operator within an organization dependent upon collaboration for optimal performance. The fifth site exhibited a hidden curriculum of collaboration and support, although the messages received were conflicting when addressing issues around teaching. Conclusions: The authors conclude by noting two possibilities for medical imaging departments to consider that of isolation or that of integration. They examine the implications of each and propose a way forward that situates Radiology as the crossroads of medicine. As such, the need for a new, generative metaphor reasserts the importance of recognizing the role and function of scholarship in teaching and learning contexts across Canada.
The hidden curriculum in radiology residency programs: A path to isolation or integration?
International Nuclear Information System (INIS)
Purpose: In this qualitative case study involving five academic Radiology centres across Canada, the authors seek to identify the hidden curriculum. Methods: A qualitative case study methodology was used for its potential to explore and provide rich descriptions and allow for the in-depth analysis of multiple data sources that include official institutional documents, surveys, observations and interviews (including undergraduate students, postgraduate, radiologists, imaging scientists, residents, faculty and administrators). This study relied on 48 interviews and involved primary data analysis by the core research team, and a secondary analysis by external examiners. Results: The results revealed that in four of the five major centres studied, a hidden curriculum of isolation prevailed, reinforcing an image of the radiologist as an independent operator within an organization dependent upon collaboration for optimal performance. The fifth site exhibited a hidden curriculum of collaboration and support, although the messages received were conflicting when addressing issues around teaching. Conclusions: The authors conclude by noting two possibilities for medical imaging departments to consider that of isolation or that of integration. They examine the implications of each and propose a way forward that situates Radiology as the crossroads of medicine. As such, the need for a new, generative metaphor reasserts the importance of recognizing the role and function of scholarship in teaching and learning contexts across Canada
Ecosystem services and integrated water resource management: different paths to the same end?
Cook, Brian R; Spray, Christopher J
2012-10-30
The two concepts that presently dominate water resource research and management are the Global Water Partnership's (GWP, 2000) interpretation of Integrated Water Resource Management (IWRM) and Ecosystem Services (ES) as interpreted by the Millennium Ecosystem Assessment (MA, 2005). Both concepts are subject to mounting criticism, with a significant number of critiques focusing on both their conceptual and methodological incompatibility with management and governance, what has come to be known as the 'implementation gap'. Emergent within the ES and IWRM literatures, then, are two parallel debates concerning the gap between conceptualisation and implementation. Our purpose for writing this review is to argue: 1) that IWRM and ES have evolved into nearly identical concepts, 2) that they face the same critical challenge of implementation, and 3) that, if those interested in water research and management are to have a positive impact on the sustainable utilisation of dwindling water resources, they must break the tendency to jump from concept to concept and confront the challenges that arise with implementation.