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.
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...
Path integrals for pedestrians
Gozzi, Ennio; Pagani, Carlo
2016-01-01
This book serves as a pedagogical tool to teach path integrals to students and provide work-out problems. It covers the path integral for Wigner functions and for classical mechanics. This book is also useful for researchers and professionals not familiar with the topics but are interested to learn.
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.)
Continuous-Discrete Path Integral Filtering
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.
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.
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.
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...
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.
Path Integration in Conical Space
Inomata, Akira; Junker, Georg
2011-01-01
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of ...
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.
Path Integrals in Quantum Mechanics
Jean Zinn-Justin's textbook Path Integrals in Quantum Mechanics aims to familiarize the reader with the path integral as a calculational tool in quantum mechanics and field theory. The emphasis is on quantum statistical mechanics, starting with the partition function Tr exp(-β H) and proceeding through the diffusion equation to barrier penetration problems and their semiclassical limit. The 'real time' path integral is defined via analytic continuation and used for the path-integral representation of the nonrelativistic S-matrix and its perturbative expansion. Holomorphic and Grassmannian path integrals are introduced and applied to nonrelativistic quantum field theory. There is also a brief discussion of path integrals in phase space. The introduction includes a brief historical review of path integrals, supported by a bibliography with some 40 entries. As emphasized in the introduction, mathematical rigour is not a central issue in the book. This allows the text to present the calculational techniques in a very readable manner: much of the text consists of worked-out examples, such as the quartic anharmonic oscillator in the barrier penetration chapter. At the end of each chapter there are exercises, some of which are of elementary coursework type, but the majority are more in the style of extended examples. Most of the exercises indeed include the solution or a sketch thereof. The book assumes minimal previous knowledge of quantum mechanics, and some basic quantum mechanical notation is collected in an appendix. The material has a large overlap with selected chapters in the author's thousand-page textbook Quantum Field Theory and Critical Phenomena (2002 Oxford: Clarendon). The stand-alone scope of the present work has, however, allowed a more focussed organization of this material, especially in the chapters on, respectively, holomorphic and Grassmannian path integrals. In my view the book accomplishes its aim admirably and is eminently usable as a textbook
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
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.
Approximate path integral methods for partition functions
We review several approximate methods for evaluating quantum mechanical partition functions with the goal of obtaining a method that is easy to implement for multidimensional systems but accurately incorporates quantum mechanical corrections to classical partition functions. A particularly promising method is one based upon an approximation to the path integral expression of the partition function. In this method, the partition-function expression has the ease of evaluation of a classical partition function, and quantum mechanical effects are included by a weight function. Anharmonicity is included exactly in the classical Boltzmann average and local quadratic expansions around the centroid of the quantum paths yield a simple analytic form for the quantum weight function. We discuss the relationship between this expression and previous approximate methods and present numerical comparisons for model one-dimensional potentials and for accurate three-dimensional vibrational force fields for H2O and SO2
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.
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.
A New Path Generation Algorithm Based on Accurate NURBS Curves
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.
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...
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...
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...
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.
Differential neural network configuration during human path integration
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 integrals for arbitrary canonical transformations
Some aspects of the path integral formulation of quantum mechanics are studied. This formalism is generalized to arbitrary canonical transformations, by means of an association between path integral probalility amplitudes and classical generators of transformations, analogous to the usual Hamiltonian time development phase space expression. Such association turns out to be equivalent to the Weyl quantization rule, and it is also shown that this formalism furnishes a path integral representation for a Lie algebra of a given set of classical generators. Some physical considerations about the path integral quantization procedure and about the relationship between classical and quantum dynamical structures are also discussed. (Author)
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
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, ...
Integrated path towards geological storage
Among solutions to contribute to CO2 emissions mitigation, sequestration is a promising path that presents the main advantage of being able to cope with the large volume at stake when considering the growing energy demand. Of particular importance, geological storage has widely been seen as an effective solution for large CO2 sources like power plants or refineries. Many R and D projects have been initiated, whereby research institutes, government agencies and end-users achieve an effective collaboration. So far, progress has been made towards reinjection of CO2, in understanding and then predicting the phenomenon and fluid dynamics inside the geological target, while monitoring the expansion of the CO2 bubble in the case of demonstration projects. A question arises however when talking about sequestration, namely the time scale to be taken into account. Time is indeed of the essence, and points out the need to understand leakage as well as trapping mechanisms. It is therefore of prime importance to be able to predict the fate of the injected fluids, in an accurate manner and over a relevant period of time. On the grounds of geology, four items are involved in geological storage reliability: the matrix itself, which is the recipient of the injected fluids; the seal, that is the mechanistic trap preventing the injected fluids to flow upward and escape; the lower part of the concerned structure, usually an aquifer, that can be a migration way for dissolved fluids; and the man- made injecting hole, the well, whose characteristics should be as good as the geological formation itself. These issues call for specific competencies such as reservoir engineering, geology and hydrodynamics, mineral chemistry, geomechanics, and well engineering. These competencies, even if put to use to a large extent in the oil industry, have never been connected with the reliability of geological storage as ultimate goal. This paper aims at providing an introduction to these interactions and
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
In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S3C. 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.)
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 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.
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
Path integral quantization of 2 D- gravity
2 D- gravity is investigated using the Hamilton-Jacobi formalism. The equations of motion and the action integral are obtained as total differential equations in many variables. The integrability conditions, lead us to obtain the path integral quantization without any need to introduce any extra un-physical variables. (author)
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...
Transformation of variables and integration measures in path integrals
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)
Phase space representations and path integrals
Within frameworks of phase space representations in quantum mechanics and quantum field theory the Wigner distribution functions are considered, which are solutions of corresponding generalized Liouville equations. A derivation is given for representation of these distribution functions (solving of the Liouville equation) in the form of functional integrals (method is analogous to the Feynman path integral one for amplitudes). This way gives a full equality of coordinates and momenta. The expressions found are also reduced to amplitudes in the form of Feynman path integrals. A formal transition to the classical limit (h=0) is considered. Some relations of the theory of phase representations are reviewed
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 integral quantization of gravitational interactions
Some of the local symmetry properties of quantum field theory in curved space-time and quantized gravitational interactions are discussed. We concentrate on local symmetry properties, and thus the asymptotically flat space-time is assumed, whenever necessary, in the hope that the precise boundary conditions will not modify the short distance structure in quantum theory. We adopt the DeWitt-Faddeev-Popov prescription of the Feynman path integral with a complete gauge fixing. The topics discussed include: (i) A brief review of the path integral derivation of chiral anomalies in flat space-time. (ii) The specification of the gravitational path integral measure, which avoids all the ''fake'' gravitational anomalies, and the applications of this path integral prescription to 1) effective potential in generalized Kaluza-Klein theory, 2) 4-dimensional conformal anomalies, 3) conformal symmetry in pure conformal gravity, 4) bosonic string theory as a gravitational theory in d = 2, 5) Virasoro condition and the Wheeler-DeWitt equation in the path integral formalism, 6) gravitational anomalies and the definition of the energy-momentum tensor. (author)
Integrated robust controller for vehicle path following
Mashadi, Behrooz; Ahmadizadeh, Pouyan, E-mail: p-ahmadizadeh@iust.ac.ir; Majidi, Majid, E-mail: m-majidi@iust.ac.ir [Iran University of Science and Technology, School of Automotive Engineering (Iran, Islamic Republic of); Mahmoodi-Kaleybar, Mehdi, E-mail: m-mahmoodi-k@iust.ac.ir [Iran University of Science and Technology, School of Mechanical Engineering (Iran, Islamic Republic of)
2015-02-15
The design of an integrated 4WS+DYC control system to guide a vehicle on a desired path is presented. The lateral dynamics of the path follower vehicle is formulated by considering important parameters. To reduce the effect of uncertainties in vehicle parameters, a robust controller is designed based on a μ-synthesis approach. Numerical simulations are performed using a nonlinear vehicle model in MATLAB environment in order to investigate the effectiveness of the designed controller. Results of simulations show that the controller has a profound ability to making the vehicle track the desired path in the presence of uncertainties.
Integrated robust controller for vehicle path following
The design of an integrated 4WS+DYC control system to guide a vehicle on a desired path is presented. The lateral dynamics of the path follower vehicle is formulated by considering important parameters. To reduce the effect of uncertainties in vehicle parameters, a robust controller is designed based on a μ-synthesis approach. Numerical simulations are performed using a nonlinear vehicle model in MATLAB environment in order to investigate the effectiveness of the designed controller. Results of simulations show that the controller has a profound ability to making the vehicle track the desired path in the presence of uncertainties
Fermionic path integrals and local anomalies
Roepstorff, G.
2003-05-01
No doubt, the subject of path integrals proved to be an immensely fruitful human, i.e. Feynman's idea. No wonder it is more timely than ever. Some even claim that it is the most daring, innovative and revolutionary idea since the days of Heisenberg and Bohr. It is thus likely to generate enthusiasm, if not addiction among physicists who seek simplicity together with perfection. Professor Devreese's long-lasting interest in, if not passion on the subject stems from his firm conviction that, beyond being the tool of choice, path integration provides the key to all quantum phenomena, be it in solid state, atomic, molecular or particle physics as evidenced by the impressive list of publications at the address http://lib.ua.ac.be/AB/a867.html. In this note, I review a pitfall of fermionic path integrals and a way to get around it in situations relevant to the Standard Model of particle physics.
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.
Efficient and Accurate Path Cost Estimation Using Trajectory Data
Dai, Jian; Yang, Bin; Guo, Chenjuan; Jensen, Christian S.
2015-01-01
Using the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road network as a graph, assigns weights to the graph's edges by fragmenting trajectories into small pieces that fit the underlying edges, and then applies a routing algorithm to the resulting graph. We propose a new paradigm that targets more accurate and more ...
Path integrals for stochastic processes an introduction
Wio, Horacio S
2013-01-01
This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920's, corresponding to a sum over random trajectories, anticipating by two decades Feynman's famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950's. The last quarter of the 20th century has witnesse
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.
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.
Path integral and noncommutative Poisson brackets
Valtancoli, P.
2015-06-01
We find that in presence of noncommutative Poisson brackets, the relation between Lagrangian and Hamiltonian is modified. We discuss this property by using the path integral formalism for non-relativistic systems. We apply this procedure to the harmonic oscillator with a minimal length.
Path integral and noncommutative poisson brackets
Valtancoli, P.
2015-01-01
We find that in presence of noncommutative poisson brackets the relation between Lagrangian and Hamiltonian is modified. We discuss this property by using the path integral formalism for non-relativistic systems. We apply this procedure to the harmonic oscillator with a minimal length.
Path integration in desert ants, Cataglyphis fortis
Müller, Martin; Wehner, Rüdiger
1988-01-01
Foraging desert ants, Cataglyphis fortis, continually keep track of their own posotions relative to home— i.e., integrate their tortuous outbound routes and return home along straight (inbound) routes. By experimentally manipulating the ants' outbound trajectories we show that the ants solve this path integration problem not by performing a true vector summation (as a human navigator does) but by employing a computationally simple approximation. This approximation is characterized by small, b...
Age differences in virtual environment and real world path integration
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
Glueball masses from ratios of path integrals
Della Morte, Michele
2011-01-01
By generalizing our previous work on the parity symmetry, the partition function of a Yang-Mills theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang-Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at two values of the lattice spacing (0.17 and 0.12 fm).
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
Path Integrals and Anomalies in Curved Space
Bastianelli and van Nieuwenhuizen's monograph 'Path Integrals and Anomalies in Curved Space' collects in one volume the results of the authors' 15-year research programme on anomalies that arise in Feynman diagrams of quantum field theories on curved manifolds. The programme was spurred by the path-integral techniques introduced in Alvarez-Gaume and Witten's renowned 1983 paper on gravitational anomalies which, together with the anomaly cancellation paper by Green and Schwarz, led to the string theory explosion of the 1980s. The authors have produced a tour de force, giving a comprehensive and pedagogical exposition of material that is central to current research. The first part of the book develops from scratch a formalism for defining and evaluating quantum mechanical path integrals in nonlinear sigma models, using time slicing regularization, mode regularization and dimensional regularization. The second part applies this formalism to quantum fields of spin 0, 1/2, 1 and 3/2 and to self-dual antisymmetric tensor fields. The book concludes with a discussion of gravitational anomalies in 10-dimensional supergravities, for both classical and exceptional gauge groups. The target audience is researchers and graduate students in curved spacetime quantum field theory and string theory, and the aims, style and pedagogical level have been chosen with this audience in mind. Path integrals are treated as calculational tools, and the notation and terminology are throughout tailored to calculational convenience, rather than to mathematical rigour. The style is closer to that of an exceedingly thorough and self-contained review article than to that of a textbook. As the authors mention, the first part of the book can be used as an introduction to path integrals in quantum mechanics, although in a classroom setting perhaps more likely as supplementary reading than a primary class text. Readers outside the core audience, including this reviewer, will gain from the book a
How to solve path integrals in quantum mechanics
A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last 15 years, including, of course, the main contributions since the invention of the path integral by Feynman in 1942. An outline of the general theory is given which will serve as a quick reference for solving path integrals. Explicit formulae for the so-called basic path integrals are presented on which our general scheme to classify and calculate path integrals in quantum mechanics is based. (orig.)
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.
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-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-...
Real-time accurate hand path tracking and joint trajectory planning for industrial robots(Ⅱ)
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.
Modeling DNA Dynamics by Path Integrals
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 (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 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 geometry peculiar of B-DNA. I discuss the interplay between twisting of the double helix and anharmonic stacking along the molecule backbone suggesting an interesting relation between intrinsic nonlinear character of the microscopic interactions and molecular topology.
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.
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
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
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)
Real-time accurate hand path tracking and joint trajectory planning for industrial robots(Ⅰ)
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.
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 solution by fractional calculus
Cottone, G; Paola, M D; Pirrotta, A [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita degli Studi di Palermo, Viale delle Scienze, 90128, Palermo (Italy)], E-mail: giuliocottone@diseg.unipa.it, E-mail: dipaola@diseg.unipa.it, E-mail: pirrotta@diseg.unipa.it
2008-02-15
In this paper, the Path Integral solution is developed in terms of complex moments. The method is applied to nonlinear systems excited by normal white noise. Crucial point of the proposed procedure is the representation of the probability density of a random variable in terms of complex moments, recently proposed by the first two authors. Advantage of this procedure is that complex moments do not exhibit hierarchy. Extension of the proposed method to the study of multi degree of freedom systems is also discussed.
Path integral solution by fractional calculus
In this paper, the Path Integral solution is developed in terms of complex moments. The method is applied to nonlinear systems excited by normal white noise. Crucial point of the proposed procedure is the representation of the probability density of a random variable in terms of complex moments, recently proposed by the first two authors. Advantage of this procedure is that complex moments do not exhibit hierarchy. Extension of the proposed method to the study of multi degree of freedom systems is also discussed
Path integral for multi-field inflation
Gong, Jinn-Ouk; Shiu, Gary
2016-01-01
We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixing conditions based on the Poisson brackets of the constraints, from which we derive two convenient gauges that are appropriate for multi-field inflation. We then adopt the in-in formalism to derive the most general expression for the power spectrum of the curvature perturbation including the corrections from the interactions of the curvature mode with other light degrees of freedom. We also discuss the contributions of the interactions to the bispectrum.
Path integral quantization of generalized quantum electrodynamics
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.
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 discussion for Smorodinsky-Winternitz potentials. Pt. 1
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
Huygens' principle and the path integral
Huygens' principle is shown to be the relativistic generalization of Feynman's path integral, i.e. the latter can be derived from the former if the speed of light goes to affinity. There are two quite different views which have to be disentangled: the well-known diffraction patterns as in the propagation of light waves through one or more slits, are associated with monochromatic light and satisfy the Helmholtz equation, whereas Huygens's wave theory is based on time-varying light pulses which satisfy the wave equation. the Helmholtz equation, or equivalently the stationary Schroedinger equation, are elliptic partial differential equation for which nothing resembling Huygens' original construction applies, as will be explained in some detail because it is often not well understood. The full wave equation leads in 1 and 3 space dimensions quite naturally to this construction in terms of spherical wave pulses, but not generally to the usual diffraction pattern. For 2 space dimensions, however, or for relativistic particles with a non-vanishing mass, and for hyperbolic partial differential equations in general, one gets only the weak form of Huygens' principle where the amplitude is propagated both on and inside the light cone. Explicit integral formulas are given for the amplitude at some later time t>0 in terms of the amplitude and its time-derivative at time t = 0 using the work of Hadamard and its explicit results as found in the treatise by Courant and Hilbert. We give a short sketch of how these formulas can be applied to the Dirac equation, and then lead directly to the path integral for the time-dependent Schroedinger equation. 11 refs, 2 figs
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. PMID:26442503
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
Development Path of Urban-rural Integration
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; Schaefer, Thomas; Sulejmanpasic, Tin; Unsal, Mithat
2016-01-01
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical 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 semi-classical expansion is in conflict with basic properties such as positive-semidefiniteness of the spectrum, and constraints of supersymmetry. Generic saddles are not only complex, but also possibly multi-valued, and even singular. This is in contrast to instanton solutions, which are real, smooth, and single-valued. The multi-valuedness of the action can be interpreted as a hidden topological angle, quantized in units of $\\pi$ in supersymmetric theories. The general ideas also apply to non-supersymmetric theories.
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...
Polymer quantum mechanics some examples using path integrals
Parra, Lorena [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F., México and Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Vergara, J. David [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F. (Mexico)
2014-01-14
In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems.
Coordinate-invariant Path Integral Methods in Conformal Field Theory
van Tonder, André
2004-01-01
We present a coordinate-invariant approach, based on a Pauli-Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in contrast to the measure used in the Fujikawa calculation, and we show the agreement, despite differ...
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...
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
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.
Two-path plasmonic interferometer with integrated detector
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
The Weyl ordering and path integrals in curved spaces
A simple framework to deal with path integrals in curved spaces is presented. The phase space path integral representation of the propagator is constructed in terms of an effective Hamiltonian which differs from the classical one by terms of order (h/2π). The general expression for this quantum correction is derived by using the Weyl ordering for non-commuting operators. When the propagator is expressed as a Lagrangian path integral with an invariant measure an additional correction is introduced. (author). 11 refs
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.
A Contracted Path Integral Solution of the Discrete Master Equation
Helbing, Dirk
1998-01-01
A new representation of the exact time dependent solution of the discrete master equation is derived. This representation can be considered as contraction of the path integral solution of Haken. It allows the calculation of the probability distribution of the occurence time for each path and is suitable as basis of new computational solution methods.
Remembered landmarks enhance the precision of path integration
Shannon O´Leary
2005-01-01
Full Text Available When navigating by path integration, knowledge of ones position becomes increasingly uncertain as one walks from a known location. This uncertainty decreases if one perceives a known landmark location nearby. We hypothesized that remembering landmarks might serve a similar purpose for path integration as directly perceiving them. If this is true, walking near a remembered landmark location should enhance response consistency in path integration tasks. To test this, we asked participants to view a target and then attempt to walk to it without vision. Some participants saw the target plus a landmark during the preview. Compared with no-landmark trials, response consistency nearly doubled when participants passed near the remembered landmark location. Similar results were obtained when participants could audibly perceive the landmark while walking. A control experiment ruled out perceptual context effects during the preview. We conclude that remembered landmarks can enhance path integration even though they are not directly perceived.
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...
Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will
Vehicle path tracking by integrated chassis control
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.
A path integral formulation of p-adic quantum mechanics
We propose a path integral formulation of some evolution operators with p-adic 'time', based on restrictions to nested invariant subspaces of test-functions. These restrictions turn the time variables into discrete ones and allow the usual path integral manipulations. We illustrate this definition with the example of the p-acid harmonic oscillator and point out realizations in the context of two-dimensional conformal field theories and Yang-Mills equations. (orig.)
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...
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...
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.
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.
Bias in Human Path Integration Is Predicted by Properties of Grid Cells.
Chen, Xiaoli; He, Qiliang; Kelly, Jonathan W; Fiete, Ila R; McNamara, Timothy P
2015-06-29
Accurate wayfinding is essential to the survival of many animal species and requires the ability to maintain spatial orientation during locomotion. One of the ways that humans and other animals stay spatially oriented is through path integration, which operates by integrating self-motion cues over time, providing information about total displacement from a starting point. The neural substrate of path integration in mammals may exist in grid cells, which are found in dorsomedial entorhinal cortex and presubiculum and parasubiculum in rats. Grid cells have also been found in mice, bats, and monkeys, and signatures of grid cell activity have been observed in humans. We demonstrate that distance estimation by humans during path integration is sensitive to geometric deformations of a familiar environment and show that patterns of path integration error are predicted qualitatively by a model in which locations in the environment are represented in the brain as phases of arrays of grid cells with unique periods and decoded by the inverse mapping from phases to locations. The periods of these grid networks are assumed to expand and contract in response to expansions and contractions of a familiar environment. Biases in distance estimation occur when the periods of the encoding and decoding grids differ. Our findings explicate the way in which grid cells could function in human path integration. PMID:26073138
INTEGRATED LAYOUT DESIGN OF CELLS AND FLOW PATHS
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.
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.
2016-01-01
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.
PathSys: integrating molecular interaction graphs for systems biology
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...
Measure of the path integral in lattice gauge theory
Paradis, F.; Kroger, H.; Luo, X. Q.; Moriarty, K. J. M.
2005-01-01
We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in contrast to the calculation of ratios of amplitudes). Single amplitudes are required for computation of the partition function and the free energy. For U(1) lattice gauge theory, we present a numerical simulation of the transition amplitude comparing the path int...
Pricing Exotic Options in a Path Integral Approach
G. Bormetti; Montagna, G.; Moreni, N.; Nicrosini, O.
2004-01-01
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 European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the cases of Asian, barrier knock out, reverse cliquet and basket call options, evaluating prices and Greeks. The numerical results are compared with those obtained with oth...
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.
Polymer density functional approach to efficient evaluation of path integrals
Brukhno, Andrey; Vorontsov-Velyaminov, Pavel N.; Bohr, Henrik
2005-01-01
A polymer density functional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly......, the path integral problem can, in principle, be solved exactly by making use of the two-particle pair correlation function (2p-PCF) for the ends of an open polymer, half of the original. This way the exact data for one-dimensional quantum harmonic oscillator are reproduced in a wide range of...... simple self-consistent iteration so as to correctly account for the interparticle interactions. The algorithm is speeded up by taking convolutions with the aid of fast Fourier transforms. We apply this approximate path integral DFT (PI-DFT) method to systems within spherical symmetry: 3D harmonic...
Path Integration Applied to Structural Systems with Uncertain Properties
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...
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.
Defect forces, defect couples and path integrals
Definition and meaning of concepts like 'J integral' are given without any assumption about material behaviour. The key of the work is the field of 'defect forces' and 'defect couples' in a continuous media. These forces and couples, which can also be called 'material forces' and 'material couples' are related to the work done by a particle moving through a solid. It is shown that the resultant of all the defect forces included in a volume is the Jsub(k) integral computer on the surface surrounding this volume. A similar result is obtained about the moment resultant. Conventional form of the principle of virtual work is not applicable to fractures mechanics because equations of compatibility are not satisfied. A generalized form is given, which is valid when (virtual) crack propagation is considered. The virtual work of 'material' forces is included in the generalized form, and can be used as a new definition of J concept. As an illustration application, a simple procedure is described which allows to obtain the curve J-Δa (the so called J-R curve) from only one experimental test
Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology
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.
Recent developments in the path integral approach to anomalies
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)
Path Integral Methods for Single Band Hubbard Model
N. Heydari; Azakov, S.
1997-01-01
We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly. Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creation and annihilation fermionic operators, with the help of the fermionic coherent states of holomorp...
Path integral approach to non-relativistic electron charge transfer
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)
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...
Group theoretical approach to path integration on spheres
The path integral over compact and non-compact spheres (denoted by Hα) is discussed. The short time propagator is decomposed in unitary irreducible representations of the corresponding transformation group G of Hα. Two cases are considered. For G ≅ Hα the Fourier analysis leads to an expansion in group characters. However, in the general case Hα ≅ G/H the decomposition gives an expansion in zonal spherical functions of G is contained in H. The path integral is performed using the orthogonality of the representations. The groups SO(n), SO(n - 1,1) SU(2) and SU(1,1) are considered. (author). 10 refs
Path integrals, BRST identities, and regularization schemes in nonstandard gauges
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
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 invariants in abelian Chern–Simons theory
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
Is the Polyakov path integral prescription too restrictive?
Mathur, S D
1993-01-01
In the first quantised description of strings, we integrate over target space co-ordinates $X^\\mu$ and world sheet metrics $g_{\\alpha\\beta}$. Such path integrals give scattering amplitudes between the `in' and `out' vacuua for a time-dependent target space geometry. For a complete description of `particle creation' and the corresponding backreaction, we need instead the causal amplitudes obtained from an `initial value formulation'. We argue, using the analogy of a scalar particle in curved space, that in the first quantised path integral one should integrate over $X^\\mu$ and world sheet {\\it zweibiens}. This extended formalism can be made to yield causal amplitudes; it also naturally allows incorporation of density matrices in a covariant manner. (This paper is an expanded version of hep-th 9301044)
Chiral symmetry in the path-integral approach
The derivation of anomalous Ward-Takahashi identities related to chiral symmetries in the path-integral framework is presented. Some two-dimensional models in both abelian and non-abelian cases are discussed. The quantization of such theories using Weyl fermions is also presented. (L.C.)
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.
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
Review of quantum path integrals in fluctuating markets
Bonnet, Frederic D. R.; Allison, Andrew G.; Abbott, Derek
2004-03-01
We review various techniques from engineering and physics applied to the theory of financial risks. We also explore at an introductory level how the quantum aspects of physics may be used to study the dynamics of financial markets. In particular we explore how the path integral methods may be used to study financial markets quantitatively.
A path integral approach to topological conservation in polymer systems
The physical application discussed here refers to polymer molecules in a condensed concentrated state, e.g. as in a melt. It is initially considered how these molecules can be described in terms of path integrals and then the topological constraints that prevents one molecule from passing through another are being discussed. 9 refs, 5 figs
A path-integral approach to the collisional Boltzmann gas
Chen, C Y
2000-01-01
Collisional effects are included in the path-integral formulation that was proposed in one of our previous paper for the collisionless Boltzmann gas. In calculating the number of molecules entering a six-dimensional phase volume element due to collisions, both the colliding molecules and the scattered molecules are allowed to have distributions; thus the calculation is done smoothly and no singularities arise.
Path integral quantization of the Poisson-Sigma model
Hirshfeld, Allen C.; Schwarzweller, Thomas
1999-01-01
We apply the antifield quantization method of Batalin and Vilkovisky to the calculation of the path integral for the Poisson-Sigma model in a general gauge. For a linear Poisson structure the model reduces to a nonabelian gauge theory, and we obtain the formula for the partition function of two-dimensional Yang-Mills theory for closed two-dimensional manifolds.
On the Path Integral of the Relativistic Electron
Kull, A.; Treumann, R. A.
1999-01-01
We revisit the path integral description of the motion of a relativistic electron. Applying a minor but well motivated conceptional change to Feynman's chessboard model, we obtain exact solutions of the Dirac equation. The calculation is performed by means of a particular simple method different from both the combinatorial approach envisaged by Feynman and its Ising model correspondence.
Path integral in holomorphic representation without gauge fixation
The way of path integral (PI) construction without a gauge fixation in holomorphic representation is proposed for finite-dimensional models with a gauge group. This PI gives a manifest gauge-invariant form for the evolution operator kernel. 10 refs
Path Integral Monte-Carlo Calculations for Relativistic Oscillator
Ivanov, Alexandr; Pavlovsky, Oleg
2014-01-01
The problem of Relativistic Oscillator has been studied in the framework of Path Integral Monte-Carlo(PIMC) approach. Ultra-relativistic and non-relativistic limits have been discussed. We show that PIMC method can be effectively used for investigation of relativistic systems.
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.
Path-integral method for the source apportionment of photochemical pollutants
Dunker, A. M.
2015-06-01
A new, path-integral method is presented for apportioning the concentrations of pollutants predicted by a photochemical model to emissions from different sources. A novel feature of the method is that it can apportion the difference in a species concentration between two simulations. For example, the anthropogenic ozone increment, which is the difference between a simulation with all emissions present and another simulation with only the background (e.g., biogenic) emissions included, can be allocated to the anthropogenic emission sources. The method is based on an existing, exact mathematical equation. This equation is applied to relate the concentration difference between simulations to line or path integrals of first-order sensitivity coefficients. The sensitivities describe the effects of changing the emissions and are accurately calculated by the decoupled direct method. The path represents a continuous variation of emissions between the two simulations, and each path can be viewed as a separate emission-control strategy. The method does not require auxiliary assumptions, e.g., whether ozone formation is limited by the availability of volatile organic compounds (VOCs) or nitrogen oxides (NOx), and can be used for all the species predicted by the model. A simplified configuration of the Comprehensive Air Quality Model with Extensions (CAMx) is used to evaluate the accuracy of different numerical integration procedures and the dependence of the source contributions on the path. A Gauss-Legendre formula using three or four points along the path gives good accuracy for apportioning the anthropogenic increments of ozone, nitrogen dioxide, formaldehyde, and nitric acid. Source contributions to these increments were obtained for paths representing proportional control of all anthropogenic emissions together, control of NOx emissions before VOC emissions, and control of VOC emissions before NOx emissions. There are similarities in the source contributions from the
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
Integral representation of the edge diffracted waves along the ray path of the transition region.
Umul, Yusuf Z
2008-09-01
The expression of the edge diffracted fields, in terms of the Fresnel integral, is transformed into a path integral. The obtained integral considers the integration of the incident field along the ray path of the transition region. The similarities of the path integral with Kirchhoff's theory of diffraction and the modified theory of physical optics are examined. PMID:18758538
Shortest Path Edit Distance for Enhancing UMLS Integration and Audit.
Rudniy, Alex; Geller, James; Song, Min
2010-01-01
Expansion of the UMLS is an important long-term research project. This paper proposes Shortest Path Edit Distance (SPED) as an algorithm for improving existing source-integration and auditing techniques. We use SPED as a string similarity measure for UMLS terms that are known to be synonyms because they are assigned to the same concept. We compare SPED with several other well known string matching algorithms using two UMLS samples as test bed. One of those samples is SNOMED-based. SPED transforms the task of calculating edit distance among two strings into a problem of finding a shortest path from a source to a destination in a node and link graph. In the algorithm, the two strings are used to construct the graph. The Pulling algorithm is applied to find a shortest path, which determines the string similarity value. SPED was superior for one of the data sets, with a precision of 0.6. PMID:21347068
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, BRS symmetry, and string and membrane theories
A unified treatment of quantum symmetries is attempted on the basis of the BRS symmetry appearing in the path integral. We first briefly review a systematic derivation of anomalous commutators and the fact that all the known non-trivial anomalous commutators are related to the anomaly. We next present a refined treatment of the reparametrization invariant path integral measure, which is then illustrated for the two-dimensional string theory. The critical dimension is shown to arise from the explicit or implicit gauge fixing of the Weyl freedom. We finally present a Faddeev-Popov-BRS treatment of the bosonic membrane. The narrow limit of the quantized closed membrane is shown to reproduce certain massless states of the closed string. (author)
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
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.
Path Integral Monte Carlo Calculation of the Deuterium Hugoniot
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
High-density amorphous ice: A path-integral simulation
Herrero, Carlos P; 10.1063/1.4750027
2012-01-01
Structural and thermodynamic properties of high-density amorphous (HDA) ice have been studied by path-integral molecular dynamics simulations in the isothermal-isobaric ensemble. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. Quantum nuclear motion is found to affect several observable properties of the amorphous solid. At low temperature (T = 50 K) the molar volume of HDA ice is found to increase by 6%, and the intramolecular O--H distance rises by 1.4% due to quantum motion. Peaks in the radial distribution function of HDA ice are broadened respect to their classical expectancy. The bulk modulus, B, is found to rise linearly with the pressure, with a slope dB/dP = 7.1. Our results are compared with those derived earlier from classical and path-integral simulations of HDA ice. We discuss similarities and discrepancies with those earlier simulations.
Path integral Liouville dynamics for thermal equilibrium systems
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 quantization of the relativistic Hopfield model
Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M.
2016-03-01
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 Solution for an Angle-Dependent Anharmonic Oscillator
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.
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...
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.
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.
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.
Feynman path integrals in the young double-slit experiment
An estimate for the value of the nonlinear interference term in the Young double-slit experiment is found using the Feynman path-integral method. In our time-dependent calculation the usual interference term becomes multiplied by 1 + e with e proportional to cos(2mλL//eta/T), where λ is the distance between the two slits (holes) and L is the length of the shortest trajectory of electrons between the source and the observation point
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...
Non linear gluon evolution in path-integral form
Blaizot, J P; Weigert, H
2003-01-01
We explore and clarify the connections between two different forms of the renormalisation group equations describing the quantum evolution of hadronic structure functions at small $x$. This connection is established via a Langevin formulation and associated path integral solutions that highlight the statistical nature of the quantum evolution, pictured here as a random walk in the space of Wilson lines. The results confirm known approximations, form the basis for numerical simulations and widen the scope for further analytical studies.
Non linear gluon evolution in path-integral form
Blaizot, Jean-Paul; Iancu, Edmond E-mail: iancu@spht.saclay.cea.fr; Weigert, Heribert
2003-01-27
We explore and clarify the connections between two different forms of the renormalization group equations describing the quantum evolution of hadronic structure functions at small x. This connection is established via a Langevin formulation and associated path integral solutions that highlight the statistical nature of the quantum evolution, pictured here as a random walk in the space of Wilson lines. The results confirm known approximations, form the basis for numerical simulations and widen the scope for further analytical studies.
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.
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...
Quantum mechanics 1. Path-integral formulation and operator formalism
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.
Efficient algorithms for semiclassical instanton calculations based on discretized path integrals
Path integral instanton method is a promising way to calculate the tunneling splitting of energies for degenerated two state systems. In order to calculate the tunneling splitting, we need to take the zero temperature limit, or the limit of infinite imaginary time duration. In the method developed by Richardson and Althorpe [J. Chem. Phys. 134, 054109 (2011)], the limit is simply replaced by the sufficiently long imaginary time. In the present study, we have developed a new formula of the tunneling splitting based on the discretized path integrals to take the limit analytically. We have applied our new formula to model systems, and found that this approach can significantly reduce the computational cost and gain the numerical accuracy. We then developed the method combined with the electronic structure calculations to obtain the accurate interatomic potential on the fly. We present an application of our ab initio instanton method to the ammonia umbrella flip motion
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.
Accurate Complex Systems Design: Integrating Serious Games with Petri Nets
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.
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.
An improved heat kernel expansion from worldline path integrals
The one-loop effective action for the case of a massive scalar loop in the background of both a scalar potential and an abelian or non-abelian gauge field is written in a one-dimensional path integral representation. From this the inverse mass expansion is obtained by Wick contractions using a suitable Green function, which allows the computation of higher order coefficients. For the scalar case, explicit results are presented up to order O(T8) in the proper time expansion. The relation to previous work is clarified. (orig.)
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...
Huang, Guo-Jiao; Bai, Chao-Ying; Greenhalgh, Stewart
2013-09-01
The traditional grid/cell-based wavefront expansion algorithms, such as the shortest path algorithm, can only find the first arrivals or multiply reflected (or mode converted) waves transmitted from subsurface interfaces, but cannot calculate the other later reflections/conversions having a minimax time path. In order to overcome the above limitations, we introduce the concept of a stationary minimax time path of Fermat's Principle into the multistage irregular shortest path method. Here we extend it from Cartesian coordinates for a flat earth model to global ray tracing of multiple phases in a 3-D complex spherical earth model. The ray tracing results for 49 different kinds of crustal, mantle and core phases show that the maximum absolute traveltime error is less than 0.12 s and the average absolute traveltime error is within 0.09 s when compared with the AK135 theoretical traveltime tables for a 1-D reference model. Numerical tests in terms of computational accuracy and CPU time consumption indicate that the new scheme is an accurate, efficient and a practical way to perform 3-D multiphase arrival tracking in regional or global traveltime tomography.
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, 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.
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
Dornheim, Tobias; Schoof, Tim; Groth, Simon; Filinov, Alexey; Bonitz, Michael
2015-11-01
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, r s = r ¯ / a B ≳ 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.
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
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.
Path integrals for the Green-Schwarz superstring
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
Investigation of the spinfoam path integral with quantum cuboid intertwiners
Bahr, Benjamin; Steinhaus, Sebastian
2016-05-01
In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the spinfoam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov. To tackle the problem, we restrict to a set of quantum geometries that reflects the large amount of lattice symmetries. In particular, the sum over intertwiners is restricted to quantum cuboids, i.e. coherent intertwiners which describe a cuboidal geometry in the large-j limit. Using asymptotic expressions for the vertex amplitude, we find several interesting properties of the state sum. First of all, the value of coupling constants in the amplitude functions determines whether geometric or nongeometric configurations dominate the path integral. Secondly, there is a critical value of the coupling constant α , which separates two phases. In both phases, the diffeomorphism symmetry appears to be broken. In one, the dominant contribution comes from highly irregular, in the other from highly regular configurations, both describing flat Euclidean space with small quantum fluctuations around them, viewed in different coordinate systems. On the critical point diffeomorphism symmetry is nearly restored, however. Thirdly, we use the state sum to compute the physical norm of kinematical states, i.e. their norm in the physical Hilbert space. We find that states which describe boundary geometry with high torsion have an exponentially suppressed physical norm. We argue that this allows one to exclude them from the state sum in calculations.
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.
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...
ACCURATE BUILDING INTEGRATED PHOTOVOLTAIC SYSTEM (BIPV) ARCHITECTURAL DESIGN TOOL
One of the leading areas of renewable energy applications for the twenty-first century is building integrated photovoltaics (BIPV). Integrating photovoltaics into building structures allows the costs of the PV system to be partially offset by the solar modules also serving a s...
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
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).
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.
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
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.)
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.
2012-06-06
... COMMISSION Certain Integrated Circuit Packages Provided With Multiple Heat- Conducting Paths and Products.... International Trade Commission has received a complaint entitled Certain Integrated Circuit Packages Provided... sale within the United States after importation of certain integrated circuit packages provided...
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, ...
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
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.
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.
Looping probabilities of elastic chains: a path integral approach.
Cotta-Ramusino, Ludovica; Maddocks, John H
2010-11-01
We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end
Path integral formulation and Feynman rules for phylogenetic branching models
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantized, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of non-equilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The 'free' theory (without branching) is solved, and the correct trilinear 'interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with two or three leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrization covariance
Geodesic optics via path integral formalism. A modified principle of minimum time
The optical propagator for the Helmoltz equation in geodesic optics is given by the Fourier transform of a path integral in curve spaces. Here it is tried to express it directly by a path integral in a Riemann space. This optical propagator is obtained as a Lagrangian path integral which let us infer a modified principle of minimum time for geodesic components, that is an effective refractive index is obtained as the usual refractive index plus a correction of order λ2
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 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...
Accurate Kirkwood-Buff Integrals from Molecular Dynamics Simulations
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...
An Integrative Approach to Accurate Vehicle Logo Detection
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.
Theory of extreme correlations using canonical Fermions and path integrals
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 Δ0 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 EQ∗∼γQ−√(Γ02+Q2), where the vanishing of Q, a momentum type variable, locates the kink minimum. Therefore the quasiparticle velocity interpolates between (γ∓1) over a width Γ0 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. •Electronic origin of low energy kinks in
Wang, Jin; Zhang, Kun; Wang, Erkwang
2010-09-01
We developed a general framework to quantify three key ingredients for dynamics of nonequilibrium systems through path integrals in length space. First, we identify dominant kinetic paths as the ones with optimal weights, leading to effective reduction of dimensionality or degrees of freedom from exponential to polynomial so large systems can be treated. Second, we uncover the underlying nonequilibrium potential landscapes from the explorations of the state space through kinetic paths. We apply our framework to a specific example of nonequilibrium network system: lambda phage genetic switch. Two distinct basins of attractions emerge. The dominant kinetic paths from one basin to another are irreversible and do not follow the usual steepest descent or gradient path along the landscape. It reflects the fact that the dynamics of nonequilibrium systems is not just determined by potential gradient but also the residual curl flux force, suggesting experiments to test theoretical predictions. Third, we have calculated dynamic transition time scales from one basin to another critical for stability of the system through instantons. Theoretical predictions are in good agreements with wild type and mutant experiments. We further uncover the correlations between the kinetic transition time scales and the underlying landscape topography: the barrier heights along the dominant paths. We found that both the dominant paths and the landscape are relatively robust against the influences of external environmental perturbations and the system tends to dissipate less with less fluctuations. Our general framework can be applied to other nonequilibrium systems.
Theory of Atom Optics: Feynman's Path Integral Approach
DENG Lü-bi
2006-01-01
The present theory of atom optics is established mainly on the Schr(o)dinger equations or the matrix mechanics equation.The authors present a new theoretical formulation of atom optics: Feynman's path integral theory.Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating),apertures,and standing wave laser field in Earth's gravitational field by using a type of wave function and calculation is simple.For this reason,we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction),double slit,N slit,rectangular aperture,circular aperture,the Mach-Zehndertype interferometer,the interferometer with the Raman beams,the Sagnac effect,the Aharonov-Casher effect,the Kapitza-Dirac diffraction effect,and the Aharonov-Bohm effect.The authors give a wave function of the state of particles on the screen in abovementioned configurations.Our formulas show good agreement with present experimental measurements.
Quantum 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
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 .
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 ...
The path integral representation kernel of evolution operator in Merton-Garman model
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.
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.
2012-12-12
..., California (collectively, ``ITRI''). 77 FR 39735 (Jul. 5, 2012). The complaint, as amended, alleges... COMMISSION Certain Integrated Circuit Packages Provided with Multiple Heat- Conducting Paths and Products... integrated circuit packages provided with multiple heat-conducting paths and products containing same...
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.
Some bounds on quantum partition functions by path-integral methods
Equilibrium statistical mechanics requires the competition of the partition function. The density matrix and hence the quantum partition function may be expressed as an integral with an integral which can be given explicitly, namely as a (Wiener-) path integral. Techniques especially designed for path integrals provide inequalities for density matrices, partition functions and spectral densities. Some of these inequalities related to density matrices and partition functions are reviewed in this paper. 39 refs
The path integral for a particle in curved spaces and Weyl anomalies
The computation of anomalies in quantum field theory may be carried out by evaluating path-integral jacobians, as first shown by Fujikawa. The evaluation of these jacobians can be cast in the form of a quantum mechanical problem, whose solution has a path integral representation. For the case of Weyl anomalies, also called trace anomalies, one is immediately led to study the path integral for a particle moving in curved spaces. We analyze the latter in a manifestly covariant way and by making use of ghost fields. The introduction of the ghost fields allows us to represent the path-integral measure in a form suitable for performing the perturbative expansion. We employ our method to compute the hamiltonian associated with the evolution kernel given by the path integral with fixed boundary conditions, and use this result to evaluate the trace needed in a field theoretic computation of Weyl anomalies in two dimensions. (orig.)
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.
Path integral, semiclassical and stochastic propagators for Markovian open quantum systems
We develop the path integral theory for master equations of general Lindblad form (positive semigroups), describing Markovian open quantum systems. First the Hamiltonian path integral expression for the propagator is derived, which exhibits nicely the decoherence of pairs of phase space histories. A very appealing picture arises in the semiclassical limit where the degree of decoherence is expressible in terms of a phase space decoherence distance functional. For the important class of (effective) Hamiltonians quadratic in the momenta, we derive the Lagrangian version of the path integral propagator. We then evaluate the path integral approximately in a stationary phase approximation, leading to a Van Vleck-type propagator valid under semiclassical ((h/2π)→0) conditions. We also derive the propagator for the soluble damped harmonic oscillator in closed form from path integrals. Finally, connections to the active field of stochastic pure-state descriptions of open quantum systems are established, here in particular to linear quantum state diffusion. (author)
On the coordinate (in)dependence of the formal path integral
Johnson-Freyd, Theo
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....
Accelerating the convergence of path integral dynamics with a generalized Langevin equation
Ceriotti, Michele; Parrinello, Michele; 10.1063/1.3556661
2012-01-01
The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasi-harmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.
Path integrals in quantum physics. Lectures given at ETH Zurich during summer semester 1997
This lectures aim at giving graduate students an introduction to a working knowledge of path integral methods in a wide variety of fields in physics. Consequently, the 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 the standard examples of quadratic Lagrangians for which the path integrals can be solved exactly. Applications include semi-classical expansions, scattering problems and the representation of Green functions as path integrals. In the last chapter of this part it is shown how (euclidean) path integrals can be treated numerically by Monte-Carlo methods with a program for the anharmonic oscillator as an explicit example. The second part deals with the application of path integrals in statistical mechanics and many-body problems. Various chapters treat the partition functions, the polaron problem as a non-relativistic field theory and path integrals over ordinary and Grassmannian coherent states. Perturbation theory and the diagrammatic rules are derived in an unified way for both bosons and fermions and illustrated by simple examples. Finally, in the third part path integrals in relativistic quantum field theory are discussed. Standard topics like the generating functional for Green functions, perturbative expansions, effective actions and quantization of gauge theories are treated. Some special applications (the wordline formalism and spin in relativistic path integrals, the derivation of anomalies by path integral methods) are contained in additional chapters. The last section tries to give a simple introduction into lattice (gauge) field theory including a numerical example which can be run on a PC. The set of problems which accompanied the lectures is also included in the present notes. (author) 15 figs., refs
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...
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.
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...
Feynman path integrals - from the prodistribution definition to the calculation of glory scattering
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)
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.
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.
Power Series Expansion of Propagator for Path Integral and Its Applications
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.
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
Path Integral Solution for the Coulomb Potential in a Curved Space of Constant Positive Curvature
Aggoun, L.; Bounouioua, N.; Benamira, F.; Guechi, L.
2016-05-01
A new path integral treatment of a hydrogen-like atom in a uniformly curved space with a constant positive curvature is presented. By converting the radial path integral into a path integral for the modified Pöschl-Teller potential with the help of the space-time transformation technique, the radial Green's function is expressed in closed form, from which the energy spectrum and the corresponding normalized wave functions of the bound states are extracted. In the limit of vanishing curvature, the Green's function, the energy spectra and the correctly normalized wave functions of bound and scattering states for a standard hydrogen-like atom are found.
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.…
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.
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.
Establishing path integral in the entangled state representation for Hamiltonians in quantum optics
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.
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
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.
Toker, Daniel; Sommer, Friedrich
2016-01-01
An outstanding challenge with the Integrated Information Theory of Consciousness (IIT) is to find a way of rapidly and accurately calculating integrated information from neural data. A number of measures of integrated information based on time series data have been proposed, but most measures require finding the Minimum Information Partition of a network, which is computationally expensive and not practical for real brain data. Here, we introduce a novel partition, the Maximum Modularity Part...
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...
By further study of the geometry of the harmonic superspace constraints, we make explicit the relation between the operator and path integral approaches to the manifestly covariant harmonic superstring. In particular we find the correct complete set of functionally independent gauge symmetries for the auxiliary variables and identify the ones corresponding to the harmonic superfield postulate in the operator formalism. Then, we deduce in a systematic way the lagrangian path integral from the well defined covariant hamiltonian formulation of the GS superstring. (authors)
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
Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates
Briggs, Andrew; Camblong, Horacio E.; Ordonez, Carlos R.
2011-01-01
The path-integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat spacetime geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics.
Dirac particle in the presence of plane wave and constant magnetic fields: Path integral approach
Bourouaine, S.
2005-01-01
The Green function (GF) related to the problem of a Dirac particle interacting with a plane wave and constant magnetic fields is calculated in the framework of path integral via Alexandrou et al. formalism according to the so-called global projection. As a tool of calculation, we introduce two identities (constraints) into this formalism, their main role is the reduction of integrals dimension and the emergence in a natural way of some classical paths, and due to the existence of constant ele...
A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results
Marco Rosa-Clot; Stefano Taddei
1999-01-01
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the multi-dimensional cases, with point dependent drift and volatility, and describe a covariant formulation which allows general changes of variables. Finally we apply the method to some economic models with analytical solutions. In particular, we evaluate the exp...
Using umbrella integration to find minimum free energy paths
Bohner, Matthias Ulrich
2015-01-01
The analysis of the detailed mechanism of chemical reactions is a key task of computational chemistry. The detailed knowledge may help to improve known processes or even contribute to the development of new ones. In this way ecological and economic demands can be reduced. Furthermore, the course of a reaction path also plays an important role in the action of drugs. Understanding the binding of the active ingredient to receptors, such as proteins, can make it possible to optimize drugs by red...
Comment on 'Path integral solution for a Mie-type potential'
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.)
Agarwal, Animesh, E-mail: animesh@zedat.fu-berlin.de; Delle Site, Luigi, E-mail: dellesite@fu-berlin.de [Institute for Mathematics, Freie Universität Berlin, Berlin (Germany)
2015-09-07
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.
Agarwal, Animesh; Delle Site, Luigi
2015-09-01
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement
Agarwal, Animesh; Delle Site, Luigi
2015-09-01
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement. PMID:26342354
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
Variational Method for Calculation of Plasma Phase Diagrams in Path Integral Representation
Madzhulis, Ilmars; Frishfelds, Vilnis
2001-01-01
The use of variational method in functional integral approach is discussed for fermion and boson systems with Coulomb interaction. The formal general expression of thermodynamic potential is obtained by Feynman path integral technique and representation of Coulomb interaction with functional integrals. Introduced additional complex field show to transform the problem to calculation of functional integrals containing third order vertices. The thermodynamic potential can be found from variation...
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.
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.
Path integral in area tensor Regge calculus and complex connections
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
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 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 and in particular, no sensible classical limit. In this paper we describe this frequently-occurring but little-appreciated phenomenon in some detail, showing clearly the connection with the quantum Zeno effect. We then show that it may be avoided by implementing the restriction on paths in the path integral in a 'softer' way. The resulting amplitudes then involve a new coarse graining parameter, which may be taken to be a timescale ε, describing the softening of the restrictions on the paths. We argue that the complications arising from the Zeno effect are then negligible as long as ε >> 1/E, where E is the energy scale of the incoming state. Our criticisms of path integral constructions largely apply to approaches to quantum theory such as the decoherent histories approach or quantum measure theory, which do not specifically involve measurements. We address some criticisms of our approach by Sokolovksi, concerning the relevance of our results to
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.
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
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...
Supersymmetric regularized path-integral measure in x space
The complete supersymmetric Liouville action for a scalar multiplet coupled to supergravity in two-dimensional x space is obtained by integrating all anomalies, and not only the conformal anomaly. The resulting action is supersymmetric, but supersymmetry is derived, and not merely used as a device to extend the integrated conformal anomaly to the complete supersymmetric Liouville action. The integration variables are obtained from the matter variables not only (as usual) by multiplication by powers of dete(x), but also by addition of terms containing products of matter fields and supergravity fields. The dependence of the action on dete, γxpsi, and S is removed by rescaling and shifting the new matter variables. As a regulator we use a matrix operator which contains the D'Alembertian in each diagonal entry and which is obtained from the matter action by squaring and introducing a ''twist'' operator. Because the regulator contains off-diagonal elements, all three anomalies (Weyl, super-Weyl, and ''auxiliary'') contribute
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
Double path-integral migration velocity analysis: a real data example
Path-integral imaging forms an image with no knowledge of the velocity model by summing over the migrated images obtained for a set of migration velocity models. Double path-integral imaging migration extracts the stationary velocities, i.e. those velocities at which common-image gathers align horizontally, as a byproduct. An application of the technique to a real data set demonstrates that quantitative information about the time migration velocity model can be determined by double path-integral migration velocity analysis. Migrated images using interpolations with different regularizations of the extracted velocities prove the high quality of the resulting time-migration velocity information. The so-obtained velocity model can then be used as a starting model for subsequent velocity analysis tools like migration tomography or other tomographic methods
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.
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.
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.
Variational Path-Integral Study on Bound Polarons in Parabolic Quantum Dots and Wires
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.
Making the gravitational path integral more Lorentzian or Life beyond Liouville gravity
Loll, R.; Ambjørn, J.; Anagnostopoulos, K. N.
2000-06-01
In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, 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 non-fractal, ii) it remains consistent when coupled to matter, even beyond the c=1 barrier, iii) it is closer to canonical quantization approaches than previous path-integral formulations, and iv) its construction generalizes to higher dimensions.
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.
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...
Resurgence theory, ghost-instantons, and analytic continuation of path integrals
Basar, Gokce; Unsal, Mithat
2013-01-01
A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles contribute to physical observables, even if the complex saddles are not on the integration path i.e., the associated Stokes multipliers are zero. We show explicitly that instanton-anti-instanton and ghost--anti-ghost saddles both affect the expansion around the perturbative vacuum. We study a self-dual model in which the analytic continuation of the partition function to negative values of coupling constant gives a pathological exponential growth, but a homotopically independent combination of integration cycles (Lefschetz thimbles) results in a sensible theory. These two choices of the integration cycles are tied with a quantum phase transition. The general set of ideas in our construction may provide new insights into non-perturbative QFT, string theory, quantum gravity, and the ...
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.
The Schwinger model on a circle: Relation between path integral and Hamiltonian approaches
We solve the massless Schwinger model exactly in Hamiltonian formalism on a circle. We construct physical states explicitly and discuss the role of the spectral flow and nonperturbative vacua. Different thermodynamical correlation functions are calculated and after performing the analytical continuation are compared with the corresponding expressions obtained for the Schwinger model on the torus in Euclidean Path Integral formalism obtained before. (author)
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.
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
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
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
Path-integral measure for Chern-Simons theory within the stochastic quantization approach
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
On the non-linear Jaynes-Cummings model: the path-integral approach
The non-linear Jaynes-Cummings model (JCM) is solved using the formalism incorporating coherent state propagators and the path integral technique. In particular, the propagators in the coherent and the occupation-number representations of the multiphoton JCM are obtained. (author). 25 refs
Integrated Flight Path Planning System and Flight Control System for Unmanned Helicopters
Yu-Hsiang Lin
2011-07-01
Full Text Available This paper focuses on the design of an integrated navigation and guidance system for unmanned helicopters. The integrated navigation system comprises two systems: the Flight Path Planning System (FPPS and the Flight Control System (FCS. The FPPS finds the shortest flight path by the A-Star (A* algorithm in an adaptive manner for different flight conditions, and the FPPS can add a forbidden zone to stop the unmanned helicopter from crossing over into dangerous areas. In this paper, the FPPS computation time is reduced by the multi-resolution scheme, and the flight path quality is improved by the path smoothing methods. Meanwhile, the FCS includes the fuzzy inference systems (FISs based on the fuzzy logic. By using expert knowledge and experience to train the FIS, the controller can operate the unmanned helicopter without dynamic models. The integrated system of the FPPS and the FCS is aimed at providing navigation and guidance to the mission destination and it is implemented by coupling the flight simulation software, X-Plane, and the computing software, MATLAB. Simulations are performed and shown in real time three-dimensional animations. Finally, the integrated system is demonstrated to work successfully in controlling the unmanned helicopter to operate in various terrains of a digital elevation model (DEM.
a Path-Integration Approach to the Correlators of XY Heisenberg Magnet and Random Walks
Bogoliubov, N. M.; Malyshev, C.
2008-11-01
The path integral approach is used for the calculation of the correlation functions of the XY Heisenberg chain. The obtained answers for the two-point correlators of the XX magnet are of the determinantal form and are interpreted in terms of the generating functions for the random turns vicious walkers.
The Schwinger Model on a circle: relation between Path Integral and Hamiltonian approaches
Azakov, Siyavush
2005-01-01
We solve the massless Schwinger model exactly in Hamiltonian formalism on a circle. We construct physical states explicitly and discuss the role of the spectral flow and nonperturbative vacua. Different thermodynamical correlation functions are calculated and after performing the analytical continuation are compared with the corresponding expressions obtained for the Schwinger model on the torus in Euclidean Path Integral formalism obtained before.
Path integral treatment of a Dirac particle in a weak gravitational plane wave
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.)
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.)
The path integral of Feynman and "information modelling" of processes and systems
Shro, O. I.
2009-01-01
The given article example of physical analogies to be entered information space-time. The opportunity of Poincare group use is shown for transition from one frame in another, for this purpose is entered invariant velocity of transition of the information. For calculation of information processes probability amplitudes is offered using path integral of Feynman.
Path integral measure and the fermion-boson equivalence in the Schwinger model
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)
Quantum mechanical path integrals with Wiener measures for all polynomial Hamiltonians
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.)
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.
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
Factors Affecting Technology Integration in K-12 Classrooms: A Path Model
Inan, Fethi A.; Lowther, Deborah L.
2010-01-01
The purpose of this study was to examine the direct and indirect effects of teachers' individual characteristics and perceptions of environmental factors that influence their technology integration in the classroom. A research-based path model was developed to explain causal relationships between these factors and was tested based on data gathered…
Effects of Quantum Nuclear Delocalisation on NMR Parameters from Path Integral Molecular Dynamics
Dračínský, Martin; Hodgkinson, P.
2014-01-01
Roč. 20, č. 8 (2014), s. 2201-2207. ISSN 0947-6539 Grant ostatní: Seventh Framework Programme of the European Union(XE) FP7-299242 People Institutional support: RVO:61388963 Keywords : density functional calculations * isotope effects * NMR spectroscopy * nuclear delocalisation * path integral molecular dynamics Subject RIV: CC - Organic Chemistry Impact factor: 5.731, year: 2014
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...
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
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 Treatment of Proton Transport Processes in BaZrO3
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 theory of an axially confined worm-like chain
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)
PRELIMINARY PROJECT PLAN FOR LANSCE INTEGRATED FLIGHT PATHS 11A, 11B, 12, and 13
D. H. BULTMAN; D. WEINACHT - AIRES CORP.
2000-08-01
This Preliminary Project Plan Summarizes the Technical, Cost, and Schedule baselines for an integrated approach to developing several flight paths at the Manual Lujan Jr. Neutron Scattering Center at the Los Alamos Neutron Science Center. For example, the cost estimate is intended to serve only as a rough order of magnitude assessment of the cost that might be incurred as the flight paths are developed. Further refinement of the requirements and interfaces for each beamline will permit additional refinement and confidence in the accuracy of all three baselines (Technical, Cost, Schedule).
PRELIMINARY PROJECT PLAN FOR LANSCE INTEGRATED FLIGHT PATHS 11A, 11B, 12, and 13
This Preliminary Project Plan Summarizes the Technical, Cost, and Schedule baselines for an integrated approach to developing several flight paths at the Manual Lujan Jr. Neutron Scattering Center at the Los Alamos Neutron Science Center. For example, the cost estimate is intended to serve only as a rough order of magnitude assessment of the cost that might be incurred as the flight paths are developed. Further refinement of the requirements and interfaces for each beamline will permit additional refinement and confidence in the accuracy of all three baselines (Technical, Cost, Schedule)
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).
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
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.
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. The path integral representation of the process is constructed, and the basic quantities are evaluated. (paper)
The method for numerical evaluation of path integrals in Eucledean quantum mechanics without lattice discretization is elaborated. The method is based on the representation of these integrals in the form of functional integrals with respect to the conditional Wiener measure and on the use of the derived approximate exact on a class of polynomial functionals of a given degree. By the computations of non-perturbative characteristics, concerned the topological structure of vacuum, the advantages of this method versus lattice Monte-Carlo calculations are demonstrated
The integration of pulsatile gonadotropin secretion by the radioimmunoassay of an acetone precipitation from a short-term urine sample was evaluated. FSH and LH excretion over a 3-h period was compared to the mean level of 10 blood samples obtained every 20 min for a similar time period from 71 patients. A highly significant correlation existed between blood and urine results. In addition, the gonadotropin levels obtained from a 3-h sample correlated well with the 24-h excretion of FSH and LH from the same individual. A 3-h urine collection can provide a simple, sensitive, and accurate means of assessing circulating FSH and LH levels. (U.S.)
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.
Li, Zhiyang
2010-10-01
A method for high precision optical wavefront reconstruction using low resolution spatial light modulators (SLMs) was proposed. It utilizes an adiabatic waveguide taper consisting of a plurality of single-mode waveguides to decompose an incident light field into simple fundamental modes of the single-mode waveguides. By digital generation of the conjugate fields of those simple fundamental modes a field proportional to the original incident light field might be reconstructed accurately based on reciprocity. Devices based on the method using transparent and reflective SLMs possess no aberration like that of a conventional optic lens and are able to achieve diffraction limited resolution. Specifically on the surface of the narrow end of a taper a resolution much higher than half of the wavelength is attainable. The device may work in linear mode and possesses unlimited theoretical 3D space-bandwidth product (SBP). The SBP of a real device is limited by the accuracy of SLMs. A pair of 8-bit SLMs with 1000 × 1000 = 10 6 pixels could provide a SBP of about 5 × 10 4. The SBP may expand by 16 times if 10-bit SLMs with the same number of pixels are employed or 16 successive frames are used to display one scene. The device might be used as high precision optical tweezers, or employed for continuous or discrete real-time 3D display, 3D measurement, machine vision, etc.
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...
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 solution of the one-dimensional Dirac quantum cellular automaton
Quantum cellular automata, which describe the discrete and exactly causal unitary evolution of a lattice of quantum systems, have been recently considered as a fundamental approach to quantum field theory and a linear automaton for the Dirac equation in one dimension has been derived. In the linear case a quantum cellular automaton is isomorphic to a quantum walk and its evolution is conveniently formulated in terms of transition matrices. The semigroup structure of the matrices leads to a new kind of discrete path-integral, different from the well known Feynman checkerboard one, that is solved analytically in terms of Jacobi polynomials of the arbitrary mass parameter. - Highlights: • Discrete path integral formulation of linear QCAs in terms of transition matrices. • Derivation of the analytical solution for the one dimensional Dirac QCA. • Solution given in terms of Jacobi polynomials versus the arbitrary mass parameter. • The discrete paths and the transition matrices of the Dirac QCA are binary encoded. • Paths are grouped in equivalence classes according to their overall transition matrix
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.
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
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.
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...
Two-scale large deviations for chemical reaction kinetics through second quantization path integral
Li, Tiejun; Lin, Feng
2016-04-01
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.
The use of a path independent integral in non-linear fracture mechanics
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
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.
Do familiar landmarks reset the global path integration system of desert ants?
Collett, M; Collett, T S; Chameron, S; Wehner, R
2003-03-01
It is often suggested that animals may link landmark memories to a global coordinate system provided by path integration, thereby obtaining a map-like representation of familiar terrain. In an attempt to discover if desert ants form such associations we have performed experiments that test whether desert ants recall a long-term memory of a global path integration vector on arriving at a familiar food site. Ants from three nests were trained along L-shaped routes to a feeder. Each route was entirely within open-topped channels that obscured all natural landmarks. Conspicuous artificial landmarks were attached to the channelling that formed the latter part of the route. The homeward vectors of ants accustomed to the route were tested with the foodward route, either as in training, or with the first leg of the L shortened or extended. These ants were taken from the feeder to a test area and released, whereupon they performed a home vector. If travelling the latter part of a familiar route and arriving at a familiar food site triggers the recall of an accustomed home vector, then the home vector should be the same under both test conditions. We find instead that the home vector tended to reflect the immediately preceding outward journey. In conjunction with earlier work, these experiments led us to conclude in the case of desert ants that landmark memories do not prime the recall of long-term global path integration memories. On the other hand, landmark memories are known to be linked to local path integration vectors that guide ants along a segment of a route. Landmarks thus seem to provide procedural information telling ants what action to perform next but not the positional information that gives an ant its location relative to its nest. PMID:12547942
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.
Path integrals with topological constraints: Aharonov-Bohm effect and polymer entanglements
Wiegel, F.W.
1981-01-01
For Wiener- and Feynman integrals over paths with certain topological properties we compare various methods for explicit calculation. This leads to a one-to-one correspondence between the Aharonov-Bohm effect and a certain polymer entanglement problem. We briefly comment on two generalizations of the Aharonov-Bohm effect. First, we consider this effect due to a closed magnetic flux loop of arbitrary shape; next, we consider the combined effect due to a gas of microscopic magnetic flux loops.
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.
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.
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.
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 ...
Using the path integral formalism and a model based on statistical arguments, we derive the correlation function which enters the description of a one-dimensional collective system coupled to an intrinsic system in terms of transport concepts. The derivation shows a finite time dependence of the correlation function in contradistinction to a former calculation. We discuss some points related to the derivation and estimate the relaxation times which characterise the memory effects in both cases of weak and strong coupling. (orig.)
L. Ingber; P.L. Nunez
2000-01-01
We present high-resolution path-integral calculations of a previously developed model of short-term memory in neocortex. These calculations, made possible with supercomputer resources, supplant similar calculations made in L. Ingber, Phys. Rev. E 49, 4652 (1994), and support coarser estimates made in L. Ingber, Phys. Rev. A 29, 3346 (1984). We also present a current experimental context for the relevance of these calculations using the approach of statistical mechanics of neocortical interact...
Yang, Sandy; Yamamoto, Takeshi; Miller, William H.
2005-01-01
The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different...
Calculation Rule for Aoyama-Tamra's Prescription for Path Integral with Quantum Tunneling
Suzuki, Hiroshi
1995-01-01
We derive a simple calculation rule for Aoyama--Tamra's prescription for path integral with degenerated potential minima. Non-perturbative corrections due to the restricted functional space (fundamental region) can systematically be computed with this rule. It becomes manifest that the prescription might give Borel summable series for finite temperature (or volume) system with quantum tunneling, while the advantage is lost at zero temperature (or infinite volume) limit.
Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator
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.
A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods
Marco Rosa-Clot; Stefano Taddei
1999-01-01
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic numerical method. Then, we apply the latter to some specific financial problems. In particular, we consider the pricing of a European option, a zero-coupon bond, a caplet, an American option, and a Bermudan swaption.
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...
Nuclear quantum effects in chemical reactions via higher-order path-integral calculations
Highlights: • The study presents path-integral calculations for chemical reactions. • The path-integrals use higher-order factorizations of the density matrix. • The Eckart potential and the H2 + H reaction are used as test cases for the methods. • The Chin higher order factorization enhances QM transmission convergence. • The higher order factorizations enhance eigenvalue and partition function convergence. - Abstract: A practical approach to treat nuclear quantum mechanical effects in simulations of condensed phases, such as enzymes, is via Feynman path integral (PI) formulations. Typically, the standard primitive approximation (PA) is employed in enzymatic PI simulations. Nonetheless, these PI simulations are computationally demanding due to the large number of beads required to obtain converged results. The efficiency of PI simulations may be greatly improved if higher-order factorizations of the density matrix operator are employed. Herein, we compare the results of model calculations obtained employing the standard PA, the improved operator of Takahashi and Imada (TI), and a gradient-based forward corrector algorithm due to Chin (CH). The quantum transmission coefficient is computed for the Eckart potential while the partition functions and rate constant are computed for the H2 + H hydrogen transfer reaction. These potentials are simple models for chemical reactions. The study of the different factorization methods reveals that in most cases the higher-order action converges faster than the PA and TI approaches, at a moderate computational cost
Chern-Simons Path Integrals in S2 × S1
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.
Fumiyoshi Kondo
2014-10-01
Full Text Available Non-dispersive infrared CO2/H2O gas analysers produce erroneous CO2 outputs when CO2 is measured in humid air, unless a correction for water vapour cross-sensitivity is applied. Spectroscopic cross-sensitivities arising from direct absorption interference and from the pressure broadening effect are significant in CO2 flux measurements by the eddy covariance technique using open-path gas analysers over the ocean, as opposed to land-surface measurements, where CO2 fluxes are orders of magnitude larger. In this study, a widely used analyser with manufacturer-determined correction coefficients for both cross-sensitivities was tested by laboratory experiments. Our results showed that the correction coefficient for direct absorption interference was not optimised to calculate CO2 flux accurately, and that the correction coefficient for the pressure broadening caused overestimation of the CO2 mixing ratio flux in the same direction as the water vapour flux. Overestimations of open-path eddy covariance measurements of upward CO2 fluxes in previous ocean observations probably resulted from inaccuracies in both of these correction coefficients. We also found that slight changes in spectroscopic cross-sensitivities due to contamination of the analyser's optical windows by sea salt caused a low bias in CO2 outputs with increasing H2O; however, this contamination effect was not always observed in repeated tests under different contamination conditions. We suggest that previously proposed methods for correcting the effect of optical window contamination is of limited value and that measurement of small CO2 fluxes by the open-path eddy covariance technique over the ocean should be performed after confirming the spectroscopic cross-sensitivity and ensuring that the optical windows are as clean as possible.
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
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
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...
Zima, V. G.; Fedoruk, S. O.
1998-01-01
The transition amplitude is obtained for a free massive particle of arbitrary spin by calculating the path integral in the index-spinor formulation within the BFV-BRST approach. None renormalizations of the path integral measure were applied. The calculation has given the Weinberg propagator written in the index-free form with the use of index spinor. The choice of boundary conditions on the index spinor determines holomorphic or antiholomorphic representation for the canonical description of...
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.
Light-front Hamiltonian and path integral formulations of large N scalar QCD2
Recently Grinstein, Jora and Polosa (2009) have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) ). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qq¯ bound states. They consider the gauge fields in the adjoint representation of SU(N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.
Light-front Hamiltonian and path integral formulations of large N scalar QCD{sub 2}
Kulshreshtha, Usha, E-mail: ushakulsh@gmail.com [Department of Physics, Kirori Mal College, University of Delhi, Delhi-110007 (India); Kulshreshtha, D.S., E-mail: dskulsh@gmail.com [Department of Physics and Astrophysics, University of Delhi, Delhi-110007 (India); Vary, J.P., E-mail: jvary@iastate.edu [Department of Physics and Astronomy, Iowa State University, Ames, IA 50011 (United States)
2012-02-14
Recently Grinstein, Jora and Polosa (2009) have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) ). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qq{sup Macron} bound states. They consider the gauge fields in the adjoint representation of SU(N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.
Light-front Hamiltonian and path integral formulations of large N scalar QCD2
Kulshreshtha, Usha; Kulshreshtha, D. S.; Vary, J. P.
2012-02-01
Recently Grinstein, Jora and Polosa (2009) [5] have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) [6]). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qqbar bound states. They consider the gauge fields in the adjoint representation of SU (N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.
Response of Non-Linear Systems to Renewal Impulses by Path Integration
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...... additional discrete-valued state variables for which the stochastic equations are also formulated....
The Salesman's Improved Paths: 3/2+1/34 Integrality Gap and Approximation Ratio
Sebő, András; van Zuylen, Anke
2016-01-01
We give a new, strongly polynomial algorithm and improved analysis of the metric $s-t$ path TSP. The algorithm finds a tour of cost less than 1.53 times the optimum of the subtour elimination LP, while known examples show that 1.5 is a lower bound for the integrality gap. A key new idea is the deletion of some edges, where the arising connectivity problems can be solved for a minor extra cost. On the one hand our algorithm and analysis extend previous tools, at the same time simplifying the f...
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
An introduction to stochastic control theory, path integrals and reinforcement learning
Kappen, Hilbert J.
2007-02-01
Control theory is a mathematical description of how to act optimally to gain future rewards. In this paper I give an introduction to deterministic and stochastic control theory and I give an overview of the possible application of control theory to the modeling of animal behavior and learning. I discuss a class of non-linear stochastic control problems that can be efficiently solved using a path integral or by MC sampling. In this control formalism the central concept of cost-to-go becomes a free energy and methods and concepts from statistical physics can be readily applied.
Temperature-dependent isovector pairing gap equations using a path integral approach
Temperature-dependent isovector neutron-proton (np) pairing gap equations have been established by means of the path integral approach. These equations generalize the BCS ones for the pairing between like particles at finite temperature. The method has been numerically tested using the one-level model. It has been shown that the gap parameter Δnp has a behavior analogous to that of Δnn and Δpp as a function of the temperature: one notes the presence of a critical temperature. Moreover, it has been shown that the isovector pairing effects remain beyond the critical temperature that corresponds to the pairing between like particles
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.
Energy levels and expectation values via accelerated path integral Monte Carlo
Stojiljkovic, D; Bogojevic, A; Balaz, A [Scientific Computing Laboratory, Institute of Physics, Belgrade (Serbia)], E-mail: danica@phy.bg.ac.yu
2008-08-15
A recently developed method systematically improved the convergence of generic path integrals for transition amplitudes, partition functions, expectation values and energy spectra. This was achieved by analytically constructing a hierarchy of discretized effective actions indexed by a level number p and converging to the continuum limit as 1/N{sup p}. Here we apply the above general method to numerical calculations using Metropolis Monte Carlo simulations of energy expectation values and energy spectra. We analyze and compare the ensuing increase in efficiency of several orders of magnitude.
Calculating splittings between energy levels of different symmetry using path-integral methods
Mátyus, Edit; Althorpe, Stuart C.
2016-03-01
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.
Sidles, J A
2002-01-01
It is shown that classical control diagrams can be mapped one-to-one onto quantum path integrals over measurement amplitudes. To show the practical utility of this method, exact closed-form expressions are derived for the control dynamics and quantum noise levels of a test mass observed by a Fabry-Perot interferometer. This formalism provides an efficient yet rigorous method for analyzing complex systems such as interferometric gravity wave detectors and magnetic resonance force microscopy (MRFM) experiments. Quantum limits are conjectured for the sensitivity of interferometric observation of test mass trajectories.
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.
Path integral Monte Carlo calculation of momentum distribution in solid He-4
Rota, Riccardo; Boronat Medico, Jordi
2011-01-01
We perform calculations of the momentum distribution n(k) in solid \\^4\\He by means of path integral Monte Carlo methods. We see that, in perfect crystal, n(k) does not depend on temperature T and that is different from the classical Gaussian shape of Maxwell-Boltzmann distribution, even though these discrepancies decrease when the density of the system increases. In crystal presenting vacancies, we see that for T \\ge 0.75K, n(k) presents the same behavior as in the perfect crystal, but, at lo...
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.
Rabi oscillation in a damped rotating magnetic field: A path integral approach
In this paper we consider a spin 1/2 particle interacting with a damped rotating magnetic field using path integral formalism. The propagator is first of all written in the standard form by replacing the spin by two fermionic oscillators via the Schwinger's model; then it is determined exactly thanks to the introduction of a particular rotations in coherent state space which has eliminated the rotation angle of the magnetic field and has simplified the Hamiltonian of the considered system. Thus, the Rabi formula are deduced.
Feynman path integral approach to electron diffraction for one and two slits: analytical results
In this paper we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulae, various approximations of the electron distribution are shown which facilitate the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could therefore also serve as an interesting pedagogical introduction to Feynman’s formulation of quantum mechanics for university students dealing with the foundations of quantum mechanics. (paper)
Public Sector Employment and the Occupational Integration Paths Taken by Young People
Vanessa di Paola; Stéphanie Moullet
2003-01-01
Nine standard integration paths were constructed from a sample of 1998 school leavers who had at least one period of employment in the civil service in the three years following 1998. The young women in this cohort found quick entry into the internal civil service market. Conversely, public sector employment more often comes later for the young men. More generally, a larger number of women work a fairly long period in a public sector job, whereas there is a greater probability of the mens pat...
Dimensional regularization of the path integral in curved space on an infinite time interval
Bastianelli, F.; Corradini, O.; van Nieuwenhuizen, P.
2000-09-01
We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general coordinates. It is shown that one only needs a covariant two-loop counterterm (VDR=ℏ2/8R) to obtain the same results as obtained earlier in other regularization schemes. It is also shown that the mass term needed in order to avoid infrared divergences explicitly breaks general covariance in the final result.
Ling, Hong; Schäfer, Klaus; Xin, Jinyuan; Qin, Min; Suppan, Peter; Wang, Yuesi
2014-08-01
Traffic emissions are a very important factor in Beijing's urban air quality. To investigate small-scale spatial variations in air pollutants, a campaign was carried out from April 2009 through March 2011 in Beijing. DOAS (differential optical absorption spectroscopy) systems and in situ instruments were used. Atmospheric NO, NO2, O3 and SO2 mixing ratios were monitored. Meanwhile, HCHO mixing ratios were measured by two different DOAS systems. Diurnal variations of these mixing ratios were analysed. Differences between the path-integrated and in situ measurements were investigated based on the results from the campaign. The influences of different weather situations, dilution conditions and light-path locations were investigated as well. The results show that the differences between path-integrated and in situ mixing ratios were affected by combinations of emission source strengths, weather conditions, chemical transformations and local convection. Path-integrated measurements satisfy the requirements of traffic emission investigations better than in situ measurements.
Spura, Thomas; Elgabarty, Hossam; Kühne, Thomas D
2015-06-14
We present an accelerated ab initio path-integral molecular dynamics technique, where the interatomic forces are calculated "on-the-fly" by accurate coupled cluster electronic structure calculations. In this way not only dynamic electron correlation, but also the harmonic and anharmonic zero-point energy, as well as tunneling effects are explicitly taken into account. This method thus allows for very precise finite temperature quantum molecular dynamics simulations. The predictive power of this novel approach is illustrated on the example of the protonated water dimer, where the impact of nuclear quantum effects on its structure and the (1)H magnetic shielding tensor are discussed in detail. PMID:25650366
A Neural Path Integration Mechanism for Adaptive Vector Navigation in Autonomous Agents
Goldschmidt, Dennis; Dasgupta, Sakyasingha; Wörgötter, Florentin;
2015-01-01
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 of......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...
Path integrals for the nonrelativistic electron interacting with the black body radiation
Feynman's method to write the polaron free energy as a functional integral is extended to the electron coupled to the radiation field at finite temperature. To actually perform the summation over the Boson degrees of freedom, we use a path-ordered version of the Feynman--Kac--Ito formula. Like in the polaron case, the resulting free energy derives from an action involving a double stochastic integral with respect to the tied-down Brownian motion. This representation is sufficiently explicit to allow us to take first steps towards solving the renormalization problem (removal of the high-energy cutoff). To order e2, the renormalized free energy is determined and is seen to behave like T2 at small temperatures. The thermodynamical effects, although very small in any laboratory, may become considerable when studying end products of stellar evolution such as white dwarfs and neutron stars. copyright 1995 Academic Press, Inc
Characterization of near-road pollutant gradients using path-integrated optical remote sensing.
Thoma, Eben D; Shores, Richard C; Isakov, Vlad; Baldauf, Richard W
2008-07-01
Understanding motor vehicle emissions, near-roadway pollutant dispersion, and their potential impact to near-roadway populations is an area of growing environmental interest. As part of ongoing U.S. Environmental Protection Agency research in this area, a field study was conducted near Interstate 440 (I-440) in Raleigh, NC, in July and August of 2006. This paper presents a subset of measurements from the study focusing on nitric oxide (NO) concentrations near the roadway. Measurements of NO in this study were facilitated by the use of a novel path-integrated optical remote sensing technique called deep ultraviolet differential optical absorption spectroscopy (DUV-DOAS). This paper reviews the development and application of this measurement system. Time-resolved near-road NO concentrations are analyzed in conjunction with wind and traffic data to provide a picture of emissions and near-road dispersion for the study. Results show peak NO concentrations in the 150 ppb range during weekday morning rush hours with winds from the road accompanied by significantly lower afternoon and weekend concentrations. Traffic volume and wind direction are shown to be primary determinants of NO concentrations with turbulent diffusion and meandering accounting for significant near-road concentrations in off-wind conditions. The enhanced source capture performance of the open-path configuration allowed for robust comparisons of measured concentrations with a composite variable of traffic intensity coupled with wind transport (R2 = 0.84) as well as investigations on the influence of wind direction on NO dilution near the roadway. The benefits of path-integrated measurements for assessing line source impacts and evaluating models is presented. The advantages of NO as a tracer compound, compared with nitrogen dioxide, for investigations of mobile source emissions and initial dispersion under crosswind conditions are also discussed. PMID:18672712
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
Path Integral Approach to a Single Polymer Chain with Random Media
Kunsombat, Ch.; Sa-Yakanit, V.
In this paper we consider the problem of a polymer chain in random media with finite correlation. We show that the mean square end-to-end distance of a polymer chain can be obtained using the Feynman path integral developed by Feynman for treating the polaron problem and successfuly applied to the theory of heavily doped semiconductor. We show that for short-range correlation or the white Gaussian model we derive the results obtained by Edwards and Muthukumar using the replica method and for long-range correlation we obtain the result of Yohannes Shiferaw and Yadin Y. Goldschimidt. The main idea of this paper is to generalize the model proposed by Edwards and Muthukumar for short-range correlation to finite correlation. Instead of using a replica method, we employ the Feynman path integral by modeling the polymer Hamiltonian as a model of non-local quadratic trial Hamiltonian. This non-local trial Hamiltonian is essential as it will reflect the translation invariant of the original Hamiltonian. The calculation is proceeded by considering the differences between the polymer propagator and the trial propagator as the first cumulant approximation. The variational principle is used to find the optimal values of the variational parameters and the mean square end-to-end distance is obtained. Several asymptotic limits are considered and a comparison between this approaches and replica approach will be discussed.
Two-scale large deviations for chemical reaction kinetics through second quantization path integral
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)
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments
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...
Relations between the EU and Republic of Kosovo - The path of Kosovo integration towards the EU
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.
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...
Path integral for coherent states of the dynamical U2 group and U2/1 supergroup
A part-integral formulation in the representation of coherent states for the unitary U2 group and U2/1 supergroup is introduced. U2 and U2/1 path integrals are shown to be defined on the coset spaces U2/U1xU1 and U2/1/U1/1xU1, respectively. These coset appears as curved classical phase spaces. Partition functions are expressed as path integrals over these spaces. In the case when U2 and U2/1 are the dynamical groups, the corresponding path integrals are evaluated with the help of linear fractional transformations that appear as the group (supergroup) action in the coset space (superspace). Possible applications for quantum models are discussed. 9 refs
Mielke, Steven L.; Truhlar, Donald G.
2015-01-01
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
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.
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
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.
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...
The commensurate Frenkel Kontorova (FK) model is studied using path-integral molecular dynamics (PIMD). We focus on the highly discrete case, in which the embedding potential has a much greater maximum curvature than the harmonic potential connecting two particles in the FK chain. When efficient sampling methods are used, the dynamical interpretation of adiabatic PIMD appears to represent quite accurately the true time correlation functions of this highly correlated many-body system. We have found that the discrete, quantum FK model shows different behavior than its continuum version. The spectral density does not show the characteristic ω-2Θ(ω-ωc) cusp of the continuum solution in the pinned phase (m>mc). We also identify a dynamical quantum hysteresis in addition to the regular classical hysteresis when an external force is applied to the FK chain. In the unpinned phase (m≤mc), we find a linear response damping coefficient which is finite and only weakly dependent on temperature T at small values of T
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 .
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
2010-01-01
Purpose Services’ integration comprises organizational, normative, economic, informational and clinical dimensions. Since 2004, the province of Quebec has devoted significant efforts to unify the governance of the main health and social care organizations of its various territories. Notwithstanding the uniformity of the national plan’s prescription, the territorial integration modalities greatly vary across the province. Theory This research is based upon a conceptual model of integration tha...
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.
A path integral approach to the full Dicke model with dipole-dipole interaction
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)
Feynman path integral - ab initio investigation of the excited-state properties of benzene
The Feynman path integral Monte Carlo formalism has been combined with an ab initio configuration interaction scheme to study the excited singlet states of benzene under consideration of the nuclear degrees of freedom. Transition energies and oscillator strengths, which have been evaluated as ensemble averages over large sets of nuclear configurations, are correlated with single-configuration results derived for the D6h minimum of benzene. The quantum fluctuations of the benzene nuclei cause a strong redistribution of transition intensities. Transitions which are dipole allowed in the rigid D6h geometry of C6H6 lose intensity due to vibronic coupling; vice versa for transitions which are dipole forbidden in the D6h case. (author)
A New Perspective on Path Integral Quantum Mechanics in Curved Space-Time
Singh Dinesh
2013-09-01
Full Text Available Abstract. A new approach to path integral quantum mechanics in curved space-time is presented for scalar particle propagation, expressed in terms of Lie transport and Fermi or Riemann normal co-ordinates to describe local curvature. While the presence of local curvature results in a strictly non-unitary representation of local time translation, the formalism nevertheless correctly recovers the free-particle Lagrangian in curved space-time, along with new terms that predict a simultaneous breakdown of time-reversal symmetry and a quantum violation of the weak equivalence principle at the particle’s Compton wavelength scale. Furthermore, the formalism reveals the prediction of a gauge-invariant phase factor interpreted as the gravitational Aharonov-Bohm effect and Berry’s phase.
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
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.
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.)
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.
Bose–Einstein condensate in a double-well potential: Feynman path integral variational approach
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-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
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.
Feynman path integral for the Dirac equation in a curved space-time
Internal angular momentum of a spinning test-particle moving in a curved space-time obeys the law of parallel transport along the particle world line. Therefore, the final spin orientation depends on the world line. Assuming that propagator of a quantum particle is formed by contributions of all its world lines, every one of which possesses some amplitude, one can see that these amplitudes actually pertain to the particle final spin states. Consequently, the law of parallel transport for spin must be taken into account in definition of world line amplitudes. In this work such amplitudes are constructed for massive spin 1/2 particles. It is shown that path integral for such a particle takes the form of a Clifford algebra-valued two-point function. (author). 9 refs
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.
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 ...
Correct Path-Integral Formulation of Quantum Thermal Field Theory in Coherent State Representation
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.
Path-integrated growth of electrostatic waves: The generation of terrestrial myriametric radiation
It is generally accepted that electrostatic wave energy is the source of terrestrial myriametric radiation (TMR), but there are several theories to suggest how this energy is converted into TMR. The linear mode conversion window theory of Jones (1976, 1980), which in the past has been considered by some to be too inefficient to account for the observed wave amplitudes, is considered here. First, the ray tracing program HOTRAY is described. This program is used to trace electromagnetic and electrostatic waves in a hot magnetized plasma and to calculate the path-integrated growth rates for a realistic unstable particle distribution function. A density model is constructed from wave observations made by DE 1 of an event where TMR was beamed to northern and southern latitudes from a source very close to the magnetic equator. Ray tracing shows that backward propagating electrostatic waves can refract into electromagnetic Z mode waves and transport energy to the so-called radio window at the equator. Path-integrated growth rates show that the electrostatic waves amplify by a factor ≥ 42 from the background fluctuation level before reaching the window. Increasing the depth of the loss cone, or increasing the hot plasma density, to within observed limits, increases the wave amplification up to a factor of 104. Strong Landau and cyclotron damping from the hot plasma component restricts the efficient transfer of energy to the radio window to within a few tenths of a degree in latitude about the magnetic equator. Thus the strongest TMR is emitted from the equator
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 ...
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.
Vorhees, Charles V.; Herring, Nicole R.; Schaefer, Tori L.; Grace, Curtis E.; Skelton, Matthew R.; Johnson, Holly L.; Williams, Michael T.
2008-01-01
Postnatal day (P)11–20 (+)-methamphetamine (MA) treatment impairs spatial learning and reference memory in the Morris water maze, but has marginal effects on path integration learning in a labyrinthine maze. A subsequent experiment showed that MA treatment on P11–15, but not P16–20, is sufficient to induce Morris maze deficits. Here we tested the effects of P11–15 MA treatment under two different rearing conditions on Morris maze performance and path integration learning in the Cincinnati wat...
Song, Linze; Shi, Qiang, E-mail: qshi@iccas.ac.cn [Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190 (China)
2015-05-07
We present a new non-perturbative method to calculate the charge carrier mobility using the imaginary time path integral approach, which is based on the Kubo formula for the conductivity, and a saddle point approximation to perform the analytic continuation. The new method is first tested using a benchmark calculation from the numerical exact hierarchical equations of motion method. Imaginary time path integral Monte Carlo simulations are then performed to explore the temperature dependence of charge carrier delocalization and mobility in organic molecular crystals (OMCs) within the Holstein and Holstein-Peierls models. The effects of nonlocal electron-phonon interaction on mobility in different charge transport regimes are also investigated.
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).
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.
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...
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.
Mielke, Steven L., E-mail: slmielke@gmail.com, E-mail: truhlar@umn.edu; Truhlar, Donald G., E-mail: slmielke@gmail.com, E-mail: truhlar@umn.edu [Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, Minnesota 55455-0431 (United States)
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{sup −6}) to O(P{sup −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.
虚拟路径整合的学习效应%The Effect of Learning in Virtual Path Integration
过继成思; 宛小昂
2015-01-01
路径整合指通过自身运动信息对自身位置进行更新的过程。本研究使用头盔式虚拟现实系统和分段式迷宫，在两个实验中检验在同样布局的外出路径上重复地进行路径完成任务是否会改善被试的反应表现。实验1中的外出路径具有相对较简单的空间布局，实验结果表明，男性和女性被试均在反应时、位置误差、角度误差上表现出了学习效应，即第二次在同样空间布局的外出路径上进行路径完成任务时的表现比第一次有了显著的改善。实验2中的外出路径具有更复杂多样化的空间布局，而实验结果表明，男性和女性被试均在反应时和比例位置误差上表现出了学习效应，但是路径更复杂时要求更多次数的重复才可以提高路径整合成绩。这些研究结果为路径整合能力训练的可行性提供了初步的实证依据。%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
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 ...
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…
We study four dimensional Effective Bosonic Field Theories for massive fermion field in the infrared region and massive fermion in ultraviolet region by using an appropriate Fermion Path Integral Chiral variable change and the Polyakov's Fermi-Bose transmutation in the 3D-Abelian Thrirring model. (author)
Khorrami, M.; Alimohammadi, M.
1996-01-01
Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) of the generalized 2D Yang-Mills theories in the Schwinger--Fock gauge. Our calculation is done for arbitrary 2D orientable, and also nonorientable surfaces.
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
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
Walters, Peter L.; Makri, Nancy
2016-01-01
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.
Iterative quantum-classical path integral with dynamically consistent state hopping
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.
Highlights: • PIMD simulations with PM6-DH+ potential are carried out for Cl−(H2O)n clusters. • The geometric isotope effects on the rearrangement of single and multi shell structures are presented. • The competition of intramolecular and intermolecular nuclear quantum effects on the cluster structures is shown. • The correlations between r(Cl…O) and other vibration motions are discussed. - Abstract: The geometric isotope effects on the structures of hydrated chloride ionic hydrogen bonded clusters are explored by carrying out path integral molecular dynamics simulations. First, an outer shell coordinate is selected to display the rearrangement of single and multi hydration shell cluster structures. Next, to show the competition of intramolecular and intermolecular nuclear quantum effects, the intramolecular OH∗ stretching and intermolecular ion–water wagging motions are studied for single and multi shell structures, respectively. The results indicate that the intermolecular nuclear quantum effects stabilize the ionic hydrogen bonds in single shell structures, while they are destabilized through the competition with intramolecular nuclear quantum effects in multi shell structures. In addition, the correlations between ion–water stretching motion and other cluster vibrational coordinates are discussed. The results indicate that the intermolecular nuclear quantum effects on the cluster structures are strongly related to the cooperation of the water–water hydrogen bond interactions
Energy estimators and calculation of energy expectation values in the path integral formalism
Grujic, J. [Scientific Computing Laboratory, Institute of Physics, P.O. Box 57, 11001 Belgrade (Serbia)]. E-mail: jelenagr@phy.bg.ac.yu; Bogojevic, A. [Scientific Computing Laboratory, Institute of Physics, P.O. Box 57, 11001 Belgrade (Serbia)]. E-mail: alex@phy.bg.ac.yu; Balaz, A. [Scientific Computing Laboratory, Institute of Physics, P.O. Box 57, 11001 Belgrade (Serbia)]. E-mail: antun@phy.bg.ac.yu
2006-12-25
A recently developed method systematically improved the convergence of generic path integrals for transition amplitudes [A. Bogojevic, A. Balaz, A. Belic, Phys. Rev. Lett. 94 (2005) 180403, A. Bogojevic, A. Balaz, A. Belic, Phys. Rev. B 72 (2005) 064302, A. Bogojevic, A. Balaz, A. Belic, Phys. Lett. A 344 (2005) 84]. This was achieved by analytically constructing a hierarchy of N-fold discretized effective actions S{sub N}{sup (p)} labeled by a whole number p and starting at p=1 from the naively discretized action in the mid-point prescription. The derivation guaranteed that the level p effective actions lead to discretized transition amplitudes differing from the continuum limit by a term of order 1/N{sup p}. Here we extend the applicability of the above method to the calculation of energy expectation values. This is done by constructing analytical expressions for energy estimators of a general theory for each level p. As a result of this energy expectation values converge to the continuum as 1/N{sup p}. Finally, we perform a series of Monte Carlo simulations of several models, show explicitly the derived increase in convergence, and the ensuing speedup in numerical calculation of energy expectation values of many orders of magnitude.
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
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.
Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom
Ruokosenmäki, Ilkka; Kylänpää, Ilkka; Rantala, Tapio T
2015-01-01
We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We...
Iterative quantum-classical path integral with dynamically consistent state hopping
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
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.)
Boosting QED and QCD bound states in the path integral formalism
Simonov, Yu A
2014-01-01
Wave functions and energy eigenvalues of the path integral Hamiltonian are studied in Lorentz frame moving with velocity $v$. The instantaneous interaction produced by the Wilson loop is shown to be reduced by an overall factor $\\sqrt{1-(\\frac{v}{c})^2}$. As a result one obtains the boosted energy eigenvalues in the Lorentz covariant form $E= \\sqrt{\\veP^2+M^2_0}$, where $M_0$ is the c.m. energy, and this form is tested for two free particles and for the Coulomb and linear interaction.Using Lorentz contracted wave functions of the bound states one obtains the scaled parton wave functions and valence quark distributions for large $P$. Matrix elements containing wave functions moving with different velocities strongly decrease with growing relative momentum, e.g. for the time-like formfactors one obtains $F_h(Q_0)\\sim (\\frac{M_h}{Q_0})^{2 n_h} $ with $n_h = 1$ and 2 for mesons and baryons, as in the "quark counting rule".
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