Path integral statistical mechanics

Path-integral statistical mechanics is obtained in strict analogy to path-integral quantum dynamics [71]. The path-integral version of quantum dynamics focuses on the fact that a quantum mechanical system is allowed to violate Hamilton s principle. For example, tunneling (a nonclassical motion) is possible within quantum mechanics. Seizing on a comment by Dirac [72] on the relationship between S and the quantum propagator... 

Path Integral Quantum Mechanics and Statistical Thermodynamics. 69... 

Tuckerman M E and Hughes A 1998 Path integral molecular dynamics a computational approach to quantum statistical mechanics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 311-57... 

H. Kleinert, Path integrals in quantum mechanics, statistics and polymer physics , World Scientific, Singapore, 1995, chapters 18.5 and 18.6. 

H. Kleinert. Path Integrals in Quantum Mechanics, Statistics and Polymer Physics. Singapore World Scientific, 1990. 

Another example of slight conceptual inaccuracy is given by the Wigner function(12) and Feynman path integral(13). Both are useful ways to look at the wave function. However, because of the prominence of classical particles in these concepts, they suggest the view that QM is a variant of statistical mechanics and that it is a theory built on top of NM. This is unfortunate, since one wants to convey the notion that NM can be recovered as an integral part of QM pertaining to for macroscopic systems. 

Feynman RP, Hibbs AR (1965) Quantum Mechanics and Path Integrals. McGraw-Hill New York, p xiv, 365 p. For the applications in quantum statistics, see chapters 10 and 11 Corrections to the errata in the book http //www.oberlin.edu/physics/dstyer/FeynmanHibbs/ and http //www.physik. fu-berlin.de/ kleinert/Feynman-Hibbs/... 

Kleinert H (2004) Path integrals in quantum mechanics, statistics, polymer physics, and financial markets. 3rd edition. World Scientific Singapore River Edge, NJ, p xxvi, 1468 p. For the quantum mechanical integral equation, see Section 1.9 For the variational perturbation theory, see Chapters... 

There is considerable interest in the use of discretized path-integral simulations to calculate free energy differences or potentials of mean force using quantum statistical mechanics for many-body systems [140], The reader has already become familiar with this approach to simulating with classical systems in Chap. 7. The theoretical basis of such methods is the Feynmann path-integral representation [141], from which is derived the isomorphism between the equilibrium canonical ensemble of a... 

A NEW SERIES EXPANSION FOR PATH INTEGRALS IN STATISTICAL MECHANICS ... 

The use of path or functional integration techniques in physics offers many apparent simplifications especially in statistical mechanics. However, in practice it is usually impossible to make an explicit evaluation of the path integrals one meets. Here we shall give a very condensed account of a possible approximation scheme for the calculation of a particular class of path integrals. 

Integrals, Path, A New Series Expansion for, in Statistical Mechanics... 

Our simulations are based on well-established mixed quantum-classical methods in which the electron is described by a fully quantum-statistical mechanical approach whereas the solvent degrees of freedom are treated classically. Details of the method are described elsewhere [27,28], The extent of the electron localization in different supercritical environments can be conveniently probed by analyzing the behavior of the correlation length R(fih/2) of the electron, represented as polymer of pseudoparticles in the Feynman path integral representation of quantum mechanics. Using the simulation trajectories, R is computed from the mean squared displacement along the polymer path, R2(t - t ) = ( r(f) - r(t )l2), where r(t) represents the electron position at imaginary time t and 1/(3 is Boltzmann constant times the temperature. 

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