Feynman path integrals

The quantity is the Feynman path integral centroid density [43] that is understood to be expressed asymptotically as... 

Voth G A 1993 Feynman path integral formulation of quantum mechanical transition state theory J. Phys. Chem. 97 8365... 

In this section we shall expand upon the problem of one-dimensional motion in a potential V x). Although it is a textbook example, we use here the less traditional Feynman path-integral formalism, the advantage of which is a possibility of straightforward extension to many dimensions. In the following portion of the theory we shall use dimensionless units, in which h = i,k = 1 and the particle has unit mass. 

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. 

Albeverio, S.A. and Hpegh-Krohn, R.J., Mathematical Theory of Feynman Path Integrals, Lecture Notes in Mathematics 523, Springer, Berlin, Heidelberg, and New York, 1976. 

The calculation of the potential of mean force, AF(z), along the reaction coordinate z, requires statistical sampling by Monte Carlo or molecular dynamics simulations that incorporate nuclear quantum effects employing an adequate potential energy function. In our approach, we use combined QM/MM methods to describe the potential energy function and Feynman path integral approaches to model nuclear quantum effects. 

Polarization fluctuations of a certain type were considered in the configuration model presented above. In principle, fluctuations of a more complicated form may be considered in the same way. A more general approach was suggested in Refs. 23 and 24, where Eq. (16) for the transition probability has been written in a mixed representation using the Feynman path integrals for the nuclear subsystem and the functional integrals over the electron wave functions of the initial and final states t) and t) for the electron ... 

The expressions for the density matrices p, and pf are written through the Feynman path integrals over x(t) and R(t).70 The path integral over x(t) can be calculated exactly for the arbitrary form of the functions /(R) and f/(R)- The path integrals over R(t) cannot, in general, be calculated exactly. However, taking into... 

A dynamic description of the effect of relaxation on the probability of the adiabatic transition may be performed using various methods, e.g., a Feynman path integral approach similar to that presented in Section III (see also Refs. 81-84). Here we shall present the results for a simple model obtained by another method.85... 

A number of papers are devoted to the effect of dissipation on tunneling.81"83,103,104 Wolynes81 was one of the first to consider this problem using the Feynman path integral approach to calculate the correlation function of the reactive flux involved in the expression for the rate constant,... 

The Feynman path integral formalism " in quantum mechanics has proven to be an important vehicle for studying the quantum properties of condensed matter, both conceptually and in computational studies. Various classical-like concepts may be more easily introduced and, in the case of equilibrium properties, the formalism provides apowerful computer simulation tool. 

The rather complicated Feynman-path-integral-like local averaging scheme due to Wang and Teter11 is consistent with the natural variable argument. 

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