Related papers: ``Classical'' Propagator and Path Integral in the …
Quantized systems whose underlying classical dynamics possess an elaborate mixture of regular and chaotic motion can exhibit rather subtle long-time quantum transport phenomena. In a short wavelength regime where semiclassical theories are…
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…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
We address the calculation of transition probabilities in multiplicative noise stochastic differential equations using a path integral approach. We show the equivalence between the conditional probability and the propagator of a quantum…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it…
We present the path-integral solutions to the distributions in classical (Gibbs) and quantum (Wigner) statistical mechanics. The kernel of the distributions are derived in two ways - one by time slicing and defining the appropriate…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
Feynman's path integral in adelic quantum mechanics is considered. The propagator K(x'',t'';x',t') for one-dimensional adelic systems with quadratic Lagrangians is analytically evaluated. Obtained exact general formula has the form which is…
We describe both quantum particles and classical particles in terms of a classical statistical ensemble, characterized by a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same…
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root-search for classical trajectories. We demonstrate its potential by…
A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…