相关论文: A Feynman-Kac Formula for Anticommuting Brownian M…
A new mathematical framework is formulated to derive the effective equations of motion for the constrained quantum system which possesses an internal clock. In the realm close to classical behavior, the quantum evolution is approximated by…
We consider functional Schr\"{o}dinger equations associated with a wide class of Hamiltonians in all Fock representations of the bosonic canonical commutation relations, in particular the Cook-Fock, Friedrichs-Fock, and Bargmann-Fock…
A general formlulation for discrete-time quantum mechanics, based on Feynman's method in ordinary quantum mechanics, is presented. It is shown that the ambiguities present in ordinary quantum mechanics (due to noncommutativity of the…
We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows…
A quantum-mechanical version of Einstein's 1905 theory of Brownian motion is presented. Starting from the Hamiltonian dynamics of an isolated composite of objective and environmental systems, subdynamics for the objective system is derived…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
In this article, we study a finite horizon linear-quadratic stochastic control problem for Brownian particles, where the cost functions depend on the state and the occupation measure of the particles. To address this problem, we develop an…
We propose a Langevin equation to describe the quantum Brownian motion of bounded particles based on a distinctive formulation concerning both the fluctuation and dissipation forces. The fluctuation force is similar to that employed in the…
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…
By using Malliavin calculus, Bismut derivative formulae are established for a class of stochastic (functional) differential equations driven by fractional Brownian motions. As applications, Harnack type inequalities and strong Feller…
A structure of generator of a quantum dynamical semigroup for the dynamics of a test particle interacting through collisions with the environment is considered, which has been obtained from a microphysical model. The related master-equation…
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.…
Functional Schr\"{o}dinger equations for interacting fields are solved via rigorous non-perturbative Feynman type integrals.
We try to clarify what are the genuine quantal effects that are associated with generalized Brownian Motion (BM). All the quantal effects that are associated with the Zwanzig-Feynman-Vernon-Caldeira-Leggett model are (formally) a solution…
By considering an ensemble of Brownian particles suspended in a heat bath as a thermodynamic system with an internal degree of freedom it is possible to obtain the Fokker-Planck equation for Brownian motion in a temperature gradient, by…
A fully quantum treatment of Einstein's Brownian motion is given, showing in particular the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
Dynamics of quantum systems which are perturbed by linear coupling to the reservoir stochastically can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…