相关论文: Quantum Diffusions and Appell Systems

Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We…

Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so called ballistic behaviour, which is generally expected for the spreading in a quantum…

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite…

Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.

A stochastic simulation algorithm for the computation of multitime correlation functions which is based on the quantum state diffusion model of open systems is developed. The crucial point of the proposed scheme is a suitable extension of…

By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…

We investigate the structure of the Schrodinger algebra and its representations in a Fock space realized in terms of canonical Appell systems. Generalized coherent states are used in the construction of a Hilbert space of functions on which…

Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum…

Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…

In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous dynamical systems and to analyze numerical integrators.…

We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an…

This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…

The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…

We propose the construction of equations of motion based on symmetries in quantum-mechanical systems, using Heisenberg's uncertainty principle as a minimal foundation. From canonical operators, two spaces of conjugate operators are…

We study the relationships among the various forms of the $q$ oscillator algebra and consider the conditions under which it supports a Hopf structure. We also present a generalization of this algebra together with its corresponding Hopf…

In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed product on a locally convex algebra, thus…

This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…

A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…