408,052 research outputs found
The non-Markovian stochastic Schrodinger equation for open systems
We present the non-Markovian generalization of the widely used stochastic
Schrodinger equation. Our result allows to describe open quantum systems in
terms of stochastic state vectors rather than density operators, without
approximation. Moreover, it unifies two recent independent attempts towards a
stochastic description of non-Markovian open systems, based on path integrals
on the one hand and coherent states on the other. The latter approach utilizes
the analytical properties of coherent states and enables a microscopic
interpretation of the stochastic states. The alternative first approach is
based on the general description of open systems using path integrals as
originated by Feynman and Vernon.Comment: 9 pages, RevTe
Linear quantum state diffusion for non-Markovian open quantum systems
We demonstrate the relevance of complex Gaussian stochastic processes to the
stochastic state vector description of non-Markovian open quantum systems.
These processes express the general Feynman-Vernon path integral propagator for
open quantum systems as the classical ensemble average over stochastic pure
state propagators in a natural way. They are the coloured generalization of
complex Wiener processes in quantum state diffusion stochastic Schrodinger
equations.Comment: 9 pages, RevTeX, appears in Physics Letters
Stochastic description for open quantum systems
A linear open quantum system consisting of a harmonic oscillator linearly
coupled to an infinite set of independent harmonic oscillators is considered;
these oscillators have a general spectral density function and are initially in
a Gaussian state. Using the influence functional formalism a formal Langevin
equation can be introduced to describe the system's fully quantum properties
even beyond the semiclassical regime. It is shown that the reduced Wigner
function for the system is exactly the formal distribution function resulting
from averaging both over the initial conditions and the stochastic source of
the formal Langevin equation. The master equation for the reduced density
matrix is then obtained in the same way a Fokker-Planck equation can always be
derived from a Langevin equation characterizing a stochastic process. We also
show that a subclass of quantum correlation functions for the system can be
deduced within the stochastic description provided by the Langevin equation. It
is emphasized that when the system is not Markovian more information can be
extracted from the Langevin equation than from the master equation.Comment: 16 pages, RevTeX, 1 figure (uses epsf.sty). Shortened version.
Partially rewritten to emphasize those aspects which are new. Some references
adde
Paths and stochastic order in open systems
The principle of maximum irreversible is proved to be a consequence of a
stochastic order of the paths inside the phase space; indeed, the system
evolves on the greatest path in the stochastic order. The result obtained is
that, at the stability, the entropy generation is maximum and, this maximum
value is consequence of the stochastic order of the paths in the phase space,
while, conversely, the stochastic order of the paths in the phase space is a
consequence of the maximum of the entropy generation at the stability
Dissipative Linear Stochastic Hamiltonian Systems
This paper is concerned with stochastic Hamiltonian systems which model a
class of open dynamical systems subject to random external forces. Their
dynamics are governed by Ito stochastic differential equations whose structure
is specified by a Hamiltonian, viscous damping parameters and
system-environment coupling functions. We consider energy balance relations for
such systems with an emphasis on linear stochastic Hamiltonian (LSH) systems
with quadratic Hamiltonians and linear coupling. For LSH systems, we also
discuss stability conditions, the structure of the invariant measure and its
relation with stochastic versions of the virial theorem. Using Lyapunov
functions, organised as deformed Hamiltonians, dissipation relations are also
considered for LSH systems driven by statistically uncertain external forces.
An application of these results to feedback connections of LSH systems is
outlined.Comment: 10 pages, 1 figure, submitted to ANZCC 201
Exact quantum jump approach to open systems in Bosonic and spin baths
A general method is developed which enables the exact treatment of the
non-Markovian quantum dynamics of open systems through a Monte Carlo simulation
technique. The method is based on a stochastic formulation of the von Neumann
equation of the composite system and employs a pair of product states following
a Markovian random jump process. The performance of the method is illustrated
by means of stochastic simulations of the dynamics of open systems interacting
with a Bosonic reservoir at zero temperature and with a spin bath in the strong
coupling regime.Comment: 4 pages, 2 figure
Energetics of Open Systems and Chemical Potential From Micro-Dynamics Viewpoints
We present the energetic aspect of open systems which may exchange particles
with their environments. Our attention shall be paid to the scale that the
motion of the particles is described by the classical Langevin dynamics. Along
a particular realization of the stochastic process, we study the energy
transfer into the open system from the environments. We are able to clarify how
much energy each particle carries when it enters or leaves the system. On the
other hand, the chemical potential should be considered as the concept in macro
scale, which is relevant to the free energy potential with respect to the
number of particles. Keywords: open systems, stochastic energetics, chemical
potentialComment: 7 pages, 1 figur
Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited
Stochastic Schr{\"o}dinger equations for quantum trajectories offer an
alternative and sometimes superior approach to the study of open quantum system
dynamics. Here we show that recently established convolutionless non-Markovian
stochastic Schr{\"o}dinger equations may serve as a powerful tool for the
derivation of convolutionless master equations for non-Markovian open quantum
systems. The most interesting example is quantum Brownian motion (QBM) of a
harmonic oscillator coupled to a heat bath of oscillators, one of the
most-employed exactly soluble models of open system dynamics. We show
explicitly how to establish the direct connection between the exact
convolutionless master equation of QBM and the corresponding convolutionless
exact stochastic Schr\"odinger equation.Comment: 18 pages, RevTe
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