77,171 research outputs found
Non-Markovian finite-temperature two-time correlation functions of system operators: beyond the quantum regression theorem
An extremely useful evolution equation that allows systematically calculating
the two-time correlation functions (CF's) of system operators for non-Markovian
open (dissipative) quantum systems is derived. The derivation is based on
perturbative quantum master equation approach, so non-Markovian open quantum
system models that are not exactly solvable can use our derived evolution
equation to easily obtain their two-time CF's of system operators, valid to
second order in the system-environment interaction. Since the form and nature
of the Hamiltonian are not specified in our derived evolution equation, our
evolution equation is applicable for bosonic and/or fermionic environments and
can be applied to a wide range of system-environment models with any factorized
(separable) system-environment initial states (pure or mixed). When applied to
a general model of a system coupled to a finite-temperature bosonic environment
with a system coupling operator L in the system-environment interaction
Hamiltonian, the resultant evolution equation is valid for both L = L^+ and L
\neq L^+ cases, in contrast to those evolution equations valid only for L = L^+
case in the literature. The derived equation that generalizes the quantum
regression theorem (QRT) to the non-Markovian case will have broad applications
in many different branches of physics. We then give conditions on which the QRT
holds in the weak system-environment coupling case, and apply the derived
evolution equation to a problem of a two-level system (atom) coupled to a
finite-temperature bosonic environment (electromagnetic fields) with L \neq
L^+.Comment: To appear in the Journal of Chemical Physics (12 pages, 1 figure
Variational Principle for Mixed Classical-Quantum Systems
An extended variational principle providing the equations of motion for a
system consisting of interacting classical, quasiclassical and quantum
components is presented, and applied to the model of bilinear coupling. The
relevant dynamical variables are expressed in the form of a quantum state
vector which includes the action of the classical subsystem in its phase
factor. It is shown that the statistical ensemble of Brownian state vectors for
a quantum particle in a classical thermal environment can be described by a
density matrix evolving according to a nonlinear quantum Fokker-Planck
equation. Exact solutions of this equation are obtained for a two-level system
in the limit of high temperatures, considering both stationary and
nonstationary initial states. A treatment of the common time shared by the
quantum system and its classical environment, as a collective variable rather
than as a parameter, is presented in the Appendix.Comment: 16 pages, LaTex; added Figure 2 and Figure
The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis
We provide an in-depth and thorough treatment of the validity of the
rotating-wave approximation (RWA) in an open quantum system. We find that when
it is introduced after tracing out the environment, all timescales of the open
system are correctly reproduced, but the details of the quantum state may not
be. The RWA made before the trace is more problematic: it results in incorrect
values for environmentally-induced shifts to system frequencies, and the
resulting theory has no Markovian limit. We point out that great care must be
taken when coupling two open systems together under the RWA. Though the RWA can
yield a master equation of Lindblad form similar to what one might get in the
Markovian limit with white noise, the master equation for the two coupled
systems is not a simple combination of the master equation for each system, as
is possible in the Markovian limit. Such a naive combination yields inaccurate
dynamics. To obtain the correct master equation for the composite system a
proper consideration of the non-Markovian dynamics is required.Comment: 17 pages, 0 figures
Phase Diffusion in Quantum Dissipative Systems
We study the dynamics of the quantum phase distribution associated with the
reduced density matrix of a system for a number of situations of practical
importance, as the system evolves under the influence of its environment,
interacting via a quantum nondemoliton type of coupling, such that there is
decoherence without dissipation, as well as when it interacts via a dissipative
interaction, resulting in decoherence as well as dissipation. The system is
taken to be either a two-level atom (or equivalently, a spin-1/2 system) or a
harmonic oscillator, and the environment is modeled as a bath of harmonic
oscillators, starting out in a squeezed thermal state. The impact of the
different environmental parameters on the dynamics of the quantum phase
distribution for the system starting out in various initial states, is
explicitly brought out. An interesting feature that emerges from our work is
that the relationship between squeezing and temperature effects depends on the
type of system-bath interaction. In the case of quantum nondemolition type of
interaction, squeezing and temperature work in tandem, producing a diffusive
effect on the phase distribution. In contrast, in case of a dissipative
interaction, the influence of temperature can be counteracted by squeezing,
which manifests as a resistence to randomization of phase. We make use of the
phase distributions to bring out a notion of complementarity in atomic systems.
We also study the dispersion of the phase using the phase distributions
conditioned on particular initial states of the system.Comment: Accepted for publication in Physical Review A; changes in section V;
20 pages, 12 figure
Markovian master equations for quantum thermal machines: local vs global approach
The study of quantum thermal machines, and more generally of open quantum
systems, often relies on master equations. Two approaches are mainly followed.
On the one hand, there is the widely used, but often criticized, local
approach, where machine sub-systems locally couple to thermal baths. On the
other hand, in the more established global approach, thermal baths couple to
global degrees of freedom of the machine. There has been debate as to which of
these two conceptually different approaches should be used in situations out of
thermal equilibrium. Here we compare the local and global approaches against an
exact solution for a particular class of thermal machines. We consider
thermodynamically relevant observables, such as heat currents, as well as the
quantum state of the machine. Our results show that the use of a local master
equation is generally well justified. In particular, for weak inter-system
coupling, the local approach agrees with the exact solution, whereas the global
approach fails for non-equilibrium situations. For intermediate coupling, the
local and the global approach both agree with the exact solution and for strong
coupling, the global approach is preferable. These results are backed by
detailed derivations of the regimes of validity for the respective approaches.Comment: Published version. See also the related work by J. Onam Gonzalez et
al. arXiv:1707.0922
- …