34 research outputs found
A perturbative method for nonequilibrium steady state of open quantum systems
We develop a method of calculating the nonequilibrium steady state (NESS) of
an open quantum system that is weakly coupled to reservoirs in different
equilibrium states. We describe the system using a Redfield-type quantum master
equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the
remaining part . Regarding the steady state of the Lindblad QME as
the unperturbed solution, we perform a perturbative calculation with respect to
to obtain the NESS of the Redfield QME. The NESS thus determined
is exact up to the first order in the system-reservoir coupling strength
(pump/loss rate), which is the same as the order of validity of the QME. An
advantage of the proposed method in numerical computation is its applicability
to systems larger than those in methods of directly solving the original
Redfield QME. We apply the method to a noninteracting fermion system to obtain
an analytical expression of the NESS density matrix. We also numerically
demonstrate the method in a nonequilibrium quantum spin chain.Comment: 15 pages, 3 figures. To appear in J. Phys. Soc. Jp
Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems
For open systems described by the quantum Markovian master equation, we study
a possible extension of the Clausius equality to quasistatic operations between
nonequilibrium steady states (NESSs). We investigate the excess heat divided by
temperature (i.e., excess entropy production) which is transferred into the
system during the operations. We derive a geometrical expression for the excess
entropy production, which is analogous to the Berry phase in unitary evolution.
Our result implies that in general one cannot define a scalar potential whose
difference coincides with the excess entropy production in a thermodynamic
process, and that a vector potential plays a crucial role in the thermodynamics
for NESSs. In the weakly nonequilibrium regime, we show that the geometrical
expression reduces to the extended Clausius equality derived by Saito and
Tasaki (J. Stat. Phys. {\bf 145}, 1275 (2011)). As an example, we investigate a
spinless electron system in quantum dots. We find that one can define a scalar
potential when the parameters of only one of the reservoirs are modified in a
non-interacting system, but this is no longer the case for an interacting
system.Comment: 28 pages, 3 figures. 'Remark on the fluctuation theorem' has been
revised in ver. 2. Brief Summary has been added in Sec. 1 in ver.
Geometrical Pumping in Quantum Transport: Quantum Master Equation Approach
For an open quantum system, we investigate the pumped current induced by a
slow modulation of control parameters on the basis of the quantum master
equation and full counting statistics. We find that the average and the
cumulant generating function of the pumped quantity are characterized by the
geometrical Berry-phase-like quantities in the parameter space, which is
associated with the generator of the master equation. From our formulation, we
can discuss the geometrical pumping under the control of the chemical
potentials and temperatures of reservoirs. We demonstrate the formulation by
spinless electrons in coupled quantum dots. We show that the geometrical
pumping is prohibited for the case of non-interacting electrons if we modulate
only temperatures and chemical potentials of reservoirs, while the geometrical
pumping occurs in the presence of an interaction between electrons