43 research outputs found
Microscopic analysis of the microscopic reversibility in quantum systems
We investigate the robustness of the microscopic reversibility in open
quantum systems which is discussed by Monnai [arXiv:1106.1982 (2011)]. We
derive an exact relation between the forward transition probability and the
reversed transition probability in the case of a general measurement basis. We
show that the microscopic reversibility acquires some corrections in general
and discuss the physical meaning of the corrections. Under certain processes,
some of the correction terms vanish and we numerically confirmed that the
remaining correction term becomes negligible; the microscopic reversibility
almost holds even when the local system cannot be regarded as macroscopic.Comment: 12 pages, 10 figure
Unified Treatment of Quantum Fluctuation Theorem and Jarzynski Equality in Terms of microscopic reversibility
There are two related theorems which hold even in far from equilibrium,
namely fluctuation theorem and Jarzynski equality. Fluctuation theorem states
the existence of symmetry of fluctuation of entropy production, while Jarzynski
equality enables us to estimate the free energy change between two states by
using irreversible processes. On the other hand, relationship between these
theorems was investigated by Crooks for the classical stochastic systems. In
this letter, we derive quantum analogues of fluctuation theorem and Jarzynski
equality microscopic reversibility condition. In other words, the quantum
analogue of the work by Crooks is presented.Comment: 7pages, revised versio
Microscopic reversibility of quantum open systems
The transition probability for time-dependent unitary evolution is invariant
under the reversal of protocols just as in the classical Liouvillian dynamics.
In this article, we generalize the expression of microscopic reversibility to
externally perturbed large quantum open systems. The time-dependent external
perturbation acts on the subsystem during a transient duration, and
subsequently the perturbation is switched off so that the total system would
thermalize. We concern with the transition probability for the subsystem
between the initial and final eigenstates of the subsystem. In the course of
time evolution, the energy is irreversibly exchanged between the subsystem and
reservoir. The time reversed probability is given by the reversal of the
protocol and the initial ensemble. Microscopic reversibility equates the time
forward and reversed probabilities, and therefore appears as a thermodynamic
symmetry for open quantum systems.Comment: numerical demonstration is correcte
Diffusion in the Markovian limit of the spatio-temporal colored noise
We explore the diffusion process in the non-Markovian spatio-temporal
noise.%the escape rate problem in the non-Markovian spatio-temporal random
noise. There is a non-trivial short memory regime, i.e., the Markovian limit
characterized by a scaling relation between the spatial and temporal
correlation lengths. In this regime, a Fokker-Planck equation is derived by
expanding the trajectory around the systematic motion and the non-Markovian
nature amounts to the systematic reduction of the potential. For a system with
the potential barrier, this fact leads to the renormalization of both the
barrier height and collisional prefactor in the Kramers escape rate, with the
resultant rate showing a maximum at some scaling limit.Comment: 4pages,2figure
Fluctuation theorem for currents in open quantum systems
A quantum-mechanical framework is set up to describe the full counting
statistics of particles flowing between reservoirs in an open system under
time-dependent driving. A symmetry relation is obtained which is the
consequence of microreversibility for the probability of the nonequilibrium
work and the transfer of particles and energy between the reservoirs. In some
appropriate long-time limit, the symmetry relation leads to a steady-state
quantum fluctuation theorem for the currents between the reservoirs. On this
basis, relationships are deduced which extend the Onsager-Casimir reciprocity
relations to the nonlinear response coefficients.Comment: 19 page
Relativistic dissipative hydrodynamics with extended matching conditions for ultra-relativistic heavy-ion collisions
Recently we proposed a novel approach to the formulation of relativistic
dissipative hydrodynamics by extending the so-called matching conditions in the
Eckart frame [Phys. Rev. {\bf C 85}, (2012) 14906]. We extend this formalism
further to the arbitrary Lorentz frame. We discuss the stability and causality
of solutions of fluid equations which are obtained by applying this formulation
to the Landau frame, which is more relevant to treat the fluid produced in
ultra-relativistic heavy-ion collisions. We derive equations of motion for a
relativistic dissipative fluid with zero baryon chemical potential and show
that linearized equations obtained from them are stable against small
perturbations. It is found that conditions for a fluid to be stable against
infinitesimal perturbations are equivalent to imposing restrictions that the
sound wave, , propagating in the fluid, must not exceed the speed of light
, i.e., . This conclusion is equivalent to that obtained in the
previous paper using the Eckart frame [Phys. Rev. {\bf C 85}, (2012) 14906].Comment: 2nd version. Typos corrected. 7 pages. Contribution to The European
Physical Journal A (Hadrons and Nuclei) topical issue about 'Relativistic
Hydro- and Thermodynamics in Nuclear Physics