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Takaaki Monnai

Publications and source records attributed to Takaaki Monnai.

26 records · Page 2Linked to original sources
arXiv2011

Relaxation to equilibrium of expectation values in macroscopic quantum systems

A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally perturbed during a finite time, and then isolated for a sufficiently long time. We show a quantitative explanation that the initial microcanonical state typically reaches to a state whose expectation values are well-approximated by the average over another microcanonical ensemble.

cond-mat.stat-mech↗
arXiv2010

Derivation of quantum master equation with counting fields by monitoring a probe

We show a microscopic derivation of a quantum master equation with counting terms which describes the electron statistics. A localized spin behaves as a probe whose precession angle monitors the net electron current by the magnetic-moment interaction. The probe Hamiltonian is proportional to the current, and is determined self-consistently for a model of a quantum dot. Then it turns out that the quantum master equation for the spin-precession contains the counting terms. As an application, we show the fluctuation theorem for the electron current.

cond-mat.stat-mech↗
arXiv2010

Nonequilibrium thermodynamics and Nose-Hoover dynamics

We show that systems driven by an external force and described by Nose-Hoover dynamics allow for a consistent nonequilibrium thermodynamics description when the thermostatted variable is initially assumed in a state of canonical equilibrium. By treating the "real" variables as the system and the thermostatted variable as the reservoir, we establish the first and second law of thermodynamics. As for Hamiltonian systems, the entropy production can be expressed as a relative entropy measuring the system-reservoir correlations established during the dynamics.

cond-mat.stat-mech↗
arXiv2008

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.

cond-mat.stat-mech↗
arXiv2008

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.

cond-mat.stat-mech↗
arXiv2006

Role of an intermediate state in homogeneous nucleation

We explore the role of an intermediate state (phase) in homogeneous nucleation phenomenon by examining the decay process through a doubly-humped potential barrier. As a generic model we use the fourth- and sixth-order Landau potentials and analyze the Fokker-Planck equation for the one-dimensional thermal diffusion in the system characterized by a triple-well potential. In the low temperature case we apply the WKB method to the decay process and obtain the decay rate which is accurate for a wide range of depth and curvature of the middle well. In the case of a deep middle well, it reduces to a doubly-humped-barrier counterpart of the Kramers escape rate: the barrier height and the curvature of an initial well in the Kramers rate are replaced by the arithmetic mean of higher(or outer) and lower(or inner) partial barriers and the geometric mean of curvatures of the initial and intermediate wells, respectively. It seems to be a universal formula. In the case of a shallow-enough middle well, Kramers escape rate is alternatively evaluated within the standard framework of the mean-first-passage time problem, which certainly supports the WKB result. The criteria whether or not the existence of an intermediate state can enhance the decay rate are revealed.

cond-mat.stat-mech↗
arXiv2004

Calculation of Correlation Functions in Terms of Fluctuation Relation

We derive a relation similar to the fluctuation theorem for work done on a system obeying Langevin dynamics with thermal and colored noises. Then, we propose a method of calculating the correlation function of the colored noise by using this fluctuation relation.

cond-mat.stat-mech↗