arXiv subjects

Kazuki Yamaga

Publications and source records attributed to Kazuki Yamaga.

4 recordsLinked to original sources

arXiv2020

Asymptotic property of current for a conduction model of Fermi particles on finite lattice

In this paper, we introduce a conduction model of Fermi particles on a finite sample, and investigate the asymptotic behavior of stationary current for large sample size. In our model a sample is described by a one-dimensional finite lattice on which Fermi particles injected at both ends move under various potentials and noise from the environment. We obtain a simple current formula. The formula has broad applicability and is used to study various potentials. When the noise is absent, it provides the asymptotic behavior of the current in terms of a transfer matrix. In particular, for dynamically defined potential cases, a relation between exponential decay of the current and the Lyapunov exponent of a relevant transfer matrix is obtained. For example, it is shown that the current decays exponentially for the Anderson model. On the other hand, when the noise exists but the potential does not, an explicit form of the current is obtained, which scales as 1/N for large sample size N. Moreover, we provide an extension to higher dimensional systems. For a three-dimensional case, it is shown that the current increases in proportion to cross section and decreases in inverse proportion to the length of the sample.

math-ph↗

arXiv2020

Stochastic process emerged from lattice fermion systems by repeated measurements and large-time limit

It is known that in quantum theory, measurements may suppress Hamiltonian dynamics of a system. A famous example is the `Quantum Zeno Effect'. This is the phenomena that if one repeats the measurements many times asking whether the system is in the same state as the one at the initial time until the fixed measurement time, then survival probability tends to 1 by taking the measurement interval to 0. This is the case for fixed measurement time. It is known that if one takes measurement time infinite at appropriate scaling, `Quantum Zeno Effect' does not occur and the effect of Hamiltonian dynamics emerges (Facchi and Ligabo 2017). In the present paper, we consider the long time repeated measurements and the dynamics of quantum many body systems in the scaling where the effect of measurements and dynamics are balanced. We show that the stochastic process, called symmetric simple exclusion process (SSEP), is obtained from the repeated and long time measurements of configuration of particles in finite lattice fermion systems. The emerging stochastic process is independent of potential and interaction of the underlying Hamiltonian of the system.

quant-ph↗

arXiv2020

Dissipative dynamics of non-interacting fermion systems and conductivity

In this paper, Non-Equilibrium Steady State induced by electric field and the conductivity of non-interacting fermion systems under the dissipative dynamics is discussed. The dissipation is taken into account within a framework of the quantum dynamical semigroup introduced by Davies (1977). We obtain a formula of the conductivity for the stationary state, which is applicable to arbitrary potentials. Our formula gives a justification of an adiabatic factor which is often introduced in practical calculation using Kubo formula. In addition the conductivity of crystals (i.e. periodic potentials) is also discussed.

math-ph↗

arXiv2018

The second law-type work relation in non-equilibrium steady states in one-dimensional quantum lattice systems

We consider the Non-Equilibrium Steady State induced by two infinite quantum thermal reservoirs at different temperatures and derive an inequality giving the upper bound of the work extracted by cyclic operations. This upper bound tends to 0 in the equilibrium limit and the inequality reproduces the second law of thermodynamics that one cannot extract any work from equilibrium states by cyclic operations. In addition, we consider global cyclic operations and obtain an upper bound of the work density in one-dimensional quantum lattice systems, which depends on the model and the temperatures of the reservoirs. This bound is independent of the operations and also tends to 0 in the equilibrium limit.

cond-mat.stat-mech↗