arXiv subjects

Keiji Saito

Publications and source records attributed to Keiji Saito.

At least 91 records · Page 5Linked to original sources

arXiv2015

Waiting for rare entropic fluctuations

Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the distribution of these observables, at large fixed time. To characterize the precise stochastic nature of the process, we here address the distribution in the time domain. In particular, we focus on the first passage time distribution (FPTD) of entropy production, in several realistic models. We find that the fluctuation relation symmetry plays a crucial role in getting the typical asymptotic behavior. Similarities and differences to the simple random walk picture are discussed. For a driven particle in the ring geometry, the mean residence time is connected to the particle current and the steady state distribution, and it leads to a fluctuation relation-like symmetry in terms of the FPTD.

cond-mat.stat-mech↗

arXiv2014

Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain

Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang (KPZ) scaling, while the heat mode correlations satisfies Levy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We find very good agreement in many cases, but also some deviations.

cond-mat.stat-mech↗

arXiv2013

Kondo signature in heat transfer via a local two-state system

We study the Kondo effect in heat transport via a local two-state system. This system is described by the spin-boson Hamiltonian with Ohmic dissipation, which can be mapped onto the Kondo model with anisotropic exchange coupling. We calculate thermal conductance by the Monte Carlo method based on the exact formula. Thermal conductance has a scaling form κ= (k_B^2 T_K/\hbar) f(α,T/T_K ), where T_K and αindicate the Kondo temperature and dimensionless coupling strength, respectively. Temperature dependence of conductance is classified by the Kondo temperature as κ\propto (T/T_K )^3 for T\ll T_K and κ\propto (k_B T / \hbarω_c)^{2α-1} for T\gg T_K. Similarities to the Kondo signature in electric transport are discussed.

cond-mat.stat-mech↗

arXiv2013

Fundamental aspects of steady state heat to work conversion

We review theoretical approaches to analyzing efficiency of steady state heat to work conversion which is crucial in the timely problem of optimizing efficiency of small-scale heat engines and refrigerators. A rather abstract perspective of non-equilibrium statistical mechanics and dynamical system's theory is taken to view at this very practical problem. Several recently discovered general mechanisms of optimizing the figure of merit of thermoelectric efficiency are discussed, also in connection to breaking time-reversal symmetry of the microscopic equations of motion. Applications of these theoretical and mathematical ideas to practically relevant models are pointed out.

cond-mat.stat-mech↗

arXiv2013

A Classical Nernst Engine

We introduce a simple model for an engine based on the Nernst effect. In the presence of a magnetic field, a vertical heat current can drive a horizontal particle current against a chemical potential. For a microscopic model invoking classical particle trajectories subject to the Lorentz force, we prove a universal bound 3-2*sqrt(2) simeq 0.172 for the ratio between maximum efficiency and Carnot efficiency. This bound, as the slightly lower one 1/6 for efficiency at maximum power, can indeed be saturated for large magnetic field and small fugacity irrespective of the aspect ratio.

cond-mat.stat-mech↗

arXiv2013

Anomalous transport and current fluctuations in a model of diffusing Levy walkers

A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a long-tailed distribution with a finite mean but an infinite variance. Here we consider an open system with boundary injection and removal of particles, at prescribed rates, and study the steady state properties of the system. In particular, we compute density profiles, current and current fluctuations in this system. We also consider the case of a finite density of Levy walkers on the ring geometry. Here we introduce a size dependent cut-off in the time of flight distribution and consider properties of current fluctuations.

cond-mat.stat-mech↗

arXiv2013

Exact solution of a Levy walk model for anomalous heat transport

The Levy walk model is studied in the context of the anomalous heat conduction of one dimensional systems. In this model the heat carriers execute Levy-walks instead of normal diffusion as expected in systems where Fourier's law holds. Here we calculate exactly the average heat current, the large deviation function of its fluctuations and the temperature profile of the Levy-walk model maintained in a steady state by contact with two heat baths (the open geometry). We find that the current is non-locally connected to the temperature gradient. As observed in recent simulations of mechanical models, all the cumulants of the current fluctuations have the same system-size dependence in the open geometry. For the ring geometry, we argue that a size dependent cut-off time is necessary for the Levy walk model to behave as mechanical models. This modification does not affect the results on transport in the open geometry for large enough system sizes.

cond-mat.stat-mech↗

arXiv2013

Strong bounds on Onsager coefficients and efficiency for three terminal thermoelectric transport in a magnetic field

For thermoelectric transport in the presence of a magnetic field that breaks time-reversal symmetry, a strong bound on the Onsager coefficients is derived within a general set-up using three terminals. Asymmetric Onsager coefficients lead to a maximum efficiency substantially smaller than the Carnot efficiency reaching only η_C/4 in the limit of strong asymmetry. Related bounds are derived for efficiency at maximum power, which can become larger than the Curzon-Ahlborn value η_C/2, and for a cooling device. Our approach reveals that in the presence of reversible currents the standard analysis based on the positivity of entropy production is incomplete without considering the role of current conservation explicitly.

cond-mat.stat-mech↗

arXiv2012

Nonequilibrium density matrix description of steady state quantum transport

With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs and, as well, the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both, electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for inter-electrode electron transport and low-dimensional phonon heat flux are elucidated.

cond-mat.stat-mech↗

arXiv2011

Additivity Principle in High-dimensional Deterministic Systems

The additivity principle (AP), conjectured by Bodineau and Derrida [Phys. Rev. Lett. vol.92, 180601 (2004)], is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated, and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high-dimensional. Surprisingly even in the anomalous regime the CGF is also well fitted by the AP. Lower dimensional systems are also studied and the importance of three-dimensionality for the validity is stressed.

cond-mat.stat-mech↗

arXiv2011

Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems

Recently, in their attempt to construct steady state thermodynamics (SST), Komatsu, Nakagwa, Sasa, and Tasaki found an extension of the Clausius relation to nonequilibrium steady states in classical stochastic processes. Here we derive a quantum mechanical version of the extended Clausius relation. We consider a small system of interest attached to large systems which play the role of heat baths. By only using the genuine quantum dynamics, we realize a heat conducting nonequilibrium steady state in the small system. We study the response of the steady state when the parameters of the system are changed abruptly, and show that the extended Clausius relation, in which "heat" is replaced by the "excess heat", is valid when the temperature difference is small. Moreover we show that the entropy that appears in the relation is similar to von Neumann entropy but has an extra symmetrization with respect to time-reversal. We believe that the present work opens a new possibility in the study of nonequilibrium phenomena in quantum systems, and also confirms the robustness of the approach by Komtatsu et al.

cond-mat.stat-mech↗

arXiv2011

Thermodynamic Bounds on Efficiency for Systems with Broken Time-reversal Symmetry

We show that for systems with broken time-reversal symmetry the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a "figure of merit" and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the so-called strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, always within linear response, it is allowed to have simultaneously Carnot efficiency and non-zero power.

cond-mat.stat-mech↗

arXiv2011

Thermopower with broken time-reversal symmetry

We show that when non-unitary noise effects are taken into account the thermopower is in general asymmetric under magnetic field reversal, even for non-interacting systems. Our findings are illustrated in the example of a three-dot ring structure pierced by an Aharonov-Bohm flux.

cond-mat.stat-mech↗

arXiv2011

Generating Function Formula of Heat Transfer in Harmonic Networks

We consider heat transfer across an arbitrary harmonic network connected to two heat baths at different temperatures. The network has $N$ positional degrees of freedom, of which $N_L$ are connected to a bath at temperature $T_L$ and $N_R$ are connected to a bath at temperature $T_R$. We derive an exact formula for the cumulant generating function for heat transfer between the two baths. The formula is valid even for $N_L \ne N_R$ and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.

cond-mat.stat-mech↗

arXiv2011

Fluctuation Theorem and Microreversibility in a Quantum Coherent Conductor

Mesoscopic systems provide us a unique experimental stage to address non-equilibrium quantum statistical physics. By using a simple tunneling model, we describe the electron exchange process via a quantum coherent conductor between two reservoirs, which yields the fluctuation theorem (FT) in mesoscopic transport. We experimentally show that such a treatment is semi-quantitatively validated in the current and noise measurement in an Aharonov-Bohm ring. The experimental proof of the microreversibility assumed in the derivation of FT is presented.

cond-mat.stat-mech↗

arXiv2010

Linear response formula for finite frequency thermal conductance of open systems

An exact linear response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present numerical results on the frequency dependence of the response function for three different one-dimensional models of coupled oscillators connected to Langevin baths with oscillating temperatures. For momentum conserving systems, a low frequency peak is seen that, is higher than the zero frequency response for large systems. For momentum non-conserving systems, there is no low frequency peak. The momentum non-conserving system is expected to satisfy Fourier's law, however, at the single bond level, we do not see any clear agreement with the predictions of the diffusion equation even at low frequencies. We also derive an exact analytical expression for the response of a chain of harmonic oscillators to a (not necessarily small) temperature difference; the agreement with the linear response simulation results for the same system is excellent.

cond-mat.stat-mech↗

arXiv2010

Chaotic Transport in the Symmetry Crossover Regime with a Spin-orbit Interaction

We study a chaotic quantum transport in the presence of a weak spin-orbit interaction. Our theory covers the whole symmetry crossover regime between time-reversal invariant systems with and without a spin-orbit interaction. This situation is experimentally realizable when the spin-orbit interaction is controlled in a conductor by applying an electric field. We utilize a semiclassical approach which has recently been developed. In this approach, the non-Abelian nature of the spin diffusion along a classical trajectory plays a crucial role. New analytical expressions with one crossover parameter are semiclassically derived for the average conductance, conductance variance and shot noise. Moreover numerical results on a random matrix model describing the crossover from the GOE (Gaussian Orthogonal Ensemble) to the GSE (Gaussian Symplectic Ensemble) are compared with the semiclassical expressions.

cond-mat.mes-hall↗

arXiv2010

A microscopic mechanism for increasing thermoelectric efficiency

We study the coupled particle and energy transport in a prototype model of interacting one-dimensional system: the disordered hard-point gas, for which numerical data suggest that the thermoelectric figure of merit ZT diverges with the system size. This result is explained in terms of a microscopic mechanism, namely the local equilibrium is characterized by the emergence of a broad stationary "modified Maxwell-Boltzmann velocity distribution", of width much larger than the mean velocity of the particle flow.

cond-mat.stat-mech↗