arXiv subjects

Takashi Mori

Publications and source records attributed to Takashi Mori.

69 records · Page 4Linked to original sources

arXiv2014

Natural correlation between a system and a thermal reservoir

Non-Markovian corrections to the Markovian quantum master equation of an open quantum system are investigated up to the second order of the interaction between the system of interest and a thermal reservoir. The concept of "natural correlation" is discussed. When the system is naturally correlated with a thermal reservoir, the time evolution of the reduced density matrix looks Markovian even in a short-time regime. If the total system was initially in an "unnatural" state, the natural correlation is established during the time evolution, and after that the time evolution becomes Markovian in a long-time regime. It is also shown that for a certain set of reduced density matrices, the naturally correlated state does not exist. If the initial reduced density matrix has no naturally correlated state, the time evolution is inevitably non-Markovian in a short-time regime.

quant-ph↗

arXiv2014

Novel symmetry-broken phase in a driven cavity system in the thermodynamic limit

We study non-equilibrium stationary states of a cavity system consisting of many atoms interacting with a quantized cavity field mode, under a driving field in a dissipative environment. We derive a quantum master equation which is suitable for treating systems with a strong driving field and a strong atom-photon interaction. We do this by making use of the fact that the mean-field dynamics are exact in the thermodynamic limit thanks to a uniform coupling between atoms and photons. We find ordered states with symmetry-broken components of the photon field and atomic excitation driven by the external field. The mechanism by which these ordered states arise is discussed from the viewpoint of the quantum interference effect.

quant-ph↗

arXiv2013

Phase transitions in systems with non-additive long-range interactions

We consider spin systems with long-range interactions in nonadditive regime. When the non-additive scaling limit is employed, the energy and the entropy compete and the system exhibits some phase transitions. Such systems do not satisfy the additivity, which results in some unfamiliar properties related to phase transitions. In this paper, the concept of additivity and its consequence are explained and the recent progress on statistical mechanics of long-range interacting systems are reviewed. It is shown that the parameter space is clearly decomposed into the three regions according to the stability of the uniform state predicted by the mean-field theory. Based on this parameter space decomposition, recent results on the exactness of MF theory are explained. When the interaction is non-negative (ferromagnetic), the analysis of the mean-field theory is exact and a typical spin configuration is always uniform in the canonical ensemble. However, in the restricted canonical ensemble, i.e., the canonical ensemble with a restriction of the value of the magnetization, it is shown that the mean-field theory does not necessarily give the exact description of the system and phase transitions between the mean-field uniform states (MF phase) and the inhomogeneous states (non-MF phase) occur. A new finding is that when the interaction potential changes its sign depending on the distance, the non-MF phase appears even in the canonical ensemble.

cond-mat.stat-mech↗

arXiv2013

Nonadditivity in Quasiequilibrium States of Spin Systems with Lattice Distortion

It is pointed out that there exists a short-range interacting system, i.e. the elastic spin model, which is extensive but nonadditive. It is numerically shown that, depending on the statistical ensemble, the specific heat or the susceptibility becomes negative in a certain parameter region, which shows ensemble inequivalence in this model. Further, we numerically estimate the effective Hamiltonian for spin variables, and it is clarified that the effective interaction among spin variables is long-ranged. Remarkably, the so called Kac's prescription, which is usually regarded as a mathematical operation to make the system extensive, naturally holds in the effective interaction.

cond-mat.stat-mech↗

arXiv2013

Exactness of the mean-field dynamics in optical cavity systems

Validity of the mean-field approach to open system dynamics in the optical cavity system is examined. It is rigorously shown that the mean-field approach is justified in the thermodynamic limit. The result is applicable to nonequilibrium situations, e.g. the thermal reservoirs may have different temperatures, and the system may be subject to a time-dependent external field. The result of this work will lead to further studies on macroscopic open quantum systems.

cond-mat.stat-mech↗

arXiv2013

Analysis of the exactness of mean-field theory in long-range interacting systems

Relationships between general long-range interacting classical systems on a lattice and the corresponding mean-field models (infinitely long-range interacting models) are investigated. We study systems in arbitrary dimension d for periodic boundary conditions and focus on the free energy for fixed value of the total magnetization. As a result, it is shown that the equilibrium free energy of the long-range interacting systems are exactly the same as that of the corresponding mean-field models (exactness of the mean-field theory). Moreover, the mean-field metastable states can be also preserved in general long-range interacting systems. It is found that in the case that the magnetization is conserved, the mean-field theory does not give correct property in some parameter region.

cond-mat.stat-mech↗

arXiv2012

Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions

We study equilibrium states of quantum spin systems with non-additive long-range interactions by adopting an appropriate scaling of the interaction strength, i.e., the so called Kac prescription. In classical spin systems, it is known that the equilibrium free energy is obtained by minimizing the free energy functional over the coarse-grained magnetization. Here we show that it is also true for quantum spin systems. From this observation, it is found that when the canonical ensemble and the microcanonical ensemble are not equivalent in some parameter region, it is not necessarily justified to replace the actual long-range interaction by the infinite-range interaction (Curie-Weiss type interaction). On the other hand, in the parameter region where the two ensembles are equivalent, this replacement is always justified. We examine the Heisenberg XXZ model as an illustrative example, and discuss the relation to experiments.

cond-mat.stat-mech↗

arXiv2012

Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems

Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called "exactness of the mean-field theory". It is found out that this expectation is not necessarily true if the microcanonical ensemble is not equivalent to the canonical ensemble in the mean-field model. Moreover, necessary and sufficient conditions for exactness of the mean-field theory are obtained. These conditions are investigated for two concrete models, the α-Potts model with annealed vacancies and the α-Potts model with invisible states.

cond-mat.stat-mech↗

arXiv2012

Critical temperature and correlation length of an elastic interaction model for spin-crossover materials

It has previously been pointed out that the coexistence of infinite-range and short-range interactions causes a system to have a phase transition of the mean-field universality class, in which the cluster size is finite even at the critical point. In the present paper, we study this property in a model of bistable molecules, whose size changes depending on the bistable states. The molecules can move in space, interacting via an elastic interaction. It is known that due to the different sizes, an effective long-range interaction between the spins appears, and thus this model has a mean-field type of phase transition. It is found that the scaling properties of the shift of the critical temperature from the pure short-range limit in the model with infinite-range and short-range interactions hold also in the present model, regarding the ratio of the size of the two states as a control parameter for the strength of the long-range interaction. By studying the structure factor, it is shown that the dependence of the cluster size at the critical temperature also shows the same scaling properties as a previously studied model with both infinite-range and short-range interactions. We therefore conclude that these scaling relations hold universally in hybrid models with both short-range and weak long-range interactions.

cond-mat.stat-mech↗

arXiv2011

Instability of the mean-field states and generalization of phase separation in long-range interacting systems

Equilibrium properties of long-range interacting systems on lattices are investigated. There was a conjecture by Cannas et. al. that the mean-field theory is exact for spin systems with non-additive long-range interactions. This is called "exactness of the mean-field theory". We show that the exactness of the mean-field theory holds for systems on a lattice with non-additive two body long-range interactions in the canonical ensemble with non-fixed order parameters. We also show that in canonical ensemble with fixed order parameters (e.g. lattice gas model with a fixed number of particles), exactness of the mean-field theory does not hold in some parameter region, which we call "non-MF region". In the non-MF region, an inhomogeneous configuration appears contrary to the uniform configuration in the region where the mean-field theory holds. This inhomogeneous configuration is not the one given by the standard phase separation. Therefore, the mean-field picture is not adequate to describe these states. We discuss phase transitions between the MF region and the non-MF region. Exactness of the mean-field theory in spin glasses is also discussed.

cond-mat.stat-mech↗

arXiv2011

Crossover between a Short-range and a Long-range Ising model

Recently, it has been found that an effective long-range interaction is realized among local bistable variables (spins) in systems where the elastic interaction causes ordering of the spins. In such systems, generally we expect both long-range and short-range interactions to exist. In the short-range Ising model, the correlation length diverges at the critical point. In contrast, in the long-range interacting model the spin configuration is always uniform and the correlation length is zero. As long as a system has non-zero long-range interactions, it shows criticality in the mean-field universality class, and the spin configuration is uniform beyond a certain scale. Here we study the crossover from the pure short-range interacting model to the long-range interacting model. We investigate the infinite-range model (Husimi-Temperley model) as a prototype of this competition, and we study how the critical temperature changes as a function of the strength of the long-range interaction. This model can also be interpreted as an approximation for the Ising model on a small-world network. We derive a formula for the critical temperature as a function of the strength of the long-range interaction. We also propose a scaling form for the spin correlation length at the critical point, which is finite as long as the long-range interaction is included, though it diverges in the limit of the pure short-range model. These properties are confirmed by extensive Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2009

Comparison among Various Expressions of Complex Admittance for Quantum System in Contact with Heat Reservoir

Relation among various expressions of the complex admittance for quantum systems in contact with heat reservoir is studied. Exact expressions of the complex admittance are derived in various types of formulations of equations of motion under contact with heat reservoir. Namely, the complex admittance is studied in the relaxation method and the external-field method. In the former method, the admittance is calculated using the Kubo formula for quantum systems in contact with heat reservoir in no external driving fields, while in the latter method the admittance is directly calculated from equations of motion with external driving terms. In each method, two types of equation of motions are considered, i.e., the time-convolution (TC) equation and time-convolutionless (TCL) equation. That is, the full of the four cases are studied. It is turned out that the expression of the complex admittance obtained by using the relaxation method with the TC equation exactly coincides with that obtained by using the external-field method with the TC equation, while other two methods give different forms. It is also explicitly demonstrated that all the expressions of the complex admittance coincide with each other in the lowest Born approximation for the systemreservoir interaction. The formulae necessary for the higher order expansions in powers of the system-reservoir interaction are derived, and also the expressions of the admittance in the n-th order approximation are given. To characterize the TC and TCL methods, we study the expressions of the admittances of two exactly solvable models. Each exact form of admittance is compared with the results of the two methods in the lowest Born approximation. It is found that depending on the model, either of TC and TCL would be the better method.

cond-mat.stat-mech↗

arXiv2009

Threshold Phenomena under Photo Excitation of Spin-crossover Materials with Cooperativity due to Elastic Interactions

Photo-induced switching from the low-spin state to the high-spin state is studied in a model of spin-crossover materials, in which long-range interactions are induced by elastic distortions due to different molecular sizes the two spin states. At a threshold value of the light intensity we observe nonequilibrium critical behavior corresponding to a mean-field spinodal point. Finite-size scaling of the divergence of the relaxation time is revealed by analysis of kinetic Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2009

Scaling properties of the relaxation time near the mean-field spinodal

We study the relaxation processes of the infinitely long-range interaction model (the Husimi-Temperley model) near the spinodal point. We propose a unified finite-size scaling function near the spinodal point, including the metastable region, the spinodal point, and the unstable region. We explicitly adopt the Glauber dynamics, derive a master equation for the probability distribution of the total magnetization, and perform the so-called van Kampen Omega expansion (an expansion in terms of the inverse of the systems size), which leads to a Fokker-Planck equation. We analyze the scaling properties of the Fokker-Planck equation and confirm the obtained scaling plot by direct numerical solution of the original master equation, and by kinetic Monte Carlo simulation of the stochastic decay process.

cond-mat.stat-mech↗

arXiv2008

Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation

We study the structure of the time evolution of the density matrix in contact with a thermal bath in a standard projection operator sheme. The reduced density matrix of the system in the steady state is obtained by tracing out the degree of freedom of the thermal bath from the equilibrium density matrix of the total system. This reduced density matrix is modified by the interaction, and is different from that of the equilibrium of the system alone. We explicitly calculate the contribution of each term in quantum master equation to the realization of the steady state density matrix, and make clear roles of each term. By making use of the role of each term, the properties of the commonly used quantum master equation are examined.

cond-mat.stat-mech↗