Search

We investigate the relationship between a diffusive motion of an interface, heat conduction, and the roughening transition in the three-dimensional Ising model. We numerically compute the thermal conductivity and the diffusion constant and find that the diffusion constant shows a crossover in its temperature dependence. The crossover temperature is equal to the roughening transition temperature in equilibrium and deviates from it when heat flows in the system. From these results, we discuss the possibility that heat conduction causes a shift of the roughening transition temperature.

We investigate properties of the diffusive motion of an interface in the two-dimensional Ising model in equilibrium or nonequilibrium situations. We focused on the relation between the power spectrum of a time sequence of spins and diffusive motion of an interface which was already clarified in one- dimensional systems with a nonequilibrium phase transition like the asymmetric simple exclusion process. It is clarified that the interface motion is a diffusion process with a drift force toward the higher-temperature side when the system is in contact with heat reservoirs at different temperatures and heat transfers through the system. Effects of the width of the interface are also discussed., 14 pages, 20 figures

We study the single-particle momentum distribution functions of a one-dimensional Hamiltonian system in the nonequilibrium steady state of heat conduction. Deviation from the Maxwellian distribution is measured by the use of the relative entropy. As a result, it is found that the total relative entropy linearly increases with the system size in an integrable model, while it decreases for large N in nonintegrable systems. Moreover, effects of a symmetry are discussed and some differences are found between the FPU model and the Φ 4 model when the boundary breaks the symmetry.

A Boltzmann-type equation is introduced as an approximation for calculating the time evolution of the probability distribution in elementary reversible cellular automata. A number of properties are discussed from the approximation. Applications to heat conduction problem are exhibited. Simulation results suggest a connection between conserved quantities and diffusive or ballistic behavior.

We discuss in detail statistical mechanical properties of quantum dynamics with the use of numerical simulations of isolated one-dimensional spin systems of various sizes. With respect to the energy distribution in a subsystem, a good agreement is observed between those obtained by the method of statistical mechanics and via long-time average over simulation, even in the system composed of a small number of spins. In particular, the distribution of energy forms the canonical distribution.

We numerically study the large deviation function of the total current, which is the sum of local currents over all bonds, for the symmetric and asymmetric simple exclusion processes with open boundary conditions. We estimate the generating function by calculating the largest eigenvalue of the modified transition matrix and by population Monte Carlo simulation. As a result, we find a number of interesting behaviors not observed in the exactly solvable cases studied previously as follows. The even and odd parts of the generating function show different system-size dependences. Different definitions of the current lead to the same generating function in small systems. The use of the total current is important in the Monte Carlo estimation. Moreover, a cusp appears in the large deviation function for the asymmetric simple exclusion process. We also discuss the convergence property of the population Monte Carlo simulation and find that in a certain parameter region, the convergence is very slow and the gap between the largest and second largest eigenvalues of the modified transition matrix rapidly tends to vanish with the system size., 31 pages, 30 figures, to be published in JPSJ

We give a necessary and sufficient condition for the existence of additive conserved quantities for one-dimensional discrete-time lattice dynamical systems such as cellular automata (CA) and coupled map lattices. Proof is given for the case of nearest-neighbor interaction rules. The obtained condition guarantees the existence of the current conservation law and is useful for finding additive conserved quantities for CA. Applications are made to Wolfram's elementary CA and elementary reversible CA of Takesue. In the latter case, the additive conserved quantities are classified into those induced by local conservation laws and propagative ones.

Fracture in a disordered lattice system is studied. In our system, particles are initially arranged on the triangular lattice and each nearest-neighbor pair is connected with a randomly chosen soft or hard Hookean spring. Every spring has the common threshold of stress at which it is cut. We make an initial crack and expand the system perpendicularly to the crack. We find that the maximum stress in the stress-strain curve is larger than those in the systems with soft or hard springs only (uniform systems). Energy required to advance fracture is also larger in some disordered systems, which indicates that the fracture toughness improves. The increase of the energy is caused by the following two factors. One is that the soft spring is able to hold larger energy than the hard one. The other is that the number of cut springs increases as the fracture surface becomes tortuous in disordered systems., 15pages, 14 figures

The relaxation properties of a number of elementary reversible cellular automata are studied. Different rules have different types of relaxation behavior. Possible relationships between the thermodynamic behavior and phase space structure are discussed.

We study a symmetry property of momentum distribution functions in the steady state of heat conduction. When the equation of motion is symmetric under change of signs for all dynamical variables, the distribution function is also symmetric. This symmetry can be broken by introduction of an asymmetric term in the interaction potential or the on-site potential, or employing the thermal walls as heat reservoirs. We numerically find differences of behavior of the models with and without the on-site potential., 13 pages. submitted to JPSJ

We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a $\omega^{-3/2}$ power spectrum. This is successfully applied to the totally asymmetric simple exclusion process (TASEP) with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and discreteness of the system is not effective., Comment: 4 pages, 4 figures

We study how energy transport in an integrable system is affected by the spectral densities of heat reservoirs. The model investigated here is the quantum harmonic chain whose both ends are in contact with two heat reservoirs at different temperatures. The master equation for the reduced density matrix is derived on the assumption that the reservoirs are composed of an infinite number of independent harmonic oscillators. We evaluate temperature profile and energy flux in the stationary state for the master equation and discuss how they depend on the types of spectral densities. When we attach the reservoirs of the same type of spectral density, we find that the temperature profile is independent of the types. On the other hand, when the two reservoirs have different types of spectral densities, the energy profile near the ends of the chain depends on the types. When the coupling is finite, the temperature profile near the ends shows wide variation of behavior dependent on spectral densities and temperatures of reservoirs. This dependence is discussed with the Fokker-Planck equations obtained in the classical limit., 20 pages including 10 eps figures, RevTeX

Nature of energy transport around a critical point is studied in the Creutz cellular automaton. Fourier heat law is confirmed to hold in this model by a direct measurement of heat flow under a temperature gradient. The thermal conductivity is carefully investigated near the phase transition by the use of the Kubo formula. As the result, the thermal conductivity is found to take a finite value at the critical point contrary to some previous works. Equal-time correlation of the heat flow is also analyzed by a mean-field type approximation to investigate the temperature dependence of thermal conductivity. A variant of the Creutz cellular automaton called the Q2R is also investigated and similar results are obtained., Comment: 27 pages including 14figures

We extend the derivation of the finite-size Kubo formula for classical systems by Kundu et al. to a finite open quantum system in contact with reservoirs. Starting with the master equation obtained from the quantum repeated interaction model, we examine the linear response, utilizing superoperators defined by virtue of a conservation law. Some generalizations of our method are also discussed.

The properties of energy transport are numerically investigated with the use of a one-dimensional cellular-automaton model called 26R. The validity of Fourier's law and the Green-Kubo formula for thermal conductivity \ensuremath{\kappa} is demonstrated for this model in the limit of large systems. Nonlinear correction to Fourier's law and the recovery of left-right symmetry are also discussed.

Reversible cellular automata are used to investigate the thermodynamic behavior of large systems. Additive conserved quantities are regarded as the energy of these models. By the consideration of a large system as the sum of a subsystem and a heat bath, it is numerically shown that a canonical distribution is realized under certain conditions concerning the conserved quantities.

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.

Effects of turbulence on nucleation are investigated in classical fluids near the critical point. Turbulence can suppress the onset of nucleation, enhance the coagulation of droplets, and break up droplets. The final characteristic droplet size strongly depends on the temperature difference Tc − T and the Reynolds number Re.

Here I introduce a family of fully discrete conservative dynamical systems named elementary reversible cellular automata (ERCAs)[1] as the minimal models to study the thermodynamic behavior of large dynamical systems.