Statistical physics and fluctuations in ballistic non-equilibrium systems

In nonequilibrium systems in the ballistic transport regime, every point of the system contains particles arriving from different regions-each of them at different temperatures-and there are only few collisions, in such a way that equilibrium between the different populations will be reached very slowly. Here, we tentatively approach the local distribution function by a superposition of local-equilibrium distribution functions with different temperatures, corresponding to the different starting positions of the particles. In a second-order expansion, we find a distribution function which depends not only on the Hamiltonian H but also on H², and we study the additional contribution to energy fluctuations.     

Towards a dynamical temperature of finite Hamiltonian systems

With the aid of numerical simulations of the β Fermi-Pasta-Ulam (FPU) system, we compare the different definitions of dynamical temperature for Hamiltonian systems. We have shown that each definition gives different values of temperature for a system with a small number of degrees of freedom (DOF). Only for systems with a sufficiently large number of DOF, do all the definitions of dynamical temperature approach the same value.     

Magnetic properties of the mixed ferrimagnetic ternary system with a single-ion anisotropy on the Bethe lattice

The magnetic properties of the ternary system ABC consisting of spins , S=1, and are investigated on the Bethe lattice by using the exact recursion relations. We consider both ferromagnetic and antiferromagnetic exchange interactions. The exact expressions for magnetizations and magnetic susceptibilities are found, and thermal behaviors of magnetizations and susceptibilities are studied. We construct the phase diagrams and find that the system exhibits one, two or even three compensation temperatures depending on the values of the interaction parameters in the Hamiltonian. Moreover, the system undergoes a second-order phase transition for the coordination number q?3 and a second- and first-order phase transitions for q>3; hence the system gives a tricritical point. The system also exhibits the reentrant behaviors.     

Performance characteristic of a Stirling refrigeration cycle in micro/nano scale

The aim of the paper is to present the performance characteristics of a Stirling refrigeration cycle in micro/nano scale, in which the working substance of cycle is an ideal Maxwellian gas. Due to the quantum boundary effect on the gas particles confined in the finite domain, the cycle no longer possesses the condition of perfect regeneration. The inherent regenerative losses, the refrigeration heat and coefficient of performance (COP) of the cycle are derived. It is found that, for the micro/nano scaled Stirling refrigeration cycle devices, the refrigeration heat and COP of cycle all depend on the surface area of the system (boundary of cycle) besides the temperature of the heat reservoirs, the volume of system and other parameters, while for the macro scaled refrigeration cycle devices, the refrigeration heat and COP of cycle are independent of the surface area of the system. Variations of the refrigeration heat ratio r_R and the COP ratio r_ε with the temperature ratio τ and volume ratio r_V for the different surface area ratio r_A are examined, which reveals the influence of the boundary of cycle on the performance of a micro/nano scaled Stirling refrigeration cycle. The results are useful for designing of a micro/nano scaled Stirling cycle device and may conduce to confirming experimentally the quantum boundary effect in the micro/nano scaled devices.     

Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation

Exact solution of the Schrödinger equation is derived for underdamped, critically damped, and overdamped harmonic oscillators with a driving force. A unitary operator transforming Hamiltonian into a simple form is introduced. The transformed Hamiltonian, represented in terms of a modified frequency ω, is identical with the Hamiltonian of the standard harmonic oscillator for the underdamped oscillator, with the Hamiltonian of a free particle for the critically damped oscillator, and with the Hamiltonian of a system with a harmonic parabolic potential for the overdamped oscillator. The eigenvalues of underdamped oscillator are discrete while those of the critically damped and the overdamped oscillators are continuous.     

Truncated forms of the second-rank orthorhombic Hamiltonians used in magnetism and electron magnetic resonance (EMR) studies are invalid—Why it went unnoticed for so long?

This paper deals with the truncated forms of the second-rank orthorhombic Hamiltonians employed in magnetism and electron magnetic resonance (EMR) studies. Consideration of the intrinsic features of orthorhombic Hamiltonians reveals that the truncations, which consist in omission of one of three interdependent orthorhombic terms, are fundamentally invalid. Implications of the invalid truncations are: loss of generality of quantized spin models, misinterpretation of physical properties of systems studied (e.g. maximum rhombicity ratio and relative parameter values), and inconsistent notations for Hamiltonian parameters that hamper direct comparison of data from various sources. Truncated Hamiltonian forms identified in our survey are categorized and systematically reviewed. Examples are taken from studies of various magnetic systems, especially those involving transition ions, as well as model magnetic systems. The pertinent studies include magnetic ordering in three- and lower dimensions, e.g. [(CH₃)₄N]MnCl₃ (TMMC), canted ferromagnets, Haldane gap antiferromagnets, single molecule magnets exhibiting macroscopic quantum tunneling, e.g. Mn₁₂ complexes with spin S=10. Our study provides better insight into magnetic and spectroscopic properties of pertinent magnetic systems, which calls for reconsideration of the experimental and theoretical results based on invalid truncated Hamiltonians. The physical nature of Hamiltonians used in magnetism and EMR studies and other types of inappropriate terminology occurring, especially in model magnetism studies, require separate discussion.     

Magnetic properties of an anti-ferromagnetic and ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model in the longitudinal magnetic field within the effective-field approximation

The magnetic properties of an anti-ferromagnetic and ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field in a longitudinal magnetic field on the honeycomb (z=3) and square lattice (z=4) are studied by using the effective-field theory with correlations. The ground state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. We also investigate the thermal variations of the sublattice and total magnetizations, and present the phase diagrams in the (Δ/|J|, ) plane. The phase diagrams have one, two or even three compensation temperatures depending on the values of the crystal-field interaction. Moreover, the susceptibility, internal energy and specific heat of the system are numerically examined, and some interesting phenomena in these quantities are found due to the applied longitudinal magnetic field.     

Phase separation of binary systems

In this paper, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the sign of a nondimensional parameter K such that if K>0, the transition is first order with latent heat and if K<0, the transition is second order. Here the parameter K is defined in terms of the coefficients in the quadratic and cubic nonlinear terms of the Cahn-Hilliard equation and the typical length scale of the container. Second, a phase diagram is derived, characterizing the order of phase transitions, and leading in particular to a prediction that there is only a second-order transition for molar fraction near 1/2. This is different from the prediction made by the classical phase diagram. Third, a TL-phase diagram is derived, characterizing the regions of both homogeneous and separation phases and their transitions.     

Phase transformation and elastic behavior of MgX (X=S, Se, Te) alkaline earth chalcogenides

Pressure induced structural aspects of NaCl-type (B1) to CsCl-type (B2) structure in alkaline earth chalcogenides (AECs) magnesium chalcogenides (MgX; X=S, Se, and Te) are presented. An effective interionic interaction potential (EIoIP) with long-range Coulomb interactions and the Hafemeister and Flygare type short-range overlap repulsion extending up to the second neighbor ions and the van der Waals (vdW) interaction is developed. The vdW coefficients are evaluated following the Slater-Kirkwood variational method, as both the ions are polarizable. The present calculations have revealed reasonably good agreement with the available experimental data on structural transition (B1-B2 structure), the phase transition pressures P_t of 167 (MgS), 170 (MgSe), and 176 (MgTe) GPa as well the elastic properties. The calculated values of the volume collapses [ΔV(P)/V(0)] are also closer to their observed data. Further, the variations of the second and third order elastic constants with pressure have followed a systematic trend, which are almost identical to those exhibited by the observed data measured for other semiconducting compounds with rocksalt (B1) type crystal structure. The Born and relative stability criteria is valid in Mg monochalcogenides.     

Computing the non-linear anomalous diffusion equation from first principles

We investigate asymptotically the occurrence of anomalous diffusion and its associated family of statistical evolution equations. Starting from a non-Markovian process à la Langevin we show that the mean probability distribution of the displacement of a particle follows a generalized non-linear Fokker-Planck equation. Thus we show that the anomalous behavior can be linked to a fast fluctuation process with memory from a microscopic dynamics level, and slow fluctuations of the dissipative variable. The general results can be applied to a wide range of physical systems that present a departure from the Brownian regime.     

Finite size effects for the Ising model on random graphs with varying dilution

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and N^γ edges, with 1<γ≤2. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the mean-field type for all the considered values of γ at the transition temperature of the fully connected Curie-Weiss model. Finite size corrections are investigated for different values of the parameter γ, using two different approaches: a replica based finite N expansion, and a cavity method. Numerical simulations are compared with theoretical predictions. The cavity based analysis is shown to agree better with numerics.     

Defect-induced transitions in synchronous asymmetric exclusion processes

The effects of a single local defect in synchronous asymmetric exclusion processes are investigated via theoretical analysis and Monte Carlo simulations. Our theoretical analysis shows that there are four possible stationary phases, i.e., the (low density, low density), (low density, high density), (high density, low density) and (high density, high density) in the system. In the (high density, low density) phase, the system can reach a maximal current which is determined by the local defect, but independent of boundary conditions. A phenomenological domain wall approach is developed to predict dynamic behavior at phase boundaries. The effects of defective hopping probability p on density profiles and currents are investigated. Our investigation shows that the value of p determines phase transitions when entrance rate α and exit rate β are fixed. Density profiles and currents obtained from theoretical calculations are in agreement with Monte Carlo simulations.     

Compressibility of a two-dimensional electron gas in a parallel magnetic field

The thermodynamic compressibility of a two-dimensional electron system in the presence of an in-plane magnetic field is calculated. We use accurate correlation energy results from quantum Monte Carlo simulations to construct the ground state energy and obtain the critical magnetic field B_c required to fully spin polarize the system. Inverse compressibility as a function of density shows a kink-like behavior in the presence of an applied magnetic field, which can be identified as B_c. Our calculations suggest an alternative approach to transport measurements of determining full spin polarization.     

Nonequilibrium phase transition in the kinetic Ising model on a two-layer square lattice under the presence of an oscillating field

The nonequilibrium or dynamic phase transitions are studied, within a mean-field approach, in the kinetic Ising model on a two-layer square lattice consisting of spin- 1/2 ions in the presence of a time varying (sinusoidal) magnetic field has been studied by using Glauber-type stochastic dynamics. The dynamic equations of motion are obtained in terms of the intralayer coupling constants J₁ and J₂ for the first and second layer, respectively, and interlayer coupling constant J₃ between these two layers. The nature (first- or second-order) of the transitions is characterized by investigating the behavior of the thermal variations of the dynamic order parameters. The dynamic phase transitions are obtained and the dynamic phase diagrams are constructed in the plane of the reduced temperature versus the amplitude of the magnetic field and found fourteen fundamental types of phase diagrams. Phase diagrams exhibit one, two or three dynamic tricritical points for various values of J₂/|J₁| and J₃/|J₁|. Besides the paramagnetic (p), ferromagnetic (f) and compensated (c) phases, there were the f+c,f+sf,c+sf,af+p,m+p,f+m and c+af, where the af, sf and m are the antiferromagnetic, surface ferromagnetic and mixed phases respectively. Coexistence phase regions also exist in the system.     

The capacity of two neighbour intersections considering the influence of the bus stop

In this paper, we use a two-lane CA model to investigate the effect of a bus stop between two neighbouring intersections on the capacity of the bus. Both the case of a bus stop with a special stopping lane and that of one without are considered. The capacity versus the distance L_B(L_D) between the stop and the upstream (downstream) intersection is studied, with respect to the entering probability P_e and the traffic light cycle T. It is found that a bus stop near an intersection can act as a bottleneck and cause a drop in the capacity when the L_B (or L_D) is below a critical point L_Bc1(or L_Dc1). However, the situation when the stop is located near the downstream intersection is worse than that of the upstream one. Furthermore, the simulation results show that the negative effect varies with the increase of the cycle time T and the capacity can be maximized by adjusting T. Comparisons between the two cases suggest that the stopping lane can improve the capacity to some extent. These results mean that the capacity can be exploited by changing the position of the bus stop or the cycle time, and adding a stopping lane if necessary. These findings may be useful in offering scientific guidance for the management and design of traffic networks.     

Monte Carlo study of the change of critical temperature in a diluted Ising model due to configuration disorder

Monte Carlo simulations on a diluted Ising Hamiltonian were used to obtain the susceptibility of virtual binary samples (conformed by ferromagnetic atoms and non-magnetic atoms) on a bcc lattice. Samples size of L=10$L=10$ were constructed with different configuration order using random mixtures. The susceptibility curves illustrate that the critical temperature decreases when the disorder in the samples increase. From fittings of the exchange interaction versus the concentration of non-magnetic atoms it was possible to reasonably describe the magnetic phase diagram of the Fe_1−qAlq${\mathrm{Fe}}_{1-q}{\mathrm{Al}}_q$ alloys.     

A new macro model with consideration of the traffic interruption probability

In this paper, we present a new macro model which involves the effects that the probability of traffic interruption has on the car-following behavior through formulating the inner relationship between micro and macro variables. Linear stability analysis shows that consideration of the traffic interruption probability can improve the stability of traffic flow if and only if the drivers’ reactive time required for adjusting their acceleration based on the traffic interruption probability p is not greater than that one based on the non-interruption probability 1−p. Numerical results verify that the new model can be used to analyze the effects of traffic interruption probability and traffic interruption on shock, rarefaction wave, small perturbation and uniform flow. The model has been applied in reproducing some complex traffic phenomena resulted by some traffic interruptions (e.g., signal light, pedestrian and tolling station).     

Anomalous dynamic scaling of the non-local growth equations

The anomalous dynamic scaling behavior of the d+1 dimensional non-local growth equations is investigated based on the scaling approach. The growth equations studied include the non-local Kardar-Parisi-Zhang (NKPZ), non-local Sun-Guo-Grant (NSGG), and non-local Lai-Das Sarma-Villain (NLDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. Our results show that non-local interactions can affect anomalous scaling properties of surface fluctuations.     

An optimum Hamiltonian for non-Hermitian quantum evolution and the complex Bloch sphere

For a quantum system governed by a non-Hermitian Hamiltonian, we studied the problem of obtaining an optimum Hamiltonian that generates nonunitary transformations of a given initial state into a certain final state in the smallest time τ. The analysis is based on the relationship between the states of the two-dimensional subspace of the Hilbert space spanned by the initial and final states and the points of the two-dimensional complex Bloch sphere.