Entropy of Non-equilibrium Stationary Measures of Boundary Driven TASEP

We examine the entropy of non-equilibrium stationary states of boundary driven totally asymmetric simple exclusion processes. As a consequence, we obtain that the Gibbs–Shannon entropy of the non equilibrium stationary state converges to the Gibbs–Shannon entropy of the local equilibrium state. Moreover, we prove that its fluctuations are Gaussian, except when the mean displacement of particles produced by the bulk dynamics agrees with the particle flux induced by the density reservoirs in the maximal phase regime.     

The ballast resistor; An electro-thermal instability in a conducting wire II; Fluctuations around homogeneous stationary states

The correlation function of temperature fluctuations around homogeneous stationary states of the ballast resistor is evaluated by extending the theory of thermal fluctuations around equilibrium states to non-equilibrium situations. It is found that equal-time temperature fluctuations become correlated over large distances if one approaches the critical point. At the “critical point” of the ballast resistor the correlation length and the amplitude of the temperature fluctuations diverge. Furthermore the theory predicts a critical slowing down for the time-dependent temperature fluctuation correlation function. The electric noise of the system is also analyzed.     

α粒子的慢化过程对D-T等离子体聚变燃烧的影响

在双温聚变燃烧点模型框架下，对比D-T等离子体聚变燃烧过程中α粒子能量逐步沉积与瞬时沉积两种描述的等离子体温度、离子数密度随时间的变化，在不同的密度条件下作了计算，考察了α粒子的慢化过程对D-T聚变点火的影响.发现考虑α粒子的慢化过程后，D-T等离子体峰值温度的出现将会推迟若干皮秒甚至几十皮秒，在较低的初始温度密度条件下，时间推迟得更多些.等离子体的峰值温度比α粒子能量瞬时沉积描述也会下降13keV左右. 关键词： α粒子 聚变燃烧 能量沉积 慢化过程     

Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions

We study the slowing down of a particle beam passing through the dusty plasma with power‐law κ‐distributions. Three plasma components, electrons, ions, and dust particles, can have a different κ‐parameter. By using Fokker‐Planck theory, the deceleration factor and slowing down time are derived and expressed by a hyper‐geometric κ‐function. Numerically, we study the slowing down property of an electron beam in the κ‐distributed dusty plasma. We show that the slowing down in the plasma depends strongly on the κ‐parameters of plasma components, and dust particles play a dominant role in the deceleration effects. We also show dependence of the slowing down on mass and charge of a dust particle in the kappa‐distributed plasma.     

Front Propagation Dynamics with Exponentially-Distributed Hopping

We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B → 2A reaction. We find that the effect of fluctuations is especially pronounced at small hopping rates. Fluctuations are treated heuristically via a density cutoff in the reaction rate. We then consider the case of propagating up a reaction rate gradient. The effect of fluctuations here is pronounced, with the front velocity increasing without limit with increasing bulk particle density. The rate of increase is faster than in the case of a reaction-gradient with nearest-neighbor hopping. We derive analytic expressions for the front velocity dependence on bulk particle density. Computer simulations are performed to confirm the analytical results.     

Activated Random Walkers: Facts, Conjectures and Challenges

We study a particle system with hopping (random walk) dynamics on the integer lattice ? ^d . The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of particles; there is no limit on the number of particles at a given site. Isolated active particles fall asleep at rate λ>0, and then remain asleep until joined by another particle at the same site. The state in which all particles are inactive is absorbing. Whether activity continues at long times depends on the relation between the particle density ζ and the sleeping rate λ. We discuss the general case, and then, for the one-dimensional totally asymmetric case, study the phase transition between an active phase (for sufficiently large particle densities and/or small λ) and an absorbing one. We also present arguments regarding the asymptotic mean hopping velocity in the active phase, the rate of fixation in the absorbing phase, and survival of the infinite system at criticality. Using mean-field theory and Monte Carlo simulation, we locate the phase boundary. The phase transition appears to be continuous in both the symmetric and asymmetric versions of the process, but the critical behavior is very different. The former case is characterized by simple integer or rational values for critical exponents (β=1, for example), and the phase diagram is in accord with the prediction of mean-field theory. We present evidence that the symmetric version belongs to the universality class of conserved stochastic sandpiles, also known as conserved directed percolation. Simulations also reveal an interesting transient phenomenon of damped oscillations in the activity density.     

Density-PDFs and Lagrangian statistics of highly compressible turbulence

In isothermal, highly compressible turbulent flows, density fluctuations follow a log-normal distribution. We establish a connection between these density fluctuations and the probability-density-functions (PDF) of Lagrangian tracer particles advected with the flow. Our predicted particle statistics is tested against large scale numerical simulations, which were performed with 512³ collocation points and 2 million tracer particles integrated over several dynamical times.     

Relaxation of ideal classical particles in a one‐dimensional box

We study the deterministic dynamics of non‐interacting classical gas particles confined to a one‐dimensional box as a pedagogical toy model for the relaxation of the Boltzmann distribution towards equilibrium. Hard container walls alone induce a uniform distribution of the gas particles at large times. For the relaxation of the velocity distribution we model the dynamical walls by independent scatterers. The Markov property guarantees a stationary but not necessarily thermal velocity distribution for the gas particles at large times. We identify the conditions for physical walls where the stationary velocity distribution is the Maxwell distribution. For our numerical simulation we represent the wall particles by independent harmonic oscillators. The corresponding dynamical map for oscillators with a fixed phase (Fermi–Ulam accelerator) is chaotic for mesoscopic box dimensions.     

Accumulating particles at the boundaries of a laminar flow

The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a Fokker-Planck equation for the particle density. It is shown that for extended spherical particles the shape of the fluid domain gives rise to inhomogeneous particle densities, thereby leading to particle accumulation and corresponding depletion. For extended spherical particles, conditions are specified that lead to inhomogeneous densities and consequently to regions with particle accumulation and depletion.     

Origin of the slow dynamics and the aging of a soft glass

We study by light microscopy a soft glass consisting of a compact arrangement of polydisperse multilamellar vesicles. We show that its slow and nonstationary dynamics results from the unavoidable small fluctuations of temperature, which induce intermittent local shear deformations in the sample, because of thermal expansion and contraction. Temperature-induced shear provokes both reversible and irreversible rearrangements whose amplitude decreases with time, leading to an exponential slowing down of the dynamics with sample age.     

Radiation propagation in random media: From positive to negative correlations in high-frequency fluctuations

We survey research on radiation propagation or ballistic particle motion through media with randomly variable material density, and we investigate the topic with an emphasis on very high spatial frequencies. Our new results are based on a specific variability model consisting of a zero-mean Gaussian scaling noise riding on a constant value that is large enough with respect to the amplitude of the noise to yield overwhelmingly non-negative density. We first generalize known results about sub-exponential transmission from regular functions, which are almost everywhere continuous, to merely “measurable” ones, which are almost everywhere discontinuous (akin to statistically stationary noises), with positively correlated fluctuations. We then use the generalized measure-theoretic formulation to address negatively correlated stochastic media without leaving the framework of conventional (continuum-limit) transport theory. We thus resolve a controversy about recent claims that only discrete-point process approaches can accommodate negative correlations, i.e., anti-clustering of the material particles. We obtain in this case the predicted super-exponential behavior, but it is rather weak. Physically, and much like the alternative discrete-point process approach, the new model applies most naturally to scales commensurate with the inter-particle distance in the material, i.e., when the notion of particle density breaks down due to Poissonian—or maybe not-so-Poissonian—number-count fluctuations occur in the sample volume. At the same time, the noisy structure must prevail up to scales commensurate with the mean-free-path to be of practical significance. Possible applications are discussed.     

A Nonequilibrium Extension of the Clausius Heat Theorem

We generalize the Clausius (in)equality to overdamped mesoscopic and macroscopic diffusions in the presence of nonconservative forces. In contrast to previous frameworks, we use a decomposition scheme for heat which is based on an exact variant of the Minimum Entropy Production Principle as obtained from dynamical fluctuation theory. This new extended heat theorem holds true for arbitrary driving and does not require assumptions of local or close to equilibrium. The argument remains exactly intact for diffusing fields where the fields correspond to macroscopic profiles of interacting particles under hydrodynamic fluctuations. We also show that the change of Shannon entropy is related to the antisymmetric part under a modified time-reversal of the time-integrated entropy flux.     

Optically driven Mott‐Hubbard systems out of thermodynamic equilibrium

We consider the Hubbard model at half filling, driven by an external, stationary laser field. This stationary, but periodic in time, electromagnetic field couples to the charge current, i.e. it induces an extra contribution to the hopping amplitude in the Hubbard Hamiltonian (photo‐induced hopping). We generalize the dynamical mean‐field theory (DMFT) for nonequilibrium with periodic‐in‐time external fields, using a Floquet mode representation and the Keldysh formalism. We calculate the non‐equilibrium electron distribution function, the density of states and the optical DC conductivity in the presence of the external laser field for laser frequencies above and below the Mott‐Hubbard gap. The results demonstrate that the system exhibits an insulator‐metal transition as the frequency of the external field is increased and exceeds the Mott‐Hubbard gap. This corresponds to photo‐induced excitations into the upper Hubbard band.     

Fluctuation,relaxation, and extensivity of macrovariables in nonequilibrium systems

The extensive property of a macrovariable is proved for a quantal system whose Hamiltonian depends on time and for a stochastic system whose temporal evolution operator depends on time. These generalized situations are concerned with bulk-contact open systems. The extensive property, fluctuation, and nonlinear relaxation are investigated explicitly by calculating rigorously generating functions in exactly soluble models such as the linear stochastic model and linearXY model. The relation between the nonlinear critical slowing down and linear critical slowing down is also discussed.     

Self-organized criticality in 1D stochastic traffic flow model

Results of computer simulations of a 1D particle hopping model of traffic flow are presented. The model is characterized by parallel update and fully asymmetric stochastic hopping dynamics which allows unbounded series of jumps to empty neighbour sites on the right. The considered case of open boundary conditions can be used to model a “bottleneck” situation in traffic. Evidence for self-organized criticality is found in two aspects: the presence of long-range spatial correlations manifested in the shape of density profiles, and long-time temporal correlations showing up in the low-frequency behaviour of the spectral density of the total particle number and flow. A plausible conjecture is to interpret the observed qualitative changes in these features, as a function of the injection rate and the hopping probability, in terms of a nonequilibrium phase transition between a low-density phase and a maximal current phase. This conjecture is supported by the phase diagram obtained in mean-field approximation.     

Edge Particle Flux with Temperature Fluctuation in the HL-2A Tokamak

Electron temperature, density, plasma potential and their fluctuation profiles at edge plasmas are measured simultaneously with a reciprocating probe system in HL-2A. The analysis results of four-tip data indicate that the temperature fluctuation has relative amplitude of 10-15%, gives more contribution to particle flux in lower （0- 25 kHz） and higher frequency （50-250 kHz） ranges. The coherence between temperature fluctuations and density or potential fluctuations implies that their coupling will impact anomalous transport. The measured diffusion coefficient is about three times of the Bohm diffusion coefficient when considering the temperature fluctuation. The particle flux with temperature fluctuation is discussed in HL-2A for the first time.     

On the theory of surface diffusion: kinetic versus lattice gas approach

The present paper extends the results of a recent analytic kinetic theory of particle-on-substrate diffusion. The approach treats explicitly the molecule–surface interaction and takes into account inter-molecular interaction within the hard particle approximation. The physics influencing the diffusion pre-exponential factor and mechanisms determining the density dependence of collective diffusivity are discussed. The kinetic results are compared with those of the traditional lattice gas hopping models. Analytical expressions for jump rates in the low density limit are derived, and the density dependence of effective jump rates at finite occupancy is discussed. It is shown how the traditional hopping model oversimplifies the picture of diffusion by neglecting the collision part of the hopping process.     

Evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wavelength and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wavelength with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by x-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.     

Quantization,coherent states and geometric phases of a generalized nonstationary mesoscopic RLC circuit

We present an alternative quantum treatment for a generalized mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Taking advantage of the Lewis and Riesenfeld quantum invariant method and using quadratic invariants we obtain exact nonstationary Schrödinger states for this electromagnetic oscillation system. Afterwards, we construct coherent and squeezed states for the quantized RLC circuit and employ them to investigate some of the system’s quantum properties, such as quantum fluctuations of the charge and the magnetic flux and the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary mesoscopic circuit. Finally we evaluate the dynamical and Berry phases for three special circuits. Surprisingly, we find identical expressions for the dynamical phase and the same formulae for the Berry’s phase.     

Anderson Localization in Dissipative Lattices

Anderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for dynamical localization. In the one-dimensional Hermitian Anderson model with uncorrelated diagonal disorder, there is a one-to-one correspondence between dynamical localization and spectral localization, that is, the exponential localization of all the Hamiltonian eigenfunctions. This correspondence can be broken when dealing with disordered dissipative lattices. When the system exchanges particles with the surrounding environment and random fluctuations of the dissipation are introduced, spectral localization is observed but without dynamical localization. Previous studies consider lattices with mixed conservative (Hamiltonian) and dissipative dynamics and are restricted to a semiclassical analysis. However, Anderson localization in purely dissipative lattices, displaying an entirely Lindbladian dynamics, remains largely unexplored. Here the purely-dissipative Anderson model in the framework of a Lindblad master equation is considered, and it is shown that, akin to the semiclassical models with conservative hopping and random dissipation, one observes dynamical delocalization in spite of strong spectral localization of the Liouvillian superoperator. This result is very distinct from delocalization observed in the Anderson model with dephasing, where dynamical delocalization arises from the delocalization of the stationary state of the Liouvillian.