Limit Processes for TASEP with Shocks and Rarefaction Fans

We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density ρ ₋ and right density ρ ₊. We study the associated height function, whose discrete gradient is given by the particle occurrences. Macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of ρ _±. We characterize the large time scaling limit of the multipoint fluctuations as a function of the densities ρ _± and of the different macroscopic regions. Moreover, using a slow decorrelation phenomena, the results are extended from fixed time to the whole space-time, except along the some directions (the characteristic solutions of the related Burgers equation) where the problem is still open.     

Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains

With focus on anharmonic chains, we develop a nonlinear version of fluctuating hydrodynamics, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added. The required model-dependent parameters are written in such a way that they can be computed numerically within seconds, once the interaction potential, pressure, and temperature are given. In principle the theory is applicable to any one-dimensional system with local conservation laws. The resulting nonlinear stochastic field theory is handled in the one-loop approximation. Some of the large scale predictions can still be worked out analytically. For more details one has to rely on numerical simulations of the corresponding mode-coupling equations. In this way we arrive at detailed predictions for the equilibrium time correlations of the locally conserved fields of an anharmonic chain.     

Scalar Domination and Normal Fluctuations in N-Vector Quantum Anharmonic Crystals

A lattice model of N-dimensional quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric pair interaction is considered. For arbitrary N , correlation inequalities, showing that the temperature Green functions of this model are dominated by the corresponding Green functions of the scalar (N=1) model, are proven. These inequalities are then used to prove that the fluctuations of displacements of particles remain normal at all temperatures provided the model parameters obey a certain condition. In particular this means that the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator should be large enough or its mass should be small enough.     

Nonlinear Dynamics and Fluctuations of Dissipative Toda Chains

The dynamics of a ring of masses including dissipative forces (passive or active friction) and Toda interactions between the masses is investigated. The characteristic attractor structure and the influence of noise by coupling to a heat bath are studied. The system may be driven from the thermodynamic equilibrium to far from equilibrium states by including negative friction. We show, that over-critical pumping with free energy may lead to a partition of the phase space into attractor regions corresponding to several types of collective motions including uniform rotations, one- and multiple soliton-like excitations and relative oscillations. The distribution functions in the phase space and the correlation functions of the forces and the spectra of nonlinear excitations are calculated. We show that a finite-size Toda ring with weak thermal coupling develops at intermediate temperatures a broadband colored noise spectrum with an 1/f tail at low frequencies.     

Thermal Disorder, Fluctuations, Growth and Fragmentation of Finite One-Dimensional Atomic Chains

Ordering in one-dimensional atomic chains is studied using computer simulation. We find that dense ordered chains may exist if the system is cold enough and not macroscopically long. Growth of finite length chains from the vapor and by vapor exchange between chains begins rapidly, then slows down exponentially in time. As temperature rises density fluctuations increase, causing the chains to fragment. Independent of fragmentation, disordering begins at the ends, a condition similar to the precursor of edge and surface melting in two and three dimensions. The chemical potential of finite ordered chains is a function of length and temperature, due to the competition between attraction and internal thermal excitation. Equilibrium of chains coexisting with one-dimensional vapor produces a distribution of sizes, peaked at a temperature dependent chain length. Several results may be relevant to experimental studies of adsorption on carbon nanotubes     

Theory of Thermal Fluctuations for Leaking and Non Leaking Surface Waves

Thermal fluctuation spectra are discussed for electromagnetic waves in magnetized, inhomogeneous, cold electron fluid plasmas.     

Traveling Waves for the Mass in Mass Model of Granular Chains

In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely, a granular chain involving additionally an internal (or, respectively, external) resonator. For these chains, we rigorously establish that under suitable “anti-resonance” conditions connecting the mass of the resonator and the speed of the wave, bell-shaped traveling-wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. We also numerically touch upon settings, where the conditions do not hold, illustrating, in line also with recent experimental work, that non-monotonic waves bearing non-vanishing tails may exist in the latter case.     

Angle of Arrival Fluctuations for Optical Waves Propagating Through Joint Moderate to Strong Atmospheric Turbulence

Satellite laser communication has gained wide attention both at home and abroad. The pointing, acquisition, and tracking (PAT) technology is the kernel of satellite laser communication systems, and the atmospheric layer is a part of the communication channel for satellite-to-ground links. Thus, angle of arrival (AOA) fluctuations caused by atmospheric turbulence inevitably influence long-distance satellite laser communication. Therefore, it is very important to analyze the impact of AOA fluctuations in satellite laser communication systems. According to the actual situation of satellite-to-ground links, a joint atmospheric turbulence power spectrum model is defined that includes Kolmogorov turbulence from the ground to 6 km in portions of the troposphere and non-Kolmogorov turbulence above 6 km in the stratosphere. Based on the extended Rytov theory, we derive the large-scale and small-scale variances of AOA fluctuations propagating in the uplink and downlink channels for a satellite laser communication system and analyze the influence of large zenith angle variations on the AOA fluctuations. It has long been a focus of concern that the expressions for the AOA variance obtained must be concise and of closed form.     

Amplitude and Phase Fluctuations of Decimeter Radio Waves Raying the Atmosphere via Satellite-to-Satellite Paths

We present the results of experimental studies of the atmospheric phase and amplitude fluctuations of decimeter radio waves in radio occultation measurements using paths connecting the MICROLAB satellite and the satellites of the GPS navigation system. The dependences of the amplitude- and phase-fluctuation variance on the minimum altitude of the ray trajectory and the frequency spectra of the fluctuations are presented. The experimental data are compared with the theory of radio-wave propagation in random media. We determine the spectral index of irregularities of the atmospheric refractive index, the external scale of the irregularities, and the variance of the refractive-index fluctuations. It is shown that the radio occultation technique allows one to monitor small-scale irregularities of the atmosphere.     

Anharmonic Excitations,Time Correlations and Electric Conductivity

We study the influence of anharmonic mechanical excitations of a classical ionic lattice on its electric properties. First, to illustrate salient features, we investigate a simple model, an one‐dimensional (1D) system consisting of ten semiclassical electrons embedded in a lattice or a ring with ten ions interacting with exponentially repulsive interactions. The lattice is embedded in a thermal bath. The behavior of the velocity autocorrelation function and the dynamic structure factor of the system are analyzed. We show that in this model the nonlinear excitations lead to long lasting time correlations and, correspondingly, to an increase of the conductivity in a narrow temperature region, where the excitations are supersonic soliton‐like. In the second part we consider the quantum statistics of general ion‐electron systems with arbitrary dimension and express ‐ following linear response transport theory ‐ the quantum‐mechanical conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the ion motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. An evaluation of the influenec of solitons predicts for 1D‐lattices a conductivity increase in the temperature region where most thermal solitons are excited, similar as shown in the classical Drude‐Lorentz‐Kubo framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

High Frequency Current and Field Fluctuations in a Magnetized Plasma

The current density and electric field fluctuations at frequencies much above the ion plasma frequency are derived for a non-relativistic plasma of arbitrary density, using the Klimontovich approach. Both longitudinal and transverse components of the interaction forces between the electrons are taken into account. The error introduced by neglecting the transverse component is discussed.     

Quantum Fluctuations of Current and Voltage for Mesoscopic Quartz Piezoelectric Crystal at Finite Temperature

The mesoscopic quartz piezoelectric crystal equivalent circuit is quantized by the method of damped harmonic oscillator quantization. It is shown that the quantum fluctuations of voltage and current of each loop are related to not only the equivalent circuit inherent parameter and squeezing parameter, but also the temperature, and decay according to exponent along with time in the thermal vacuum state, the thermal coherent state and the thermal squeezed state.     

Quantum Thermodynamic Uncertainty Relations,Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities

Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper [Dong et al., Entropy 2022, 24, 870], we show how TURs are rooted in the quantum uncertainty principles and the fluctuation–dissipation inequalities (FDI) under fully nonequilibrium conditions. In this paper, we shift our attention from the quantum basis to the thermal manifests. Using a microscopic model for the bath’s spectral density in quantum Brownian motion studies, we formulate a “thermal” FDI in the quantum nonequilibrium dynamics which is valid at high temperatures. This brings the quantum TURs we derive here to the classical domain and can thus be compared with some popular forms of TURs. In the thermal-energy-dominated regimes, our FDIs provide better estimates on the uncertainty of thermodynamic quantities. Our treatment includes full back-action from the environment onto the system. As a concrete example of the generalized current, we examine the energy flux or power entering the Brownian particle and find an exact expression of the corresponding current–current correlations. In so doing, we show that the statistical properties of the bath and the causality of the system+bath interaction both enter into the TURs obeyed by the thermodynamic quantities.     

Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems

We prove Lieb-Robinson bounds for systems defined on infinite dimensional Hilbert spaces and described by unbounded Hamiltonians. In particular, we consider harmonic and certain anharmonic lattice systems.     

Microscopic Structure of Shocks and Antishocks in the ASEP Conditioned on Low Current

We study the time evolution of the ASEP on a one-dimensional torus with L sites, conditioned on an atypically low current up to a finite time t. For a certain one-parameter family of initial measures with a shock we prove that the shock position performs a biased random walk on the torus and that the measure seen from the shock position remains invariant. We compute explicitly the transition rates of the random walk. For the large scale behavior this result suggests that there is an atypically low current such that the optimal density profile that realizes this current is a hyperbolic tangent with a traveling shock discontinuity. For an atypically low local current across a single bond of the torus we prove that a product measure with a shock at an arbitrary position and an antishock at the conditioned bond remains a convex combination of such measures at all times which implies that the antishock remains microscopically stable under the locally conditioned dynamics. We compute the coefficients of the convex combinations.     

Quantum Fluctuations of the Current and Voltage in Thermal Vacuum State for Mesoscopic Quartz Piezoelectric Crystal

The mesoscopic quartz piezoelectric crystal equivalent circuit is quantized by the method of damped harmonic oscillator quantization. It is shown that, when each branch is in the thermal vacuum states, the quantum fluctuations of the voltage, and current of each loop relate with not only the equivalent circuit inherent parameter, but also the temperature and decay according to exponent along with time.