Kinetic theory of electromagnetic ion waves in relativistic plasmas

A kinetic theory for electromagnetic ion waves in a cold relativistic plasma is derived. The kinetic equation for the broadband electromagnetic ion waves is coupled to the slow density response via an acoustic equation driven by ponderomotive force like term linear in the electromagnetic field amplitude. The modulational instability growth rate is derived for an arbitrary spectrum of waves. The monochromatic and random phase cases are studied.Comment: 7 pages, 4 figures, to appear in Physics of Plasma

Ion structure in warm dense matter: benchmarking solutions of hypernetted-chain equations by first-principle simulations

We investigate the microscopic structure of strongly coupled ions in warm dense matter using ab initio simulations and hypernetted chain (HNC) equations. We demonstrate that an approximate treatment of quantum effects by weak pseudopotentials fails to describe the highly degenerate electrons in warm dense matter correctly. However, one-component HNC calculations for the ions agree well with first-principles simulations if a linearly screened Coulomb potential is used. These HNC results can be further improved by adding a short-range repulsion that accounts for bound electrons. Examples are given for recently studied light elements, lithium and beryllium, and for aluminum where the extra short-range repulsion is essential

Quantum kinetic theory of the filamentation instability

The quantum electromagnetic dielectric tensor for a multi species plasma is re-derived from the gauge invariant Wigner-Maxwell system and presented under a form very similar to the classical one. The resulting expression is then applied to a quantum kinetic theory of the electromagnetic filamentation instability. Comparison is made with the quantum fluid theory including a Bohm pressure term, and with the cold classical plasma result. A number of analytical expressions are derived for the cutoff wave vector, the largest growth rate and the most unstable wave vector

Dispersion and damping of potential surface waves in a degenerate plasma

Potential (electrostatic) surface waves in plasma half-space with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The wave spectrum and the collisionless damping rate are obtained numerically for a wide range of wavelengths. In the limit of long wavelengths, the wave frequency $\omega$ approaches the cold-plasma limit $\omega=\omega_p/\sqrt{2}$ with $\omega_p$ being the plasma frequency, while at short wavelengths, the wave spectrum asymptotically approaches the spectrum of zero-sound mode propagating along the boundary. It is shown that the surface waves in this system remain weakly damped at all wavelengths (in contrast to strongly damped surface waves in Maxwellian electron plasmas), and the damping rate nonmonotonically depends on the wavelength, with the maximum (yet small) damping occuring for surface waves with wavelength of $\approx5\pi\lambda_{F}$, where $\lambda_{F}$ is the Thomas-Fermi length.Comment: 22 pages, 6 figure

Heat exchange mediated by a quantum system

We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large, but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the STM tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.Comment: 16 pages, 6 figure

Swimming suppresses correlations in dilute suspensions of pusher microorganisms

Active matter exhibits various forms of non-equilibrium states in the absence of external forcing, including macroscopic steady-state currents. Such states are often too complex to be modelled from first principles and our understanding of their physics relies heavily on minimal models. These have mostly been studied in the case of "dry" active matter, where particle dynamics are dominated by friction with their surroundings. Significantly less is known about systems with long-range hydrodynamic interactions that belong to "wet" active matter. Dilute suspensions of motile bacteria, modelled as self-propelled dipolar particles interacting solely through long-ranged hydrodynamic fields, are arguably the most studied example from this class of active systems. Their phenomenology is well-established: at sufficiently high density of bacteria, there appear large-scale vortices and jets comprising many individual organisms, forming a chaotic state commonly known as bacterial turbulence. As revealed by computer simulations, below the onset of collective motion, the suspension exhibits very strong correlations between individual microswimmers stemming from the long-ranged nature of dipolar fields. Here we demonstrate that this phenomenology is captured by the minimal model of microswimmers. We develop a kinetic theory that goes beyond the commonly used mean-field assumption, and explicitly takes into account such correlations. Notably, these can be computed exactly within our theory. We calculate the fluid velocity variance, spatial and temporal correlation functions, the fluid velocity spectrum, and the enhanced diffusivity of tracer particles. We find that correlations are suppressed by particle self-propulsion, although the mean-field behaviour is not restored even in the limit of very fast swimming.Comment: 23 pages, 9 figure

Colloquium: Nonlinear collective interactions in quantum plasmas with degenerate electron fluids

The current understanding of some important nonlinear collective processes in quantum plasmas with degenerate electrons is presented. After reviewing the basic properties of quantum plasmas, we present model equations (e.g. the quantum hydrodynamic and effective nonlinear Schr\"odinger-Poisson equations) that describe collective nonlinear phenomena at nanoscales. The effects of the electron degeneracy arise due to Heisenberg's uncertainty principle and Pauli's exclusion principle for overlapping electron wavefunctions that result in tunneling of electrons and the electron degeneracy pressure. Since electrons are Fermions (spin-1/2), there also appears an electron spin current and a spin force acting on electrons due to the Bohr magnetization. The quantum effects produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a quantum plasma that are summarized in here. Furthermore, we discuss nonlinear features of ES ion waves and electron plasma oscillations (ESOs), as well as the trapping of intense EM waves in quantum electron density cavities. Specifically, simulation studies of the coupled nonlinear Schr\"odinger (NLS) and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. We also discuss the effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic (Q-MHD) equations. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects, in plasma-assisted nanotechnology, and in the next-generation of intense laser-solid density plasma interaction experiments.Comment: 25 pages, 14 figures. To be published in Reviews of Modern Physic

Bimodality and hysteresis in systems driven by confined L\'evy flights

We demonstrate occurrence of bimodality and dynamical hysteresis in a system describing an overdamped quartic oscillator perturbed by additive white and asymmetric L\'evy noise. Investigated estimators of the stationary probability density profiles display not only a turnover from unimodal to bimodal character but also a change in a relative stability of stationary states that depends on the asymmetry parameter of the underlying noise term. When varying the asymmetry parameter cyclically, the system exhibits a hysteresis in the occupation of a chosen stationary state.Comment: 4 pages, 5 figures, 30 reference

Quantifying Self-Organization with Optimal Predictors

Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we propose a new criterion, namely an internally-generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. We precisely define this complexity for spatially-extended dynamical systems, using the probabilistic ideas of mutual information and minimal sufficient statistics. This leads to a general method for predicting such systems, and a simple algorithm for estimating statistical complexity. The results of applying this algorithm to a class of models of excitable media (cyclic cellular automata) strongly support our proposal.Comment: Four pages, two color figure

Quantum many-body dynamics in a Lagrangian frame: II. Geometric formulation of time-dependent density functional theory

We formulate equations of time-dependent density functional theory (TDDFT) in the co-moving Lagrangian reference frame. The main advantage of the Lagrangian description of many-body dynamics is that in the co-moving frame the current density vanishes, while the density of particles becomes independent of time. Therefore a co-moving observer will see the picture which is very similar to that seen in the equilibrium system from the laboratory frame. It is shown that the most natural set of basic variables in TDDFT includes the Lagrangian coordinate, $\bm\xi$, a symmetric deformation tensor $g_{\mu\nu}$, and a skew-symmetric vorticity tensor, $F_{\mu\nu}$. These three quantities, respectively, describe the translation, deformation, and the rotation of an infinitesimal fluid element. Reformulation of TDDFT in terms of new basic variables resolves the problem of nonlocality and thus allows to regularly derive a local nonadiabatic approximation for exchange correlation (xc) potential. Stationarity of the density in the co-moving frame makes the derivation to a large extent similar to the derivation of the standard static local density approximation. We present a few explicit examples of nonlinear nonadiabatic xc functionals in a form convenient for practical applications.Comment: RevTeX4, 18 pages, Corrected final version. The first part of this work is cond-mat/040835