arXiv subjects

Joel L. Lebowitz

Publications and source records attributed to Joel L. Lebowitz.

107 records · Page 6Linked to original sources

arXiv2003

Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Contact matrices provide a coarse grained description of the configuration omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when the distance between the position of the i-th and j-th step are less than or equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and SAW, with "a" the minimal permissible distance. We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n <= 2, but differs for n >= 3.

math-ph↗

arXiv2003

Space Charge Limited 2-d Electron Flow between Two Flat Electrodes in a Strong Magnetic Field

An approximate analytic solution is constructed for the 2-d space charge limited emission by a cathode surrounded by non emitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.

physics.plasm-ph↗

arXiv2002

Hydrodynamics of binary fluid phase segregation

Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field $\bm{u}$ when the system is segregated into two phases (at low temperatures) with a sharp interface between them. $\bm{u}$ satisfies the incompressible Navier-Stokes equations together with a jump boundary condition for the pressure across the interface which, in turn, moves with a velocity given by the normal component of $\bm{u} $. Numerical simulations of the Vlasov-Boltzmann equations for shear flows parallel and perpendicular to the interface in a phase segregated mixture support this analysis. We expect similar behavior in real fluid mixtures.

cond-mat.stat-mech↗

arXiv2001

Surface-Directed Spinodal Decomposition in Binary Fluid Mixtures

We consider the phase separation of binary fluids in contact with a surface which is preferentially wetted by one of the components of the mixture. We review the results available for this problem and present new numerical results obtained using a mesoscopic-level simulation technique for the 3-dimensional problem.

cond-mat.stat-mech↗

arXiv2000

Statistical Mechanics: A Selective Review of Two Central Issues

I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These phenomena are emergent collective properties not discernible in the behavior of individual atoms. They are given precise and elegant mathematical formulations when the ratio between macroscopic and microscopic scales becomes very large.

math-ph↗

arXiv2000

Ionization of a Model Atom by Perturbations of the Potential

We study the time evolution of the wave function of a particle bound by an attractive $δ$-function potential when it is subjected to time dependent variations of the binding strength (parametric excitation). The simplicity of this model permits certain nonperturbative calculations to be carried out analytically both in one and three dimensions. Thus the survival probability of bound state $|θ(t)|^2$, following a pulse of strength $r$ and duration $t$, behaves as $|θ(t)|^2 -|θ(\infty)|^2 \sim t^{-α}$, with both $θ(\infty)$ and $α$ depending on $r$. On the other hand a sequence of strong short pulses produces an exponential decay over an intermediate time scale.

math-ph↗

arXiv1999

Large deviations for ideal quantum systems

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.

math-ph↗

arXiv1999

Ionization of a Model Atom: Exact Results and Connection with Experiment

We prove that a model atom having one bound state will be fully ionized by a time periodic potential of arbitrary strength $r$ and frequency $ω$. The survival probability is for small $r$ given by $e^{-Γt}$ for times of order $Γ^{-1} \sim r^{-2n}$, where $n$ is the number of ``photons'' required for ionization, with enhanced stability at resonances. For late times the decay is like $t^{-3}$. Results are for a 1d system with a delta function potential of strength $-g(1 + η(t))$ but comparison with experiments on the microwave ionization of excited hydrogen atoms and with recent analytical work indicate that many features are universal.

physics.atom-ph↗

arXiv1998

Critical droplets in Metastable States of Probabilistic Cellular Automata

We consider the problem of metastability in a probabilistic cellular automaton (PCA) with a parallel updating rule which is reversible with respect to a Gibbs measure. The dynamical rules contain two parameters $β$ and $h$ which resemble, but are not identical to, the inverse temperature and external magnetic field in a ferromagnetic Ising model; in particular, the phase diagram of the system has two stable phases when $β$ is large enough and $h$ is zero, and a unique phase when $h$ is nonzero. When the system evolves, at small positive values of $h$, from an initial state with all spins down, the PCA dynamics give rise to a transition from a metastable to a stable phase when a droplet of the favored $+$ phase inside the metastable $-$ phase reaches a critical size. We give heuristic arguments to estimate the critical size in the limit of zero ``temperature'' ($β\to\infty$), as well as estimates of the time required for the formation of such a droplet in a finite system. Monte Carlo simulations give results in good agreement with the theoretical predictions.

cond-mat.stat-mech↗

arXiv1998

Hydrodynamic Limit of Brownian Particles Interacting with Short and Long Range Forces

We investigate the time evolution of a model system of interacting particles, moving in a $d$-dimensional torus. The microscopic dynamics are first order in time with velocities set equal to the negative gradient of a potential energy term $Ψ$ plus independent Brownian motions: $Ψ$ is the sum of pair potentials, $V(r)+γ^d J(γr)$, the second term has the form of a Kac potential with inverse range $γ$. Using diffusive hydrodynamical scaling (spatial scale $γ^{-1}$, temporal scale $γ^{-2}$) we obtain, in the limit $γ\downarrow 0$, a diffusive type integro-differential equation describing the time evolution of the macroscopic density profile.

cond-mat.stat-mech↗

arXiv1997

Solutions to the Boltzmann equation in the Boussinesq regime

We consider a gas in a horizontal slab, in which the top and bottom walls are kept at different temperatures. The system is described by the Boltzmann equation (BE) with Maxwellian boundary conditions specifying the wall temperatures. We study the behavior of the system when the Knudsen number $ε$ is small and the temperature difference between the walls as well as the velocity field is of order $ε$, while the gravitational force is of order $ε^2$. We prove that there exists a solution to the BE for which is near a global Maxwellian, and whose moments are close, up to order $ε^2$ to the density, velocity and temperature obtained from the smooth solution of the Oberbeck-Boussinesq equations, up to the time this one stays regular.

cond-mat.stat-mech↗

arXiv1997

Current-Voltage Characteristic of a Partially Ionized Plasma in Cylindrical Geometry

The properties of a partially ionized plasma in a long cylindrical tube subject to a uniform axial electric field are investigated. The plasma is maintained by an external ionizing source balanced by bulk and surface recombinations. Collisions between neutrals, whose density greatly exceeds the density of charged particles, and of neutrals with ions are sufficiently effective for their velocity distribution to be close to a Maxwellian with the same uniform temperature, independent of the external field. The behavior of the plasma is described by a collisional two-fluid scheme with charge neutrality in the interior of the tube. Approximate nonlinear equations for the hydrodynamical moments are obtained from a Boltzmann equation in which electron-neutral, electron-ion and electron-electron collisions are all important. It is found that under certain circumstances the current, and the temperature of the electrons undergo a drastic change, with hysteresis, as the electric field is varied.

physics.plasm-ph↗

arXiv1997

Stationary Nonequilibrium States in Boundary Driven Hamiltonian Systems: Shear Flow

We investigate stationary nonequilibrium states of systems of particles moving according to Hamiltonian dynamics with specified potentials. The systems are driven away from equilibrium by Maxwell demon ``reflection rules'' at the walls. These deterministic rules conserve energy but not phase space volume, and the resulting global dynamics may or may not be time reversible (or even invertible). Using rules designed to simulate moving walls we can obtain a stationary shear flow. Assuming that for macroscopic systems this flow satisfies the Navier-Stokes equations, we compare the hydrodynamic entropy production with the average rate of phase space volume compression. We find that they are equal when the velocity distribution of particles incident on the walls is a local Maxwellian. An argument for a general equality of this kind, based on the assumption of local thermodynamic equilibrium, is given. Molecular dynamic simulations of hard disks in a channel produce a steady shear flow with the predicted behavior.

cond-mat.stat-mech↗

arXiv1996

Microscopic Reversibility and Macroscopic Behavior: Physical Explanations and Mathematical Derivations

The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More specific features of macroscopic evolution depend on the nature of the microscopic dynamics. In particular, short range interactions with good mixing properties lead, for simple systems, to the quantitative description of such evolutions by means of autonomous hydrodynamic equations, e.g., the diffusion equation. These deterministic time-asymmetric equations accurately describe the observed behavior of {\it individual} macro systems. Derivations using ensembles (or probability distributions) must therefore, to be relevant, hold for almost all members of the ensemble, i.e., occur with probability close to one. Equating observed irreversible macroscopic behavior with the time evolution of ensembles describing systems having only a few degrees of freedom, where no such typicality holds, is misguided and misleading.

cond-mat↗

arXiv1995

Does the Wave Function Provide a Complete Description of Physical Reality?

This is the introduction to the section on Quantum Mechanics in the centennial collection of noteworthy articles appearing in The Physical Review and Physical Review Letters through 1983, since it all began in 1893. The selections for this section are "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" by Einstein, Podolsky and Rosen; Bohr's response, with the same title; Bohm's first hidden variables paper: "A Suggested Interpretation of the Quantum Theory in Terms of `Hidden' Variables. I"; Aharonov and Bohm's "Significance of Electromagnetic Potentials in the Quantum Theory"; and "Experimental Test of Bell's Inequalities Using Time-Varying Analyzers" by Aspect, Dalibard and Roger.

quant-ph↗

arXiv1994

Gaussian Fluctuation in Random Matrices

Let $N(L)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of ${\cal N}$ by ${\cal N}$ matrices, in the limit ${\cal N}\rightarrow\infty$. We prove that $[N(L) - \langle N(L)\rangle]/\sqrt{\log L}$ has a Gaussian distribution when $L\rightarrow\infty$. This theorem, which requires control of all the higher moments of the distribution, elucidates numerical and exact results on chaotic quantum systems and on the statistics of zeros of the Riemann zeta function. \noindent PACS nos. 05.45.+b, 03.65.-w

chao-dyn↗

arXiv1993

Exact Results for the Asymmetric Simple Exclusion Process with a Blockage

We present new results for the current as a function of transmission rate in the one dimensional totally asymmetric simple exclusion process (TASEP) with a blockage that lowers the jump rate at one site from one to r < 1. Exact finite volume results serve to bound the allowed values for the current in the infinite system. This proves the existence of a gap in allowed density corresponding to a nonequilibrium ``phase transition'' in the infinite system. A series expansion in r, derived from the finite systems, is proven to be asymptotic for all sufficiently large systems. Pade approximants based on this series, which make specific assumptions about the nature of the singularity at r = 1, match numerical data for the ``infinite'' system to a part in 10^4.

comp-gas↗