Mean field kinetic theory of a classical electron gas in a periodic potential. III. The high-temperature limit in two dimensions

The Vlasov-like mean field kinetic equation for a classical electron plasma in the periodic field of an ionic lattice is solved in the high-temperature limit in two dimensions. The predictions for the one-electron density, the static structure factor, and the long-wavelength charge fluctuation spectrum are compared to the results of extensive molecular dynamics simulations. The predicted shift and damping of the plasma oscillation mode are in reasonable agreement with the simulation data at intermediate couplings (=e ²/k _B T1), but the agreement deteriorates as the temperature or the density is lowered, because mean field theory does not lead to the expected Kosterlitz-Thouless transition to the dielectric phase where electrons are localized.     

Mean field kinetic theory of a classical electron gas in a periodic potential. II. Qualitative analysis of the mean-field solution in one dimension

A qualitative analysis is made of the static and dynamic behavior of a one-dimensional classical electron gas in a periodic potential in the framework of a mean-field kinetic theory. The mean-field equations have been formally solved elsewhere in terms of the trajectories of one electron in the mean-field equilibrium potential, which determines the local electronic density. Taking advantage of the relative simplicity of the mean-field expressions in one dimension, we study the effects of the temperature upon the local electronic density, the static structure factor, and the spectrum of the fluctuations in the long-wavelength limit. At high temperatures, the system tends to behave like a homogeneous electron gas; however, the collective plasmon mode at zero wavenumber is damped and shifted below the plasma frequency. At low temperatures, the system behaves as an ensemble of independent electrons strongly localized in the neighborhood of the fixed ions that create the periodic potential; the plasmon mode then vanishes. We consider the physical relevance of these predictions. They turn out to be quite reasonable, despite the failure of meanfield theory to predict the phase of the model.     

Part I. The 2D classical Coulomb gas near the zero-density Kosterlitz-Thouless critical point: Correlations and critical line

The 2D classical Coulomb gas undergoes the famous Kosterlitz-Thouless (KT) transition between a high-temperature conducting phase and a low-temperature insulating phase. We present various studies of the correlations in the insulating phase near the zero-density critical point. First, we briefly recall the phenomenological approach of Kosterlitz and Thouless. This theory predicts that the decay of the charge correlation is entirely controlled by the bare Coulomb potential between opposite charges only renormalized by the dielectric constante. Then, we present an analysis of the low-fugacity expansions of the correlations. The particle correlations are found to decay as 1/r⁴. The large-distance decay of the charge correlation is shown to be tightly related to the behavior of l/s in the regime of interest. Systematic resummations allow one to recover the algebraic decay predicted by the heuristic KT model. This settles on a rigorous basis various assumptions of this model. In particular, the nested pair mechanism naturally arises in the resummation scheme. Finally, we describe the phase diagram of the system according to the most recent calculations which include finite-density effects.     

Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.     

Correlations in the Kosterlitz-Thouless phase of the two-dimensional Coulomb gas

The particle and charge correlations of the two-dimensional Coulomb gas are studied in the dielectric phase. A term-by-term analysis of the low-fugacity expansions suggests that the large-distance behaviors of the particle correlations are governed by multipolar interactions, similar to what happens in a system of permanent dipoles. These behaviors are compatible with the asymptotic structure of the BGY hierarchy equations; on the other hand, a new identity for the dielectric constant is used to show that the four-particle correlations decay as the dipole-dipole potential 1/r² when two neutral pairs are separated by a large distancer. Near the zero-density critical point of the Kosterlitz-Thouless transition, we resum the low-fugacity expansions of both 1/ and the charge correlation C(r). We thus retrieve the coupling constant flow equations of the renormalization group as well as the effective interaction energy of the iterated mean-field theory by Kosterlitz and Thouless. The coupling constant at the RG fixed point is then identified with 1/. The nonanalyticity of 1/ at the transition turns out to coincide with the divergence of the low-fugacity series for this quantity. The leading term in the large-distance behavior of C(r) is found to be the same as for external charges. Moreover, we exhibit the subleading terms which also contribute to 1/.     

A new rigorous upper bound for the inverse critical temperature of the two-dimensional Coulomb gas

In this paper we show how to improve the recent result _c 17.2 on the inverse critical temperature for the two-dimensional Coulomb gas at low density to get the following upper bound: _c 16.     

Collective modes and dynamic structure factor of a two-dimensional electron fluid

The electrons bound to the surface of liquid dielectrics by image forces are described as a two-dimensional, classical, one-component plasma with inverse distance interactions. Exact expressions for the collective modes and the dynamic structure factor are obtained from first principles in the limit of long wavelengths. The differences and analogies with uncharged particle fluids and with the three-dimensional one-component plasma are explicitly displayed. The previously used mean-field approximation is shown not to describe weakly coupled systems and to be inadequate in the long-wavelength region.     

Derivation and classical limit of the mean-field equation for a quantum Coulomb system: Maxwell-Boltzmann statistics

The mean-field density matrix of a changed plasma of quantum particles with Maxwell-Boltzmann statistics in a confining external potential is obtained as a limit of theN-body canonical states for suitably scaled charges. Also, it is shown that the density profile of the quantum mean-field theory converges to the solution of the classical mean-field equation when the Planck's constant tends to zero.     

Dynamic chaos in the solution of the Gross-Pitaevskii equation for a periodic potential

We analytically and numerically investigate the solution to the stationary Gross-Pitaevskii equation for a one-dimensional potential of the optical lattice in the case of repulsive nonlinearity. From the mathematical viewpoint, this problem is similar to the well-known problem of the classical mathematical Kapitza pendulum perturbed by a weak high-frequency force. At certain values of the parameters, dynamic chaos is produced in the considered problem. It is modeled analytically by a nonlinear diffusion equation.     

The exact solution of an elimination problem in kinetic theory: I. The one-dimensional hard sphere gas

A class of initial value problems for a one-dimensional hard sphere gas is considered where a specified particle has a given distribution f⁽¹⁾(z₁; 0) and the rest are in equilibrium at t=0. An exact expansion is obtained for a certain n-particle reduced distribution function f⁽ⁿ⁾(z₁;…;z_n; t) in terms of the 1-particle reduced distribution function f⁽¹⁾(z₁; t) for the specified particle by starting with separate expressions for these functions in terms of f⁽¹⁾(z₁; 0). Expansions for the corresponding cluster functions are first obtained and then graph theoretic methods applied to obtain a solution.     

Driven quasi-one-dimensional classical electron gas in the presence of a constriction: Pinning and depinning

We studied the properties of a quasi-one-dimensional system of charged particles in the presence of a local Lorentzian-shaped constriction. We investigated the response of the system when a time-independent external driving force is applied in the unconfined direction. Langevin molecular dynamics simulations for different values of the drive and temperature are performed. We found that the particles are pinned unless a threshold value of the driving force is reached. We investigated in detail the depinning phenomenon. The system can depin “elastically”, with particles moving together and keeping their neighbors, or “quasi-elastically”, with particles moving together through a complex net of conducting channels without keeping their neighbors. In the case of elastic depinning the velocity vs applied drive curves is characterized by a critical exponent β consistent with the value , while in the case of quasi-elastic depinning the critical exponent β has on average the value 0.94. The model is relevant e.g. for electrons on liquid helium, colloids and dusty plasma.     

On the Coulomb energy of a finite-temperature electron gas

We rederive the Coulomb expansion of the electron gas average energy at finite temperature, starting from scratch, i.e., using only the framework of the grand canonical ensemble and not the finite-T Green's function formalism. We recover the analytical expressions of the exchange and correlation energy in both the high-T and theT=0 limits. We explicitly show the origin of the crossover of the correlation energy leading term frome ⁴ lne ² at zero temperature toe ³ at finiteT. We also discuss the relative importance of exchange and correlation in both limits.     

高增益型气体电子倍增微网结构探测器的性能研究

随着微结构气体探测器的不断发展, 不同的探测需求相继提出.为了实现气体探测器在高增益和低打火率的条件下长时间稳定工作, 结合气体电子倍增器(GEM)与微网结构气体探测器(MicroMegas)的探测优势, 成功研制出一种基于GEM作为预放大的MicroMegas探测器, 详细介绍了探测器结构和工作原理, 并利用⁵⁵Fe放射源对探测器增益、打火率、能量分辨和工作稳定性等性能进行了实验测量. 分析结果显示GEM-MicroMegas探测器可以连续工作30 h 以上, 探测器增益可以超过10⁶, 相对于无GEM膜的MicroMegas探测器, 相同增益下打火率可以降低近100倍. 关键词： 微网结构气体探测器 能量分辨率 增益 打火率     

Computer simulation of some dynamical properties of the Lorentz gas

We carried out molecular dynamics simulations of a Lorentz gas, consisting of a lone hydrogen molecule moving in a sea of stationary argon atoms. A Lennard-Jones form was assumed for the H₂-Ar potential. The calculations were performed at a reduced temperatureK ^* =kT/_{H 2–Ar} = 4.64 and at reduced densities ^*= _{Ar Ar} ³ in the range 0.074–0.414. The placement of Ar atoms was assumed to be random rather than dictated by equilibrium considerations. We followed the trajectories of many H₂ molecules, each of which is assigned in turn a velocity given by the Maxwell-Boltzmann distribution at the temperature of the simulation. Solving the equations of motion classically, we obtained the translational part of the incoherent dynamic structure factor for the H₂ molecule,S _tr(q, ). This was convoluted with the rotational structure factorS _rot(q, ) calculated assuming unhindered rotation to obtain the total structure factorS(q, ). Our results agree well with experimental data on this function obtained by Egelstaffet al. At the highest density ( ^*=0.414) we studied the dependence ofS(q, ) on system size (number of Ar atoms), number of H₂ molecules for which trajectories are generated, and the length of time over which these trajectories are followed.     

An electrochemomechanical theory of defects in ionic solids. I. Theory

Charged defects diffuse through an ionic solid under electrochemical driving forces. Such a diffusion process can be affected by mechanical stresses in the solid. A deviation of defect concentration from its stoichiometric value during diffusion can cause volumetric strains in the solid. Such strains will result in mechanical stresses if the ionic solid is under mechanical constraint, or if the defect distribution is non-uniform. We develop a framework to account for the coupling between mechanical stresses and diffusion of charged defects in ionic solids. The framework consists of a system of nonlinear differential/algebraic equations governing the defect concentrations, electrostatic potential and the mechanical stresses. It is believed that this framework is the first fully coupled theory for the interaction between mechanical stresses and electrochemical forces in ionic solids.     

Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method

In this Letter, the Dirac equation is exactly solved for spatially-dependent mass Coulomb potential including a Coulomb-like tensor potential under pseudospin symmetry limit by using asymptotic iteration method with arbitrary spin-orbit coupling number κ. The energy eigenvalues and corresponding eigenfunctions are obtained and some numerical results are given.     

Hilbert-Enskog-Chapman expansion in the turbulent kinetic theory of gases. I

Giving up the assumption of molecular chaos, we get a hierarchy of equations, instead of the Boltzmann equation, governing the motion of a dilute gas. The Hilbert-Enskog-Chapman expansion methods for the hierarchy are studied in this paper and its continuations.     

Kinetic theory of long time tails in velocity correlation functions in a moderately dense electron gas

The long time tails of the correlation functions that determine the self-diffusion coefficient and the kinetic parts of the shear viscosity and heat conductivity in a one-component plasma are calculated using a systematic kinetic theory. The results are in agreement with those obtained from the phenomenological mode coupling theory. The formal kinetic theory calculations of previous workers, who obtained incomplete long time tail results, are also discussed.     

On the absence of intermediate phases in the two-dimensional Coulomb gas

For a simple, continuum two-dimensional Coulomb gas (with soft cutoff), Gallavotti and Nicoló [J. Stat. Phys. 38:133–156 (1985)] have proved the existence of finite coefficients in the Mayer activity expansion up to order 2n below a series of temperature thresholdsT _n =T [1+(2n–1)^–1] (n=1, 2,...). With this in mind they conjectured that an infinite sequence of intermediate, multipole phases appears between the exponentially screened plasma phase aboveT ₁ and the full, unscreened Kosterilitz-Thouless phase belowT T _KT. We demonstrate that Debye-Hückel-Bjerrum theory, as recently investigated ford=2 dimensions, provides a natural and quite probably correct explanation of the pattern of finite Mayer coefficients while indicating the totalabsence of any intermediate phases at nonzero density ; only the KT phase extends to >0.     

Determination of the structure factor for the rare gas fluids based on the ORPA theory and LIR equation of state

Linear isotherm regularity is applied to generate an expression for the direct correlation function (DCF), based on the optimized random-phase approximation theory. We use the Lennard-Jones potential in the modelling of real fluids, in which its molecular parameters are state-dependent. Based on the perturbation theory, we assume that the core contribution of the DCF is related to the geometric effect via a linear form, which arises from the excluded volume, and the tail contribution is related to the long-range intermolecular interactions of the system via a non-linear form. We use this model to predict the behaviour of the structure factor, S(k), in a wide range of k values for the xenon and krypton liquids. Finally, we compare our results with the experimental and theoretical data available in literature. The model is also successful in the presentation of the Ornstein–Zernike behaviour of S(k) at the low-k region.