Solvable models of classical lattice gases

We study classical lattice gases at fixed temperature but variable fugacity. It is shown how the thermodynamic functions may be calculated exactly provided the Boltzmann weights are representable as principal minors of a convolution operator. We explicitly construct this operator for the cluster models of Fisher and Felderhof.On leave from the Institute for Theoritical Physics, RWTH Aachen, Germany.     

On the statistical mechanics of classical Coulomb and dipole gases

A detailed, rigorous study of the statistical mechanics-screening- and critical properties, phase diagrams, etc., of classical Coulomb monopole and dipole gases in two or more dimensions is presented. The statistical mechanics of the two-dimensionalXY and Villain models is reconsidered and related to the one of two-dimensional lattice Coulomb gases. At low temperatures and moderate densities those gases behave like dipole gases. The Kosterlitz-Thouless transition is analyzed in that perspective and characterized by an order parameter. Techniques useful for a proof of existence of such a transition in a two-dimensional hard-core Coulomb gas are developed and applied to the study of dipole gases.A Sloan Fellow, and supported in part by NSF grant No. DMR 7904355.     

Negative-viscosity lattice gases

A new irreversible collision rule is introduced for lattice-gas automata. The rule maximizes the flux of momentum in the direction of the local momentum gradient, yielding a negative shear viscosity. Numerical results in 2D show that the negative viscosity leads to the spontaneous ordering of the velocity field, with vorticity resolvable down to one lattice-link length. The new rule may be used in conjunction with previously proposed collision rules to yield a positive shear viscosity lower than the previous rules provide. In particular, Poiseuille flow tests demonstrate a decrease in viscosity by more than a factor of 2.     

The cluster expansion for classical and quantum lattice systems

We develop a high-temperature expansion for general lattice systems which can be applied to classical as well as quantum systems. Applying the expansion we prove analyticity of correlation functions, uniqueness of equilibrium states, and cluster properties for classical and quantum lattice systems in the high-temperature region.     

Low-viscosity lattice gases

A class of lattice gas models are studied which are variants of the FCHC model. The aim is to achieve the highest possible Reynolds coefficient (inverse dimensionless viscosity) for efficient simulations of the three-dimensional incompressible Navier-Stokes equations. The models include an arbitrary number of rest particles and violation of semi-detailed balance. Within the framework of the Boltzmann approximation exact expressions are obtained for the Reynolds coefficients. The minimization of the viscosity is done by solving a Hitchcock-type optimization problem for the fine tuning of the collision rules. When the number of rest particles exceeds one, there is a range of densities at which the viscosity takes negative values. Various optimal models with up to 26 bits per node have been implemented on a CRAY-2 and their true transport coefficients have been measured with good accuracy. Fairly large discrepancies with Boltzmann values are observed when semi-detailed balance is violated; in particular, no negative viscosity is obtained. Still, the best model has a Reynolds coefficient of 13.5, twice that of the best previously implemented model, and thus is about 16 times more efficient computationally. Suggestions are made for further improvements. It is proposed to use models with very high Reynolds coefficients for sub-grid-scale modeling of turbulent flows.     

Tracer diffusion in lattice gases

It has been proved that a tracer particle in a reversible lattice gas converges to Brownian motion. However, only in a few particular cases has a strictly positive self-diffusion coefficientD been established. Here we supply the missing piece and show thatD>0 in general. The exceptions are one-dimensional lattice gases with nearest neighbor jumps only, for whichD=0. The proof establishes a variational formula forD which could be used to obtain realistic bounds.     

Quantum corrections for lattice gases

Classical lattice gases consisting of structureless particles (with spin) have been quantized by introducing a kinetic energy operator that produces nearest-neighbor hops. Systematic quantum corrections for the partition function and the particle distribution functions appear naturally as power series inX = ²/2ml ² ( ^–1 =k _B T,m is the mass,l is a distance related to lattice spacing). These corrections require knowledge of certain particle displacement probabilities in the corresponding classical lattice gases. Leading-order corrections have been derived in forms that should facilitate their use in computer simulation studies of lattice gases by the standard Monte Carlo method.     

Iterated Mayer expansion for classical gases at low temperatures

We derive iterated Mayer expansions for classical gases and establish recursive bounds which control their convergence. These bounds are useful for gases with two body forces which are strong and possibly attractive at distances that are short compared to their range. Our procedure is based on splitting the potential into pieces of decreasing strength and increasing range. This may be called a renormalization group treatment of a classical gas. We apply our results to Yukawa lattice gas models and obtain convergence of series expansions for the pressure for a range of parameters (temperature, fugacities, range of the interaction) that was inaccessible before. Application to 3-dimensionalU(1) lattice gauge theory (Coulomb gas,Z-ferromagnet) will be made elsewhere.Work supported in part by Deutsche Forschungsgemeinschaft     

Global invariants and equilibrium states in lattice gases

It is now well known that, in addition to the physical conserved quantities, lattice gases also have other unphysical ones related to the discretization of their phase space. From an abstract point of view a lattice gas can be considered like a full discrete Markov processL and these spurious conserved quantities yield the existence of a nonspatially homogeneous equilibrium state forL ^k. We show that a particular set of these conserved quantities is of special interest: Its elements will be called regular. These regular invariants are simply built from the local ones and their projection on each node is always a locally conserved quantity. Moreover, for most models they are one-to-one related to the Gibbs states ofL ^k which remain factorized. It turns out that all the classical known spurious invariants are regular and one can exhibit simple conditions to build models with only regular invariants. For the latter it is then justified to determine the transport coefficients of the locally conserved densities with the Green-Kubo procedure.     

Lorentz lattice gases: Basic theory

We present several ballistic models of the Lorentz gas in two-dimensional lattices with deterministic and stochastic deflection rules, and their corresponding Liouville equations. Boltzmann-level-equation results are obtained for the diffusion coefficient and velocity autocorrelation function for models with stochastic deflection rules. The long-time behavior of the mean square displacement is briefly discussed and the possibility of abnormal diffusion indicated. Even if the diffusion coefficient exists, its low-density limit may not be given correctly by the Boltzmann equation.     

A renormalization group analysis of correlation functions for the dipole gas

We develop a renormalization group method for analyzing the generating functional for charge correlations of a dilute classical dipole gas. It is based on and extends the renormalization group analysis introduced by Brydges and Yau for the dipole gas partition function. Our method leads to systematic formulas for the large-distance behavior of correlation functions of all orders. We prove that in any dimensiond2, at any value>0 of the inverse temperature, and at sufficiently small activityz, the correlation functions exhibit at large distances the same behavior as for a vacuum (z=0), but with a new dielectric constant 1+ over which we have good control. The results proved here extend existing results on the two-point correlations to all higher correlations, and constitute a general confirmation of the fact that dipoles do not screen.     

High-temperature expansion for nonequilibrium steady states in driven lattice gases

We develop a controlled high-temperature expansion for nonequilibrium steady states of the driven lattice gas, the "Ising model" for nonequilibrium physics. We represent the steady state as P(eta) alpha e(-betaH(eta)-psi(eta)) and evaluate the lowest order contribution to the nonequilibrium effective interaction psi(eta). We see that, in dimensions d > or = 2, all models with nonsingular transition rates yield the same summable psi(eta), suggesting the possibility of describing the state as a Gibbs state similar to equilibrium. The models with the Metropolis rule show exceptional behavior.     

Diffusion of lattice gases without double occupancy on three-dimensional percolation lattices

We examined the diffusion of lattice gases, where double occupancy of sites is excluded, on three-dimensional percolation lattices at the percolation thresholdp _c . The critical exponent for the root-mean-square displacement was determined to bek=0.183±0.010, which is similiar to the result of Roman for the problem of the ant in the labyrinth. Furthermore, we found a plateau value fork at intermediate times for systems with higher concentrations of lattice gas particles.     

Convergent expansions for asymptotically degenerate inverse correlation lengths of classical lattice spin systems

We obtain convergent expansions for the inverse correlation length associated with various spin-spin correlation functions for some weakly coupled multicomponent classical lattice spin systems. In terms of the lattice quantum field theory associated with the models the expansions provide a convergent perturbation theory for particle masses which are asymptotically degenerate in the limit of zero coupling.Reseach partially supported by CNPq, Brazil.     

Long-time tails in lattice Lorentz gases

We consider a Lorentz gas on a square lattice with a fraction c of scattering sites. The collision laws are deterministic (fixed mirror model) or stochastic (with transmission, reflection, and deflection probabilities ,, and respectively). If all mirrors are parallel, the mirror model is exactly solvable. For the general case a self-consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function (0) (t) and the tensor correlation Q(0)Q(t) withQ= _{x y} . Both functions showt ^–2 tails, as opposed to the continuous Lorentz gas, where the tails are respectivelyt ^–2 andt ^–3. Inclusion of the self-consistent ring collisions increases the low-density coefficient of the tail in (0)(t) by 30–100% as compared to the simple ring collisions, depending on the model parameters.     

Bulk diffusivity of lattice gases close to criticality

We consider lattice gases where particles jump at random times constrained by hard-core exclusion (simple exclusion process with speed change). The conventional theory of critical slowing down predicts that close to a critical point the bulk diffusivity vanishes as the inverse compressibility. We confirm this claim by proving a strictly positive lower bound for the conductivity.     

Experimental realization of two-dimensional single-layer ultracold gases of 87Rb in an accordion lattice

We experimentally realize two-dimensional (2D) single-layer ultracold gases of ⁸⁷Rb by dynamically tuning the periodicity of a standing wave, known as accordion lattice. In order to load ⁸⁷Rb Bose—Einstein condensate into single dark fringe node of the blue detuning optical lattice, we reduce the lattice periodicity from 26.7 μ to 3.5 μ with the help of an acousto-optic deflector (AOD) to compress the three-dimensional BEC adiabatically into a flat and uniform quasi-2D single-layer. We describe the experimental procedure of the atoms loading into the accordion lattice in detail and present the characteristics of the quasi-2D ultracold gases. This setup provides an important platform for studying in- and out-of equilibrium physics, phase transition and 2D topological matter.     

HIRFL-CSRe二极铁积分磁场测量

 介绍了兰州重力加速器冷却储存环实验环二极磁铁积分长线圈测磁装置的构成,描述了实验环二极铁的分散性测量、横向分布测量、传递函数等测量内容及测量方法。实验环二极铁采用不断地加减硅钢铁片垫补和加调整线圈电流的方法来调整二极磁铁的有效长度来改变分散性。通过垫补和测量,二极磁铁的分散性在优化磁场时达到±2×10^-4。同时给出了二极铁的横向分布和传递函数的测量结果。对二极铁的设计和加工进行了修正。     

偶极子接收换能器驻波场校准系统的研究

本文研究了设计偶极子接收换能器的驻波场校准系统，利用该系统可以实现偶极子类型接收换能器的校准，包括接收灵敏度及偶极子方向性的测量，频率范围为２０－２０００Ｈｚ校准误差小于１ｄＢ。     

Collapse transition and asymptotic scaling behavior of lattice animals: Low-temperature expansion

A low-temperature expansion for the free energy density of lattice animals is derived. Analysis of the series yields a collapse transition temperature ofT _c - 0.54, in close agreement with previous estimates. It is demonstrated that _p,k, the number ofp-particle,p-bond animals, obeys the asymptotic scaling law log _p,k pg(k/p) + o(p). The low-temperature series and numerical data are used to estimate the scaling function.