理想量子气体的尺度效应

根据欧拉-麦克劳林(Euler-MacLaurin)公式,导出有限理想量子气体的热力学量表达式,揭示系统尺度和边界形状对其性质的影响.结果表明,有限尺度效应导致了一系列与热力学极限条件下不同的性质特征,如系统的非广延性和压强的各向异性等.     

On thermodynamics of RN-dS black hole surrounded by the quintessence

De Sitter black holes have the black hole horizon and the cosmological horizon, and the thermodynamic quantities on the two horizons all satisfy the first law of thermodynamics. The thermodynamic quantities on the two horizons are not independent but are correlated to each other. Taking de Sitter space-time as thermodynamic system, we investigated the effective thermodynamic quantities of Reissner–Nordström de Sitter black hole surrounded by the quintessence (RN-DSQ). We obtained the effective temperature and entropy of the system by considering the corrections between the black hole horizon and the cosmological horizon. We found that the entropy of the RN-DSQ is in agreement with that of Reissner–Nordström de Sitter black hole. It offers a basis for further studying of the thermodynamic properties of de Sitter space-time.     

Finite-size corrections for inclined interfaces in two dimensions: Exact results for Ising and solid-on-solid models

Analysis of finite-size corrections for the surface tension and surface stiffness coefficients in two-dimensional models with inclined interfaces is presented. We obtain a universal leading contribution proportional to (lnL)/L for the 2D system of sizeL. By explicit calculations for restricted and unrestricted solid-on-solid models and the square lattice Ising model, we demonstrate the Gaussian nature of rough interfaces with fixed ends, and derive the leading 1/L-type corrections for appropriate surface quantities.     

Critical dynamics of cluster algorithms in the dilute Ising model

Autocorrelation times for thermodynamic quantities atT _C are calculated from Monte Carlo simulations of the site-diluted simple cubic Ising model, using the Swendsen-Wang and Wolff cluster algorithms. Our results show that for these algorithms the autocorrelation timesdecrease when reducing the concentration of magnetic sites from 100% down to 40%. This is of crucial importance when estimating static properties of the model, since the variances of these estimators increase with autocorrelation time. The dynamical critical exponents are calculated for both algorithms, observing pronounced finite-size effects in the energy autocorrelation data for the algorithm of Wolff. We conclude that, when applied to the dilute Ising model, cluster algorithms become even more effective than local algorithms, for whichincreasing autocorrelation times are expected.     

有限尺度下弱相互作用费米气体的热力学性质

基于巨正则系综理论和数值模拟方法，研究有限尺度下弱相互作用费米气体的热力学性质，给出系统低温下的化学势、能量及热容量的解析式，分析弱相互作用、有限尺度效应对系统热力学性质的影响.研究表明，有限尺度和排斥相互作用增大了系统的化学势、能量,吸引相互作用减小了系统的化学势、能量.相互作用受到尺度的调制，尺度变大，相互作用影响变小，相互作用和尺度效应都受到温度的调制，温度升高，相互作用和尺度的影响减小.尺度和相互作用的一级修正对热容量无影响.     

有限尺度下弱相互作用费米气体的热力学性质

基于巨正则系综理论和数值模拟方法,研究有限尺度下弱相互作用费米气体的热力学性质,给出系统低温下的化学势、能量及热容量的解析式,分析弱相互作用、有限尺度效应对系统热力学性质的影响.研究表明,有限尺度和排斥相互作用增大了系统的化学势、能量,吸引相互作用减小了系统的化学势、能量.相互作用受到尺度的调制,尺度变大,相互作用影响变小,相互作用和尺度效应都受到温度的调制,温度升高,相互作用和尺度的影响减小.尺度和相互作用的一级修正对热容量无影响.     

弱磁场中弱相互作用费米气体的有限粒子数效应(英文)

由弱磁场中弱相互作用费米气体的配分函数,导出有限粒子数条件下系统的配分函数G(β,N ).在此基础上,运用统计平均方法求解有限粒子数弱相互作用费米气体热力学量的解析表达式,给出各种温度条件下的热力学性质.研究结果表明,有限粒子数效应使各个热力学量都产生了一个修正项,除温度趋于0外,粒子数对化学势的修正项有直接影响,对内能和热容量的修正项并不产生直接影响.并且有限粒子数效应总是降低化学势,从而使化学势的0点向低温漂移,粒子数增大,会削弱这种效应,粒子间的相互排斥会加强这种效应.     

弱磁场中弱相互作用玻色气体的热力学性质

运用外势中弱相互作用玻色体系的理论结论,研究弱磁场中弱相互作用玻色气体的高温热力学性质,给出系统总能和热容量的解析式,分析粒子之间的相互作用及磁场对系统热力学性质的影响.研究结果表明,排斥(吸引)对粒子和能量的空间分布有集中(分散)作用,并使得系统的化学势、总能、热容量都增大(减小);加强磁场既可使得粒子和能量的空间分布趋于分散又可削弱相互作用对粒子和能量空间分布的影响.相互作用对各个特征量的影响也有着不同的个性表现.     

Isobaric expansion coefficient and isothermal compressibility for a finite-size ideal Fermi gas system

Due to quantum size effects (QSEs), the isobaric thermal expansion coefficient and isothermal compressibility well defined for macroscopic systems are invalid for finite-size systems. The two parameters are redefined and calculated for a finite-size ideal Fermi gas confined in a rectangular container. It is found that the isobaric thermal expansion coefficient and isothermal compressibility are generally anisotropic, i.e., they are generally different in different directions. Moreover, it is found the thermal expansion coefficient may be negative in some directions under the condition that the pressures in all directions are kept constant.     

Statistic properties of Fermi gas in a strong magnetic field

Based on the thermodynamic potential function of Fermi gas in a strong magnetic field, using the thermodynamics method, the integrated analytical expressions of thermodynamic quantities of the system at low temperatures are derived, and the effects of the magnetic field on the statistic properties of the system are analysed. It is shown that, as long as the temperature is not zero, the effects of the magnetic field on the thermodynamic quantities of the system contain both oscillatory and non-oscillatory parts. For the non-oscillatory part, compared with the situation of Fermi gas in a weak magnetic field, the influence of the magnetic field on the thermodynamic quantities is not exactly the same. For the oscillatory part, the period and amplitude of the oscillation are all related to the magnetic field. Due to the oscillation, the chemical potential may be greater than Ferim energy of the system, but the oscillation does not affect the thermodynamic stability of the system.     

Statistical multifragmentation of nuclei: (I). Formulation of the model

A statistical formulation of the multifragmentation of finite nuclei is given. The approach considers the generalization of the liquid-drop model for hot nuclei and allows one to calculate thermodynamic quantities characterizing the nuclear ensemble at the disassembly stage. It is shown how to determine probabilities of definite partitions of finite nuclei and how to apply a Monte Carlo method. The importance of including finite-size effects is shown by comparison with infinite-like systems.     

Linear and nonlinear transport across carbon nanotube quantum dots

We present a low energy-theory for non-linear transport in finite-size interacting single-wall carbon nanotubes. It is based on a microscopic model for the interacting p_z electrons and successive bosonization. We consider weak coupling to the leads and derive equations of motion for the reduced density matrix. We focus on the case of large-diameter nanotubes where exchange effects can be neglected. In this situation the energy spectrum is highly degenerate. Due to the multiple degeneracy, diagonal as well as off-diagonal (coherences) elements of the density matrix contribute to the nonlinear transport. At low bias, a four-electron periodicity with a characteristic ratio between adjacent peaks is predicted. Our results are in quantitative agreement with recent experiments.     

Multiscaling and multifractality in an one-dimensional Ising model

Scaling properties of the Gibbs distribution of a finite-size one-dimensional Ising model are investigated as the thermodynamic limit is approached. It is shown that, for each nonzero temperature, coarse-grained probabilities of the appearance of particular energy levels display multiscaling with the scaling length ℓ = 1/M _n, where n denotes the number of spins and M_n is the total number of energy levels. Using the multifractal formalism, the probabilities are argued to reveal also multifractal properties. Received 10 July 2000 and Received in final form 6 November 2000     

Finite-size scaling studies of one-dimensional reaction-diffusion systems. Part I. Analytical results

We consider two single-species reaction-diffusion models on one-dimensional lattices of lengthL: the coagulation-decoagulation model and the annihilation model. For the coagulation model the system of differential equations describing the time evolution of the empty interval probabilities is derived for periodic as well as for open boundary conditions. This system of differential equations grows quadratically withL in the latter case. The equations are solved analytically and exact expressions for the concentration are derived. We investigate the finite-size behavior of the concentration and calculate the corresponding scaling functions and the leading corrections for both types of boundary conditions. We show that the scaling functions are independent of the initial conditions but do depend on the boundary conditions. A similarity transformation between the two models is derived and used to connect the corresponding scaling functions.     

Bethe ansatz results for Hubbard chains with toroidal boundary conditions

We solve exactly the problem of a one-dimensional repulsive-U Hubbard chain with toroidal boundary conditions (HTB) using the Bethe ansatz approach. We calculate analytically the finite-size corrections to the ground-state energy in the half-filled case and use this expression to derive charge and spin stiffnesses with no assumptions. We then use a particle-hole transformation to calculate the finite-size corrections for the half-filledattractive- U case, and again derive the resulting expressions for the charge and spin stiffnesses. Lastly, we discuss how the repulsive-U corrections relate to those of a Heisenberg model with toroidal boundary conditions.On leave from Departamento de Fisica, Universidade Federal de S. Carlos, S. Carlos, 13560, Brazil.     

Bethe ansatz calculations for the eight-vertex model on a finite strip

Bethe ansatz equations for the eigenvalues of the transfer matrix of the eight-vertex model are solved numerically to yield mass gap data on infinitely long strips of up to 512 sites in width. The finite-size corrections, at criticality, to the free energy per site and polarization gap are found to be in agreement with recent studies of theXXZ spin chain. The leading corrections to the finite-size scaling estimates of the critical line and thermal exponent are also found, providing an explanation of the poor convergence seen in earlier studies. Away from criticality, the linear scaling fields are derived exactly in the full parameter space of the spin system, allowing a thorough test of a recently proposed method of extracting linear scaling fields and related exponents from finite lattice data.     

Zur Elektronenstreuung an ionisierten Störstellen in Halbleitern mit isotroper effektiver Masse

A selfconsistent scattering-potential for a ionized impurity in a semiconductor with a isotropic effective mass and arbitrary degree of degeneracy is derived. For this scattering-potential the mobility formula for electrons is deduced, the corrections to the Brooks-Herring-formula are evaluated for the case of n-type GaAs.     

Effects of a finite number of particles on the thermodynamic properties of a harmonically trapped ideal charged Bose gas in a constant magnetic field

We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose–Einstein transition temperature, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties,particularly the Bose–Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N →∞.     

Spin coupling and magnetic field effects on the finite-size free energy and its non-extensivity for 1-D Ising model with nearest and next-nearest neighbor interactions in nanosystem

The effects of second-neighbor spin coupling interactions and a magnetic field are investigated on the free energies of a finite-size 1-D Ising model. For both ferromagnetic of nearest neighbor (NN) and next-nearest neighbor (NNN) spin coupling interactions, the finite-size free energy first increases and then approaches a constant value for any size of the spin chain. In contrast, when NNN and NN spin coupling interactions are antiferromagnetic and ferromagnetic, respectively, the finite-size free energy gradually decreases by increasing the competition factor and eventually vanishes for large values of it. When a magnetic field is applied, the finite-size free energy decreases with respect to the case of zero magnetic fields for both ferromagnetic and antiferromagnetic spin coupling interactions. Deviation of free energy per size for finite-size systems relative to the infinite system increases when the spin coupling interactions as well as the f parameter (the ratio of the magnetic field to NN spin coupling interaction) increase.     

Casimir amplitudes in a quantum spherical model with long-range interaction

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is . Received 3 June 1999 and Received in final form 16 August 1999