双时间—温度格临函数的二元碰撞展开

应用李政道和杨振宁提出的二元碰撞展开法,对于有强短程排斥互作用的多粒子系发展了一种按图形计算双时间-温度格临函数的规则,其各级近似由二体散射相移的各次幂所表征。文中得出了玻色和费米统计情形的计算规则,并且研究了有凝聚相存在的玻色系统。本文主要讨论了单粒子格临函数的图形技术,但容易将它们推广应用于计算各种时间-温度格临函数。     

From fractional exclusion statistics back to Bose and Fermi distributions

Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this Letter I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.     

A path integral centroid molecular dynamics method for Bose and Fermi statistics

We propose a path integral centroid molecular dynamics (CMD) method extended to Bose and Fermi statistics. An extended method of path integral molecular dynamics (PIMD) for such statistics is also developed as a technique of calculations of static properties. Bose PIMD and CMD simulations have been performed for bulk liquid ⁴He and ideal Bose gas, respectively. The remnant of λ transition is observed for bulk liquid ⁴He, while the effect of Bose statistics on the centroid dynamics spanning several nanoseconds is observed for ideal Bose gas.     

A characterization of clustering states

A characterization of states, over quasi-local algebras, which satsfy a strong cluster property is derived. The discussion is applicable to classical systems and quantum systems with Bose or Fermi statistics.     

Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice

In combination with Laughlin's treatment of the quantized Hall conductivity, the Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number on a periodic lattice in arbitrary dimensions. Regardless of dimensionality, interaction strength, and particle statistics (Bose or Fermi), a finite excitation gap is possible only when the particle number per unit cell of the ground state is an integer.     

Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems, as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order l≥ 3 contribute to an exponential which corresponds to a mean-field energy involving the second operator U₂, instead of the potential itself as usual - in other words, the mean-field correction is expressed in terms of a modification of a local Boltzmann equilibrium. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator U_n with n≥ 3 contains a “tree-reducible part”, which groups naturally with U₂ through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics. Received 18 October 2001     

Exact Maxwell–Boltzmann,Bose–Einstein and Fermi–Dirac statistics

The exact Maxwell–Boltzmann (MB), Bose–Einstein (BE) and Fermi–Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a “binary decision”, exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems.     

The vacuum violates Bell's inequalities

It is found that the vacuum state in any Bose or Fermi free quantum field theory violates Bell's inequalities maximally, i.e. in principle, with suitable detectors maximal violations of Bell's inequalities may be obtained without setting up a source. We explain, however, why it would be difficult to measure such violations.     

Correlation inequalities and the thermodynamic limit for classical and quantum continuous systems

We use Ginibre's general formulation of Griffiths' inequalities to derive new correlation inequalities for two-component classical and quantum mechanical systems of distinguishable particles interacting via two body potentials of positive type. As a consequence we obtain existence of the thermodynamic limit of the thermodynamic and correlation functions in the grand canonical ensemble at arbitrary temperatures and chemical potentials. For a large class of systems we show that the limiting correlation functions are clustering. (In a subsequent article these results are extended to the correlation functions of two-component quantum mechanical gases with Bose-Einstein statistics). Finally, a general construction of the thermodynamic limit of the pressure for gases which are not H-stable, above collapse temperature, is presented.Research supported in part by the U.S. National Science Foundation under grant MPS 75-11864A Sloan Foundation Fellow     

Ultracold Atomic Fermi–Bose Mixtures in Bichromatic Optical Dipole Traps: A Novel Route to Study Fermion Superfluidity

The study of low density, ultracold atomic Fermi gases is a promising avenue to understand fermion superfluidity from first principles. One technique currently used to bring Fermi gases in the degenerate regime is sympathetic cooling through a reservoir made of an ultracold Bose gas. We discuss a proposal for trapping and cooling of two-species Fermi–Bose mixtures into optical dipole traps made from combinations of laser beams having two different wavelengths. In these bichromatic traps it is possible, by a proper choice of the relative laser powers, to selectively trap the two species in such a way that fermions experience a stronger confinement than bosons. As a consequence, a deep Fermi degeneracy can be reached having at the same time a softer degenerate regime for the Bose gas. This leads to an increase in the sympathetic cooling efficiency and allows for higher precision thermometry of the Fermi–Bose mixture.     

Mathematical inequalities for some divergences

Some natural phenomena are deviating from standard statistical behavior and their study has increased interest in obtaining new definitions of information measures. But the steps for deriving the best definition of the entropy of a given dynamical system remain unknown. In this paper, we introduce some parametric extended divergences combining Jeffreys divergence and Tsallis entropy defined by generalized logarithmic functions, which lead to new inequalities. In addition, we give lower bounds for one-parameter extended Fermi–Dirac and Bose–Einstein divergences. Finally, we establish some inequalities for the Tsallis entropy, the Tsallis relative entropy and some divergences by the use of the Young’s inequality.     

Renormalization of boundary conditions for distribution functions of quasiparticles obeying quantum statistics at interfaces between crystalline grains

Boundary conditions for distribution functions of quasiparticles scattered by an interface between two crystalline grains are presented. In contradistinction to former formulations where the Maxwell-Boltzmann statistics was considered, the present boundary conditions take into account the quantum (Fermi-Dirac or Bose-Einstein) statistics of the quasiparticles. Provided that small deviations from the thermodynamical equilibrium only are present, the boundary conditions are linearized, and then their “renormalization” is investigated in case of the elastic scattering. The final results of the renormalization, which are obtained for a simplified model of an interface, suggest that the portion of the Fermi (Bose)-quasiparticles reflected or transmitted specularly is decreased (increased) in comparison with the case of quasiparticles obeying the Maxwell-Boltzmann statistics.     

Network synchronization under periodic coupling of both positive and negative values

The European Physical Journal B - We show that all the Bose–Einstein (BE) condensations of Bose and Fermi systems can be formulated using the common ‘boson’ operator (valid below...     

On the exact mean-field description of continuous quantum systems in equilibrium

The thermodynamic limit of free energy density is investigated for quantum systems of n particles obeying Boltzmann, Fermi and Bose statistics, interacting via spin-independent 2-body bounded separable potentials and confined to a bounded region Λ ? R^v. The technique used exploits the Feynman-Kac theorem in finite volume and the saddle-point method of Tindemans and Capel. It is shown that the limiting free energy density of such systems is equal to that of a system of noninteracting particles subject to a mean field which is equal to the averaged 2-body interaction. The equations for the mean field of n particles obeying Boltzmann, Fermi or Bose statistics represent self-consistent field problems and their forms comply with the well-known theorems on mean occupation numbers of single-particle eigenstates of ideal quantum gases at inverse temperature β.     

A unified grand canonical description of the nonextensive thermostatistics of the quantum gases: Fractal and fractional approach

In this paper, the particles of quantum gases, that is, bosons and fermions are regarded as g-ons which obey fractional exclusion statistics. With this point of departure the thermostatistical relations concerning the Bose and Fermi systems are unified under the g-on formulation where a fractal approach is adopted. The fractal inspired entropy, the partition function, distribution function, the thermodynamics potential and the total number of g-ons have been found for a grand canonical g-on system. It is shown that from the g-on formulation; by a suitable choice of the parameters of the nonextensivity q, the parameter of the fractional exclusion statistics g, nonextensive Tsallis as well as extensive (q=1) standard thermostatistical relations of the Bose and Fermi systems are recovered. Received 17 September 1999     

Quantum statistics and isospin invariance

The level density of an ideal Bose or Fermi gas is written in terms of usual phase-space integrals taking isospin conservation into accoutt. This cluster decomposition includes quantum statistics corrections between equal as well as unequal charge states of the considered particles. The isospin weights are given. These results are used to formulate a simple isospin-invariant statistical bootstrap model with Bose statistics. In the framework of this model the production of neutral pions in e⁺e^? and $\text{N}\text{N}$ annihilation is investigated.     

An algebraic geometry study of theb−c system with arbitrary twist fields and arbitrary statistics

We present an analysis of the generalb–c system (including the – system) on a compact Riemann surface of arbitrary genusg0 by postulating that its correlation functions should only have the singularities imposed by the operator product expansion (OPE) of the system. Studying a very (in fact optimally) general form of theb–c system, we prove rigorously that the standard practice of eliminating zero modes, and even the standard lagrangian, follow from the analyticity structure dictated by the OPE alone. We extend the analysis to consider the most general case of the presence of twist (e.g. spin) fields. We then determine all the possible correlation functions of theb–c system, with statistics unspecified, compatible with the OPE. On imposing Fermi and Bose statistics, we obtain the correlation functions of the fermionicb–c and – systems, respectively.     

Temperature correlators in the two-component one-dimensional gas

The quantum non-relativistic two-component Bose and Fermi gases with infinitely strong point-like coupling between particles in one space dimension are considered. Time- and temperature-dependent correlation functions are represented in the thermodynamic limit as Fredholm determinants of integrable linear integral operators.     

Correlation inequalities and contour estimates

We give a simple estimate on the probability of contours in classical ferromagnetic spin systems, based on Griffiths' or Ginibre's correlation inequalities. This includes quite general one- and two-component spin models. Some extension also holds for alln-component anisotropic or isotropic rotators.Supported by NSF grant No. MCS78-01885.On leave from: Institut de Physique Théorique, Université de Louvain, Belgium.Supported by NSF grant No. PHY78-15920.     

Path integral hybrid Monte Carlo calculation of the bosonic oscillators

In this paper, various correlation functions for a bosonic many-body system have been calculated using the path integral hybrid Monte Carlo method proposed by the authors [Chem. Phys. Lett. 308, 115 (1999)]. A system consisting of 32 independent particles in a harmonic well was chosen as a model problem. Calculations were carried out at two temperatures for the Boltzmann and Bose statistics. The large amplitude of the bosonic pair-correlation function around origin was found in comparison with the boltzmannoniac counterpart. This behavior can be interpreted by effective “attractive interaction” between particles arising from the Bose statistics.