表紙、裏表紙、奥付

In this work liquid helium-4 is studied for the first time within the framework of the so-called static fluctuation approximation. This is based on the replacement of the square of the local-field operator with its mean value. A closed set of nonlinear integral equations is derived for weakly as well as for strongly interacting systems. This set is solved numerically by an iteration method for a realistic interhelium potential. The thermodynamic properties are then obtained for both the weakly interacting system, liquid 4He in Vycor glass, and the strongly interacting system, liquid 4He. It turns out, however, that the present quadratic-fluctuation approximation is valid in the latter, strongly interacting case only in the low-temperature limit (≤0.15 K). Our results are presented in a set of figures. The role of the interaction is emphasized and the functional dependence of key thermodynamic quantities on the temperature is derived for both weakly and strongly interacting 4He systems. © 2001 Plenum Publishing Corporation

The classical two-dimensional Ising model in the static fluctuation approximation

The classical two-dimensional Ising model is studied in the framework of the so-called static fluctuation approximation. This approximation hinges on the replacement of the square of the local-field operator with its mean value. The physical implication is that the true quantum-mechanical spectrum of this operator is replaced with a distribution; the moments of this distribution as well as the expectation value of the operator are then calculated self-consistently. With this single controllable approximation, the full thermodynamics and the pair correlation function of the classical two-dimensional Ising model are determined for the regular infinite lattice. The possible application to ultrathin ferroelectric films is discussed. © 1999 Elsevier Science Ltd. All rights reserved

Applications of Excel VBA for the Psychology (1) VBA Programming

Viewed as a prototype for strongly interacting many-body systems, the spin-1/2 n-dimensional Ising model (n = 1, 2, 3) is studied within the so-called static fluctuation approximation (SFA). The underlying physical picture is that the local field operator σz f with quadratic fluctuations is replaced with its mean value [(σz f)2 ≅

Thermodynamic properties of an interacting hard-sphere Bose gas in a trap using the static fluctuation approximation

A hard-sphere (HS) Bose gas in a trap is investigated at finite temperatures in the weakly-interacting regime and its thermodynamic properties are evaluated using the static fluctuation approximation (SFA). The energies are calculated with a second-quantized many-body Hamiltonian and a harmonic oscillator wave function. The specific heat capacity, internal energy, pressure, entropy and the Bose-Einstein (BE) occupation number of the system are determined as functions of temperature and for various values of interaction strength and number of particles. It is found that the number of particles plays a more profound role in the determination of the thermodynamic properties of the system than the HS diameter characterizing the interaction, that the critical temperature drops with the increase of the repulsion between the bosons, and that the fluctuations in the energy are much smaller than the energy itself in the weakly-interacting regime.Comment: 34 pages, 24 Figures. To appear in the International Journal of Modern Physics

Proton model of ferroelectrics with tunneling in the static fluctuation approximation

The transverse Ising model is considered in the static fluctuation approximation. This hinges on the replacement of the local field operator with its mean value; only the quadratic fluctuations of the local field are retained. The model is applied to ferroelectrics of the order-disorder type, such as monoaxial crystalline threeglycinsulfate. Analytic expressions are derived for the spontaneous polarization, the specific heat, the pair correlation function, and the static susceptibility of this ferroelectric. Its main characteristics are then determined numerically as functions of the temperature. In particular, its critical behavior is obtained automatically for a specific value of some "control" parameter. It is predicted that, with respect to this parameter, the specific heat exhibits a logarithmic behavior to the right of the critical point; this is interpreted as a consequence of the long range and axial anisotropy of the dipole-dipole interaction. In passing, the behavior of the lattice Green function for the anisotropic dipole-dipole potential near the critical point is thoroughly examined

One-, two-, and three-dimensional ising model in the static fluctuation approximation

Viewed as a prototype for strongly interacting many-body systems, the spin-1/2 n-dimensional Ising model (n = 1, 2, 3) is studied within the so-called static fluctuation approximation (SFA). The underlying physical picture is that the local field operator σz f with quadratic fluctuations is replaced with its mean value [(σz f)2 ≅

Asymmetric Bethe-Salpeter equation for pairing and condensation

The Martin-Schwinger hierarchy of correlations are reexamined and the three-particle correlations are investigated under various partial summations. Besides the known approximations of screened, ladder and maximally crossed diagrams the pair-pair correlations are considered. It is shown that the recently proposed asymmetric Bethe-Salpeter equation to avoid unphysical repeated collisions is derived as a result of the hierarchical dependencies of correlations. Exceeding the parquet approximation we show that an asymmetry appears in the selfconsistent propagators. This form is superior over the symmetric selfconsistent one since it provides the Nambu-Gorkov equations and gap equation for fermions and the Beliaev equations for bosons while from the symmetric form no gap equation results. The selfenergy diagrams which account for the subtraction of unphysical repeated collisions are derived from the pair-pair correlation in the three-particle Greenfunction. It is suggested to distinguish between two types of selfconsistency, the channel-dressed propagators and the completely dressed propagators, with the help of which the asymmetric expansion completes the Ward identity and is $\Phi$-derivable.Comment: 12 pages. 26 figure

Basics of Bose-Einstein Condensation

The review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate. Understanding these challenging problems is necessary for the correct description of Bose-condensed systems. The principal problems considered in the review are as follows: (i) What is the relation between Bose-Einstein condensation and global gauge symmetry breaking? (ii) How to resolve the Hohenberg-Martin dilemma of conserving versus gapless theories? (iii) How to describe Bose-condensed systems in strong spatially random potentials? (iv) Whether thermodynamically anomalous fluctuations in Bose systems are admissible? (v) How to create nonground-state condensates? Detailed answers to these questions are given in the review. As examples of nonequilibrium condensates, three cases are described: coherent modes, turbulent superfluids, and heterophase fluids.Comment: Review articl