The gas-liquid surface of the penetrable sphere model. II

1978 ◽  
Vol 358 (1694) ◽  
pp. 267-280 ◽  
Keyword(s):  
Surface Tension ◽  
Correlation Function ◽  
Liquid Surface ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Intermolecular Potential ◽  
Direct Correlation Function ◽  
Sphere Model ◽  
One Dimensional

The direct correlation function between two points in the gas-liquid surface of the penetrable sphere model is obtained in a mean-field approximation. This function is used to show explicitly that three apparently different ways of calculating the surface tension all lead to the same result. They are (1) from the virial of the intermolecular potential, (2) from the direct correlation function, and (3) from the energy density. The equality of (1) and (2) is shown analytically at all temperatures 0 < T < T c where T c is the critical temperature; the equality of (2) and (3) is shown analytically for T ≈ T c , and by numerical integration at lower temperatures. The equality of (2) and (3) is shown analytically at all temperatures for a one-dimensional potential.

Stochastic Properties of a One-Dimensional Discrete Ginzburg-Landau Field

1981 ◽  
Vol 36 (1) ◽  
pp. 1-9
Author(s):  
M. Jaspers ◽  
W. Schattke
Keyword(s):  
Mean Field ◽  
Planck Equation ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ginzburg Landau ◽  
Mean Values ◽  
One Dimensional ◽  
Slowing Down ◽  
Set Up ◽  
Stochastic Properties

Starting from a master equation for a discrete order parameter a dynamical model is set up via mean-field approximation in the Fokker-Planck equation. The time evolution of some mean values is calculated numerically, showing two transitions with characteristic slowing down of the relaxation time

COLLAPSE OF K-Rb FERMI-BOSE MIXTURES IN OPTICAL LATTICES

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5199-5203
Author(s):  
D. M. JEZEK ◽  
H. M. CATALDO
Keyword(s):  
Low Temperature ◽  
Optical Lattice ◽  
Optical Lattices ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
One Dimensional ◽  
Different Types ◽  
The Mean ◽  
Number Of Particles

We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quanta1 degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain values of the number of particles the mixture collapses. We investigate, in the mean-field approximation, the curve for which this phenomenon occurs, in the space of number of particles of both species. This is done for different types of optical lattices.

FRÖHLICH'S ONE-DIMENSIONAL SUPERCONDUCTOR WITH PARA-FERMI STATISTICS

1994 ◽  
Vol 08 (19) ◽  
pp. 1195-1200 ◽  
Author(s):  
V. L. SAFONOV ◽  
A. V. ROZHKOV
Keyword(s):  
Density Wave ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Wave State ◽  
One Dimensional ◽  
Fermi Statistics ◽  
The Mean ◽  
A Charge ◽  
Dimensional Crystal

The hypothesis that conduction electrons in a one-dimensional crystal obey para-Fermi statistics is discussed. Thermal properties of Fröhlich's model in the mean-field approximation are calculated within the framework of this hypothesis. It is shown that the temperature of the phase transition to a charge density wave state is greater in a system with parastatistics.

Modulated Phases on the FCC(110) Surfaces with Adsorbate-Induced Reconstructions

2003 ◽  
Vol 10 (02n03) ◽  
pp. 189-194
Author(s):  
Min Kang ◽  
Makoto Kaburagi
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Correlation Function ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Modulated Phases ◽  
The Mean ◽  
Beg Model

We theoretically investigate the fcc(110) surfaces with missing row reconstructions induced by adatoms using the Blume–Emmery–Griffith (BEG) model. In the model, Kij is introduced to denote interactions between surface atoms and Jij to describe interactions between dipoles. The investigation by the mean field approximation has predicted that there appear modulated phases on the surfaces as the next-nearest-neighbor (NNN) and the nearest-neighbor (NN) interactions along the [001] direction become competitive. In this study, Monte Carlo simulations are performed to confirm the prediction. A correlation function defined by concentration operators in wave vector q space is calculated. The results show that the concentration modulations appear. The temperature versus the ratio of the NNN interaction K2 to the NN interaction K1 phase diagram is obtained. The possible features of the modulated phases in experiments are discussed.

scholarly journals Impurities in a one-dimensional Bose gas: the flow equation approach

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fabian Brauneis ◽  
Hans-Werner Hammer ◽  
Mikhail Lemeshko ◽  
Artem Volosniev
Keyword(s):  
Mean Field ◽  
Interaction Strength ◽  
Field Approximation ◽  
Flow Equation ◽  
Mean Field Approximation ◽  
Bose Gases ◽  
One Dimensional ◽  
Flow Equations ◽  
Impurity Interaction ◽  
The Mean

A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities[1,2]. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.

scholarly journals NONLINEAR EFFECT ON THE TRANSMISSION OF LIGHT IN A CAVITY ARRAY

2011 ◽  
Vol 09 (02) ◽  
pp. 677-687
Author(s):  
H. D. LIU ◽  
W. WANG ◽  
X. X. YI
Keyword(s):  
Nonlinear Effect ◽  
Transmission Rate ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Level System ◽  
One Dimensional ◽  
Coherent Transport ◽  
The Mean ◽  
Cavity Array

Taking nonlinear effect into account, we study theoretically the transmission properties of photons in a one-dimensional coupled cavity, the cavity located at the center of the cavity array being coupled to a two-level system. By using the traditional scattering theory and the mean-field approximation, we calculate the transmission rate of photons along the cavities, and discuss the effect of nonlinearity and the cavity-atom coupling on the photon transport. The results show that the cavity-atom couplings affect the coherent transport of photons. The dynamics of such a system is also studied by numerical simulations, the effect of the atom-field detuning and nonlinearity on the dynamics is shown and discussed.

MAGNETIZATION CURVES OF QUASI-ONE-DIMENSIONAL HALDANE SYSTEMS

2002 ◽  
Vol 16 (20n22) ◽  
pp. 3339-3342
Author(s):  
A. KAWAGUCHI ◽  
A. KOGA ◽  
N. KAWAKAMI ◽  
K. OKUNISHI
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Group Method ◽  
Density Matrix Renormalization Group ◽  
One Dimensional ◽  
Density Matrix Renormalization ◽  
Antiferromagnetic Correlation ◽  
Bond Alternation ◽  
Theoretical Results

We study the magnetization process of a quasi-one-dimensional S=1 antiferromagnet with bond alternation by using the density matrix renormalization group method combined with interchain mean-field approximation. Particularly, we discuss how the interchain couplings affect the magnetization curve around a plateau structure in both of the Haldane phase and the dimer phase. It is shown that the antiferromagnetic correlation induced by the interchain couplings reduces the region of the plateau significantly, which will play an important role when the theoretical results are compared with actual measurements of the magnetization.

Librational motion in the α phase of solid nitrogen. I. Basic theory and results

1977 ◽  
Vol 55 (6) ◽  
pp. 554-572 ◽  
Author(s):  
Paul V. Dunmore
Keyword(s):  
Single Molecule ◽  
Translational Motion ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Intermolecular Potential ◽  
Α Phase ◽  
Solid Nitrogen ◽  
Librational Motion ◽  
The Mean

Librational motion in the α phase of solid nitrogen is studied on the basis of a model that ignores the translational motion of the molecular centres of mass. A general expansion in spherical harmonics is written down for an arbitrary two-body intermolecular potential, and methods are presented for obtaining the expansion coefficients for a particular potential model. The crystal Hamiltonian is written down and the mean-field approximation is briefly discussed. The eigenstates of the mean-field Hamiltonian are shown to correspond formally to the eigenstatesof the two-dimensional isotropic harmonic oscillator, and this correspondence is exploited to define boson creation and annihilation operators for excitations of a single molecule. The full crystal Hamiltonian is expressed in terms of these operators and the bilinear terms are diagonalized by an RPA treatment which is an extension of one given by Raich and Etters. Numerical results for the libron frequencies at the Γ and R points in the Brillouin zone are presented for the potential models proposed by Kohin and by Raich and Mills, the calculations having been performed with the intermolecular potential including terms as far as l = 6. The temperature dependence of the nuclear quadrupole resonance (NQR) frequency calculated with the Raich–Mills potential is shown to be in very good agreement with the measurements of Brookeman, McEnnan, and Scott. Finally the orientational probability density is presented as a function of temperature.

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