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1.
2.
We study global existence and long time behaviour for the inhomogeneous nonlinear BGK model for the Boltzmann equation with
an external confining potential. For an initial datum f
0≥0 with bounded mass, entropy and total energy we prove existence and strong convergence in L
1 to a Maxwellian equilibrium state, by compactness arguments and multipliers techniques. Of particular interest is the case
with an isotropic harmonic potential, in which Boltzmann himself found infinitely many time-periodic Maxwellian steady states.
This behaviour is shared with the Boltzmann equation and other kinetic models. For all these systems we study the multistability
of the time-periodic Maxwellians and provide necessary conditions on f
0 to identify the equilibrium state, both in L
1 and in Lyapunov sense. Under further assumptions on f, these conditions become also sufficient for the identification of the equilibrium in L
1. 相似文献
3.
We show how hot QCD equations of states can be adapted to make definite predictions for quarkgluon plasma at RHIC.We consider
equations of state up to O(g5) and O[g6(ln(1/g)+δ)]. Our method involves the extraction of equilibrium distribution functions for gluons and quarks from these equations of
state by capturing the interaction effects entirely in the effective chemical potentials. We further utilize these distribution
functions to study the screening length in hot QCD and dissociation phenomenon of heavy quarkonia states by combining this
understanding with the semi-classical transport theory. 相似文献
4.
Based on suitable choice of states, this paper studies the stability
of the equilibrium state of the EZ model by regarding the evolution of
the EZ model as a Markov chain and by showing that the Markov chain is
ergodic. The Markov analysis is applied to the EZ model with small
number of agents, the exact equilibrium state for N = 5 and
numerical results for N=18 are obtained. 相似文献
5.
Given a thermodynamic process which carries a system from one equilibrium state to another, we construct a quantity whose average, over an ensemble of microscopic realizations of the process, depends only on these end states, even if at intermediate times the system is out of equilibrium. This result (1) can be used to express the entropy difference between two equilibrium states in terms of an irreversible process connecting them, (2) leads to two statistical statements of the Clausius–Duhem inequality, and (3) can be generalized to situations in which the system begins and/or ends in nonequilibrium states. 相似文献
6.
A variational approach for the ab initio handling of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules is presented. The model Hamiltonian involves four nuclear degrees of freedom which correlate for a linear nuclear arrangement with two doubly degenerate bending modes. The bond lengths are assumed to be kept fixed at their equilibrium values and the effect of end-over-end rotations is neglected. The kinetic energy operator and the general form of the potential surfaces employed allow in principle for a treatment of large amplitude bending vibrations. However, because of restrictions implied, such as neglect of coupling between bending and stretching vibrations and interactions with other electronic states, the approach is aimed primarily at molecules bending with relatively small amplitudes around their linear equilibrium geometries. Two algorithms are developed, one for symmetric acetylene-like (A-B-B-A) molecules, the other for asymmetric (A-B-C-D) species. The approach is applied to calculate the vibronic spectrum of the lowest lying excited state, 1Δg, of B2H2, employing ab initio computed potential energy surfaces. 相似文献
7.
This paper considers the problem of return to equilibrium for perturbations of the dynamics of the one-sided and two-sidedXY-models with external field. We find that, in the presence of multiple ground states, return to equilibrium fails for certain perturbations while still holding wen there is a unique ground state. 相似文献
8.
A. S. Rudyi 《Technical Physics》1998,43(3):342-344
Two-phase states of equilibrium of a thin superconducting film carrying a current under conditions of convective heat exchange
at the free surface of the film are studied. It is shown that for a classical superconductor the two-phase state of the film
remains a single-front state over a wide range of parameters of the system. For high-T
c superconductors there exists a maximum value of the Steckl number above which weakly nonequilibrium stationary states can
only be multifront states. The solutions of the boundary-value problem modeling a two-front state of equilibrium are investigated,
and the conditions under which they obtain are examined.
Zh. Tekh. Fiz. 68, 84–87 (March 1998) 相似文献
9.
We study the branches of equilibrium states of rigid polymer rods with the Onsager excluded volume potential in two-dimensional space. Since the probability density and the potential are related by the Boltzmann relation at equilibrium, we represent an equilibrium state using the Fourier coefficients of the Onsager potential. We derive a non-linear system for the Fourier coefficients of the equilibrium state. We describe a procedure for solving the non-linear system. The procedure yields multiple branches of ordered states. This suggests that the phase diagram of rigid polymer rods with the Onsager potential has a more complex structure than that with the Maier-Saupe potential. A study of free energy indicates that the first branch of ordered states is stable while the subsequent branches are unstable. However, the instability of the subsequent branches does not mean they are not interesting. Each of these unstable branches, under certain external potential, can be made metastable, and thus may be observed. 相似文献
10.
Tom Kempton 《Journal of statistical physics》2011,143(4):795-806
We prove that, given a uniformly locally constant potential f on a countable state Markov shift and suitable conditions which guarantee the existence of the equilibrium states μ
tf
for all t, the measures μ
tf
converge in the weak star topology as t tends to infinity. 相似文献
11.
采用从头计算的多参考组态相互作用方法和含扩散基的3个基组aug-cc-PVXZ (X=D,T,Q) 计算了SO和ClO分子及其分子离子的势能曲线,确定了平衡几何结构、离解能,并采用Feller拟合递推方法得到了基函数为无穷大计算水平值. 确定了SO-,ClO+,ClO-分子离子的基态. 通过Murrell-Sorbie势能函数和最小二乘法拟合得到了解析势能函数. 基于所得的势能函数,通过解核运动的薛定谔方程得到振
关键词:
多参考组态相互作用
势能曲线
解析势能函数
光谱常数 相似文献
12.
The dynamic behavior of a spin-1 Ising system with arbitrary bilinear and biquadratic pair interactions is studied by using
the path probability method, and approaches of the system toward the stable or metastable equilibrium states according to
the ratio of interaction parameters and rate constants are presented. In particular, we investigate the relaxation of the
order parameters for temperatures less than, equal to, and greater than the second-order and first-order phase transitions.
From this investigation, the “flatness” property of metastable states is seen explicitly. We also show how a system freezes
in a metastable state as well as how it escapes from one metastable state to the other. 相似文献
13.
H. HOGREVE 《Molecular physics》2013,111(4):249-254
The low lying quartet spectrum of the molecular helium cation is investigated by configuration interaction calculations. Using large Gaussian basis sets, potential energy curves for n 4Σ+ u,g and n 4Πu,g are computed for the states n = 1,…, 5. Several of these states lead to equilibrium configurations having rather extended bond lengths and some of them also a relatively large dissociation energy. The spectroscopic properties of these equilibrium configurations are studied. Quartet He+ 2 is most strongly bound in its lowest state 1 4Σu with R e = 3.424 Å and D e = 1.348 eV. 相似文献
14.
The behaviour ofS-matrix for potentials generating bound states in continuum in the neighbourhood of the positive bound state energies is studied.
It is shown that unlike the case of usual negative energy bound states, theS-matrix does not have a pole at the positive bound state energy but becomes unity at the energy corresponding to bound states
in continuum. Calculations ofS-waveS-matrix for a local potential constructed by Stillinger and Herrick and a separable nonlocal potential constructed by the
present authors verify these results. Our results indicate that the bound states embedded in continuum constructedvia the von Neumann and Wigner procedure cannot be interpreted as resonances with zero width. 相似文献
15.
In this paper we develop the ergodic theory for a horseshoe map f which is uniformly hyperbolic, except at one parabolic fixed point ω and possibly also on W
s
(ω). We call f a parabolic horseshoe map. In order to analyze dynamical and geometric properties of such horseshoes, by making use of induced
maps, we establish, in the context of σ-finite measures, an appropriate version of the variational principle for continuous potentials with mild distortion defined
on subshifts of finite type. Staying in this setting, we propose a concept of σ-finite equilibrium states (each classical probability equilibrium state is a σ-finite equilibrium state). We then study the unstable pressure function , the corresponding finite and σ-finite equilibrium states and their associated conditional measures. The main idea is to relate the pressure function to
the pressure of an embedded parabolic iterated function system and to apply the developed theory of the symbolic σ-finite thermodynamic formalism. We prove, in particular, an appropriate form of the Bowen-Ruelle-Manning-McCluskey formula,
the existence of exactly two σ-finite ergodic conservative equilibrium states for the potential –t
u
log |Df|E
u
| (where t
u
denotes the unstable dimension), one of which is the Dirac δ-measure supported at the parabolic fixed point and the other being non-atomic. We also show that the conditional measures
of this non-atomic equilibrium state on unstable manifolds, are equivalent to (finite and positive) packing measures, whereas
the Hausdorff measures vanish. As an application of our results we obtain a classification for the existence of a generalized
physical measure, as well as a criteria implying the non-existence of an ergodic measure of maximal dimension.
The research of the first author was supported in part by the NSF Grant DMS 0400481.
The research of the second author was supported in part by the National Science Foundation under Grant No. EPS-0236913 and
matching support from the State of Kansas through Kansas Technology Enterprise Corporation. 相似文献
16.
M. A.?de?Ponte A.?Cacheffo C. J.?Villas-B?as S. S.?Mizrahi M. H.Y.?Moussa 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2010,59(3):487-496
In this work, we identify the set of time-dependent pure states building the
statistical mixture to which a system, initially in a pure state, is driven by
the reservoir. This set of time-dependent pure states, composing what we term
a pure basis, are those that diagonalize the reduced density operator
of the system. Next, we show that the evolution of the pure-basis
states reveals an interesting phenomenon as the system, after decoherence,
evolves toward the equilibrium: the spontaneous recoherence of quantum
states. Around our defined recoherence time, the statistical mixture
associated with a special kind of initial states termed even-symmetric,
spontaneously undergoes a recoherence process, by which the initial state of
the system emerges from the mixture except for its reduced excitation drained
into the reservoir. This phenomenon reveals that the reservoir only shuffle
the original information carried out by the initial state of the system
instead of erasing it. Moreover, as the spontaneously recohered state occurs
only for asymptotic time, we also present a protocol to extract it from the
mixture through specific projective measurements. The password to retrieve the
original information stems is the knowledge of both the initial state itself
and the associated pure basis. A definition of the decoherence time of
an N-state superposition is also presented. 相似文献
17.
Recently experiments have been reported about phonon sidebands in doped crystals, which may originate from coherent phonon states. The corresponding modes are either confined phonon modes in nanocrystals or localized phonon modes in bulk materials, both showing small damping due to phonon-phonon interaction. We present a theory of the lineshape of vibronic sideband spectra due to coherent phonon states using the conventional model of linear electron-phonon coupling and displaced equilibrium positions of the oscillators in the initial and final electronic states. Unlike in the conventional theory, the initial state of the oscillator is taken as a coherent phonon state and not as a thermalized one. Under these conditions we got an exact analytical solution for the lineshape of the vibronic sideband. The lineshape is determined by two parameters, the Huang-Rhys parameter S and the coherence parameter α of the phonon state. For α = 0 the lineshape converts into the standard Pekarian form for T = 0. 相似文献
18.
Marco Merkli 《Communications in Mathematical Physics》2001,223(2):327-362
The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential
tool in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive temperatures, i.e. to
non-equilibrium quantum statistical mechanics. We use the positive commutator technique to give an alternative proof of a
fundamental property of a certain class of large quantum systems, called Return to Equilibrium. This property says that equilibrium states are (asymptotically) stable: if a system is slightly perturbed from its equilibrium
state, then it converges back to that equilibrium state as time goes to infinity.
Received: 27 December 2000 / Accepted: 21 June 2001 相似文献
19.
《Physica B: Condensed Matter》2000,275(1-3):69-74
It is suggested that solutions to micromagnetic problems could be obtained more quickly by enumerating equilibrium states. An outline of how to enumerate states is given. The details of these states still need to be calculated micromagnetically. However, vortices interact with one another via force laws. To obtain a good initial state, we examine how vortices interact with each another. 相似文献
20.
Photophysical characterization of some pyrazino[2,3-c][1,2,6]thiadiazine 2,2-dioxides derivatives in DMSO and acetonitrile has been carried out. Acid-base processes have been found to occur in the ground and excited states. In DMSO and acetonitrile equilibrium between the neutral and deprotonated molecules is established in the ground state. In acetonitrile, a second equilibrium between the neutral and protonated form is also present at a lower pH, and can be treated independently of the first one. Absorption, emission, and excitation spectra of the species involved have been measured; data analysis allows us to calculate pK
aand quantum efficiencies. The change of the decay lifetimes with pH, along with steady state fluorescence measurements show the existence of communication between the excited states and enable us to estimate the excited state kinetic rate constants.A discussion about their possible use as laser dyes based on the energy threshold condition is also given. 相似文献