共查询到20条相似文献,搜索用时 968 毫秒
1.
F. Büyükkiliç D. Demirhan 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,14(4):705-711
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 相似文献
2.
The quantum discrete kinetic equations are solved to study the propagation of plane waves in a system of composite particles
with hard-sphere interactions and the filling factor (ν) being 1/2. We compare the dispersion relations thus obtained by the
relevant Pauli-blocking parameter B which describes the different-statistics particles for the quantum analog of the discrete Boltzmann system when B is positive (Bose gases), zero (Boltzmann gases), and negative (Fermi Gases). We found, as the effective magnetic field being
zero (ν = 1/2 using the composite fermion formulation), the electric field effect will induce anomalous dispersion relations. 相似文献
3.
J. Maćkowiak 《Physica A》1983,117(1):47-75
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 ? Rv. 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. 相似文献
4.
M. Holzmann P. Grüter F. Laloë 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(4):739-760
We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures
above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle
density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an
ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson
approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second
step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated.
This introduces new physical effects, such as a change of the velocity profile just above the transition: the proportion of
atoms with low velocities is higher than in an ideal gas. A consequence of this distortion is an increase of the critical
temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations
for hard spheres.
Received 13 November 1998 相似文献
5.
A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebrau(n) and its quantum analogU
q(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for
the subalgebrau(n−1) (U
q(u(n−1))). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form of the projection
operator ofu(n) andU
q(u(n)). It is shown that theU
q(u(n)) CGCs can be presented in terms of theU
q(u)(n−1)) q−9j-symbols.
Presented at the 9th International Colloquium: “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.
Supported by Russian Foundation for Fundamental Research, grant 99-01-01163.
Supported in part by the U.S. National Science Foundation under Grant PHY-9970769 and Cooperative Agreement EPS-9720652 that
includes matching from the Louisiana Board of Regents Support Fund. 相似文献
6.
Abdullah Algin 《Czechoslovak Journal of Physics》2005,55(11):1309-1313
The high and low temperature thermodynamical properties of the two-parameter deformed quantum group Bose and Fermi gases with
SU
p/q
(2) symmetry are studied. Starting with a SU
p/q
(2)-invariant bosonic as well as fermionic Hamiltonian, several thermodynamical functions of the system such as the average
number of particles, internal energy and equation of state are derived. The effects of two real independent deformation parameters
p and q on the properties of the systems are discussed. Particular emphasis is given to a discussion of the Bose-Einstein condensation
phenomenon for the two-parameter deformed quantum group Bose gas. The results are also compared with earlier undeformed and
one-parameter deformed versions of Bose and Fermi gas models.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
7.
R. F. Snider 《Journal of statistical physics》1990,61(1-2):443-465
Binary correlations are a recognized part of the pair density operator, but the influence of binary correlations on the singlet density operator is usually not emphasized. Here free motion and binary correlations are taken as independent building blocks for the structure of the nonequilibrium singlet and pair density operators. Binary correlations are assumed to arise from the collision of twofree particles. Together with the first BBGKY equation and a retention of all terms that are second order in gas density, a generalization of the Boltzmann equation is obtained. This is an equation for thefree particle density operator rather than for the (full) singlet density operator. The form for the pressure tensor calculated from this equation reduces at equilibrium to give the correct (Beth-Uhlenbeck) second virial coefficient, in contrast to a previous quantum Boltzmann equation, which gave only part of the quantum second virial coefficient. Generalizations to include higher-order correlations and collision types are indicated. 相似文献
8.
S. De Toro Arias X. Waintal J.-L. Pichard 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(1):149-158
The interplay between the quantum interferences responsible for one particle localization over a length L1, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over a length L
2
> L
1
, is illustrated by a study of the motion of two particles put close to each other at the initial time. Localization is reached
in two steps. First, before the time t1 necessary to propagate over L1, the interaction slows down the ballistic motion. On the contrary, after t1 the interaction favors a very slow delocalization, characterized by a spreading of the center of mass, until L2 is reached. This slow motion is related to the absence of quantum chaos in this one dimensional model, the interaction being
only able to induce weaker chaos with critical spectral statistics. Under appropriate initial conditions, the motion remains
invariant under the duality transformation mapping the behavior at small U onto the behavior at large U.
Received 24 August 1998 相似文献
9.
The mean-field density matrix of a changed plasma of quantum particles with Maxwell-Boltzmann statistics in a confining external potential is obtained as a limit of theN-body canonical states for suitably scaled charges. Also, it is shown that the density profile of the quantum mean-field theory converges to the solution of the classical mean-field equation when the Planck's constant tends to zero. 相似文献
10.
S. B. Isakov 《International Journal of Theoretical Physics》1993,32(5):737-767
We propose a generalization of quantum statistics in the framework of statistical mechanics. We derive a general formula which involves a wide class of equilibrium quantum statistical distributions, including the Bose and Fermi distributions. We suggest a way of evaluating the statistical distributions with the help of many-particle partition functions and apply it to studying some interesting distributions. A question on the statistical distribution for anyons is discussed, and the term following the Boltzmann one in the expansion of this distribution in powers of the Boltzmann factor, exp[(-i)], is estimated. An ansatz is proposed for evaluating the statistical distribution forquons (particles whose creation and annihilation operators satisfy theq-commutation relations). We also treat non-equilibrium statistical mechanics, obtaining unified expressions for the entropy of a nonequilibrium quantum gas and for a collision integral which are valid for a wide class of statistics. 相似文献
11.
Jürg?Fr?hlich Antti?Knowles Simon?Schwarz 《Communications in Mathematical Physics》2009,288(3):1023-1059
In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method
for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes
large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable
for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the
Heisenberg- picture dynamics of “observables”, thus avoiding the use of coherent states. Our formulation shows that the mean-field
limit is a “semi-classical” limit. 相似文献
12.
We study the effect of quantum fluctuations in an Ising
spin system on a scale-free network of
degree exponent γ>5 using
a quantum Monte Carlo simulation technique. In our model,
one can adjust the magnitude of the magnetic field perpendicular
to the Ising spin direction and can therefore control the
strength of quantum fluctuations for
each spin. Our numerical analysis
shows that quantum fluctuations reduce the transition
temperature Tc of the ferromagnetic-paramagnetic phase
transition. However, the phase transition belongs to
the same mean-field type universality class both with
and without the quantum fluctuations.
We also study the role of hubs by turning on the
quantum fluctuations exclusively
at the nodes with the most links. When only a small number of hub
spins fluctuate quantum mechanically, Tc
decreases with increasing magnetic field
until it saturates at high fields. This effect
becomes stronger as the number of hub spins increases.
In contrast, quantum fluctuations at the same number of
“non-hub” spins do not affect Tc. This implies
that the hubs play an important role in
maintaining order in the whole network. 相似文献
13.
Dirk-André Deckert Jürg Fröhlich Peter Pickl Alessandro Pizzo 《Communications in Mathematical Physics》2014,328(2):597-624
We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density ${\to \infty}$ ). Our estimates allow us to interchange the thermodynamic with the mean-field limit. 相似文献
14.
We consider a hierarchy of Hamilton operators Ĥ
N
in finite dimensional Hilbert spaces . We show that the eigenstates of Ĥ
N
are fully entangled for N even. We also calculate the unitary operator U
N
(t) = exp(—Ĥ
N
t/ħ) for the time evolution and show that unentangled states can be transformed into entangled states using this operator. We
also investigate energy level crossing for this hierarchy of Hamilton operators.
相似文献
15.
V. Korepin N. Slavnov 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):555-557
We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one-dimensional
Bose gas and XXZ Heisenberg quantum spin chain.
Received: 4 December 1997 / Accepted: 17 March 1998 相似文献
16.
The expansion of the modified two-particle Ursell functionU(r) of a hardsphere quantal fluid is obtained in terms of a series of derivatives of δ-function. This expansion has been used
to expand the second virial co-efficientB
2 of the fluid. The expansion is correct up to the fourth power in thermal wavelength and the terms of the order of λ8 and λ4 in the first expa nsion are new. 相似文献
17.
Q. H. Liu 《International Journal of Theoretical Physics》2006,45(11):2137-2142
When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2m)∑ p
i
2 with hermitian form of Cartesian momentum p
i
(i = 1,2,3), and the operator ordering should be taken into account in the kinetic energy which turns out to be 1/(2m)∑ (1/f
i
)p
i
f
i
p
i
where the functions f
i
are dummy factors in classical mechanics and nontrivial in quantum mechanics. The existence of non-trivial f
i
shows the universality of this constraint induced operator ordering in quantum kinetic energy operator for the constraint systems. 相似文献
18.
19.
Jun Song Hong-Yi Fan Ye-Jun Xu Jun Zhou 《International Journal of Theoretical Physics》2011,50(6):1946-1952
By employing the technique of an integral within an ordered product (IWOP) of operators we recast the complex wavelet transform
to a matrix element of the two-mode squeezing-displacing operator U
2(μ,σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed, i.e., we propose that 〈ψ|U
2(μ,σ)|f〉 can be considered as a new kind of spectra for analyzing |f〉, this may have some potential applications in quantum information and calculation. As an example, we numerically calculate
wavelet-transform spectrum for the Bell states, which may play a role of distinguishing them one from another. 相似文献
20.
Naihuan Jing Seok-Jin Kang Yoshitaka Koyama 《Communications in Mathematical Physics》1995,174(2):367-392
We give an explicit formula for the vertex operators related to the level 1 representations of the quantum affine Lie algebrasU
q
(D
n
(1)
) in terms of bosons. As an application, we derive an integral formula for the correlation functions of the vertex models withU
q
(D
n
(1)
)-symmetry.NJ was supported in part by NSA grant MDA904-93-H-3005 and University of Kansas General Research allocation.SJK was supported in part by Basic Science Research Institute Program, Ministry of Education of Korea, BSRI-94-1414 and GARC-KOSEF at Seoul National University, Korea. 相似文献