Searcharxiv⌕ Search

arXiv subjects

Mi Xie

Publications and source records attributed to Mi Xie.

33 records · Page 2Linked to original sources
arXiv2008

The relation between the counting function N(lambda) and the heat kernel K(t)

For a given spectrum {lambda_{n}} of the Laplace operator on a Riemannian manifold, in this paper, we present a relation between the counting function N(lambda), the number of eigenvalues (with multiplicity) smaller than λ, and the heat kernel K(t), defined by K(t)=\sum_{n}e^{-lambda_{n}t}. Moreover, we also give an asymptotic formula for N(λ) and discuss when lambda \to \infty in what cases N(lambda)=K(1/lambda).

math.SP↗
arXiv2007

Upper limit on the transition temperature for non-ideal Bose gases

In this paper we show that for a non-ideal Bose gas there exists an upper limit on the transition temperature above which Bose-Einstein condensation cannot occur regardless of the pressure applied. Such upper limits for some realistic Bose gases are estimated. This result implies that there may also exist an upper limit on the transition temperature of superconductors.

cond-mat.stat-mech↗
arXiv2007

Gentile statistics with a large maximum occupation number

In Gentile statistics the maximum occupation number can take on unrestricted integers: $1 1 the Bose-Einstein case is not recovered from Gentile statistics as n goes to % N . Attention is also concentrated on the contribution of the ground state which was ignored in related literature. The thermodynamic behavior of a $% ν$-dimensional Gentile ideal gas of particle of dispersion $E=\frac{p^{s}%}{2m}$, where $ν$ and s are arbitrary, is analyzed in detail. Moreover, we provide an alternative derivation of the partition function for Gentile statistics.

cond-mat.stat-mech↗
arXiv2007

Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum (su(2)) algebra

In this paper, we first discuss the general properties of an intermediate-statistics quantum bracket, $[ u,v]_{n}=uv-e^{i2π/(n+1)}vu$, which corresponds to intermediate statistics in which the maximum occupation number of one quantum state is an arbitrary integer, $n$. A further study of the operator realization of intermediate statistics is given. We construct the intermediate-statistics coherent state. An intermediate-statistics oscillator is constructed, which returns to bosonic and fermionic oscillators respectively when $n\to \infty $ and $n=1$. The energy spectrum of such an intermediate-statistics oscillator is calculated. Finally, we discuss the intermediate-statistics representation of angular momentum ($su(2)$) algebra. Moreover, a further study of the operator realization of intermediate statistics is given in the Appendix.

quant-ph↗
arXiv2006

The difference of boundary effects between Bose and Fermi systems

In this paper, we show that there exists an essential difference of boundary effects between Bose and Fermi systems both for Dirichlet and Neumann boundary conditions: at low temperatures and high densities the influence of the boundary on the Bose system depends on the temperature but is independent of the density, but for the Fermi case the influence of the boundary is independent of the temperature but depends on the density, after omitting the negligible high-order corrections. We also show that at high temperatures and low densities the difference of the influence of the boundary between Bose and Fermi systems appears in the next-to-leading order boundary contribution, and the leading boundary contribution is independent of the density. Moreover, for calculating the boundary effects at high temperatures and low densities, since the existence of the boundary modification causes the standard virial expansion to be invalid, we introduce a modified virial expansion.

cond-mat.stat-mech↗
arXiv2006

The equation of state for two-dimensional hard-sphere gases: Hard-sphere gases as ideal gases with multi-core boundaries

The equation of state for a two-dimensional hard-sphere gas is difficult to calculate by usual methods. In this paper we develop an approach for calculating the equation of state of hard-sphere gases, both for two- and three-dimensional cases. By regarding a hard-sphere gas as an ideal gas confined in a container with a multi-core (excluded sphere) boundary, we treat the hard-sphere interaction in an interacting gas as the boundary effect on an ideal quantum gas; this enables us to treat an interacting gas as an ideal one. We calculate the equation of state for a three-dimensional hard-sphere gas with spin $j$, and compare it with the results obtained by other methods. By this approach the equation of state for a two-dimensional hard-sphere gas can be calculated directly.

cond-mat.stat-mech↗
arXiv2004

A representation of angular momentum (SU(2)) algebra

This paper seeks to construct a representation of the algebra of angular momentum (SU(2) algebra) in terms of the operator relations corresponding to Gentile statistics in which one quantum state can be occupied by $n$ particles. First, we present an operator realization of Gentile statistics. Then, we propose a representation of angular momenta. The result shows that there exist certain underlying connections between the operator realization of Gentile statistics and the angular momentum (SU(2)) algebra.

cond-mat.stat-mech↗
arXiv2004

Geometry effects in confined space

In this paper we calculate some exact solutions of the grand partition functions for quantum gases in confined space, such as ideal gases in two- and three-dimensional boxes, in tubes, in annular containers, on the lateral surface of cylinders, and photon gases in three-dimensional boxes. Based on these exact solutions, which, of course, contain the complete information about the system, we discuss the geometry effect which is neglected in the calculation with the thermodynamic limit $V\to \infty $, and analyze the validity of the quantum statistical method which can be used to calculate the geometry effect on ideal quantum gases confined in two-dimensional irregular containers. We also calculate the grand partition function for phonon gases in confined space. Finally, we discuss the geometry effects in realistic systems.

cond-mat.stat-mech↗
arXiv2003

Quantum statistics of ideal gases in confined space

In this paper, the effects of boundary and connectivity on ideal gases in two-dimensional confined space and three-dimensional tubes are discussed in detail based on the analytical result. The implication of such effects on the mesoscopic system is also revealed.

quant-ph↗
arXiv2002

Comment on "Bose-Einstein condensation in low-dimensional traps"

We show that the critical temperature of a one-dimensional gas confined by a power-law potential should be lower than that in the paper of Vanderlei Bagnato and Daniel Kleppner. Moreover, a sketch of the critical temperature is given in some more details.

quant-ph↗
arXiv2002

Electromagnetic Transition in Waveguide with Application to Lasers

The electromagnetic transition of two-level atomic systems in a waveguide is calculated. Compared with the result in free space, the spontaneous emission rate decrease because the phase space is smaller, and meanwhile, some resonance appears in some cases. Moreover, the influence of non-uniform electromagnetic field in a waveguide on absorption and stimulated emission is considered. Applying the results to lasers, a method to enhance the laser power is proposed.

quant-ph↗
arXiv1998

Overtone spectra and intensities of tetrahedral molecules in boson-realization models

The stretching and bending vibrational spectrum and the intensities of infrared transitions in a tetrahedral molecule are studied in two boson-realization models, where the interactions between stretching and bending vibrations are described by a quadratic cross term and by Fermi resonance terms, called harmonically coupled and Fermi resonance boson-realization model, respectively. The later is a development of our recent model. As an example, the two models are applied to the overtone spectrum and the intensities of silicon tetrafluorde. Those models provide fits to the published experimental vibrational eigenvalues with standard deviations 1.956 cm$^{-1}$ and 0.908 cm$^{-1}$, respectively. The intensities of infrared transitions of its complete vibrations are calculated in the two models, and results show a good agreement with the observed data.

physics.chem-ph↗
arXiv1996

Boson-realization model for the vibrational spectra of tetrahedral molecules

An algebraic model of Boson-realization is proposed to study the vibrational spectra of a tetrahedral molecule, where ten sets of boson creation and annihilation operators are used to construct the Hamiltonian with $T_{d}$ symmetry. There are two schemes in our model. The first scheme provides an eight-parameter fit to the published experimental vibrational eigenvalues of methane with a root-mean-square deviation 11.61 $cm^{-1}$. The second scheme, where the bending oscillators are assumed to be harmonic and the interactions between the bending vibrations are neglected, provided a five-parameter fit with a root-mean-square deviation 12.42 $cm^{-1}$

chem-ph↗
arXiv1995

$L^{\pm}$ Operators and Quantum Enveloping Algebras

The relations between $L^{\pm}$ operators and the generators in the quantum enveloping algebras are studied. The $L^{\pm}$ operators for $U_{q}A_{N}$ and $U_{q}G_{2}$ algebras are explicitly expressed by the generators as examples.

q-alg↗