Three-dimensional anisotropic harmonic oscillator in a magnetic field

The problem of the energy levels of a three-dimensional anisotropic harmonic oscillator in a uniform magnetic field with an arbitrary strength and orientation is exactly solved. It is shown that, in the magnetic field, the levels continue to be equidistant: the energy spectrum is a superposition of three groups of levels separated by the same spacing dependent on the field strength. The results obtained can be used in modeling the magneto-optical properties of diverse quantum-mechanical systems.     

Quasi-two-dimensional superfluid fermionic gases

We study a quasi-two-dimensional superfluid Fermi gas where the confinement in the third direction is due to a strong harmonic trapping. We investigate the behavior of such a system when the chemical potential is varied and find strong modifications of the superfluid properties due to the discrete harmonic oscillator states. We show that such quasi-two-dimensional behavior can be created and observed with current experimental capabilities.     

Analytical relationship for the cranking inertia

The wave functions of a spheroidal harmonic oscillator without spin-orbit interaction are expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained as a function of the main quantum numbers and potential derivative. They may be used to test complex computer codes developed in a realistic approach of the fission dynamics. Results given for the ²⁴⁰Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed.     

The finite depth of the nuclear potential well in the exciton model of preequilibrium decay

The density of states and the transition rates are derived for the equidistant spacing model with the limitation on the hole maximum energy. The previous results of Blann are generalized. The influence of the finite depth of nuclear potential well on the pre-equilibrium decay within the exciton model is investigated. The calculations of proton and deuteron spectra from the reaction¹²⁰Sn+p are presented.     

A relativistic quark-diquark model for the nucleon

We developed a constituent quark-diquark model for the nucleon and its resonances using a harmonic oscillator potential for the interaction. The effects due to relativistic kinetic energy correction are studied. Finally, charge form factor of the model is calculated and compared with experimental data.      

Relaxation and dephasing in a many-fermion generalization of the Caldeira-Leggett model

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a fluctuating force generated by a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate Green's functions and discuss relaxation and dephasing of a single extra particle added above the Fermi sea. We also extend our analysis to a more generic coupling between system and bath that results in complete thermalization of the system.     

Non-universal thermodynamics of a strongly interacting inhomogeneous Fermi gas using the quantum virial expansion

Within a quantum virial expansion, we investigate theoretically the violation of universal thermodynamics for a strongly interacting unitary Fermi gas trapped in a harmonic potential. The violation is caused by the existence and anisotropy of the trapping potential and a finite-range of the two-body interaction. We calculate the second virial coefficient by solving a two-fermion problem in 3D uniform harmonic traps, as well as in anisotropic traps. In the unitarity limit, the universal value of the trapped second virial coefficient is 1/4. We discuss in detail the non-universal correction to the second virial coefficient and to the equation of state.     

弱相互作用费米气体的热力学性质

根据赝势法导出无外势时弱相互作用费米气体的化学势、内能和定容热容的解析表达式.在此基础上，采用局域密度近似研究谐振势中弱相互作用费米气体的热力学性质，探讨粒子间相互作用对系统性质的影响. 关键词： 费米气体 相互作用 赝势法 局域密度近似 热力学性质     

Quantum algorithm for distributed clock synchronization

We study theoretically the coherent nonlinear optical response of doped quantum wells with several subbands. When the Fermi energy approaches the exciton level of an upper subband, the absorption spectrum acquires a characteristic double-peak shape originating from the interference between the Fermi-edge singularity and the exciton resonance. We demonstrate that, for off-resonant pump excitation, the pump-probe spectrum undergoes a striking transformation, with a time-dependent exchange of oscillator strength between the Fermi-edge singularity and exciton peaks. This effect originates from the many-body electron-hole correlations which determine the dynamical response of the Fermi sea.     

Harmonically trapped jellium

We discuss the model of a D-dimensional confined electron gas in which the particles are trapped by a harmonic potential. In particular, we study the non-interacting kinetic and exchange energies of finite-size inhomogeneous systems, and compare the resulting Thomas–Fermi and Dirac coefficients with various uniform electron gas paradigms. We show that, in the thermodynamic limit, the properties of this model are identical to those of the D-dimensional Fermi gas.     

Thermal distribution functions and finite-size effects for lattice fermions

We perform, analytically, the sum over the finite set of Matsubara frequencies that arises in the lattice thermodynamics of a free Fermi gas. The resultant expressions provide an easy demonstration that the correction continuum expressions are obtained in the limit of small lattice spacing.     

Splitting between quadrupole modes of dilute quantum gas in a two-dimensional anisotropic trap

We consider quadrupole excitations of quasi-two-dimensional interacting quantum gas in an anisotropic harmonic oscillator potential at zero temperature. Using the time-dependent variational approach, we calculate a few low-lying collective excitation frequencies of a two-dimensional anisotropic Bose gas. Within the energy weighted sum-rule approach, we derive a general dispersion relation of two quadrupole excitations of a two-dimensional deformed trapped quantum gas. This dispersion relation is valid for both statistics. We show that the quadrupole excitation frequencies obtained from both methods are exactly the same. Using this general dispersion relation, we also calculate the quadrupole frequencies of a two-dimensional unpolarized Fermi gas in an anisotropic trap. For both cases, we obtain analytic expressions for the quadrupole frequencies and the splitting between them for arbitrary value of trap deformation. This splitting decreases with increasing interaction strength for both statistics. For a two-dimensional anisotropic Fermi gas, the two quadrupole frequencies and the splitting between them become independent of the particle number within the Thomas-Fermi approach. Received 21 September 2001 and Received in final form 9 December 2001     

Harmonic Oscillator in External Fields: Applications to Trapped Bosons and Fermions

Properties of harmonic oscillator in external fields are studied. The formalism developed is applied to a harmonic oscillator in a nonhomogeneous gravitational field. Partition functions and thermodynamic potentials for trapped Bose and Fermi gases are found. Thermodynamics of trapped Bosons and Fermions in external fields is discussed.     

New modified oscillator potential for nuclei in the actinide region

A modified oscillator potential with a new form of correction term giving the proper value of the dynamical moment of inertia is investigated. A set of parametersκ andμ for nuclei in the actinide region is given. The single particle levels around the Fermi surface obtained here are close to those calculated with the Nilsson potential with the traditional correction term.     

The equivalence of the Strutinsky type smoothing and the temperature averaging method

The Fermi gas model of the nucleus at high temperatures can be used to define a ground state shell correction. We demonstrate analytically that the shell correction so obtained is the same as that obtained from the Strutinsky type method.     

Instability of a trapped ultracold Fermi gas with attractive interactions: quantum effects

We consider the possible mechanical instability of an ultracold Fermi gas due to the attractive interactions between fermions of different species. We investigate how the instability, predicted by a mean field calculation, is modified when the gas is trapped in a harmonic potential and quantum effects are included.Received: 19 July 2004, Published online: 6 December 2004PACS: 03.75.Ss Degenerate Fermi gases - 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow     

均匀分布费米系统的组态路径积分蒙特卡罗模拟

改进了组态路径积分蒙卡方法,简化采样过程,开发相应程序并对无库伦相互作用谐振子以及均匀电子气进行模拟.谐振子平衡态能量与Fermi-Dirac分布符合较好,均匀电子气平衡态能量和动量基本符合Fermi-Dirac分布规律.对两种费米子系统的研究表明,组态路径积分蒙卡方法对费米子的交换效应具有较好的描述.本文探讨了费米交换符号问题的解决途径,同时对均匀电子气模型进行研究,为后续温热稠密物质的研究奠定基础.     

Semiclassical shell-structure moment of inertia for equilibrium rotation of a simple Fermi system

Semiclassical shell-structure components of the collectivemoment of inertia are derived within the mean-field cranking model in the adiabatic approximation in terms of the free-energy shell corrections through those of a rigid body for the statistically equilibriumrotation of a Fermi system at finite temperature by using the nonperturbative extended Gutzwiller periodic-orbit theory. Their analytical structure in terms of the equatorial and 3-dimensional periodic orbits for the axially symmetric harmonic oscillator potential is in perfect agreement with the quantum results for different critical bifurcation deformations and different temperatures.     

Shell effects in quantum dots in tilted magnetic fields

The motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The ground state of the Fermi system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape on the electron number, the magnetic field parameters and the slab thickness is found.     

One-dimensional mappings of the eigenelements of the Schrodinger problem

An approach is proposed for analyzing the inverse spectral problems for the Schrodinger equation based on writing the equation for the analog of the number-of-quanta operator for a harmonic oscillator. This equation makes it possible to determine not only the one-dimensional mapping of the energy eigenvalues but also the linear equation for the point spectrum shift operator of the Schrodinger problem. The solvability conditions of the latter lead to a nonlinear equation that determines the class of allowable potentials. Two classes of potentials regular in R(1) and symmetrical are isolated on the basis of the proposed approach. The first of these leads to equidistant spectra with a gap of arbitrary size and location. The spectrum of the second potential class is a combination of three rigorously equidistant spectra with ground states that are shifted by an arbitrary amount. Generalizations to the case of essentially nonequidistant spectra are shown to be possible.