谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似方法研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC)．导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响．以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合．     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC).导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响.以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合.     

Thermodynamic properties of rotating trapped ideal Bose gases

Ultracold atomic gases can be spined up either by confining them in rotating frame, or by introducing “synthetic” magnetic field. In this paper, thermodynamics of rotating ideal Bose gases are investigated within truncated-summation approach which keeps to take into account the discrete nature of energy levels, rather than to approximate the summation over single-particle energy levels by an integral as it does in semi-classical approximation. Our results show that Bose gases in rotating frame exhibit much stronger dependence on rotation frequency than those in “synthetic” magnetic field. Consequently, BEC can be more easily suppressed in rotating frame than in “synthetic” magnetic field.     

Quality of potential harmonics expansion method for dilute Bose-Einstein condensate

We present and examine an approximate but ab initio many-body approach, viz., potential harmonics expansion method (PHEM), which includes two-body correlations for dilute Bose-Einstein condensates. Comparing the total ground state energy for three trapped interacting bosons calculated in PHEM with the exact energy, the new method is shown to be very good in the low density limit which is necessary for achieving Bose-Einstein condensation experimentally.      

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

A theoretical analysis of the thermodynamic properties of the Robin wall characterized by the extrapolation length Λ in the electric field that pushes the particle to the surface is presented both in the canonical and two grand canonical representations and in the whole range of the Robin distance with the emphasis on its negative values which for the voltage‐free configuration support negative‐energy bound state. For the canonical ensemble, the heat capacity at exhibits a nonmonotonic behavior as a function of the temperature T with its pronounced maximum unrestrictedly increasing for the decreasing fields as and its location being proportional to . For the Fermi‐Dirac distribution, the specific heat per particle is a nonmonotonic function of the temperature too with the conspicuous extremum being preceded on the T axis by the plateau whose magnitude at the vanishing is defined as , with N being a number of the particles. The maximum of is the largest for and, similar to the canonical ensemble, grows to infinity as the field goes to zero. For the Bose‐Einstein ensemble, a formation of the sharp asymmetric feature on the ‐T dependence with the increase of N is shown to be more prominent at the lower voltages. This cusp‐like dependence of the heat capacity on the temperature, which for the infinite number of bosons transforms into the discontinuity of , is an indication of the phase transition to the condensate state. Some other physical characteristics such as the critical temperature and ground‐level population of the Bose‐Einstein condensate are calculated and analyzed as a function of the field and extrapolation length. Qualitative and quantitative explanation of these physical phenomena is based on the variation of the energy spectrum by the electric field.     

Effective area and expansion energy of trapped Bose gas in a combined magnetic-optical potential

In this Letter a conventional method of statistical physics and quantum mechanics is used to calculate the effective area and the expansion energy for trapped Bose gas in a combined optical-magnetic potential. Correction due to the finite number of particles, interatomic interaction and the deepness of the lattice potential are given simultaneously. It is found that the system possess two different phases which are superfluid phase and Mott insulator phase. The critical temperature which separate these two phases is calculated. In the superfluid phase both the effective area and expansion energy is sensitive to the variation of temperature and lattice depth. Mott insulator phase is characterized by vanishing of the condensed fraction and freezing of the effective area at the value which corresponding to BEC transition temperature. So these parameters can serve as a practical thermometer for such system. The expansion energy shows that the lack of expansion in any direction is due to the strong anisotropy of the trapping potential in this direction. The obtained results provide a solid theoretical foundation for the current experiments.     

Application of asymptotic iteration method to the Khare-Mandal and its PT-symmetric QES partner potential

We study the application of the asymptotic iteration method to the Khare-Mandal potential and its PT-symmetric partner. The eigenvalues and eigenfunctions for both potentials are obtained analytically. We have shown that although the quasi-exactly solvable energy eigenvalues of the Khare-Mandal potential are found to be in complex conjugate pairs for certain values of potential parameters, its PT-symmetric partner exhibits real energy eigenvalues in all cases.      

Hyperspherical harmonics approach to the trinucleon system with Reid soft core potential: Calculation of geometrical structure coefficients

We present the full set of equations for the solution of the trinucleon problem by the hyperspherical harmonics expansion (HHE) method where nucleons interact via the Reid soft core (RSC) potential. The coupling potential matrix elements are expressed in terms of geometrical structure coefficients (GSC) and potential multipoles (PM). Introduction of GSC greatly simplifies the calculation of the potential matrix and makes the numerical algorithm efficient. A method for calculating all the twelve independent sets of GSC needed, by using the completeness property of the Jacobi polynomials has been presented. A convenient sum rule for each set of GSC has also been derived and precision of the calculated GSC has been checked by the sum rule. Such calculations of GSC are efficient and fast, in view of the complexity of the HHE equations.     

Dynamics of atoms in strong laser fields I: A quasi analytical model in momentum space based on a Sturmian expansion of the interacting nonlocal Coulomb potential

In this study we present a model that we have formulated in the momentum space to describe atoms interacting with intense laser fields. As a further step, it follows our recent theoretical approach in which the kernel of the reciprocal-space time-dependent Schrödinger equation (TDSE) is replaced by a finite sum of separable potentials, each of them supporting one bound state of atomic hydrogen (Tetchou Nganso et al. 2013). The key point of the model is that the nonlocal interacting Coulomb potential is expanded in a Coulomb Sturmian basis set derived itself from a Sturmian representation of Bessel functions of the first kind in the position space. As a result, this decomposition allows a simple spectral treatment of the TDSE in the momentum space. In order to illustrate the credibility of the model, we have considered the test case of atomic hydrogen driven by a linearly polarized laser pulse, and have evaluated analytically matrix elements of the atomic Hamiltonian and dipole coupling interaction. For various regimes of the laser parameters used in computations our results are in very good agreement with data obtained from other time-dependent calculations.     

Scattering problem with nonlocal separable potential of rank-two: Application to statistical mechanics

In this paper, we present a formulation of statistical mechanics of a thermodynamic system consisting of free particles and independent correlated pairs interacting via nonlocal potential in terms of the scattering properties. Some quantum statistical properties such as energy, heat capacity, second virial coefficient, virial pressure and quantum correction of kinetic energy are described analytically. The difference between the resolvents of the interacting and free Hamiltonians, represented as , that is associated with particle correlations is used for the evaluation of the properties. The statistical properties are related to correlated states, when making a pole expansion of the analytically continued momentum matrix element of . The present work illustrates these relations for a three-dimensional nonlocal separable potential of rank-two.     

Self-consistent Shaw optimized model potential: Application to the determination of structural and atomic transport properties of liquid alkali metals by molecular dynamics simulations

The ‘first-principles’ fully non-local and energy-dependent optimized model potential (OMP) derived by Shaw is developed further. In contrast to Shaw's original paper, OMP parameters are derived in a self-consistent manner that does not rely on knowledge of experimental values of the ionization and cohesive energies. To our knowledge, this is the first time that this method has been used for effective potential calculations. In an application to liquid Li, Na, and K alkali metals, we used OMP pseudopotential-based interactions between ions to carry out standard molecular dynamics simulations. In the calculations, the ionic structure for the liquid state was first checked at a temperature near the melting point. Similar accurate calculations, but for atomic transport properties, predict the temperature dependence of the self-diffusion coefficients. The theoretical results obtained are in overall agreement with available experimental measurements. Thus, one can have some confidence in the ability of the optimized model potential to give a good representation of the physical properties of these alkali ions in the liquid environment.     

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer–Wolff transformation extending the latter to driven systems.     

Improved techniques for the calculation of ab initio ion-neutral interaction potentials: application to coinage metal ions interacting with rare gas atoms

Ab initio values for the potential energy functions for ion–neutral interactions can be tested by comparison with gaseous ion transport coefficients, but only if special care is taken to compute the interaction potentials accurately over wide ranges of internuclear separation. This is illustrated here by a reanalysis of the ab initio values for the coinage metal ions interacting with rare gas atoms, precise calculations of the transport cross sections over extremely wide ranges of energy, and similarly precise calculations of the zero-field ion mobilities as functions of gas temperature and the field-dependent ion mobilities at various fixed temperatures. The calculations indicate that the mobilities for Ag⁺(¹S) moving in Ne or Ar can distinguish between the existing, very similar ab initio potentials. They also show that substantial differences exist among the mobilities of the coinage metal anions and the ground and excited states of the cations. The techniques implemented are recommended for future ab initio calculations.     

Gaussian basis set of triple zeta valence quality for the atoms from K to Kr: Application in DFT and CCSD(T) calculations of molecular properties

A contracted basis set of triple zeta (TZ) valence quality for the atoms from K to Kr was constructed from fully-optimized Gaussian basis sets generated in this work. Gaussian polarization functions (d, f, and g symmetries), which were optimized at the second-order Mφller–Plesset level, were added to the TZ set. This extends earlier work on segmented contracted TZ basis set for atoms H-Ar. This set along with the BP86 non-hybrid and B3LYP hybrid functionals were used to calculate geometric parameters, dissociation energy, harmonic vibrational frequency, and electric dipole moment of a sample of molecules and, then, comparison with results obtained with other basis sets and with experimental data reported in the literature is done. CCSD(T) atomic excitation energies and bond lengths, dissociation energies, and harmonic vibrational frequencies of some diatomics were also evaluated. Using density functional theory and gauge-including atomic orbitals, ⁵⁷Fe and ⁷⁷Se nuclear magnetic resonance chemical shifts in Fe(C₅H₅)₂, H₂Se, (CH₃)SeH, CSe₂, SeCO, H₂CSe, and SeF₆ were calculated. Comparison with theoretical and experimental values previously published in the literature was done. It is verified that in general these results give good agreement with experimental and benchmark values.