Systems obeying Gentile statistics in oscillator traps under rotation

We put forward a concise approach to calculate the α decay preformation probabilities by defining the microscopic valence nucleon and hole numbers based on the single particle energy spectra, which is obtained within the relativistic Hartree–Bogoliubov model. The residual interactions including neutron–neutron, proton–proton pairing and proton–neutron correlations could trigger the collective motions among the valence nucleons and holes, along with the independent particle motions under the mean field assumption. Therefore the more the number of valence nucleons and holes, the stronger the collective motions such as α particle clustering. We assume that the valence orbits locate around the Fermi surface obeying a Fermi–Dirac distribution, i.e. nucleons (holes) occupying the orbits with much lower (higher) energies away from the Fermi surface can not be considered as the valence nucleons (holes). The α decay preformation probabilities Pα are calculated within the Np Nn scheme in terms of the valence proton–neutron interaction. As an example, in the case of even–even polonium, radon, radium and thorium isotopes the extracted α decay preformation probabilities , which are obtained within the generalized liquid drop model, can be well reproduced by employing two different formulas to take into account the shell effect at N = 126 shell closure.

The interacting Kane–Mele model with a long-range hopping is studied using analytical method. The original Kane–Mele model is defined on a honeycomb lattice. In the work, we introduce a four-lattice-constant range hopping and the on-site Hubbard interaction into the model and keep its lattice structure unchanged. From the single-particle energy spectrum, we obtain the critical strength of the long-range hopping tL at which the topological transition occurs in the non-interacting limit of the model and our results show that it is independent of the spin–orbit coupling. After introducing the Hubbard interaction, we investigate the Mott transition and the magnetic transition of the generalized strongly correlated Kane–Mele model using the slave-rotor mean field theory and Hartree–Fock mean field theory respectively. In the small long-range hopping region, it is a correlated quantum spin Hall state below the Mott transition, while a topological Mott insulator above the Mott transition. By comparing the energy band of spin degree of freedom with the one of electrons in non-interacting limit, we find a condition for the tL-driven topological transition. Under the condition, critical values of tL at which the topological transition occurs are obtained numerically from seven self-consistency equations in both regions below and above the Mott transition. Influences of the interaction and the spin–orbit coupling on the topological transition are discussed in this work. Finally, we show complete phase diagrams of the generalized interacting topological model at some strength of spin–orbital coupling.

The Bose-Einstein condensation mechanism is shown to be capable of accounting for the existence of separate hydrodynamic velocity fields for the normal and the superfluid, provided suitable assumptions are made with regard to the single-particle energy spectrum. We consider the effect on the microcanonical gas distribution of imposing a nonzero value of the total momentum P. For an ordinary gas the effect is trivial, the whole distribution being merely shifted in momentum space. However, in the case of a degenerate Bose gas whose single-particle energy spectrum has a sharp minimum (gap or cusp), only the excited part of the gas (normal fluid) participates in the imposed motion, the condensate (superfluid) remaining "frozen" in momentum space. This rigidity of the condensate in momentum space plays the same role as the rigidity of the superelectrons on imposition of a magnetic field in the London theory of superconductivity. P acts as an additional thermodynamic variable, states with P \ensuremath{\ne} 0 being macroscopically metastable and corresponding to the existence of a relative velocity between normal and superfluid. The basic hydrodynamic assumption of the two-fluid model is thus reduced to an assumption concerning the form of an effective single-particle energy spectrum, and the parallelism between the theories of superconductivity and superfluidity is clearly exhibited. The present theory permits, in particular, the introduction of the mathematical form of Landau's phonon and "roton" spectra within the framework of the Bose-Einstein condensation picture. The statistical-thermodynamic formulas are derived and are shown to lead to characteristic two-fluid equations derived previously from a variational principle.

We present a nonperturbative, self-consistent calculation for the zero-temperature electron gas based on a modified Hartree-Fock approximation in which the Coulomb potential is replaced by a Debye screened potential. The single particle energy spectrum and the screening length are determined in a self-consistent manner; the resulting energy spectrum is used to compute the specific heat, the ground-state energy and the pressure. The specific heat compares favorably with that calculated by Hedin, but the correlation energy turns out to have the wrong sign. We compute the pressure in two different ways to check the thermodynamic consistency (in the sense of Baym) of the theory; in the metallic density region the deviation from thermodynamic consistency varies from 6% to 10%.

It is shown that the nuclear single-particle energy spectra obtained in the selfconsistent way obey similar particle number dependence as the spectrum of a pure 3D harmonic oscillator potential. This effect was used to improve the quality of evaluation of the shell correction energy in weakly bound nuclei. The magnitude of the traditional Strutinsky shell correction energy obtained by the smearing of the single-particle energy spectrum of light nuclei is compared with that obtained by the smoothing of the single-particle energy sums in the particle number space.

The quantum phase transitions of one-dimensional period-two anisotropic XY models in a transverse field with the Hamiltonian where the anisotropy parameters i take and alternately, are studied. The Hamiltonian can be reduced to the diagonal form by Jordan-Wigner and Bogoliubov transformations. The long-range correlations Cx and Cy are calculated numerically. The phase with Cx Cy0 (or Cy Cx0) is referred to as the ferromagnetic (FM) phase along the x (or y) direction, while the phase with Cx=Cy=0 is the paramagnetic (PM) phase. It is found that the phase diagrams with the ratio -1 and =-1 are different obviously. For the case with -1, the line h=hc1=1-[(1-)/2]2 separates an FM phase from a PM phase, while the line =0 is the boundary between a ferromagnetic phase along the x direction (FMx) and a ferromagnetic phase along the y direction (FMy). These are similar to those of the uniform XY chains in a transverse field (i.e., =1). When =-1, the FMx and FMy phases disappear and there appears a new FM phase. The line h=hc2=1-2 separates this new FM phase from the PM phase. The new phase is gapless with two zeros in single particle energy spectrum. This is due to the new symmetry in the system with =-1, i.e., the Hamiltonian is invariant under the transformation 2ix 2i+1y,2iy 2i+1x. The correlation function between the 2i-1 and 2i lattice points along the x (y) direction is equal to that between the 2i and 2i+1 lattice points along the y (x) direction. As a result, the long-range correlation functions along two directions are equivalent. In order to facilitate the description, we call this gapless phase the isotropic ferromagnetic (FMxx) phase. Finally, the relationship between quantum entanglement and quantum phase transitions of the system is studied. The scaling behaviour of the von Neumann entropy at each point in the FMxx phase is SL~1/3log2L+ Const, which is similar to that at the anisotropic phase transition point of the uniform XY model in a transverse field, and different from those in the FMx and FMy phases.

We devise an algorithm to enumerate the microstates of a system comprising N independent, distinguishable particles. The algorithm is applicable to a wide class of systems such as harmonic oscillators, free particles, spins, and other models for which there are no analytical solutions, for example, a system with single particle energy spectrum given by ɛ(p,q) = ɛ0(p2 + q4), where p and q are non-negative integers. Our algorithm enables us to determine the approach to the limit N → ∞ within the microcanonical ensemble, and makes manifest the equivalence with the canonical ensemble. Various thermodynamic quantities as a function of N can be computed using our methods.

Using the single particle energy spectrum and Bethe's formula for nuclear level density, the mass distribution of fission fragments is calculated for nuclei $^{236}\mathrm{U}$, $^{258}\mathrm{Fm}$, and $^{240}\mathrm{Pu}$, and also for the compound systems $^{84}\mathrm{Kr}$ + $^{238}\mathrm{U}$ and $^{129}\mathrm{Xe}$ + $^{197}\mathrm{Au}$ at different excitation energies. The results are in reasonable agreement with experimental yield curves.RADIOACTIVITY, FISSION Nuclear level density, mass and charge distribution of fission fragments.

The free expansion of a Bose–Einstein condensate is analyzed, assuming that the single particle energy spectrum is modified due to some quantum structure of space time. The condensate’s free velocity expansion leads in a natural way to a deformed uncertainty principle. We show that large expansion times are required in order to amplify some possible traces of the Planck scale regime. The analysis presented in this work opens up the opportunity to use Bose–Einstein condensates as tools in quantum gravity phenomenology with a solid experimental basis.

The sine-square deformation of the lattice model of one-dimensional p-wave topological superconductor is studied focusing on the existence of the zero energy Majorana fermion localized at the ends of the superconductor. The deformation is applied in two distinct ways depending on whether the interaction in the Hamiltonian is defined on the lattice link and/or the lattice site. The zero energy Majorana fermion is found to survive both kinds of the deformations while the overall single particle energy spectrum is substantially modified.

In this paper, we present a theoretical and numerical analysis of the free expansion of a Bose–Einstein condensate, where we assume that the single particle energy spectrum is deformed due to a possible quantum structure of spacetime. Also, we consider the presence of interparticle interactions in order to study more realistic and specific scenarios. The modified free velocity expansion of the condensate leads in a natural way to a modification of the uncertainty principle, which allows us to investigate some possible features of the Planck scale regime in low-energy earth-based experiments.

: We have investigated the microwave absorption of clean two-dimensional (2D) electron systems (with mobility exceeding 1 0(exp 7)cm(exp 2)/Vs) in GaAs/Al(x)Ga(1-x)As heterostructures in high magnetic fields when the single particle energy spectrum is a series of discrete Landau levels. Our results, as summarized below, give direct evidence for the existence of several new phases of 2D electron matter and provide us new insights into the strong correlation physics therein.

In this work, a model based on single particle plus pairing residual interaction was used to study the low-lying excited states of the 193Ir nucleus. In this model, the deformation parameters in equilibrium were obtained by minimizing the total energy calculated by the Strutinsky prescription; the macroscopic contribution to the potential was taken from the Liquid Droplet Model, with the shell and paring corrections used as as microscopic contributions. The nuclear shape was described using the Cassinian ovoids as base figures; the single particle energy spectra and wave functions for protons and neutrons were calculated in a deformed Woods-Saxon potential, where the parameters for neutrons were obtained from the literature and the parameters for protons were adjusted in order to describe the main sequence of angular momentum and parity of the bandheads, as well as the proton binding energy of 193Ir. The residual pairing interaction was calculated using the BCS prescription with Lipkin-Nogami approximation. The results obtained for the first three bandheads (the 3/2+ ground state, the 1/2+ excited state at E » 73keV and the the 11/2- isomeric state at E » 80keV) showed a very good agreement, but the model so far greatly overestimated the energy of the next bandhead, a 7/2- at E » 299keV.

Time dependent Bogoliubov de Gennes equations for superconductors with anisotropic pairing interaction

Magnetocrystalline anisotropy energy and spin polarization of Fe 3Si in bulk and on Si(001) and Si(111) substrates