Quantum macroscopic equations from Bohm potential and propagation of waves

Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation. In the present work, moments of this kinetic equation are taken, thus deriving conservation equations. These macroscopic equations are then applied to study the propagation of longitudinal density perturbations in neutral gases and plasmas, of either fermions or bosons. The dispersion relation is derived and the effect of the Bohm potential shown; the speed of propagation calculated and the difference between fermions and bosons investigated. Pseudosonic waves in quantum plasmas are obtained including the effect of the Bohm potential.     

Fractional exclusion statistics in general systems of interacting particles

I show that fractional exclusion statistics is manifested in general interacting systems and I calculate the exclusion statistics parameters. Most importantly, I prove that the mutual exclusion statistics parameters are proportional to the dimension of the Hilbert space on which they act [D.V. Anghel, J. Phys. A: Math. Theor. 40 (2007) F1013].     

Do bosons obey Bose-Einstein distribution: Two iterated limits of Gentile distribution

It is a common impression that by only setting the maximum occupation number to infinity, which is the demand of the indistinguishability of bosons, one can achieve the statistical distribution that bosons obey — the Bose-Einstein distribution. In this Letter, however, we show that only with an infinite maximum occupation number one cannot uniquely achieve the Bose-Einstein distribution, since in the derivation of the Bose-Einstein distribution, the problem of iterated limit is encountered. For achieving the Bose-Einstein distribution, one needs to take both the maximum occupation number and the total number of particles to infinities, and, then, the problem of the order of taking limits arises. Different orders of the limit operations will lead to different statistical distributions. For achieving the Bose-Einstein distribution, besides setting the maximum occupation number, we also need to state the order of the limit operations.     

Statistical Interaction Term of One-Dimensional Anyon Models

A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.     

Boson-like quantum dynamics of association in ultracold Fermi gases

We study the collective association dynamics of a cold Fermi gas of 2N atoms in M atomic modes into a single molecular bosonic mode. When the atomic translational motion is slow compared to the atom-molecule conversion rate, the many-body fermionic problem for 2^M amplitudes is effectively reduced to a dynamical system of min{N, M} + 1 amplitudes, making the solution no more complex than the solution of a two-mode Bose-Einstein condensate and allowing realistic calculations with up to 10⁴ particles. The many-body dynamics is shown to be formally similar to the dynamics of the bosonic system under the mapping of boson particles to fermion holes, producing collective enhancement effects due to many-particle constructive interference.     

First-order density matrices in one dimension for independent fermions and impenetrable bosons in harmonic traps

To complement existing knowledge of the density matrix γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ of independent fermions for N   particles in one dimension under harmonic confinement, the corresponding matrix γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ for impenetrable bosons is given for N=2$N=2$ and 3 (with the N=4$N=4$ form available also). For fermions the momentum density is then obtained and illustrated numerically for N=10$N=10$. The boson momentum density is studied analytically at high momentum p  , the coefficients of the p⁻⁴$p^{\mathrm{-4}}$ and p⁻⁶$p^{\mathrm{-6}}$ terms being tabulated for N=2–5$N=2\text{–}5$ inclusive. Their dependence on powers of N   is exhibited numerically. Finally, the functional relationship between γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ and γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ is formally set out and illustrated.     

Gentile statistics with a large maximum occupation number

In Gentile statistics the maximum occupation number can take on unrestricted integers: 1<n<∞. It is usually believed that Gentile statistics will reduce to Bose-Einstein statistics when n equals the total number of particles in the system N. In this paper, we will show that this statement is valid only when the fugacity z<1; nevertheless, if z>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=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.     

Complete state counting for Gentile's generalization of the Pauli exclusion principle

In the present work, we perform the complete state counting for Gentile's approach to the generalized Pauli exclusion principle (GPEP), which has been lacking in the literature. We count the total number of ways to allocate n identical particles occupying a group of g states with up to q particles in each state, in order to derive an exact expression for the statistical weight. Our obtained expression for the statistical weight gives the fermionic one for q=1; and for q>1, it tends fast to a bosonic weight. Moreover, we perform a numerical comparison between our state counting and Wu's (corresponding to the Haldane-Wu's formulation of the GPEP), which implies that Gentile's formulation gives rise to more boson-like behavior while Haldane-Wu's approach to more fermion-like behavior; this difference lies on the fact that each formulation has its own state-occupation rules on which correlation plays a key role.     

Increase of temperature of an ideal nondegenerate quantum gas in a suddenly expanding box due to energy quantization

We show that due to energy quantization the temperature of an ideal nondegenerate quantum gas in a rectangular box always increases after a sudden expansion of the box and a subsequent thermalization. The maximal increment of temperature is proportional to the square root of the product of the initial absolute temperature by the energy of the first discrete quantum level, i.e., it is proportional to the first power of the Planck constant.     

Impossibility to describe repulsion with contact interaction

Contact interactions always lead to attractive behavior. Arguments are presented to show why a repulsive interacting system, e.g. Bose gases, cannot be described by contact interactions and corresponding treatments are possibly obscured by the appearance of bound states. The usually used cut-offs are identified as finite range parameters.     

Bose-Einstein condensation in a cavity

The effect of the physically correct boundary conditions and the nonvanishing ground state energy on Bose-Einstein condensation of quantum particles confined to a cubic volumeV=L ³ is evaluated. The transition point is shifted towards higher temperatures by the confinement, the specific heat below the onset of condensation is no longer proportional toT ^3/2, and the pressure does depend on the volume. Precise expressions for the modification of the ground state population and for the shift of the condensation temperature are derived, together with an expansion of the internal energy and of the specific heat. Numerical computations confirm the accuracy of our analytical approximations.Dedicated to Herbert Wagner, whose work on quantum Fermi liquids proved to be also very stimulating for quantum Bose liquids.     

Spectrum of the non-abelian phase in Kitaev’s honeycomb lattice model

The spectral properties of Kitaev’s honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the 2ⁿ-fold ground state degeneracy in the presence of 2n well separated vortices and the lifting of the degeneracy due to their short-range interactions. The calculations are performed on an infinite lattice. In addition to the analytic treatment, a numerical study of finite size systems is performed which is in exact agreement with the theoretical considerations. The general spectral properties of the non-abelian phase are considered for various finite toroidal systems.     

One- plus two-body random matrix ensembles with spin: Results for pairing correlations

For EGOE(1+2)-s ensemble for fermions, in the strong coupling region, partial densities over pairing subspaces follow Gaussian form and propagation formulas for their centroids and variances are derived. Similarly for this ensemble: (i) pair transfer strength sums, a statistic for chaos, are shown to follow a simple form; (ii) a quantity used in conductance peak spacings analysis is shown to exhibit bimodal form when pairing is stronger than the exchange interaction.     

General kinetic equation and irreversibility in statistical systems

General kinetic equation for statistical systems is presented. A kinetic equation with source that is fluctuation of physical values was obtained. A new statistical criterion of systems evolution was determined. Nonequilibrium statistical and variational derivations of general kinetic equations are considered. Evolution of nonequilibrium Boltzmann-Gibbs-Shannon entropy, Hamilton function and Hamilton function production are examined.     

The q-deformed Bose gas: integrability and thermodynamics

We investigate the exact solution of the q-deformed one-dimensional Bose gas to derive all integrals of motion and their corresponding eigenvalues. As an application, the thermodynamics is given and compared to an effective field theory at low temperatures.     

Quantum Degenerate Fermi--Bose Mixtures of 40K and 87Rb Atoms in a Quadrupole-Ioffe Configuration Trap

We report on the attainment of quantum degeneracy of 40^K by means of efficient thermal collisions with the evaporatively cooled 87^Rb atoms. In a quadrupole-Ioffe configuration trap, potassium atoms axe cooled to 0.5 times the Fermi temperature. We obtain up to 7.59 × 10^5 degenerate fermions 40^K.     

Bose-Einstein condensation of bouncing balls

Microscopic bouncing balls, i.e., particles confined within a positive one-half-dimensional gravitational potential, display Bose-Einstein condensation (BEC) not only in the thermodynamic limit but also in the case of a finite number of particles, and the critical temperature with a finite number of particles is higher than that in the thermodynamic limit. This system is different from the one-dimensional harmonic potential one, for which the standard result indicates that the BEC is not possible unless the number of particles is finite.     

Hubbard-type solution in the planar approximation

The Hubbard solution to the Hubbard model showed a non-trivial metal-insulator transition. The value of the one-particle density of states at the Fermi energy in that solution decreased continuously with increasing value of the Hubbard interaction and vanished at a critical value of the interaction. Such a solution is derived from a planar model, as an approximation to the exact construction of the model's one-particle Green function.     

Functional integral for ultracold fermionic atoms

We develop a functional integral formalism for ultracold gases of fermionic atoms. It describes the BEC–BCS crossover and involves both atom and molecule fields. Beyond mean field theory we include the fluctuations of the molecule field by the solution of gap equations. In the BEC limit, we find that the low temperature behavior is described by a Bogoliubov theory for bosons. For a narrow Feshbach resonance these bosons can be associated with microscopic molecules. In contrast, for a broad resonance the interaction between the atoms is approximately pointlike and microscopic molecules are irrelevant. The bosons represent now correlated atom pairs or composite “dressed molecules”. The low temperature results agree with quantum Monte Carlo simulations. Our formalism can treat with general inhomogeneous situations in a trap. For not too strong inhomogeneities the detailed properties of the trap are not needed for the computation of the fluctuation effects—they enter only in the solutions of the field equations.