Finite Bose Systems Research Articles

Mid-range order in trapped quasi-condensates of bosonic atoms

Finite Bose systems cannot display a genuine Bose–Einstein condensate with infinite long-range order. But, if the number of trapped atoms is sufficiently large, a kind of Bose–Einstein condensation does occur, with the properties of the arising quasi-condensate being very close to the genuine condensate. Although the quasi-condensate does not enjoy long-range order, it has mid-range order. This paper shows that the level of mid-range order in finite Bose systems can be characterized by order indices of density matrices.

An exactly solvable model for equilibration in bosonic systems

An analytical model for the kinetic equilibration of finite Bose systems is outlined. The corresponding transport equation is solved exactly through a nonlinear transformation. The model is applied to the equilibration of a cold quantum gas including implicitly the formation of a Bose-Einstein condensate through particle-number conservation.

Equilibration in finite Bose systems

The equilibration of a finite Bose system is modeled using a gradient expansion of the collision integral that leads to a nonlinear transport equation. For constant transport coefficients, it is solved in closed form through a nonlinear transformation. Using schematic initial conditions, the exact solution and the equilibration time are derived and compared to the corresponding case for fermions. Applications to the fast equilibration of the gluon system created initially in relativistic heavy-ion collisions, and to cold quantum gases are envisaged.

Microcanonical finite-size scaling of an ideal Bose gas in a box

We derive an exact recursive scheme to determine exactly the microcanonical partition function of a finite Bose system. Such a recursive approach is identical to that previously obtained within the context of counting statistics. Within the exact microcanonical ensemble, we study microcanonical finite-size scaling behaviors of condensate fraction and specific heat around the critical energy ϵ c for the finite ideal Bose system. We show that the microcanonical scaling functions governing the various critical behaviors are universal in the ideal Bose-Einstein condensates.

Bose-Einstein condensation and heat capacity of two-dimensional spin-polarized atomic hydrogen

The static fluctuation approximation (SFA) is used to study the condensate fraction and the specific heat capacity of finite two-dimensional spin-polarized atomic hydrogen. It is found that Bose-Einstein condensation occurs in this system. The transition temperature at different densities decreases as the number of particles of the system increases. At low density, a sharp peak in the specific heat capacity is observed at the transition temperature. On the other hand, as the density of the system increases, the transition temperature becomes no longer well-defined, and a hump is observed in the specific heat capacity around the transition temperature. A qualitative comparison of our results to published results for finite Bose systems shows good agreement.

Trap-size scaling of finite Bose systems within an exact canonical ensemble

Based on an exact canonical partition function, we investigate the trap-size scaling for ideal Bose gases with a finite number of particles N confined in a cubic box or in a harmonic trap. We study the trap-size scaling behaviors of condensate fraction 〈 n 0〉/ N and specific heat C N around the transition temperature T c ( i. e., t = T/ T c − 1 → 0) for the three different traps, where a trap exponent θ in dependence of the trapping potential and the universality class of transition are introduced. In the box trap with periodic and Dirichlet boundary conditions, where θ → 1, we find that the scaling functions governing the various critical behaviors are universal but respective of the boundary conditions. The calculated critical exponents are in nice agreement with analytical scaling predictions. The borders of universality validity are obtained numerically. In the case of the harmonic trap, the critical behavior of the system is also found to be universal, and the trap exponent is obtained as θ ≃ 0.068.

Thermodynamics of Finite Bose Systems: An Exact Canonical-Ensemble Treatment with Different Traps

Based on an exact canonical partition function, we investigate the thermodynamics and trap-size scaling behaviors for a finite number of ideal bosons confined in a cubic box or in a harmonic trap. Both in the box trap imposed by either periodic or Dirichlet boundary conditions (BCs) and in the harmonic trap, we calculate several physical quantities including the chemical potential μ, specific heat C N , condensate fraction 〈n 0〉/N, root-mean-square fluctuations δ n 0 of the condensate population, and transition temperature T c , and compare these quantities under different traps. We discuss the particle-number dependence of T c through proposing several T c definitions, where the differences among these values are considerable for the finite systems.

Many-body dynamics of a Bose system with attractive interactions on a ring

We investigate the many-body dynamics of an effectively attractive one-dimensional Bose system confined in a toroidal trap. The mean-field theory predicts that a bright-soliton state will be formed when increasing the interparticle interaction over a critical point. The study of quantum many-body dynamics in this paper reveals that there is a modulation instability in a finite Bose system correspondingly. We show that Shannon entropy becomes irregular near and above the critical point due to quantum correlations. We also study the dynamical behavior of the instability by exploring the momentum distribution and the fringe visibility, which can be verified experimentally by releasing the trap

The Finite-Size Effect on the Correlation Functions of a Bose Gas in a Trap and Vanishing of the Order Parameter in the Finite Bose Systems

The influence of the finite sizes on the coherent properties of 3D Bose systems is considered. As is shown, the correlation functions of a Bose gas in a trap have essential differences from analogous correlation functions in an infinite system. Thus, the anomalous correlation function vanishes due to the divergency of phase fluctuations which destruct the order parameter too. The normal correlation function decays exponentially in time for sufficiently large time interval.

Phases in weakly interacting finite Bose systems

We study precursors of thermal phase transitions in finite systems of interacting Bose gases. For weakly repulsive interactions there is a phase transition to the one-vortex state. The distribution of zeros of the partition function indicates that this transition is first order, and the precursors of the phase transition are already displayed in systems of a few dozen bosons. Systems of this size do not exhibit new phases as more vortices are added to the system.

Influence of boundary conditions on the growth of condensate fraction in a finite Bose system

In a recent paper we carried out a rigorous, asymptotic analysis of the low-temperature behavior of a Bose gas confined to a finite cubic geometry and subjected to periodic boundary conditions. That analysis is now extended to Dirichlet, Neumann, and antiperiodic boundary conditions. As before, the thermogeometric parameter $y$ and the condensate fraction $\frac{{N}_{0}}{N}$ are studied as functions of temperature and are evaluated explicity for cubes with $\frac{L}{\overline{l}}=40 \mathrm{and} 100$, where $L$ is the edge length of the enclosure and $\overline{l}$ the mean interparticle distance in the system. The finite-size corrections to the condensate fraction under Dirichlet or Neumann boundary conditions turn out to be qualitatively different from those under periodic or antiperiodic boundary conditions. This difference becomes manifest when one tries to express these corrections in a form consistent with the standard scaling theory for finite-size effects.