Ideal Bose Gas Research Articles

Infinite cycles of interacting bosons

Abstract In the first-quantized description of bosonic systems permutation cycles formed by the particles play a fundamental role. In the ideal Bose gas Bose-Enstein condensation (BEC) is signaled by the appearance of infinite cycles. When the particles interact, the two phenomena may not be simultaneous, the existence of infinite cycles is necessary but not sufficient for BEC. We demonstrate that their appearance is always accompanied by a singularity
in the thermodynamic quantities
which in three and four dimensions can be as strong as a one-sided divergence of the isothermal compressibility. Arguments are presented that long-range interactions can give rise to unexpected results, such as the absence of infinite cycles in three dimensions for long-range repulsion or their presence in one and two dimensions if the pair potential has a long attractive tail.

One-dimensional magnetic excitonic insulators

Abstract Dimensionality significantly affects exciton production and condensation. Despite the report of excitonic instability in one-dimensional materials, it remains unclear whether these spontaneously produced excitons can form Bose–Einstein condensates. In this work, we first prove statistically that one-dimensional condensation exists when the spontaneously generated excitons are thought of as an ideal neutral Bose gas, which is quite different from the inability of free bosons to condense. We then derive a general expression for the critical temperature in different dimensions and find that the critical temperature increases with decreasing dimension. We finally predict by first-principles GW-Bethe–Salpeter equation calculations that experimentally accessible single-chain staircase Scandocene and Chromocene wires are an antiferromagnetic spin-triplet excitonic insulator and a ferromagnetic half-excitonic insulator, respectively.

On Dunkl-Bose-Einstein Condensation in Harmonic Traps

The use of the Dunkl derivative, defined by a combination of the difference-differential and reflection operators, allows the classification of the solutions according to even and odd solutions. Recently, we considered the Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose gas confined in a gravitational field. In this work, we address another essential problem and examine an ideal Bose gas trapped by a three-dimensional harmonic oscillator within the Dunkl formalism. To this end, we derive an analytic expression for the critical temperature of the N particle system, discuss its value at large-N limit andfinally derive and compare the ground state population with the usual case result. In addition, we explore two thermal quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity functions.

Breakdown of Temporal Coherence in Photon Condensates.

The temporal coherence of an ideal Bose gas increases as the system approaches the Bose-Einstein condensation threshold from below, with coherence time diverging at the critical point. However, counterexamples have been observed for condensates of photons formed in an externally pumped, dye-filled microcavity, wherein the coherence time decreases rapidly for increasing particle number above threshold. This Letter establishes intermode correlations as the central explanation for the experimentally observed dramatic decrease in the coherence time beyond critical pump power.

Quantum degeneracy and spin entanglement in ideal quantum gases

Quantum degeneracy is the central many-body feature of ideal quantum gases stemming from quantum mechanics. In this work we address its relationship to the most fundamental form of non-classicality in many-body system, i.e. many-body entanglement. We aim at establishing a quantitative link between quantum degeneracy and entanglement in spinful ideal gases, using entanglement witness criteria based on the variance of the collective spin of the spin ensemble. We show that spin-1/2 ideal Bose gases do not possess entanglement which can be revealed from such entanglement criteria. On the contrary, ideal spin-1/2 Fermi gases exhibit spin entanglement revealed by the collective-spin variances upon entering quantum degeneracy, due to the formation of highly non-local spin singlets. We map out the regime of detectable spin entanglement for Fermi gases in free space as well as in a parabolic trap, and probe the robustness of spin entanglement to thermal effects and spin imbalance. Spin entanglement in degenerate Fermi gases is amenable to experimental observation using state-of-the-art spin detection techniques in ultracold atoms.

Performance enhancement of quantum Brayton engine via Bose-Einstein condensation.

Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.

Critical exponents and fluctuations at BEC in a 2D harmonically trapped ideal gas

The critical properties displayed by an ideal 2D Bose gas trapped in a harmonic potential are determined and characterized in an exact numerical fashion. Beyond thermodynamics, addressed in terms of the global pressure and volume which are the appropriate variables of a fluid confined in a non-uniform harmonic potential, the density-density correlation function is also calculated and the corresponding correlation length is found. Evaluation of all these quantities as Bose–Einstein condensation (BEC) is approached manifest its critical continuous phase transition character. The divergence of the correlation length as the critical temperature is reached, unveils the expected spatial scale invariance proper of a critical transition. The logarithmic singularities of this transition are traced back to the non-analytic behavior of the thermodynamic variables at vanishing chemical potential, which is the onset of BEC. The critical exponents associated with the ideal BEC transition in the 2D inhomogeneous fluid reveals its own universality class.

Linear rotor in an ideal Bose gas near the threshold for binding

Linear rotor in an ideal Bose gas near the threshold for binding

Possibility of Exciton Bose-Einstein Condensation in CdSe Nanoplatelets.

The quasi-two-dimensional exciton subsystem in CdSe nanoplatelets is considered. It is theoretically shown that Bose-Einstein condensation (BEC) of excitons is possible at a nonzero temperature in the approximation of an ideal Bose gas and in the presence of an "energy gap" between the ground and the first excited states of the two-dimensional exciton center of inertia of the translational motion. The condensation temperature (Tc) increases with the width of the "gap" between the ground and the first excited levels of size quantization. It is shown that when the screening effect of free electrons and holes on bound excitons is considered, the BEC temperature of the exciton subsystem increases as compared to the case where this effect is absent. The energy spectrum of the exciton condensate in a CdSe nanoplate is calculated within the framework of the weakly nonideal Bose gas approximation, considering the specifics of two-dimensional Born scattering.

Quantum Brayton Refrigeration Cycle with Finite-Size Bose–Einstein Condensates

We consider a quantum Brayton refrigeration cycle consisting of two isobaric and two adiabatic processes, using an ideal Bose gas of finite particles confined in a harmonic trap as its working substance. Quite generally, such a machine falls into three different cases, classified as the condensed region, non-condensed phase, and regime across the critical point. When the refrigerator works near the critical region, both figure of merit and cooling load are significantly improved due to the singular behavior of the specific heat, and the coefficient of performance at maximum figure of merit is much larger than the Curzon–Ahlborn value. With the machine in the non-condensed regime, the coefficient of performance for maximum figure of merit agrees well with the Curzon–Ahlborn value.

The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic

In the framework of the theory of Dunkl-deformed bosons, Bose-Einstein condensation of two and three-dimensional Dunkl-boson gases confined in the one-dimensional gravitational field is investigated. Using the semi-classical approximation method, we calculate the expressions of the Dunkl-critical temperature $T_{c}^{D}$, the ground state population $\frac{N_{0}^{D}}{N}$ and the Dunkl-mean energy and Dunkl-specific heat functions. Further numerical calculation shows that the condensation temperature ratio $\frac{T_{c}^{D}}{T_{c}^{B}}$ increases with the increasing Wigner parameter.

Effective binding potential from Casimir interactions: the case of the Bose gas

We consider the thermal Casimir effect in ideal Bose gases, where the dispersion relation involves both terms quadratic and quartic in momentum. We demonstrate that if macroscopic objects are immersed in such a fluid in spatial dimensionality and at the critical temperature , the Casimir force acting between them is characterized by a sign which depends on the separation D between the bodies and changes from attractive at large distances to repulsive at smaller separations. In consequence, an effective potential which binds the two objects at a finite separation arises. We demonstrate that for odd integer dimensionality , the Casimir energy is a polynomial of degree in D −2. We point out a very special role of dimensionality d = 3, where we derive a strikingly simple form of the Casimir energy as a function of D at Bose–Einstein condensation. We discuss crossover between monotonous and oscillatory decay of the Casimir interaction above the condensation temperature.

The Casimir effect in a dilute Bose gas in broken symmetry phase within the improve Hartree–Fock approximation

The Casimir effect in a weakly interacting Bose gas confined between two parallel plates is studied at finite temperature, which is smaller than the phase transition temperature, within improved Hartree–Fock (IHF) approximation, in which the number of the Goldstone bosons are conserved. When condensate and non-condensate phases co-exist, considering the contribution of the two-loop diagrams, the order-parameter and effective mass are not constant. The Casimir energy and resulting Casimir force are separated into two parts: the one corresponds to the corresponding one-loop approximation, and the other is associated with the contribution of the two-loop diagrams. Our result can be reduced to the one for weakly interacting gas at zero temperature, or for the ideal Bose gas.

Medium-induced interaction between impurities in a Bose-Einstein condensate

We consider two heavy particles immersed in a Bose-Einstein condensate in three dimensions and compute their mutual interaction induced by excitations of the medium. For an ideal Bose gas, the induced interaction is Newtonian up to a shift in distance, which depends on the coupling strength between impurities and Bosons. For a real BEC, we find that, on short distances, the induced potential is dominated by three-body physics of a single Boson bound to the impurities, leading to an Efimov potential. At large distances of the order of the healing length, a Yukawa potential emerges instead. In particular, we find that both regimes are realized for all impurity-boson couplings and determine the corresponding crossover scales. The transition from the real to the ideal condensate at low gas parameters is investigated.

Ideal Bose gas and blackbody radiation in the Dunkl formalism

Recently, deformed quantum systems have received lots of attention in the literature. Dunkl formalism differs from others by containing the difference-differential and reflection operator. It is one of the most interesting deformations since it let us discuss the solutions according to the even and odd solutions. In this work, we studied the ideal Bose gas and the blackbody radiation via the Dunkl formalism. To this end, we made a liaison between the coordinate and momentum operators with the creation and annihilation operators, which allowed us to obtain the expressions of the partition function, the condensation temperature, and the ground state population of the Bose gas. We found that Dunkl-condensation temperature increases with increasing θ value. In the blackbody radiation phenomena, we found how the Dunkl formalism modifies total radiated energy. Then, we examined the thermal quantities of the system. We found that the Dunkl deformation causes an increase in entropy and specific heat functions as well as in the total radiation energy. However, we observed a decrease in the Dunk-corrected Helmholtz free energy in this scenario. Finally, we found that the equation of state is invariant even in the considered formalism.

Trapped Ideal Bose Gas with a Few Heavy Impurities

In this article, we formulate a general scheme for the calculation of the thermodynamic properties of an ideal Bose gas with one or two immersed static impurities, when the bosonic particles are trapped in a harmonic potential with either a quasi-1D or quasi-2D configuration. The binding energy of a single impurity and the medium-induced Casimir-like forces between the two impurities are numerically calculated for a wide range of temperatures and boson–impurity interaction strengths.

The thermodynamic limit of an ideal Bose gas by asymptotic expansions and spectral ζ-functions

We analyze the thermodynamic limit—modeled as the open-trap limit of an isotropic harmonic potential—of an ideal, non-relativistic Bose gas with a special emphasis on the phenomenon of Bose–Einstein condensation. This is accomplished by the use of an asymptotic expansion of the grand potential, which is derived by ζ-regularization techniques. Herewith, we can show that the singularity structure of this expansion is directly interwoven with the phase structure of the system: In the non-condensation phase, the expansion has a form that resembles usual heat kernel expansions. By this, thermodynamic observables are directly calculable. In contrast, the expansion exhibits a singularity of infinite order above a critical density, and a renormalization of the chemical potential is needed to ensure well-defined thermodynamic observables. Furthermore, the renormalization procedure forces the system to exhibit condensation. In addition, we show that characteristic features of the thermodynamic limit, such as the critical density or the internal energy, are entirely encoded in the coefficients of the asymptotic expansion.

Comparative Study on the Models of Thermoreversible Gelation.

A critical survey on the various theoretical models of thermoreversible gelation, such as the droplet model of condensation, associated-particle model, site–bond percolation model, and adhesive hard sphere model, is presented, with a focus on the nature of the phase transition predicted by them. On the basis of the classical tree statistics of gelation, combined with a thermodynamic theory of associating polymer solutions, it is shown that, within the mean-field description, the thermoreversible gelation of polyfunctional molecules is a third-order phase transition analogous to the Bose–Einstein condensation of an ideal Bose gas. It is condensation without surface tension. The osmotic compressibility is continuous, but its derivative with respect to the concentration of the functional molecule reveals a discontinuity at the sol–gel transition point. The width of the discontinuity is directly related to the amplitude of the divergent term in the weight-average molecular weight of the cross-linked three-dimensional polymers. The solution remains homogeneous in the position space, but separates into two phases in the momentum space; particles with finite translational momentum (sol) and a network with zero translational momentum (gel) coexist in a spatially homogeneous state. Experimental methods used to detect the singularity at the sol–gel transition point are suggested.

On the Features of Ideal Bose-Gas Thermodynamic Prop-erties at a Finite Particle Number

The paper is devoted to the theory of an ideal Bose-gas with a finite number N of particles. The exact expressions for the partition functions and occupation numbers of the model in the grand canonical, canonical, and microcanonical ensembles are found. From the calculations, it is followed that, oppositely to the accepted opinion that the chemical potential μ of an ideal Bose-gas is only negative, it can take values in the range −∞ < μ < ∞. The asymptotic expressions (in the case N ≫ 1) for the partition functions and occupation numbers for all above-mentioned thermodynamic ensembles are also evaluated.

Variance of the Casimir force in an ideal Bose gas

We consider an ideal Bose gas enclosed in a d-dimensional slab of thickness D. Using the grand canonical ensemble we calculate the variance of the thermal Casimir force acting on the slab’s walls. The variance evaluated per unit wall area is shown to decay like Δvar/D for large D. The amplitude Δvar is a non-universal function of two scaling variables λ/ξ and D/ξ, where λ is the thermal de Broglie wavelength and ξ is the bulk correlation length. It can be expressed via the bulk pressure, the Casimir force per unit wall area, and its derivative with respect to chemical potential. For thermodynamic states corresponding to the presence of the Bose–Einstein condensate the amplitude Δvar retains its non-universal character while the ratio of the mean standard deviation and the Casimir force takes the scaling form , where L is the linear size of the wall.