Condensate fraction and momentum distribution of liquid helium

An expansion is presented which allows practical evaluation of the one-particle density matrix of the ground state of a Bose fluid in terms of its two-body, three-body, … spatial distribution functions.     

Off-diagonal long-range order in Bose liquids: irrotational flow and quantization of circulation

On the basis of gauge invariance, it is proven in an elementary and straightforward manner, but without invoking any ad hoc assumption, that the existence of off-diagonal long-range order in one-particle reduced density matrix in Bose liquids implies both the irrotational flow in a simply connected region and the quantization of circulation in a multiply connected region, the two fundamental properties of a Bose superfluid. The origin for both is the phase coherence of condensate wave functions. Some relevant issues are also addressed.     

The Excitation Spectrum for Weakly Interacting Bosons in a Trap

We investigate the low-energy excitation spectrum of a Bose gas confined in a trap, with weak long-range repulsive interactions. In particular, we prove that the spectrum can be described in terms of the eigenvalues of an effective one-particle operator, as predicted by the Bogoliubov approximation.     

Entropy Chaos and Bose-Einstein Condensation

We prove the entropy-chaos property for the system of N indistinguishable interacting diffusions rigorously associated with the ground state of N trapped Bose particles in the Gross–Pitaevskii scaling limit of infinitely many particles. On the path-space we show that the sequence of probability measures of the one-particle interacting diffusion weakly converges to a limit probability measure, uniquely associated with the minimizer of the Gross-Pitaevskii functional.     

On the Nature of Bose-Einstein Condensation in Disordered Systems

We study the perfect Bose gas in random external potentials and show that there is generalized Bose-Einstein condensation in the random eigenstates if and only if the same occurs in the one-particle kinetic-energy eigenstates, which corresponds to the generalized condensation of the free Bose gas. Moreover, we prove that the amounts of both condensate densities are equal. Our method is based on the derivation of an explicit formula for the occupation measure in the one-body kinetic-energy eigenstates which describes the repartition of particles among these non-random states. This technique can be adapted to re-examine the properties of the perfect Bose gas in the presence of weak (scaled) non-random potentials, for which we establish similar results. In addition some of our results can be applied to models with diagonal interactions, that is, models which conserve the occupation density in each single particle eigenstate.     

Ideal bose gas in an oscillator potential (exact solution)

Exact expressions for the statistical sum of the grand canonical ensemble and the one-particle density matrix are derived based on the definition of the density matrix for a system of N identical noninteracting Bose particles in an oscillator potential as a sum with respect to the symmetric exchange of the density matrix coordinates of distinguishable particles. A quasi-classical scenario is analyzed in detail.     

Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases

We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.     

Dispersion and nonlinear frequancy shift of natural waves in the Bose–Einstein condensate

Quantum mechanics equations for a system of the Bose particles are represented in the form of material field equations. A nonlinear equation for the macroscopic one-particle wave function is derived. Using the Krylov–Bogolyubov–Mitropol’skii method for equations in partial derivatives, nonlinear waves in the Bose–Einstein condensate are investigated. In the cubic approximation, dispersion relations for waves are derived and nonlinear frequency shift is calculated in the first- and third-order approximations for the interaction radius.     

Bose–Einstein condensation in random potentials

We present a rigorous study of the perfect Bose-gas in the presence of a homogeneous ergodic random potential. It is demonstrated that the Lifshitz tail behaviour of the one-particle spectrum reduces the critical dimensionality of the (generalized) Bose–Einstein Condensation (BEC) to d=1. To tackle the Off-Diagonal Long-Range Order (ODLRO) we introduce the space average one-body reduced density matrix. For a one-dimensional Poisson-type random potential we prove that randomness enhances the exponential decay of this matrix in domain free of the BEC. To cite this article: O. Lenoble et al., C. R. Physique 5 (2004).     

Bose-Einstein condensation in interacting gases

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a change of the velocity profile just above the transition: the proportion of atoms with low velocities is higher than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres. Received 13 November 1998     

One-particle and few-particle billiards

We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and against each other. In the one-particle case, we investigate the formation and destruction of resonance islands in (generalized) mushroom billiards, which are a recently discovered class of Hamiltonian systems with mixed regular-chaotic dynamics. In the few-particle case, we compare the dynamics in container geometries whose counterpart one-particle billiards are integrable, chaotic, and mixed. One of our findings is that two-, three-, and four-particle billiards confined to containers with integrable one-particle counterparts inherit some integrals of motion and exhibit a regular partition of phase space into ergodic components of positive measure. Therefore, the shape of a container matters not only for noninteracting particles but also for interacting particles.     

理想玻色气体的焦汤系数

应用玻色系统的基本方程，玻色积分的特性以及热力学理论，导得理想玻色气体焦汤系数的解析表达式，详细讨论了低温下玻色气体的定压热容和焦汤系数，阐明了系统的量子本性对焦汤系数的贡献，表明理想玻色气体适用于低温制冷系统。     

Analyticity properties and many-particle structure in general quantum field theory

The extraction of one-particle singularities from then-point functions is performed in the framework of L.S.Z. field theory in the case of a single massive scalar field. It is proved that the “one-particle irreducible” functions thus obtained enjoy the analytic and algebraic primitive structure of generaln-point functions (up to a finite number of generalized C.D.D. singularities). Finally under an additional technical assumption, it is shown that the Glaser-Lehmann-Zimmermann relations stating the completeness of asymptotic states yield similar relations satisfied in any given channel by the corresponding one-particle irreducible functions.     

Helium-4 Bose fluids formed in one-dimensional 18 A diameter pores

Bose fluids restricted in one dimension (1D) are realized by adsorbing 4He atoms on the 1D pore walls with a diameter of about 18 A. The Bose fluid appears above an adsorbed amount after the pore walls are coated with the inert 4He atoms. Heat capacity of the fluid was observed to have a temperature-linear term at low temperatures. This corresponds to the phonon heat capacity of the Bose fluid in the 1D pores. We estimate the phonon velocity and the interaction of the 1D Bose fluid.     

The multiple scattering model analysis of high energy multiparticle production on emulsion nuclei

Data on multiparticle production on emulsion nuclei in the range 50–400 GeV/c have been analyzed in the framework of multiple scattering model developed by Capella and Krzywicki. It is shown that under some reasonable assumptions multiple scattering type models qualitatively reproduce multiplicity distributions of relativistic charged particles, one-particle spectra and two-particle inclusive correlations. When considering one-particle distributions a particular attention was given to the regions of small and large pseudorapidities. In the first region we found an apparent evidence for low-energy cascading, contribution and main features of which have been discussed. It is also discussed how strongly the behaviour of one-particle spectra at large rapidities would depend on the internal structure of a projectile particle.     

On the theory of superfluidity

We investigate the properties of dispersion spectra of one-dimensional periodic Bose systems with repulsive interparticle interactions. These systems with sufficient large interactions can support metastable supercurrent states, which correspond to the local minima of the dispersion spectra at non-zero momenta. The existence of local minima in the spectra and the energy barriers, which separate the minima, can be explained in terms of Bose exchange symmetry. We extend our study to the case of higher dimensional Bose systems. We suggest that superfluidity could be understood as a Bose exchange effect.     

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.     

A path integral centroid molecular dynamics method for Bose and Fermi statistics

We propose a path integral centroid molecular dynamics (CMD) method extended to Bose and Fermi statistics. An extended method of path integral molecular dynamics (PIMD) for such statistics is also developed as a technique of calculations of static properties. Bose PIMD and CMD simulations have been performed for bulk liquid ⁴He and ideal Bose gas, respectively. The remnant of λ transition is observed for bulk liquid ⁴He, while the effect of Bose statistics on the centroid dynamics spanning several nanoseconds is observed for ideal Bose gas.