EXCITATIONS IN CONFINED LIQUID 4He

2005 ◽  
Vol 19 (04) ◽  
pp. 135-156
Author(s):  
FRANCESCO ALBERGAMO

The spectacular properties of liquid helium at low temperature are generally accepted as the signature of the bosonic nature of this system. Particularly the superfluid phase is identified with a Bose–Einstein condensed fluid. However, the relationship between the superfluidity and the Bose–Einstein condensation is still largely unknown. Studying a perturbed liquid 4 He system would provide information on the relationship between the two phenomena. Liquid 4 He confined in porous media provides an excellent example of a boson system submitted to disorder and finite-size effects. Much care should be paid to the sample preparation, particularly the confining condition should be defined quantitatively. To achieve homogeneous confinement conditions, firstly a suitable porous sample should be selected, the experiments should then be conducted at a lower pressure than the saturated vapor pressure of bulk helium. Several interesting effects have been shown in confined 4 He samples prepared as described above. Particularly we report the observation of the separation of the superfluid-normal fluid transition temperature, T c , from the temperature at which the Bose–Einstein condensation is believed to start, T BEC , the existence of metastable densities for the confined liquid accessible to the bulk system as a short-lived metastable state only and strong clues for a finite lifetime of the elementary excitations at temperatures as low as 0.4 K .

1983 ◽  
Vol 61 (2) ◽  
pp. 228-238 ◽  
Author(s):  
R. K. Pathria

Mathematical singularities, which are known to be at the heart of phase transitions and are responsible for making the thermodynamic functions of the given system nonanalytic, are a consequence of the thermodynamic limit, viz. N and V → ∞ with N/V staying constant. When a system containing a finite number of particles and confined to a restricted geometry undergoes a phase transition, these singularities get rounded off, with the result that all thermodynamic functions become analytic and vary smoothly with the relevant parameters of the problem. Theoretical analysis of such situations requires the use of special mathematical techniques which may vary drastically from case to case.In the present communication we report the results of a rigorous analysis of the problem of "Bose–Einstein condensation in restricted geometries", which has been carried out by making an extensive use of the Poisson summation formula. Particular emphasis is laid on the growth of the condensate fraction [Formula: see text] as the temperature of the system is lowered, and on the influence of the boundary conditions imposed on the wave functions of the particles. The relevance of these results, in relation to the scaling theory of finite size effects, is also discussed.


Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 300
Author(s):  
Run Cheng ◽  
Qian-Yi Wang ◽  
Yong-Long Wang ◽  
Hong-Shi Zong

We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume V=L3. By changing linear size L and imposing different boundary conditions on the system, we present a numerical analysis on the characteristic temperature and condensate fraction and find that a smaller linear size is efficient to increase the characteristic temperature and condensate fraction. Moreover, there is a singularity under the antiperiodic boundary condition.


1991 ◽  
Vol 69 (7) ◽  
pp. 813-821
Author(s):  
J. Hugo Souto ◽  
A. N. Chaba

We show that the expression for the density of states of a particle in a three-dimensional rectangular box of finite size can be obtained by using directly the Poisson's summation formula instead of using the Walfisz formula or the generalized Euler formula both of which can be derived from the former. We also derive the expression for the density of states in the case of an enclosure in the form of an infinite rectangular slab and apply it to the problem of the Bose–Einstein condensation of a Bose gas of noninteracting particles confined to a thin-film geometry.


Author(s):  
Klaus Morawetz

The Bose–Einstein condensation and appearance of superfluidity and superconductivity are introduced from basic phenomena. A systematic theory based on the asymmetric expansion of chapter 11 is shown to correct the T-matrix from unphysical multiple-scattering events. The resulting generalised Soven scheme provides the Beliaev equations for Boson’s and the Nambu–Gorkov equations for fermions without the usage of anomalous and non-conserving propagators. This systematic theory allows calculating the fluctuations above and below the critical parameters. Gap equations and Bogoliubov–DeGennes equations are derived from this theory. Interacting Bose systems with finite temperatures are discussed with successively better approximations ranging from Bogoliubov and Popov up to corrected T-matrices. For superconductivity, the asymmetric theory leading to the corrected T-matrix allows for establishing the stability of the condensate and decides correctly about the pair-breaking mechanisms in contrast to conventional approaches. The relation between the correlated density from nonlocal kinetic theory and the density of Cooper pairs is shown.


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