scholarly journals Finite-Size Effects with Boundary Conditions on Bose-Einstein Condensation

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 300
Author(s):  
Run Cheng ◽  
Qian-Yi Wang ◽  
Yong-Long Wang ◽  
Hong-Shi Zong
Keyword(s):  
Boundary Conditions ◽  
Particle Density ◽  
Characteristic Temperature ◽  
Finite Size ◽  
Linear Size ◽  
Einstein Condensation ◽  
Condensate Fraction ◽  
Finite Size Effects ◽  
Antiperiodic Boundary Condition ◽  
Bose Einstein

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.

Phase transitions in finite systems

1983 ◽  
Vol 61 (2) ◽  
pp. 228-238 ◽  
Author(s):  
R. K. Pathria
Keyword(s):  
Phase Transitions ◽  
Thermodynamic Functions ◽  
Finite Size ◽  
Summation Formula ◽  
Einstein Condensation ◽  
Restricted Geometry ◽  
Finite Size Effects ◽  
Mathematical Techniques ◽  
Bose Einstein ◽  
The Given

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.

EXCITATIONS IN CONFINED LIQUID 4He

2005 ◽  
Vol 19 (04) ◽  
pp. 135-156
Author(s):  
FRANCESCO ALBERGAMO
Keyword(s):  
Saturated Vapor Pressure ◽  
Saturated Vapor ◽  
Finite Size ◽  
Einstein Condensation ◽  
Normal Fluid ◽  
Finite Size Effects ◽  
Bose Einstein Condensation ◽  
Bulk System ◽  
Bose Einstein ◽  
The Relationship

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 .

scholarly journals Thermal Simulations, Open Boundary Conditions and Switches

2018 ◽  
Vol 175 ◽  
pp. 07004 ◽  
Author(s):  
Yannis Burnier ◽  
Adrien Florio ◽  
Olaf Kaczmarek ◽  
Lukas Mazur
Keyword(s):  
Boundary Conditions ◽  
Topological Charge ◽  
Finite Size ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Finite Size Effects ◽  
Compact Spaces ◽  
Integral Current ◽  
Thermal Simulations ◽  
The Continuum

SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.

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