scholarly journals INEQUIVALENT REPRESENTATIONS OF A q-OSCILLATOR ALGEBRA IN A QUANTUM q-GAS

1995 ◽  
Vol 09 (14) ◽  
pp. 883-887 ◽  
Author(s):  
M. R-MONTEIRO ◽  
L. M. C. S. RODRIGUES
Keyword(s):  
Critical Temperature ◽  
Virial Expansion ◽  
Einstein Condensation ◽  
Oscillator Algebra ◽  
Fundamental Representation ◽  
Bose Einstein Condensation ◽  
Condensation Phenomenon ◽  
Bose Einstein ◽  
Inequivalent Representations ◽  
Λ Point

We study the consequences of inequivalent representations of a q-oscillator algebra on a quantum q-gas. As in the "fundamental" representation of the algebra, the q-gas presents the Bose-Einstein condensation phenomenon and a λ-point transition. The virial expansion and the critical temperature of condensation are very sensible to the representation chosen; instead, the discontinuity in the λ-point transition is unaffected.

ν-DIMENSIONAL IDEAL QUANTUM q-GAS: BOSE-EINSTEIN CONDENSATION AND λ-POINT TRANSITION

1994 ◽  
Vol 08 (23) ◽  
pp. 3281-3298 ◽  
Author(s):  
M. R-MONTEIRO ◽  
ITZHAK RODITI ◽  
LIGIA M.C.S. RODRIGUES
Keyword(s):  
Critical Temperature ◽  
Chemical Potential ◽  
Ideal Gas ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Spatial Dimensions ◽  
Quantum Symmetries ◽  
Ideal Quantum ◽  
Bose Einstein ◽  
Λ Point

We consider an ideal quantum q-gas in ν spatial dimensions and energy spectrum ωiα pα Departing from the Hamiltonian H=ω[N], we study the effect of the deformation on thermodynamic functions and equation of state of that system. The virial expansion is obtained for the high temperature (or low density) regime. The critical temperature is higher than in non-deformed ideal gases. We show that Bose-Einstein condensation always exists (unless when ν/α=1) for finite q but not for q=∞. Employing numerical calculations and selecting for v/α the values 3/2, 2 and 3, we show the critical temperature as a function of q, the specific heat CV and the chemical potential µ as functions of [Formula: see text] for q=1.05 and q=4.5. CV exhibits a λ-point discontinuity in all cases, instead of the cusp singularity found in the usual ideal gas. Our results indicate that physical systems which have quantum symmetries can exhibit Bose-Einstein condensation phenomenon, the critical temperature being favored by the deformation parameter.

A MODEL OF BOSE–EINSTEIN CONDENSATION WITH ITINERANT AND LOCALIZED STATES

2005 ◽  
Vol 19 (21) ◽  
pp. 1011-1034
Author(s):  
FUXIANG HAN ◽  
ZHIRU REN ◽  
YUN'E GAO
Keyword(s):  
Critical Temperature ◽  
Anderson Model ◽  
Localized States ◽  
Mean Field Approximation ◽  
Einstein Condensation ◽  
Model Parameters ◽  
Zeroth Order ◽  
Energy Bands ◽  
Bose Einstein Condensation ◽  
Bose Einstein

We propose a model that includes itinerant and localized states to study Bose–Einstein condensation of ultracold atoms in optical lattices (Bose–Anderson model). It is found that the original itinerant and localized states intermix to give rise to a new energy band structure with two quasiparticle energy bands. We have computed the critical temperature Tc of the Bose–Einstein condensation of the quasiparticles in the Bose–Anderson model using our newly developed numerical algorithm and found that Tc increases as na3 (the number density times the lattice constant cubed) increases according to the power law Tc≈18.93(na3)0.59 nK for na3<0.125 and according to the linear relation Tc≈8.75+10.53na3 nK for 1.25<na3<12.5 for the given model parameters. With the self-consistent equations for the condensation fractions obtained within the Bogoliubov mean-field approximation, the effects of the on-site repulsion U on the quasiparticle condensation are investigated. We have found that, for values up to several times the zeroth-order critical temperature, U enhances the zeroth-order condensation fraction at intermediate temperatures and effectively raises the critical temperature, while it slightly suppresses the zeroth-order condensation fraction at very low temperatures.

Possible Bose-Einstein Condensation of Polygonal Clusters in 2D-Materials

2019 ◽  
Vol 297 ◽  
pp. 204-208
Author(s):  
Abid Boudiar
Keyword(s):  
Free Energy ◽  
Critical Temperature ◽  
Ground State ◽  
Low Temperatures ◽  
2D Materials ◽  
Equilibrium Structure ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Exchange Approximation ◽  
Bose Einstein

This study investigates the possibility of Bose-Einstein condensation (BEC) in 2D-nanoclusters. A ground state equilibrium structure involves the single phonon exchange approximation. At critical temperature, the specific heat, entropy, and free energy of the system can be determined. The results support the existence of BEC in nanoclusters, and they lead to predictions of the behaviour of 2Dmaterials at low temperatures.

Bose–Einstein condensation at different temperatures below the critical temperature

2018 ◽  
Vol 32 (17) ◽  
pp. 1850194 ◽  
Author(s):  
Abhishek Das
Keyword(s):  
Critical Temperature ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Different Temperatures ◽  
Bose Einstein

In this paper, we endeavor to show that the phenomenon of Bose–Einstein condensation can take place at discrete temperatures lower than the known critical temperature value.

On the Bose-Einstein condensation

1950 ◽  
Vol 203 (1073) ◽  
pp. 266-286 ◽  
Keyword(s):  
Specific Heat ◽  
Transition Point ◽  
Energy Levels ◽  
Three Dimensional ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Quantum Numbers ◽  
The Mean ◽  
Bose Einstein ◽  
Λ Point

The Bose-Einstein condensation of a gas is investigated. Starting from the well-known formulae for Bose statistics, the problem has been generalized to include a variety of potential fields in which the particles of the gas move, and the number w of dimensions has not been restricted to three. The energy levels are taken to be ε i ≡ ε s 1 , . . . . , s 10 = constant h 2 m s 1 α − 1 a 1 2 + . . . + s w α a w 2 ( 1 ≤ α ≤ 2 ) the quantum numbers being s 1 , w = 1, 2, ..., and a 1 , ..., a w being certain characteristic lengths. (For α = 2, the potential field is that of the w -dimensional rectangular box; for α = 1, we obtain the w -dimensional harmonic oscillator field.) A direct rigorous method is used similar to that proposed by Fowler & Jones (1938). It is shown that the number q = w /α determines the appearance of an Einstein transition temperature T 0 ·For q≤ 1 there is no such point, while for q > 1 a transition point exists. For 1 < q≤ 2, the mean energy ϵ - per particle and the specific heat dϵ - /dT are continuous at T = T 0 · For q > 2, the specific heat is discontinuous at T = T 0 , giving rise to a A λ-point. A well-defined transition point only appears for a very large (theoretically infinite) number N of particles. T 0 is finite only if the quantity v = N/(a 1 .... a w )2/ α ¯ is finite. For a rectangular box, v is equal to the mean density of the gas. If v tends to zero or infinity as N→ ∞, then T 0 likewise tends to zero or infinity. In the case q > 1, and at temperatures T < T 0 ' there is a finite fraction N 0 /N of the particles, given by N 0 /N = 1-(T/T 0 ) q , in the lowest state. London’s formula (1938 b ) for the three-dimensional box is an example of this equation. Some further results are also compared with those given by London’s continuous spectrum approximation.

GAUSSIAN DOMINATION AND BOSE–EINSTEIN CONDENSATION IN THE INTERACTING BOSON GAS

1999 ◽  
Vol 13 (27) ◽  
pp. 3235-3243 ◽  
Author(s):  
M. CORGINI ◽  
D. P. SANKOVICH
Keyword(s):  
Critical Temperature ◽  
Einstein Condensation ◽  
Sufficient Condition ◽  
Interaction Function ◽  
Bose Einstein Condensation ◽  
Bose Einstein

A Davies model of an imperfect boson gas is considered. The model includes not only a convex, but also a concave type of an interaction function which depends on a dencity operator. A sufficient condition of the Bose–Einstein condensation is proved. An exact value of the critical temperature is obtained.

Sign in / Sign up

Export Citation Format

Share Document