scholarly journals Fisher zeros of a unitary Bose gas

2015 ◽  
Vol 93 (8) ◽  
pp. 830-835 ◽  
Author(s):  
Wytse van Dijk ◽  
Calvin Lobo ◽  
Allison MacDonald ◽  
Rajat K. Bhaduri
Keyword(s):  
Partition Function ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Direct Calculation ◽  
Bose Gas ◽  
Einstein Condensation ◽  
Condensation Temperature ◽  
Canonical Partition Function ◽  
Fisher Zeros ◽  
Unitary Gas

For real inverse temperature β, the canonical partition function is always positive, being a sum of positive terms. There are zeros, however, on the complex β plane that are called Fisher zeros. In the thermodynamic limit, the Fisher zeros coalesce into continuous curves. In case there is a phase transition, the zeros tend to pinch the real-β axis. For an ideal trapped Bose gas in an isotropic three-dimensional harmonic oscillator, this tendency is clearly seen, signalling Bose–Einstein condensation (BEC). The calculation can be formulated exactly in terms of the virial expansion with temperature-dependent virial coefficients. When the second virial coefficient of a strongly interacting attractive unitary gas is included in the calculation, BEC seems to survive, with the condensation temperature shifted to a lower value for the unitary gas. This shift is consistent with a direct calculation of the heat capacity from the canonical partition function of the ideal and the unitary gas.

scholarly journals Particle Fluctuations in Mesoscopic Bose Systems

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 603 ◽  
Author(s):  
Vyacheslav I. Yukalov
Keyword(s):  
Condensed System ◽  
Spatial Dimension ◽  
Bose Gas ◽  
Einstein Condensation ◽  
Condensation Temperature ◽  
Bose System ◽  
Bose Einstein Condensation ◽  
Spatial Dimensionality ◽  
Bose Einstein ◽  
Ideal Bose Gas

Particle fluctuations in mesoscopic Bose systems of arbitrary spatial dimensionality are considered. Both ideal Bose gases and interacting Bose systems are studied in the regions above the Bose–Einstein condensation temperature T c , as well as below this temperature. The strength of particle fluctuations defines whether the system is stable or not. Stability conditions depend on the spatial dimensionality d and on the confining dimension D of the system. The consideration shows that mesoscopic systems, experiencing Bose–Einstein condensation, are stable when: (i) ideal Bose gas is confined in a rectangular box of spatial dimension d > 2 above T c and in a box of d > 4 below T c ; (ii) ideal Bose gas is confined in a power-law trap of a confining dimension D > 2 above T c and of a confining dimension D > 4 below T c ; (iii) the interacting Bose system is confined in a rectangular box of dimension d > 2 above T c , while below T c , particle interactions stabilize the Bose-condensed system, making it stable for d = 3 ; (iv) nonlocal interactions diminish the condensation temperature, as compared with the fluctuations in a system with contact interactions.

scholarly journals On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 846
Author(s):  
Donya Ohadi ◽  
David S. Corti ◽  
Mark J. Uline
Keyword(s):  
Equation Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Pure Component ◽  
Excluded Volume ◽  
Theory Approach ◽  
Prolate Spheroidal ◽  
Empirical Correction ◽  
Prolate Spheroids ◽  
Onsager Theory

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

scholarly journals APPLICATIONS OF DENSITY MATRICES IN A TRAPPED BOSE GAS

2006 ◽  
Vol 20 (15) ◽  
pp. 2189-2221 ◽  
Author(s):  
K. CH. CHATZISAVVAS ◽  
S. E. MASSEN ◽  
CH. C. MOUSTAKIDIS ◽  
C. P. PANOS
Keyword(s):  
Quantum Information ◽  
Bose Gas ◽  
Einstein Condensation ◽  
Density Distributions ◽  
Occupation Numbers ◽  
The One ◽  
Bose Einstein ◽  
Jensen Shannon Divergence ◽  
Analytical Expressions ◽  
Short Range Correlations

An overview of the Bose–Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback–Leibler relative entropy and the recently proposed Jensen–Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross–Piatevskii equation is solved, giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.

Sign in / Sign up

Export Citation Format

Share Document