scholarly journals WAVE FUNCTION AND PAIR DISTRIBUTION FUNCTION OF A DILUTE BOSE GAS

2009 ◽  
Vol 23 (15) ◽  
pp. 1843-1845
Author(s):  
BO-BO WEI
Keyword(s):  
Wave Function ◽  
Distribution Function ◽  
Low Temperatures ◽  
Hard Sphere ◽  
Pair Distribution Function ◽  
Bose Gas ◽  
Dilute Bose Gas

The wave function of a dilute hard sphere Bose gas at low temperatures is revisited. Errors in an early 1957 paper are corrected. The pair distribution function is calculated for two values of [Formula: see text].

The pair distribution function of a dilute hard sphere bose gas

Physica ◽  
1964 ◽  
Vol 30 (12) ◽  
pp. 2123-2136 ◽  
Author(s):  
A. Isihara ◽  
D.D.H. Yee
Keyword(s):  
Distribution Function ◽  
Hard Sphere ◽  
Pair Distribution Function ◽  
Bose Gas

New Approximate Analytical Formula for the Solute-Solvent Contact Distribution Function in an Infinitely Dilute Binary Hard-Sphere Mixture

2008 ◽  
Vol 73 (3) ◽  
pp. 314-321 ◽  
Author(s):  
Stanislav Labík ◽  
William R. Smith
Keyword(s):  
Distribution Function ◽  
Hard Sphere ◽  
Pair Distribution Function ◽  
Analytical Formula ◽  
Diameter Ratio ◽  
Scaled Particle Theory ◽  
Perfect Agreement ◽  
Simulation Results ◽  
Contact Distribution ◽  
Contact Distribution Function

A new analytical expression for the contact value of the solute-solvent pair distribution function of a binary hard-sphere mixture at infinite dilution is proposed, based on scaled-particle-theory-like arguments. For high solute-solvent diameter ratio it predicts perfect agreement with the simulation results.

On the Pair Distribution Function of a Hard Sphere Bose System

1960 ◽  
Vol 1 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Leopoldo S. Garcia‐Colin ◽  
Jean Peretti
Keyword(s):  
Distribution Function ◽  
Hard Sphere ◽  
Pair Distribution Function ◽  
Bose System

A variational method for the ground state of a Bose fluid

1960 ◽  
Vol 256 (1284) ◽  
pp. 106-114 ◽  
Keyword(s):  
Integral Equation ◽  
Wave Function ◽  
Distribution Function ◽  
Variational Principle ◽  
Variational Method ◽  
Ground State ◽  
Pair Distribution Function ◽  
Wave Functions ◽  
Absolute Zero ◽  
Superposition Approximation

A modification of the Rayleigh—Ritz variational principle is described which makes possible a calculation of the energy, wave function, and pair distribution function f 12 ≡ f ( x 1 , x 2 ) of a Bose fluid, such as liquid 4 He, at absolute zero. The assumptions made are: (i) two-body interactions with potential U ij , (ii) trial wave functions of the form f 12 ≡ f ( x 1 , x 2 ) and (iii) the Kirkwood ‘superposition' approximation. Under these approximations, the expectation energy is E = 1 2 n 2 ∫ ∫ d 3 X 1 d 3 X 2 f 12 U 12 − h 2 m − 1 ( ∇ 1 8 ϕ 12 ) + ( ∇ 1 ϕ 12 ) 2 + n ∫ d 3 X 2 f 13 f 23 ϕ 12 ⋅ ∇ 1 ϕ 13 , where n ≡ N/V . It is shown here that making E stationary with respect to independent variations in f and ɸ corresponds to simultaneously applying the ordinary Rayleigh-Ritz principle and solving the Born-Green-Yvon integral equation for f . The method is illustrated by reproducing Bogolyubov’s results for the case where U is small. The case where U is large must be dealt with numerically, but transformations for simplifying the computations are given here.

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