Recursion relations for the classical partition function of the hard‐sphere gas in two and three dimensions

1975 ◽  
Vol 63 (11) ◽  
pp. 5048-5049 ◽  
Author(s):  
Arthur M. Lesk
Keyword(s):  
Partition Function ◽  
Hard Sphere ◽  
Three Dimensions ◽  
Recursion Relations ◽  
Classical Partition Function

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

A REMARK ON PRIME DIVISORS OF PARTITION FUNCTIONS

2014 ◽  
Vol 10 (01) ◽  
pp. 125-131
Author(s):  
PAUL POLLACK
Keyword(s):  
Partition Function ◽  
Wide Class ◽  
Analogous Result ◽  
Partition Functions ◽  
Prime Divisors ◽  
Classical Partition Function

Schinzel showed that the set of primes that divide some value of the classical partition function is infinite. For a wide class of sets 𝒜, we prove an analogous result for the function p𝒜(n) that counts partitions of n into terms belonging to 𝒜.

scholarly journals Phase behavior of a hard sphere Maier-Saupe nematogenic system in three dimensions

2006 ◽  
Vol 74 (2) ◽  
Author(s):  
E. Lomba ◽  
C. Martín ◽  
N. G. Almarza ◽  
F. Lado
Keyword(s):  
Phase Behavior ◽  
Hard Sphere ◽  
Three Dimensions

Thermodynamic Functions of Pendular Molecules

1993 ◽  
Vol 58 (10) ◽  
pp. 2458-2473 ◽  
Author(s):  
Břetislav Friedrich ◽  
Dudley R. Herschbach
Keyword(s):  
Partition Function ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Quantum Statistical Mechanics ◽  
Rotational Constant ◽  
Chemical Equilibria ◽  
Rotational States ◽  
Dipolar Molecules ◽  
Linear Molecules ◽  
Classical Partition Function

External electric or magnetic fields can hybridize rotational states of individual dipolar molecules and thus create pendular states whose field-dependent eigenproperties differ qualitatively from those of a rotor or an oscilator. The pendular eigenfunctions are directional, so the molecular axis id oriented. Here we use quantum statistical mechanics to evaluate ensamble properties of the pendular states. For linear molecules, the partition function and the averages that determine the thermodynamic functions can be specified by two reduced variables involving the dipole moment, field strength, rotational constant, and temperature. We examine a simple approximation due to Pitzer that employs the classical partition function with quantum corrections. This provides explicit analytic formulas which permit thermodynamic properties to be evaluated to good accuracy without computing energy levels. As applications we evaluate the high-field average orientation of the molecular dipoles and field-induced shifts of chemical equilibria.

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