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Equation of state of a classical anharmonic oscillator

Authors
Journal
Physica A Statistical Mechanics and its Applications
0378-4371
Publisher
Elsevier
Publication Date
Volume
81
Issue
1
Identifiers
DOI: 10.1016/0378-4371(75)90040-0
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract Static properties of a particle moving in an anharmonic potential in equilibrium with a temperature bath and an external field are discussed in the framework of classical statistical mechanics. This model system represents the basic unit in current theories of structural phase transitions. Hierarchies of equations for the correlations (cumulants) and irreducible vertices are derived from the equilibrium condition. Approximate solutions are obtained from the hierarchies by truncation. Alternatively, one can write the equilibrium condition as differential equation which may be solved exactly, if appropriate initial conditions are known. Both methods have been worked out for a single- and a double-well potential. By truncation of the hierarchies one obtains as quantitatively correct result only a low-temperature expansion for the single-well potential.

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