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Calculation of the partition function using quantum genetic algorithms

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  • Grigorenko, I
  • Garcia, M.E

Abstract

We present a new method based on genetic algorithms which permits to determine efficiently the partition function and the excitation spectrum of few-body quantum systems. In our approach, we use a variational formulation for the partition function Z of the system as a functional of its eigenfunctions. Z is obtained by applying the procedure of survival of the fittest, starting from initial random population. During the evolution the best representative converges to a set of eigenfunctions for a given Hamiltonian, while the partition function attains its global extremum (maximum) for a given temperature. We calculate the spectrum and the partition function in the case of few interacting particles in one-dimensional infinite potential well. We investigate formation of the Wigner crystal and study its melting induced by termal and quantum fluctuations.

Suggested Citation

  • Grigorenko, I & Garcia, M.E, 2002. "Calculation of the partition function using quantum genetic algorithms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 463-470.
    • Handle: RePEc:eee:phsmap:v:313:y:2002:i:3:p:463-470
    DOI: 10.1016/S0378-4371(02)00988-3
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