Calculation of the partition function using quantum genetic algorithms

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.