F. Mohling — Statistical mechanics. Methods and applications

Quantum Monte Carlo Methods in Statistical Mechanics

This paper deals with the optimization of trial states for the computation of dominant eigenvalues of operators and very large matrices. In addition to preliminary results for the energy spectrum of van der Waals clusters, we review results of the application of this method to the computation of relaxation times of independent relaxation modes at the Ising critical point in two dimensions.

Applications of statistical mechanics in number theory

The links between statistical physics and number theory are discussed. First the attempts to prove the Riemann Hypothesis by means of the suitable spin model and the Lee–Yang theorem about zeros of the partition function are shortly reviewed. Next, the analogies between random walks and prime numbers are mentioned. In the last section the partition function of the system whose energies are de n...

Applications of methods of quantum statistical mechanics to two - dimensional electron systems

1 Abstract The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. T...

Statistical Decision Theory: Concepts, Methods and Applications

Statistical mechanics methods and phase transitions in optimization problems

Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer science and statistical physics. This review aims at presenting the tools and concepts designed by physicists to deal with optimization or decision problems in...