PUB - Publikationen an der Universität Bielefeld

A lattice system of interacting quantum particles of mass m performing anharmonic oscillations around their unstable equilibrium positions is considered. It is proved that quantum effects may stabilize such a system, which means that, for any temperature, the spatial decay of two point correlation functions is not less than that for the system of harmonic oscillators with the same interaction and stable equilibria. It is exponential for short-range interaction potentials. The condition of this stabilization is that the 'quantum rigidity' mdelta(2) of such an oscillator ought to exceed the total force Sigma(l') J(ll'). Here delta is the minimal difference between the eigenvalues of the one particle Hamiltonian. For the anharmonic potentials which grow at infinity faster than x(2), the parameter mdelta(2) --> +infinity as m --> 0, hence the stabilization occurs when m < m(*), with m(*) independent of thermodynamic parameters including β.