Quantum Stabilization and Decay of Correlations in Anharmonic Crystals

ISSN： 0377-9017

Source： Letters in Mathematical Physics, Vol.65, Iss.1, 2003-07, pp. : 1-14

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Abstract

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' mδ² of such an oscillator ought to exceed the total force ∑_l' J_ll'. Here δ is the minimal differencebetween the eigenvalues of the one particle Hamiltonian. For the anharmonic potentials which grow at ∞ faster than x², the parameter mδ²→+∞ as m→0, hence the stabilization occurs when m<m_*, with m_* independent of thermodynamic parameters including β.