Crossover Phenomena and Resonances in Quantum Systems

PABLO SERRA; SABRE KAIS; NIMROD MOISEYEV

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2001 vol. 64 p. 62502 - 62502

1050-2947

The finite-size scaling method is used to calculate the critical parameters of a two-parameter model Hamiltonian that exhibit resonances. We show the existence of a crossover phenomenon for the energy spectrum; the transition from a bound state to a continuum is a ?second-order phase transition? in one region and a ?first-order phase transition? in another region. As the parameters varied, the numerical value of the critical exponent of the energy levels changed from two to one. In the zone where the critical exponent equals one, the system has narrow resonances and they disappear when the exponent is two. The method has potential applicability in predicting stable and metastable atomic and molecular states. We also show that finite-size scaling methods are capable of detecting multicritical points.