Spectral density method for the damping of boson elementary excitations in one-dimensional spin S chain

Spectral density method in quantum nonextensive thermostatistics and magnetic systems with long-range interactions

“…In case of the Heisenberg model (15), the polar ansatz (19) yields reasonable results for the excitation spectrum and the relevant thermodynamic q-quantities in the low temperature regime. For describing other thermodynamic regimes in a wider range of temperatures, one could to adopt a new set of approximations involving additional decoupling procedures and higher order moment equations, consistently with the spirit of the SDM [4,5,6,7,8].…”

“…A comparison of the previous relations with the corresponding extensive ones [4,6] suggests that the Tsallis' statistics does not influence the meaning of GF singularities, but drastically modifies the structure of the spectral weights introducing a mixing of energy levels.…”

“…In strict analogy with the extensive case [4,6,8], Eq. ( 11) suggests that the real poles ω mn of G qAB (ω) represent the exact energy spectrum of undamped excitations in the system.…”

“…In several situations of experimental interest, also the damping of excitations may be quite relevant so that the polar approximation ( 13) is inadequate. In this case, to take properly into account the finite life-time of quasi-particles, one can assume, as in the extensive case [6,8], the so called modified Gaussian ansatz…”

“…There exists at present a large variety of methods and techniques for calculation of the GF's both in classical and quantum thermostatistics [1,2,3,4,5]. In particular, the related spectral density method (SDM), originally formulated by Kalashnikov and Fradkin [4] for quantum many-body systems, is a powerful nonperturbative tool which allows a direct study of the macroscopic properties of interacting quantum and classical many-body systems [4,5,6,7,8] also involving phase transitions.…”