Collective Modes in the Quantum Lattice or ThreeDimensional XY Model. I
Abstract
The collective motions in the XY model are investigated with the help of Mori's generalized theory of Brownian motion. By supplementing the set of macrovariables in a previous paper by dot{S}_{q}^{z}, the collective mode with soundlike spectrum which survives at the critical point is derived, where dot{S}_{q}^{z} is the time derivative of the orthogonal zcomponent of spin operator in the Fourier transform. This variable represents the temporal change of the density of liquid helium and therefore is related to the longitudinal momentum in long wavelength. This mode is shown to reduce to the spin wave in the limit of vanishing temperature and to behave like the first sound near the critical point.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 September 1981
 DOI:
 10.1143/PTP.66.861
 Bibcode:
 1981PThPh..66..861A