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Annals of the New York Academy of Sciences

Two‐Time States of a Spin‐Half Particle in a Uniform Magnetic Field

Susan S. D’Amato

Published Dec 1, 1986• 0 citations
Publisher
DOI
10.1111/j.1749-6632.1986.tb12461.x

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arXiv:cond-mat/9608025•Aug 6, 1996•0 citations
A rather complete discussion of the electrodynamic behavior of a gas of spin-\textonehalf{} particles in a uniform external magnetic field is presented. The method presented here is based on the general principles of elementary nonrelativistic quantum theory and takes account of the Doppler-broadening effects arising from the random thermal motion of the particles and the Compton recoil effects arising from the emission (spontaneous plus the induced or the stimulated emission) and absorption of photons by the spin-\textonehalf{} particles. In the first half of the paper a method is presented for calculating the spin permeability tensor which determines the propagation of transverse electromagnetic radiation through a gas of spin-\textonehalf{} particles in a uniform external magnetic field. It is shown that the spin permeability tensor thus obtained yields the familiar results of solid-state physics, such as the nuclear and electronic-spin radiofrequency susceptibility and the spin paramagnetism. In the second half of this paper the subject of spin-radiative equilibrium of a gas of spin-\textonehalf{} particles in a uniform external magnetic field is discussed in some detail. Simple closed-form expressions for the steady-state photon number density and the spin-radiative relaxation time of the system under study are thus derived. It is shown that the steady-state photon number density is the familiar distribution function corresponding to Bose---Einstein statistics for "complete thermodynamic equilibrium." The conditions under which the system of spin-\textonehalf{} particles in a uniform magnetic field can become unstable for transverse electromagnetic radiations are also discussed.
We study quantum phases of an anisotropic (XYZ) Heisenberg spin-1/2 chain under a mixed magnetic field (uniform and staggered), along with its variant. Our model consists of two competing relevant operators, anisotropy a, and staggered magnetic field hs. Depending on the sign of a this model describes either the physics of solitonic confinement, or the Ising transition between gapped phases. In our case excitations are the integer spin particle in contrast to the half-integer spin particle of frustrated dimerized spin chain. We do all analysis in weak coupling limit.
The dynamical evolution of a two-site Hubbard model is derived in the presence of an uniform external magnetic field for a general initial state. The time evolution of the half-filled (two-particle) case has a complex behaviour. Under certain initial conditions, the average number of fermions in one-particle state, in the half-filled case, is not necessarily periodic, even though the magnetization remains periodic. The results obtained may be applied to study the magnetization and the transition dipole moment of the organic charge-transfer salts in the in-phase mode.