Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Generalized Bloch equations and dissipation of longitudinal magnetic-field energy

Anatoly Yu. Smirnov

Published Aug 1, 1997• 7 citations

Abstract

For a spin-$\frac{1}{2}$ coupled to a Gaussian heat bath in the presence of an external magnetic field, we generalize the Bloch equations to the non-Markovian case. Using this generalization as the base, we show that the time-varying component of the magnetic field parallel to its constant part is absorbed by the spin system, especially at high temperatures of the heat bath. For the spectral density and dispersion of longitudinal spin fluctuations, we obtain expressions that are in good agreement with known results.

DOI: 10.1103/physreve.56.1484

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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Generalized Bloch equations and dissipation of longitudinal magnetic-field energy

Anatoly Yu. Smirnov

Published Aug 1, 1997• 7 citations

Publisher

Abstract

For a spin-

\frac{1}{2}

coupled to a Gaussian heat bath in the presence of an external magnetic field, we generalize the Bloch equations to the non-Markovian case. Using this generalization as the base, we show that the time-varying component of the magnetic field parallel to its constant part is absorbed by the spin system, especially at high temperatures of the heat bath. For the spectral density and dispersion of longitudinal spin fluctuations, we obtain expressions that are in good agreement with known results.

DOI: 10.1103/physreve.56.1484

Related papers

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arXiv:2106.07509Physical review. EDec 10, 202116 citations

For a spin-

\frac{1}{2}

The time evolution of a spin-

\frac{1}{2}

particle under the influence of a locally applied external magnetic field, and interacting with anisotropic spin environment in thermal equilibrium at temperature

T

is studied. The exact analytical form of the reduced density matrix of the central spin is calculated explicitly for a finite number of bath spins. The case of an infinite number of environmental spins is investigated using the convergence of the rescaled bath operators to normal Gaussian random variables. In this limit, we derive the analytical form of the components of the Bloch vector for antiferromagnetic interactions within the bath, and we investigate the short-time and long-time behavior of reduced dynamics. The effect of the external magnetic field, the anisotropy, and the temperature of the bath on the decoherence of the central spin are discussed.

{\mathcal{E}}_{k}

and

{\mathcal{E}}_{p}

denote the average kinetic and potential energies of individual thermostat oscillators. The net averaging is twofold; the first one is over the Gibbs canonical state for the thermostat, giving

{\mathcal{E}}_{k}

and

{\mathcal{E}}_{p}

, and the second one, denoted by $\ensuremath{\langle}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\rangle}$, is over the frequencies $\ensuremath{\omega}$ of the bath oscillators which contribute to

{E}_{k}

and

{E}_{p}

according to probability distributions ${\mathcal{P}}_{k}(\ensuremath{\omega})$ and ${\mathcal{P}}_{p}(\ensuremath{\omega})$, respectively. The relationship of the present quantum version of the equipartition theorem with that of the fluctuation-dissipation theorem (within the linear-response theory framework) is also explored. Further, we investigate the influence of the external magnetic field and the effect of different dissipation processes through Gaussian decay and Drude and radiation bath spectral density functions on the typical properties of ${\mathcal{P}}_{k}(\ensuremath{\omega})$ and ${\mathcal{P}}_{p}(\ensuremath{\omega})$. Finally, the role of system-bath coupling strength and the memory effect is analyzed in the context of average kinetic and potential energies of the dissipative charged magneto-oscillator.