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International Journal of Modern Physics C

RELAXATION OF METASTABLE STATES BY QUANTUM FLUCTUATION

Seiji Miyashita, Keiji Saito

Published Dec 1, 1999• 0 citations
Publisher

Abstract

An investigation for numerical method to study quantum dynamics in dissipative environments is presented, studying the resonant tunneling phenomena of the low temperature magnetization process of Mn 12. It is pointed out that information of pure quantum transition can be obtained from deceptive nonadiabatic transitions due to the dissipative environments.

DOI
10.1142/s0129183199001194

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An investigation for numerical method to study quantum dynamics in dissipative environments is presented, studying the resonant tunneling phenomena of the low temperature magnetization process of Mn 12. It is pointed out that information of pure quantum transition can be obtained from deceptive nonadiabatic transitions due to the dissipative environments.
We have constructed an algorithm to treat quantum mechanical dynamics, such as the nonadiabatic transitions in a dissipative environment, by making use of the formula of reduced density matrix, i.e., Quantum Master Equation (QME). We applied the method to investigate dynamics of magnetization of nanoscale magnets, such as Mn12 and Fe8, in a time dependent field. Due to the discreteness of the energy levels in small systems the resonating tunneling phenomena play an important role. At relatively high temperatures the excited levels contribute to the transition and the transition rate depends significantly on the temperature. On the other hand, at very low temperatures the magnetization process does not depend on the temperature. Even at such a low temperature, the effect of environments is still relevant. We demonstrate such a process with the method of QME. We also analyze temperature dependent phenomena of hysteresis of the nanoscale magnets.
A new approach to the magnetic hysteresis loop and magnetization relaxation of molecule magnet, Mn12, is presented. The method, so called "quasi-thermal equilibrium (QTE) + erase phase (EP)" (QTE + EP), leads the dissipation in state evolution. The method gives an method to approach an irreversible quantum dynamic tunnelling and time evolution of system and straightly leads the hysteresis loops. The QTE can work well for the double-well system and is able to be extended to the multi-wells quantum system. The EP is based on the physics of random interaction with the environment that results the phase de-coherence or say "re-initial" of the phase of quantum state during the time evolution. The stairs in the magnetic loops of Mn12 we have obtained quantitatively show the quantum resonant tunnelling. The relaxation of magnetization from initial lowest state is calculated for different temperatures and well shows the exponential behavior. The theoretical results well agree with the experiments.
A comprehensive investigation of the transition dynamics of a level-crossing system with quantum dissipation is carried out for the Landau-Zener model coupled with a system of phonons. Analytical study by the formal perturbation expansion series with respect to the off-diagonal matrix element shows that the transition dynamics is characterized by the competition between the energy fluctuation and the energy dissipation. Closed expressions of the transition rate are derived for various limiting situations in a unified way. In the case of strong decoherence, a formula of the transition rate is obtained, which covers the high-temperature limit and the low-temperature, strong-coupling limit. Numerical calculation by utilizing the damping hyperoperator technique is performed, which clarifies the overall features of the time evolution of the system.