6,605 research outputs found
Quantum Environments: Spin Baths, Oscillator Baths, and applications to Quantum Magnetism
The low-energy physics of systems coupled to their surroundings is understood
by truncating to effective Hamiltonians; these tend to reduce to a few
canonical forms, involving coupling to "baths" of oscillators or spins. The
method for doing this is demonstrated using examples from magnetism,
superconductivity, and measurement theory, as is the way one then solves for
the low-energy dynamics. Finally, detailed application is given to the exciting
recent Quantum relaxation and tunneling work in naomagnets.Comment: Chapter in "Tunneling in Complex Systems" (World Sci., edited T.
Tomsovic); 97 pages. Published in June 199
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Theory of the spin bath
The quantum dynamics of mesoscopic or macroscopic systems is always
complicated by their coupling to many "environmental" modes.At low T these
environmental effects are dominated by localised modes, such as nuclear and
paramagnetic spins, and defects (which also dominate the entropy and specific
heat). This environment, at low energies, maps onto a "spin bath" model. This
contrasts with "oscillator bath" models (originated by Feynman and Vernon)
which describe {\it delocalised} environmental modes such as electrons,
phonons, photons, magnons, etc. One cannot in general map a spin bath to an
oscillator bath (or vice-versa); they constitute distinct "universality
classes" of quantum environment. We show how the mapping to spin bath models is
made, and then discuss several examples in detail, including moving particles,
magnetic solitons, nanomagnets, and SQUIDs, coupled to nuclear and paramagnetic
spin environments. We show how to average over spin bath modes, using an
operator instanton technique, to find the system dynamics, and give analytic
results for the correlation functions, under various conditions. We then
describe the application of this theory to magnetic and superconducting
systems.Particular attention is given to recent work on tunneling magnetic
macromolecules, where the role of the nuclear spin bath in controlling the
tunneling is very clear; we also discuss other magnetic systems in the quantum
regime, and the influence of nuclear and paramagnetic spins on flux dynamics in
SQUIDs.Comment: Invited article for Rep. Prog. Phys. to appear in April, 2000 (41
pages, latex, 13 figures. This is a strongly revised and extended version of
previous preprint cond-mat/9511011
Dynamics of a Pair of Interacting Spins Coupled to an Environmental Sea
We solve for the dynamics of a pair of spins, coupled to each other and also
to an environmental sea of oscillators. The environment mediates an indirect
interaction between the spins, causing both mutual coherence effects and
dissipation. This model describes a wide variety of physical systems, ranging
from 2 coupled microscopic systems (eg., magnetic impurities, bromophores,
etc), to 2 coupled macroscopic quantum systems. We obtain analytic results for
3 regimes, viz., (i) The locked regime, where the 2 spins lock together; (ii)
The correlated relaxation regime (mutually correlated incoherent relaxation);
and (iii) The mutual coherence regime, with correlated damped oscillations.
These results cover most of the parameter space of the system.Comment: 49 pages, To appear in Int J. Mod. Phys.
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