70 research outputs found
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
Comment on ``Hausdorff Dimension of Critical Fluctuations in Abelian Gauge Theories"
Hove, Mo, and Sudbo [Phys. Rev. Lett. 85, 2368 (2000)] derived a simple
connection, , between the anomalous scaling dimension of
the U(1) universality class order parameter and the Hausdorff dimension
of critical loops in loop representations of U(1) models. We show that the
above relation is wrong and establish a correct relation that contains a new
critical exponent.Comment: In 1 revtex page with 1 figur
Two-Dimensional Weakly Interacting Bose Gas in the Fluctuation Region
We study the crossover between the mean-field and critical behavior of the
two-dimensional Bose gas throughout the fluctuation region of the
Berezinskii--Kosterlitz--Thouless phase transition point. We argue that this
crossover is described by universal (for all weakly interacting |psi|^4 models)
relations between thermodynamic parameters of the system, including superfluid
and quasi-condensate densities. We establish these relations with
high-precision Monte Carlo simulations of the classical |psi|^4 model on a
lattice, and check their asymptotic forms against analytic expressions derived
on the basis of the mean-field theory.Comment: Revtex, 8 pages, 8 figures; submitted to Phys. Rev. A; extended
discussion of effective interaction and of a trapped gas; corrected typo in
Eq. (32
Comment on "Phase Diagram of a Disordered Boson Hubbard Model in Two Dimensions"
We prove that previous claims of observing a direct superfluid-Mott insulator
transition in the disordered J-current model are in error because numerical
simulations were done for too small system sizes and the authors ignored the
rigorous theorem.Comment: 1 page, Latex, 1 figur
Weakly interacting Bose gas in the vicinity of the critical point
We consider a three-dimensional weakly interacting Bose gas in the
fluctuation region (and its vicinity) of the normal-superfluid phase transition
point. We establish relations between basic thermodynamic functions: density,
, superfluid density , and condensate density, . Being universal for all weakly interacting systems,
these relations are obtained from Monte Carlo simulations of the classical
model on a lattice. Comparing with the mean-field results yields a
quantitative estimate of the fluctuation region size. Away from the fluctuation
region, on the superfluid side, all the data perfectly agree with the
predictions of the quasicondensate mean field theory.--This demonstrates that
the only effect of the leading above-the-mean-field corrections in the
condensate based treatments is to replace the condensate density with the
quasicondensate one in all local thermodynamic relations. Surprisingly, we find
that a significant fraction of the density profile of a loosely trapped atomic
gas might correspond to the fluctuation region.Comment: 14 pages, Latex, 8 figure
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