16,479 research outputs found
Coupled spin models for magnetic variation of planets and stars
Geomagnetism is characterized by intermittent polarity reversals and rapid
fluctuations. We have recently proposed a coupled macro-spin model to describe
these dynamics based on the idea that the whole dynamo mechanism is described
by the coherent interactions of many small dynamo elements. In this paper, we
further develop this idea and construct a minimal model for magnetic
variations. This simple model naturally yields many of the observed features of
geomagnetism: its time evolution, the power spectrum, the frequency
distribution of stable polarity periods, etc. This model has coexistent two
phases; i.e. the cluster phase which determines the global dipole magnetic
moment and the expanded phase which gives random perpetual perturbations that
yield intermittent polarity flip of the dipole moment. This model can also
describe the synchronization of the spin oscillation. This corresponds to the
case of sun and the model well describes the quasi-regular cycles of the solar
magnetism. Furthermore, by analyzing the relevant terms of MHD equation based
on our model, we have obtained a scaling relation for the magnetism for
planets, satellites, sun, and stars. Comparing it with various observations, we
can estimate the scale of the macro-spins.Comment: 16 pages, 9 figure
A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is
generalized to apply to a gas with an exact large number of particles.
This generalization yields a description of the Schr\"odinger picture field
operators as the product of an annihilation operator for the total number
of particles and the sum of a ``condensate wavefunction'' and a phonon
field operator in the form when the field operator acts on the N particle subspace. It
is then possible to expand the Hamiltonian in decreasing powers of ,
an thus obtain solutions for eigenvalues and eigenstates as an asymptotic
expansion of the same kind. It is also possible to compute all matrix elements
of field operators between states of different N.Comment: RevTeX, 11 page
Fluctuational Electrodynamics in Atomic and Macroscopic Systems: van der Waals Interactions and Radiative Heat Transfer
We present an approach to describing fluctuational electrodynamic (FED)
interactions, particularly van der Waals (vdW) interactions as well as
radiative heat transfer (RHT), between material bodies of vastly different
length scales, allowing for going between atomistic and continuum treatments of
the response of each of these bodies as desired. Any local continuum
description of electromagnetic (EM) response is compatible with our approach,
while atomistic descriptions in our approach are based on effective electronic
and nuclear oscillator degrees of freedom, encapsulating dissipation,
short-range electronic correlations, and collective nuclear vibrations
(phonons). While our previous works using this approach have focused on
presenting novel results, this work focuses on the derivations underlying these
methods. First, we show how the distinction between "atomic" and "macroscopic"
bodies is ultimately somewhat arbitrary, as formulas for vdW free energies and
RHT look very similar regardless of how the distinction is drawn. Next, we
demonstrate that the atomistic description of material response in our approach
yields EM interaction matrix elements which are expressed in terms of
analytical formulas for compact bodies or semianalytical formulas based on
Ewald summation for periodic media; we use this to compute vdW interaction free
energies as well as RHT powers among small biological molecules in the presence
of a metallic plate as well as between parallel graphene sheets in vacuum,
showing strong deviations from conventional macroscopic theories due to the
confluence of geometry, phonons, and EM retardation effects. Finally, we
propose formulas for efficient computation of FED interactions among material
bodies in which those that are treated atomistically as well as those treated
through continuum methods may have arbitrary shapes, extending previous
surface-integral techniques.Comment: 25 pages, 5 figures, 2 appendice
Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach
The number-conserving quantum phase space description of the Bose-Hubbard
model is discussed for the illustrative case of two and three modes, as well as
the generalization of the two-mode case to an open quantum system. The
phase-space description based on generalized SU(M) coherent states yields a
Liouvillian flow in the macroscopic limit, which can be efficiently simulated
using Monte Carlo methods even for large systems. We show that this description
clearly goes beyond the common mean-field limit. In particular it resolves
well-known problems where the common mean-field approach fails, like the
description of dynamical instabilities and chaotic dynamics. Moreover, it
provides a valuable tool for a semi-classical approximation of many interesting
quantities, which depend on higher moments of the quantum state and are
therefore not accessible within the common approach. As a prominent example, we
analyse the depletion and heating of the condensate. A comparison to methods
ignoring the fixed particle number shows that in this case artificial number
fluctuations lead to ambiguities and large deviations even for quite simple
examples.Comment: Significantly enhanced and revised version (20 pages, 20 figures
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