1,678 research outputs found
Effective rate equations for the over-damped motion in fluctuating potentials
We discuss physical and mathematical aspects of the over-damped motion of a
Brownian particle in fluctuating potentials. It is shown that such a system can
be described quantitatively by fluctuating rates if the potential fluctuations
are slow compared to relaxation within the minima of the potential, and if the
position of the minima does not fluctuate. Effective rates can be calculated;
they describe the long-time dynamics of the system. Furthermore, we show the
existence of a stationary solution of the Fokker-Planck equation that describes
the motion within the fluctuating potential under some general conditions. We
also show that a stationary solution of the rate equations with fluctuating
rates exists.Comment: 18 pages, 2 figures, standard LaTeX2
Temperature in One-Dimensional Bosonic Mott insulators
The Mott insulating phase of a one-dimensional bosonic gas trapped in optical
lattices is described by a Bose-Hubbard model. A continuous unitary
transformation is used to map this model onto an effective model conserving the
number of elementary excitations. We obtain quantitative results for the
kinetics and for the spectral weights of the low-energy excitations for a broad
range of parameters in the insulating phase. By these results, recent Bragg
spectroscopy experiments are explained. Evidence for a significant temperature
of the order of the microscopic energy scales is found.Comment: 8 pages, 7 figure
Variationnal study of ferromagnetism in the t1-t2 Hubbard chain
A one-dimensional Hubbard model with nearest and (negative) next-nearest
neighbour hopping is studied variationally. This allows to exclude saturated
ferromagnetism for . The variational boundary has a minimum
at a ``critical density'' and diverges for .Comment: 5 pages, LateX and 1 postscript figure. To appear in Physica
Calculating critical temperatures of superconductivity from a renormalized Hamiltonian
It is shown that one can obtain quantitatively accurate values for the
superconducting critical temperature within a Hamiltonian framework. This is
possible if one uses a renormalized Hamiltonian that contains an attractive
electron-electron interaction and renormalized single particle energies. It can
be obtained by similarity renormalization or using flow equations for
Hamiltonians. We calculate the critical temperature as a function of the
coupling using the standard BCS-theory. For small coupling we rederive the
McMillan formula for Tc. We compare our results with Eliashberg theory and with
experimental data from various materials. The theoretical results agree with
the experimental data within 10%. Renormalization theory of Hamiltonians
provides a promising way to investigate electron-phonon interactions in
strongly correlated systems.Comment: 6 pages, LaTeX, using EuroPhys.sty, one eps figure included, accepted
for publication in Europhys. Let
spl(2,1) dynamical supersymmetry and suppression of ferromagnetism in flat band double-exchange models
The low energy spectrum of the ferromagnetic Kondo lattice model on a N-site
complete graph extended with on-site repulsion is obtained from the underlying
spl(2,1) algebra properties in the strong coupling limit. The ferromagnetic
ground state is realized for 1 and N+1 electrons only. We identify the large
density of states to be responsible for the suppression of the ferromagnetic
state and argue that a similar situation is encountered in the Kagome,
pyrochlore, and other lattices with flat bands in their one-particle density of
states.Comment: 7 pages, 1 figur
Complexity for extended dynamical systems
We consider dynamical systems for which the spatial extension plays an
important role. For these systems, the notions of attractor, epsilon-entropy
and topological entropy per unit time and volume have been introduced
previously. In this paper we use the notion of Kolmogorov complexity to
introduce, for extended dynamical systems, a notion of complexity per unit time
and volume which plays the same role as the metric entropy for classical
dynamical systems. We introduce this notion as an almost sure limit on orbits
of the system. Moreover we prove a kind of variational principle for this
complexity.Comment: 29 page
The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's
We define the topological entropy per unit volume in parabolic PDE's such as
the complex Ginzburg-Landau equation, and show that it exists, and is bounded
by the upper Hausdorff dimension times the maximal expansion rate. We then give
a constructive implementation of a bound on the inertial range of such
equations. Using this bound, we are able to propose a finite sampling algorithm
which allows (in principle) to measure this entropy from experimental data.Comment: 26 pages, 1 small figur
Supersymmetric quantum cosmology for Bianchi class A models
The canonical theory of (N=1) supergravity, with a matrix representation for
the gravitino covector-spinor, is applied to the Bianchi class A spatially
homogeneous cosmologies. The full Lorentz constraint and its implications for
the wave function of the universe are analyzed in detail. We found that in this
model no physical states other than the trivial "rest frame" type occur.Comment: 10 pages, Revte
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