98 research outputs found
Linearly edge-reinforced random walks
We review results on linearly edge-reinforced random walks. On finite graphs,
the process has the same distribution as a mixture of reversible Markov chains.
This has applications in Bayesian statistics and it has been used in studying
the random walk on infinite graphs. On trees, one has a representation as a
random walk in an independent random environment. We review recent results for
the random walk on ladders: recurrence, a representation as a random walk in a
random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Purification of quantum trajectories
We prove that the quantum trajectory of repeated perfect measurement on a
finite quantum system either asymptotically purifies, or hits upon a family of
`dark' subspaces, where the time evolution is unitary.Comment: 10 page
Fluctuation Effects And Order Parameter Symmetry In The Cuprate Superconductors
Effect of phase fluctuations on superconducting states with anisotropic order
parameters is studied in a BCS like lattice model of cuprate superconductors.
The degradation of the mean field transition temperature due to phase
fluctuations is estimated within a Kosterlitz-Thouless scenario. Values of the
interaction parameters for optimal doping, corresponding to a stable
superconducting state of symmetry, which fit the nodal structure of
the superconducting order parameter in the Bi2212 compound, are obtained. The
angular position of the node is found to be insensitive to the dopant
concentration.Comment: Latex file, 8 output pages, 5 figures (available from Authors on
request), to appear in Europhysics Letter
Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons
A strong-coupling expansion for the antiferromagnetic phase of the Hubbard
model is derived in the framework of the slave-boson mean-field approximation.
The expansion can be obtained in terms of moments of the density of states of
freely hopping electrons on a lattice, which in turn are obtained for
hypercubic lattices in arbitrary dimension. The expansion is given for the case
of half-filling and for the energy up to fifth order in the ratio of hopping
integral over on-site interaction , but can straightforwardly be
generalized to the non-half-filled case and be extended to higher orders in
. For the energy the expansion is found to have an accuracy of better than
for . A comparison is given with an earlier perturbation
expansion based on the Linear Spin Wave approximation and with a similar
expansion based on the Hartree-Fock approximation. The case of an infinite
number of spatial dimensions is discussed.Comment: 12 pages, LaTeX2e, to be published in Phys. Rev.
Spin Stiffness in the Hubbard model
The spin stiffness of the repulsive Hubbard model that occurs
in the hydrodynamic theory of antiferromagnetic spin waves is shown to be the
same as the thermodynamically defined stiffness involved in twisting the order
parameter. New expressions for are derived, which enable easier
interpretation, and connections with superconducting weight and gauge
invariance are discussed.Comment: 21 Pages LaTeX2e, to be published in Journal of Physics
Helicity Modulus and Effective Hopping in the Two-Dimensional Hubbard Model Using Slave-Boson Methods
The slave-boson mean-field method is used to study the two-dimensional
Hubbard model. A magnetic phase diagram allowing for paramagnetism, weak- and
strong ferromagnetism and antiferromagnetism, including all continuous and
first-order transitions, is constructed and compared to the corresponding phase
diagram using the Hartree-Fock approximation (HFA). Magnetically ordered
regions are reduced by a factor of about 3 along both the and density
axes compared to the HFA. Using the spin-rotation invariant formulation of the
slave-boson method the helicity modulus is computed and for half-filling is
found to practically coincide with that found using variational Monte Carlo
calculations using the Gutzwiller wave function. Off half-filling the results
can be used to compare with Quantum Monte Carlo calculations of the effective
hopping parameter. Contrary to the case of half-filling, the slave-boson
approach is seen to greatly improve the results of the HFA when off
half-filling. (Submitted to: Journal of Physics: Condensed Matter)Comment: 27 pages, LaTeX2e, 7 figures available upon request, INLO-PUB-10/9
Ultracold atoms in optical lattices
Bosonic atoms trapped in an optical lattice at very low temperatures, can be
modeled by the Bose-Hubbard model. In this paper, we propose a slave-boson
approach for dealing with the Bose-Hubbard model, which enables us to
analytically describe the physics of this model at nonzero temperatures. With
our approach the phase diagram for this model at nonzero temperatures can be
quantified.Comment: 29 pages, 10 figure
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