79 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
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
Ising Expansion for the Hubbard Model
We develop series expansions for the ground state properties of the Hubbard
model, by introducing an Ising anisotropy into the Hamiltonian. For the
two-dimensional (2D) square lattice half-filled Hubbard model, the ground state
energy, local moment, sublattice magnetization, uniform magnetic susceptibility
and spin stiffness are calculated as a function of , where is the
Coulomb constant and is the hopping parameter. Magnetic susceptibility data
indicate a crossover around between spin density wave
antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte
Carlo simulations, RPA result and mean field solutions are also made.Comment: 22 pages, 6 Postscript figures, Revte
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