6,780 research outputs found
Analytical study of tunneling times in flat histogram Monte Carlo
We present a model for the dynamics in energy space of multicanonical
simulation methods that lends itself to a rather complete analytic
characterization. The dynamics is completely determined by the density of
states. In the \pm J 2D spin glass the transitions between the ground state
level and the first excited one control the long time dynamics. We are able to
calculate the distribution of tunneling times and relate it to the
equilibration time of a starting probability distribution. In this model, and
possibly in any model in which entering and exiting regions with low density of
states are the slowest processes in the simulations, tunneling time can be much
larger (by a factor of O(N)) than the equilibration time of the probability
distribution. We find that these features also hold for the energy projection
of single spin flip dynamics.Comment: 7 pages, 4 figures, published in Europhysics Letters (2005
Phenomenological study of the electronic transport coefficients of graphene
Using a semi-classical approach and input from experiments on the
conductivity of graphene, we determine the electronic density dependence of the
electronic transport coefficients -- conductivity, thermal conductivity and
thermopower -- of doped graphene. Also the electronic density dependence of the
optical conductivity is obtained. Finally we show that the classical Hall
effect (low field) in graphene has the same form as for the independent
electron case, characterized by a parabolic dispersion, as long as the
relaxation time is proportional to the momentum.Comment: 4 pages, 1 figur
Exact Solution of Ising Model on a Small-World Network
We present an exact solution of a one-dimensional Ising chain with both
nearest neighbor and random long-range interactions. Not surprisingly, the
solution confirms the mean field character of the transition. This solution
also predicts the finite-size scaling that we observe in numerical simulations.Comment: 9 pages, 7 figures, submitted to pr
A Polynomial Approach to the Spectrum of Dirac-Weyl Polygonal Billiards
The Schr\"odinger equation in a square or rectangle with hard walls is solved
in every introductory quantum mechanics course. Solutions for other polygonal
enclosures only exist in a very restricted class of polygons, and are all based
on a result obtained by Lam\'e in 1852. Any enclosure can, of course, be
addressed by finite element methods for partial differential equations. In this
paper, we present a variational method to approximate the low-energy spectrum
and wave-functions for arbitrary convex polygonal enclosures, developed
initially for the study of vibrational modes of plates. In view of the recent
interest in the spectrum of quantum dots of two dimensional materials,
described by effective models with massless electrons, we extend the method to
the Dirac-Weyl equation for a spin-1/2 fermion confined in a quantum billiard
of polygonal shape, with different types of boundary conditions. We illustrate
the method's convergence in cases where the spectrum in known exactly and apply
it to cases where no exact solution exists.Comment: 17 pages, 10 figure
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