680 research outputs found
Comment to "Packing Hyperspheres in High-Dimensional Euclidean Space"
It is shown that the numerical data in cond-mat/0608362 are in very good
agreement with the predictions of cond-mat/0601573.Comment: comment to cond-mat/0608362; 3 pages, 1 figur
AKLT Models with Quantum Spin Glass Ground States
We study AKLT models on locally tree-like lattices of fixed connectivity and
find that they exhibit a variety of ground states depending upon the spin,
coordination and global (graph) topology. We find a) quantum paramagnetic or
valence bond solid ground states, b) critical and ordered N\'eel states on
bipartite infinite Cayley trees and c) critical and ordered quantum vector spin
glass states on random graphs of fixed connectivity. We argue, in consonance
with a previous analysis, that all phases are characterized by gaps to local
excitations. The spin glass states we report arise from random long ranged
loops which frustrate N\'eel ordering despite the lack of randomness in the
coupling strengths.Comment: 10 pages, 1 figur
Generalized fluctuation relation and effective temperatures in a driven fluid
By numerical simulation of a Lennard-Jones like liquid driven by a velocity
gradient \gamma we test the fluctuation relation (FR) below the (numerical)
glass transition temperature T_g. We show that, in this region, the FR deserves
to be generalized introducing a numerical factor X(T,\gamma)<1 that defines an
``effective temperature'' T_{FR}=T/X. On the same system we also measure the
effective temperature T_{eff}, as defined from the generalized
fluctuation-dissipation relation, and find a qualitative agreement between the
two different nonequilibrium temperatures.Comment: Version accepted for publication on Phys.Rev.E; major changes, 1
figure adde
First-order transitions and the performance of quantum algorithms in random optimization problems
We present a study of the phase diagram of a random optimization problem in
presence of quantum fluctuations. Our main result is the characterization of
the nature of the phase transition, which we find to be a first-order quantum
phase transition. We provide evidence that the gap vanishes exponentially with
the system size at the transition. This indicates that the Quantum Adiabatic
Algorithm requires a time growing exponentially with system size to find the
ground state of this problem.Comment: 4 pages, 4 figures; final version accepted on Phys.Rev.Let
Time-dependent Nonlinear Optical Susceptibility of an Out-of-Equilibrium Soft Material
We investigate the time-dependent nonlinear optical absorption of a clay
dispersion (Laponite) in organic dye (Rhodamine B) water solution displaying
liquid-arrested state transition. Specifically, we determine the characteristic
time of the nonlinear susceptibility build-up due as to the Soret
effect. By comparing with the relaxation time provided by standard
dynamic light scattering measurements we report on the decoupling of the two
collective diffusion times at the two very different length scales during the
aging of the out-of-equilibrium system. With this demonstration experiment we
also show the potentiality of nonlinear optics measurements in the study of the
late stage of arrest in soft materials
Effective temperatures of a heated Brownian particle
We investigate various possible definitions of an effective temperature for a
particularly simple nonequilibrium stationary system, namely a heated Brownian
particle suspended in a fluid. The effective temperature based on the
fluctuation dissipation ratio depends on the time scale under consideration, so
that a simple Langevin description of the heated particle is impossible. The
short and long time limits of this effective temperature are shown to be
consistent with the temperatures estimated from the kinetic energy and Einstein
relation, respectively. The fluctuation theorem provides still another
definition of the temperature, which is shown to coincide with the short time
value of the fluctuation dissipation ratio
Exact solution of the Bose-Hubbard model on the Bethe lattice
The exact solution of a quantum Bethe lattice model in the thermodynamic
limit amounts to solve a functional self-consistent equation. In this paper we
obtain this equation for the Bose-Hubbard model on the Bethe lattice, under two
equivalent forms. The first one, based on a coherent state path integral, leads
in the large connectivity limit to the mean field treatment of Fisher et al.
[Phys. Rev. B {\bf 40}, 546 (1989)] at the leading order, and to the bosonic
Dynamical Mean Field Theory as a first correction, as recently derived by
Byczuk and Vollhardt [Phys. Rev. B {\bf 77}, 235106 (2008)]. We obtain an
alternative form of the equation using the occupation number representation,
which can be easily solved with an arbitrary numerical precision, for any
finite connectivity. We thus compute the transition line between the superfluid
and Mott insulator phases of the model, along with thermodynamic observables
and the space and imaginary time dependence of correlation functions. The
finite connectivity of the Bethe lattice induces a richer physical content with
respect to its infinitely connected counterpart: a notion of distance between
sites of the lattice is preserved, and the bosons are still weakly mobile in
the Mott insulator phase. The Bethe lattice construction can be viewed as an
approximation to the finite dimensional version of the model. We show indeed a
quantitatively reasonable agreement between our predictions and the results of
Quantum Monte Carlo simulations in two and three dimensions.Comment: 27 pages, 16 figures, minor correction
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