1,411 research outputs found
Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model
We perform a matrix product state based density matrix renormalisation group
analysis of the phases for the disordered one-dimensional Bose-Hubbard model.
For particle densities N/L = 1, 1/2 and 2 we show that it is possible to obtain
a full phase diagram using only the entanglement properties, which come "for
free" when performing an update. We confirm the presence of Mott insulating,
superfluid and Bose glass phases when N/L = 1 and 1/2 (without the Mott
insulator) as found in previous studies. For the N/L = 2 system we find a
double lobed superfluid phase with possible reentrance.Comment: 6 pages, 4 figure
Finite-Size Scaling of the Level Compressibility at the Anderson Transition
We compute the number level variance and the level
compressibility from high precision data for the Anderson model of
localization and show that they can be used in order to estimate the critical
properties at the metal-insulator transition by means of finite-size scaling.
With , , and denoting, respectively, system size, disorder strength,
and the average number of levels in units of the mean level spacing, we find
that both and the integrated obey finite-size scaling.
The high precision data was obtained for an anisotropic three-dimensional
Anderson model with disorder given by a box distribution of width . We
compute the critical exponent as and the critical
disorder as in agreement with previous
transfer-matrix studies in the anisotropic model. Furthermore, we find
at the metal-insulator transition in very close
agreement with previous results.Comment: Revised version of paper, to be published: Eur. Phys. J. B (2002
An exact-diagonalization study of rare events in disordered conductors
We determine the statistical properties of wave functions in disordered
quantum systems by exact diagonalization of one-, two- and quasi-one
dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we
find that the tails of the distribution of wave-function amplitudes are
described by the non-linear sigma-model. In two dimensions, the tails of the
distribution function are consistent with a recent prediction based on a direct
optimal fluctuation method.Comment: 13 pages, 5 figure
Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs
We study the leaf-to-leaf distances on full and complete m-ary graphs using a
recursive approach. In our formulation, leaves are ordered along a line. We
find explicit analytical formulae for the sum of all paths for arbitrary
leaf-to-leaf distance r as well as the average path lengths and the moments
thereof. We show that the resulting explicit expressions can be recast in terms
of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For
incomplete random binary trees, we provide first results by numerical
techniques; we find a rapid drop of leaf-to-leaf distances for large r.Comment: 10 pages, 7 figure
Localisation and finite-size effects in graphene flakes
We show that electron states in disordered graphene, with an onsite potential that induces inter-valley scattering, are localised for all energies at disorder as small as of the band width of clean graphene. We clarify that, in order for this Anderson-type localisation to be manifested, graphene flakes of size or larger are needed. For smaller samples, due to the surprisingly large extent of the electronic wave functions, a regime of apparently extended (or even critical) states is identified. Our results complement earlier studies of macroscopically large samples and can explain the divergence of results for finite-size graphene flakes
Hamiltonian Multivector Fields and Poisson Forms in Multisymplectic Field Theory
We present a general classification of Hamiltonian multivector fields and of
Poisson forms on the extended multiphase space appearing in the geometric
formulation of first order classical field theories. This is a prerequisite for
computing explicit expressions for the Poisson bracket between two Poisson
forms.Comment: 50 page
Cooper pair delocalization in disordered media
We discuss the effect of disorder on the coherent propagation of the bound
state of two attracting particles. It is shown that a result analogous to the
Anderson theorem for dirty superconductors is also valid for the Cooper
problem, namely, that the pair wave function is extended beyond the
single-particle localization length if the latter is large. A physical
justification is given in terms of the Thouless block-scaling picture of
localization. These arguments are supplemented by numerical simulations. With
increasing disorder we find a transition from a regime in which the interaction
delocalizes the pair to a regime in which the interaction enhances
localization.Comment: 5 pages, RevTex with 2 figures include
Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics
In this letter, the first spin noise spectroscopy measurements in
semiconductor systems of reduced effective dimensionality are reported. The
non-demolition measurement technique gives access to the otherwise concealed
intrinsic, low temperature electron spin relaxation time of n-doped GaAs (110)
quantum wells and to the corresponding low temperature anisotropic spin
relaxation. The Brownian motion of the electrons within the spin noise probe
laser spot becomes manifest in a modification of the spin noise line width.
Thereby, the spatially resolved observation of the stochastic spin polarization
uniquely allows to study electron dynamics at equilibrium conditions with a
vanishing total momentum of the electron system
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