21,429 research outputs found
Random permutations of a regular lattice
Spatial random permutations were originally studied due to their connections
to Bose-Einstein condensation, but they possess many interesting properties of
their own. For random permutations of a regular lattice with periodic boundary
conditions, we prove existence of the infinite volume limit under fairly weak
assumptions. When the dimension of the lattice is two, we give numerical
evidence of a Kosterlitz-Thouless transition, and of long cycles having an
almost sure fractal dimension in the scaling limit. Finally we comment on
possible connections to Schramm-L\"owner curves.Comment: 23 pages, 8 figure
Dynamical mean field theory for strongly correlated inhomogeneous multilayered nanostructures
Dynamical mean field theory is employed to calculate the properties of
multilayered inhomogeneous devices composed of semi-infinite metallic lead
layers coupled via barrier planes that are made from a strongly correlated
material (and can be tuned through the metal-insulator Mott transition). We
find that the Friedel oscillations in the metallic leads are immediately frozen
in and don't change as the thickness of the barrier increases from one to
eighty planes. We also identify a generalization of the Thouless energy that
describes the crossover from tunneling to incoherent Ohmic transport in the
insulating barrier. We qualitatively compare the results of these
self-consistent many-body calculations with the assumptions of
non-self-consistent Landauer-based approaches to shed light on when such
approaches are likely to yield good results for the transport.Comment: 15 pages, 12 figures, submitted to Phys. Rev.
Holography principle and arithmetic of algebraic curves
According to the holography principle (due to G.`t Hooft, L. Susskind, J.
Maldacena, et al.), quantum gravity and string theory on certain manifolds with
boundary can be studied in terms of a conformal field theory on the boundary.
Only a few mathematically exact results corroborating this exciting program are
known. In this paper we interpret from this perspective several constructions
which arose initially in the arithmetic geometry of algebraic curves. We show
that the relation between hyperbolic geometry and Arakelov geometry at
arithmetic infinity involves exactly the same geometric data as the Euclidean
AdS_3 holography of black holes. Moreover, in the case of Euclidean AdS_2
holography, we present some results on bulk/boundary correspondence where the
boundary is a non-commutative space.Comment: AMSTeX 30 pages, 7 figure
Transverse Meissner Physics of Planar Superconductors with Columnar Pins
The statistical mechanics of thermally excited vortex lines with columnar
defects can be mapped onto the physics of interacting quantum particles with
quenched random disorder in one less dimension. The destruction of the Bose
glass phase in Type II superconductors, when the external magnetic field is
tilted sufficiently far from the column direction, is described by a poorly
understood non-Hermitian quantum phase transition. We present here exact
results for this transition in (1+1)-dimensions, obtained by mapping the
problem in the hard core limit onto one-dimensional fermions described by a
non-Hermitian tight binding model. Both site randomness and the relatively
unexplored case of bond randomness are considered. Analysis near the mobility
edge and near the band center in the latter case is facilitated by a real space
renormalization group procedure used previously for Hermitian quantum problems
with quenched randomness in one dimension.Comment: 23 pages, 22 figure
- …