41,596 research outputs found
Discrete Fractal Dimensions of the Ranges of Random Walks in Associate with Random Conductances
Let X= {X_t, t \ge 0} be a continuous time random walk in an environment of
i.i.d. random conductances {\mu_e \in [1, \infty), e \in E_d}, where E_d is the
set of nonoriented nearest neighbor bonds on the Euclidean lattice Z^d and d\ge
3. Let R = {x \in Z^d: X_t = x for some t \ge 0} be the range of X. It is
proved that, for almost every realization of the environment, dim_H (R) = dim_P
(R) = 2 almost surely, where dim_H and dim_P denote respectively the discrete
Hausdorff and packing dimension. Furthermore, given any set A \subseteq Z^d, a
criterion for A to be hit by X_t for arbitrarily large t>0 is given in terms of
dim_H(A). Similar results for Bouchoud's trap model in Z^d (d \ge 3) are also
proven
Microscopic Realization of 2-Dimensional Bosonic Topological Insulators
It is well known that a Bosonic Mott insulator can be realized by condensing
vortices of a bo- son condensate. Usually, a vortex becomes an anti-vortex (and
vice-versa) under time reversal symmetry, and the condensation of vortices
results in a trivial Mott insulator. However, if each vortex or anti-vortex
interacts with a spin trapped at its core, the time reversal transformation of
the composite vortex operator will contain an extra minus sign. It turns out
that such a composite vortex condensed state is a bosonic topological insulator
(BTI) with gapless boundary excitations protected by
symmetry. We point out that in BTI, an external flux monodromy defect
carries a Kramers doublet. We propose lattice model Hamiltonians to realize the
BTI phase, which might be implemented in cold atom systems or spin-1 solid
state systems.Comment: 5 pages + supplementary materia
- β¦