92,539 research outputs found
Log-Harnack Inequality for Stochastic Burgers Equations and Applications
By proving an -gradient estimate for the corresponding Galerkin
approximations, the log-Harnack inequality is established for the semigroup
associated to a class of stochastic Burgers equations. As applications, we
derive the strong Feller property of the semigroup, the irreducibility of the
solution, the entropy-cost inequality for the adjoint semigroup, and entropy
upper bounds of the transition density
Entanglement in a second order topological insulator on a square lattice
In a -dimensional topological insulator of order , there are zero
energy states on its corners which have close relationship with its
entanglement behaviors. We studied the bipartite entanglement spectra for
different subsystem shapes and found that only when the entanglement boundary
has corners matching the lattice, exact zero modes exist in the entanglement
spectrum corresponding to the zero energy states caused by the same physical
corners. We then considered finite size systems in which case these corner
states are coupled together by long range hybridizations to form a multipartite
entangled state. We proposed a scheme to calculate the quadripartite
entanglement entropy on the square lattice, which is well described by a
four-sites toy model and thus provides another way to identify the higher order
topological insulators from the multipartite entanglement point of view.Comment: 5 pages, 3 figure
Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups
We consider stochastic equations in Hilbert spaces with singular drift in the
framework of [Da Prato, R\"ockner, PTRF 2002]. We prove a Harnack inequality
(in the sense of [Wang, PTRF 1997]) for its transition semigroup and exploit
its consequences. In particular, we prove regularizing and ultraboundedness
properties of the transition semigroup as well as that the corresponding
Kolmogorov operator has at most one infinitesimally invariant measure
(satisfying some mild integrability conditions). Finally, we prove existence of
such a measure for non-continuous drifts
Detecting edge degeneracy in interacting topological insulators through entanglement entropy
The existence of degenerate or gapless edge states is a characteristic
feature of topological insulators, but is difficult to detect in the presence
of interactons. We propose a new method to obtain the degeneracy of the edge
states from the perspective of entanglement entropy, which is very useful to
identify interacting topological states. Employing the determinant quantum
Monte Carlo technique, we investigate the interaction effect on two
representative models of fermionic topological insulators in one and two
dimensions, respectively. In the two topologically nontrivial phases, the edge
degeneracies are reduced by interactions but remain to be nontrivial.Comment: 6 pages, 4 figure
Electronic structure near an impurity and terrace on the surface of a 3-dimensional topological insulator
Motivated by recent scanning tunneling microscopy experiments on surfaces of
BiSb\cite{yazdanistm,gomesstm} and
BiTe,\cite{kaptunikstm,xuestm} we theoretically study the electronic
structure of a 3-dimensional (3D) topological insulator in the presence of a
local impurity or a domain wall on its surface using a 3D lattice model. While
the local density of states (LDOS) oscillates significantly in space at
energies above the bulk gap, the oscillation due to the in-gap surface Dirac
fermions are very weak. The extracted modulation wave number as a function of
energy satisfies the Dirac dispersion for in-gap energies and follows the
border of the bulk continuum above the bulk gap. We have also examined
analytically the effects of the defects by using a pure Dirac fermion model for
the surface states and found that the LDOS decays asymptotically faster at
least by a factor of 1/r than that in normal metals, consistent with the
results obtained from our lattice model.Comment: 7 pages, 5 figure
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