55,649 research outputs found
The Classification of Dimensional Reduced Hopf Insulators
The Hopf insulators are characterized by a topological invariant called Hopf
index which classifies maps from three-sphere to two-sphere, instead of a Chern
number or a Chern parity. In contrast to topological insulator, the Hopf
insulator is not protected by any kind of symmetry. By dimensional reduction,
we argue that there exists a new type of index for 2D
Hamiltonian with vanishing Chern number. Specific model Hamiltonian with this
nontrivial index is constructed. We also numerically calculate
the topological protected edge modes of this dimensional reduced Hopf insulator
and show that they are consistent with the classification.Comment: 6 pages, 3 figure
Basmajian-type identities and Hausdorff dimension of limit sets
In this paper, we study Basmajian-type series identities on holomorphic
families of Cantor sets associated to one-dimensional complex dynamical
systems. We show that the series is absolutely summable if and only if the
Hausdorff dimension of the Cantor set is strictly less than one. Throughout the
domain of convergence, these identities can be analytically continued and they
exhibit nontrivial monodromy
On the displacement of generators of free Fuchsian groups
We prove an inequality that must be satisfied by displacement of generators
of free Fuchsian groups, which is the two-dimensional version of the Theorem for Kleinian groups due to Anderson-Canary-Culler-Shalen. As
applications, we obtain quantitative results on the geometry of hyperbolic
surfaces such as the two-dimensional Margulis constant and lengths of closed
curves, which improves a result of Buser's
Local estimates for elliptic equations arising in conformal geometry
In this paper we consider Yamabe type problem for higher order curvatures on
manifolds with totally geodesic boundaries. We prove local gradient and second
derivative estimates for solutions to the fully nonlinear elliptic equations
associated with the problems.Comment: 30 page
Quantum Spin Hall Effect in a Three-orbital Tight-binding Hamiltonian
We consider the quantum spin hall state in a three orbital model due to
certain loop current order induced by spin-dependent interactions. This type of
order is motivated by the loop current model which is proposed to describe the
pseudogap phase of cuprates. It is shown that this model has nontrivial Chern
parity by directly counting the zeros of the Pfaffian of time reversal
operator. By connecting to the second order Chern number, we explicitly show
the singularities of wave-functions and how they depend on gauge choices. In
this case, it is shown that the Berry phase can be mapped to Nonabelian
instanton.Comment: 16 pages, 1 figur
Sharp weak bounds and limiting weak-type behavior for Hardy type operators
In this paper, Hardy type operator on \bR^{n} and its adjoint
operator are investigated. We use novel methods to obtain two
main results. One is that we obtain the operators and
being bounded from to
, and the bounds of the operators and
are sharp worked out. In particular, when ,
the norm of is equal to . The other is that we study limiting
weak-type behavior for the operator and its optimal form was
obtained
Dynamic density structure factor of a unitary Fermi gas at finite temperature
We present a theoretical investigation of the dynamic density structure
factor of a strongly interacting Fermi gas near a Feshbach resonance at finite
temperature. The study is based on a gauge invariant linear response theory.
The theory is consistent with a diagrammatic approach for the equilibrium state
taking into account the pair fluctuation effects and respects some important
restrictions like the -sum rule. Our numerical results show that the dynamic
density structure factor at large incoming momentum and at half recoil
frequency has a qualitatively similar behavior as the order parameter, which
can signify the appearance of the condensate. This qualitatively agrees with
the recent Bragg spectroscopy experiment results. We also present the results
at small incoming momentum.Comment: 7 pages, 4 figure
Ring frustration and factorizable correlation functions of critical spin rings
Basing on the exactly solvable prototypical model, the critical transverse
Ising ring with or without ring frustration, we establish the concept of
nonlocality in a many-body system in the thermodynamic limit by defining the
nonlocal factors embedded in its factorizable correlation functions. In the
context of nonlocality, the valuable traditional finite-size scaling analysis
is reappraised. The factorizable correlation functions of the isotropic
and the spin-1/2 Heisenberg models are also demonstrated with the emphasis on
the effect of ring frustration.Comment: 15 pages, 4 figure
Gauge Invariant Linear Response Theories for Ultracold Fermi Gases with Pseudogap
Recent experimental progresses allow for exploring some important physical
quantities of ultracold Fermi gases, such as the compressibility, spin
susceptibility, viscosity, optical conductivity and spin diffusivity.
Theoretically, these quantities can be evaluated from suitable linear response
theories. For BCS superfluid, it has been found that the gauge invariant linear
response theories can be fully consistent with some stringent consistency
constraints. When the theory is generalized to stronger-than-BCS regime, one
may meet serious difficulties to satisfy the gauge invariance conditions. In
this paper, we try to construct density and spin linear response theories which
are formally gauge invariant for a Fermi gas undergoing BCS-Bose-Einstein
Condensation (BEC) crossover, especially below the superfluid transition
temperature . We adapt a particular -matrix approach which is close to
the formalism to incorporate non-condensed pairing in the normal state.
We explicitly show that the fundamental constraints imposed by the Ward
identities, -limit Ward identity are indeed satisfied.Comment: 8 pages, 5 figure
Drag-Tracking Guidance for Entry Vehicles Without Drag Rate Measurement
A robust entry guidance law without drag rate measurement is designed for
drag-tracking in this paper. The bank angle is regarded as the control
variable. First, a state feedback guidance law (bank angle magnitude) that
requires the drag and its rate as feedback information is designed to make the
drag-tracking error be input-to-state stable (ISS) with respect to
uncertainties. Then a high gain observer is utilized to estimate the drag rate
which is difficult for a vehicle to measure accurately in practice. Stability
analysis as well as simulation results show the efficiency of the presented
approach.Comment: 23 pages, 11 figure
- …