5,831 research outputs found
Classification of Interacting Topological Floquet Phases in One Dimension
Periodic driving of a quantum system can enable new topological phases with
no analog in static systems. In this paper we systematically classify
one-dimensional topological and symmetry-protected topological (SPT) phases in
interacting fermionic and bosonic quantum systems subject to periodic driving,
which we dub Floquet SPTs (FSPTs). For physical realizations of interacting
FSPTs, many-body localization by disorder is a crucial ingredient, required to
obtain a stable phase that does not catastrophically heat to infinite
temperature. We demonstrate that bosonic and fermionic FSPTs phases are
classified by the same criteria as equilibrium phases, but with an enlarged
symmetry group , that now includes discrete time translation symmetry
associated with the Floquet evolution. In particular, 1D bosonic FSPTs are
classified by projective representations of the enlarged symmetry group
. We construct explicit lattice models for a variety of
systems, and then formalize the classification to demonstrate the completeness
of this construction. We also derive general constraints on localization and
symmetry based on the representation theory of the symmetry group, and show
that symmetry-preserving localized phases are possible only for Abelian
symmetry groups. In particular, this rules out the possibility of many-body
localized SPTs with continuous spin symmetry.Comment: 17 pages, 3 figures, v3: title changed to reflect published versio
Regularizing effect and local existence for non-cutoff Boltzmann equation
The Boltzmann equation without Grad's angular cutoff assumption is believed
to have regularizing effect on the solution because of the non-integrable
angular singularity of the cross-section. However, even though so far this has
been justified satisfactorily for the spatially homogeneous Boltzmann equation,
it is still basically unsolved for the spatially inhomogeneous Boltzmann
equation. In this paper, by sharpening the coercivity and upper bound estimates
for the collision operator, establishing the hypo-ellipticity of the Boltzmann
operator based on a generalized version of the uncertainty principle, and
analyzing the commutators between the collision operator and some weighted
pseudo differential operators, we prove the regularizing effect in all (time,
space and velocity) variables on solutions when some mild regularity is imposed
on these solutions. For completeness, we also show that when the initial data
has this mild regularity and Maxwellian type decay in velocity variable, there
exists a unique local solution with the same regularity, so that this solution
enjoys the regularity for positive time
Effect of the atmosphere on the classification of LANDSAT data
The author has identified the following significant results. In conjunction with Turner's model for the correction of satellite data for atmospheric interference, the LOWTRAN-3 computer was used to calculate the atmospheric interference. Use of the program improved the contrast between different natural targets in the MSS LANDSAT data of Brasilia, Brazil. The classification accuracy of sugar canes was improved by about 9% in the multispectral data of Ribeirao Preto, Sao Paulo
The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential
As a continuation of our series works on the Boltzmann equation without
angular cutoff assumption, in this part, the global existence of solution to
the Cauchy problem in the whole space is proved in some suitable weighted
Sobolev spaces for hard potential when the solution is a small perturbation of
a global equilibrium
Global existence and full regularity of the Boltzmann equation without angular cutoff
We prove the global existence and uniqueness of classical solutions around an
equilibrium to the Boltzmann equation without angular cutoff in some Sobolev
spaces. In addition, the solutions thus obtained are shown to be non-negative
and in all variables for any positive time. In this paper, we study
the Maxwellian molecule type collision operator with mild singularity. One of
the key observations is the introduction of a new important norm related to the
singular behavior of the cross section in the collision operator. This norm
captures the essential properties of the singularity and yields precisely the
dissipation of the linearized collision operator through the celebrated
H-theorem
Optical Hall Effect in the Integer Quantum Hall Regime
Optical Hall conductivity is measured from the Faraday
rotation for a GaAs/AlGaAs heterojunction quantum Hall system in the terahertz
frequency regime. The Faraday rotation angle ( fine structure constant
mrad) is found to significantly deviate from the Drude-like behavior to
exhibit a plateau-like structure around the Landau-level filling . The
result, which fits with the behavior expected from the carrier localization
effect in the ac regime, indicates that the plateau structure, although not
quantized, still exists in the terahertz regime.Comment: 4 pages, 4 figure
Hamilton-Jacobi Theory in k-Symplectic Field Theories
In this paper we extend the geometric formalism of Hamilton-Jacobi theory for
Mechanics to the case of classical field theories in the k-symplectic
framework
Spontaneous magnetization under a pseudovector interaction between quarks in high density quark matter
Spontaneous magnetization and magnetic susceptibility originated from the
pseudovector-type four-point interaction between quarks are calculated in quark
matter with zero temperature and finite quark chemical potential by using the
two-flavor Nambu-Jona-Lasinio model. It is shown that both the chiral
condensate and spin polarized condensate coexist in a narrow region of the
quark chemical potential. And then, it is also shown that, in this narrow
region, the spontaneous magnetization appears. Also, the magnetic
susceptibility due to quarks with the positive energy is evaluated in the spin
polarized phase.Comment: 15 pages, 2 figure
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