相关论文: Lifshitz Tails in Constant Magnetic Fields

The properties of semiconductors, insulators, and photonic crystals are defined by their electronic or photonic bands, and the gaps between them. When the material is disordered, Lifshitz tails appear: these are localized states that…

We prove an upper bound for the (differentiated) density of states of the Anderson model at the bottom of the spectrum. The density of states is shown to exhibit the same Lifshitz tails upper bound as the integrated density of states.

We calculate the local density of states of a two-dimensional electron system under strong crossed magnetic and electric fields. We assume a strong perpendicular magnetic field which, in the absence of in-plane electric fields and collision…

We present a simple construction of a random Schr\"odinger operator subject to a magnetic field with a regularity as low as $0^-$-H\"older and a Gaussian white noise electric potential on a two-dimensional bounded box. This construction is…

We investigate Weyl semimetals with tilted conical bands in a magnetic field. Even when the cones are overtilted (type-II Weyl semimetal), Landau-level quantization can be possible as long as the magnetic field is oriented close to the tilt…

We consider the asymptotic behavior of the spectrum of the Landau Hamiltonian plus a rapidly decaying potential, as the magnetic field strength, $B$, tends to infinity. After a suitable rescaling, this becomes a semiclassical problem where…

The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in…

We construct random Schr\"odinger operators, called Anderson Hamiltonians, with Dirichlet and Neumann boundary conditions for a fairly general class of singular random potentials on bounded domains. Furthermore, we construct the integrated…

We study the local asymptotic behavior of divergence-like functionals of a family of $d$-dimensional Infinitely Divisible Random Fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of…

By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index $z$. The Lifshitz scale invariant ground state of the theory is constructed…

Superconductivity in the presence of a step magnetic field has been recently the focus of many works. This contribution examines the behavior of a two-dimensional superconducting domain, when superconductivity is lost in the whole domain…

In contrast to the neatly bounded spectra of densely populated large random matrices, sparse random matrices often exhibit unbounded eigenvalue tails on the real and imaginary axis, called Lifshitz tails. In the case of asymmetric matrices,…

Based on the generalized Ginzburg-Landau theory, chiral phase transition is discussed in the presence of magnetic field. Considering the chiral density wave we show chiral anomaly gives rise to an inhomogeneous chiral phase for nonzero…

We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disordered-broadened Landau band, this implies the existence of…

We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the…

We construct the supergravity duals of marginal deformations of a (0,2) Landau-Ginsburg theory that describes the supersymmetric lowest Landau level. These deformations preserve supersymmetry and it is proposed that they are associated with…

We consider a random Schro\"dinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the spectrum in the…

As of now, the phenomenological classical Landau-Lifshitz (LL) damping of magnetic order is not conceptually linked to the quantum theory of dissipation of the Lindbladian formalism which is unsatisfactory for the booming research on…

We give a survey on some recent results concerning the Landau-Lifshitz equation, a fundamental nonlinear PDE with a strong geometric content, describing the dynamics of the magnetization in ferromagnetic materials. We revisit the Cauchy…

The Landau Hamiltonian, describing the behavior of a quantum particle in dimension 2 in a constant magnetic field, is perturbed by a magnetic field with power-like decay at infinity and a similar electric potential. We describe how the…