Related papers: Relaxation operator for quasiparticles in a solid
An analytical theory is presented for the damping of low-frequency adsorbate vibrations via resonant coupling to the substrate phonons. The system is treated classically, with the substrate modeled as a semi-infinite elastic continuum and…
We consider dispersive shock wave to the focusing nonlinear Schr\"odinger equation generated by a discontinuous initial condition which is periodic or quasi-periodic on the left semi-axis and zero on the right semi-axis. As an initial…
We extend the study of fermionic particle-hole symmetric semi-Dirac (alternatively, semi-Weyo) dispersion of quasiparticles, $\varepsilon_K = \pm \sqrt{(k_x^2/2m)^2 + (vk_y)^2)} = \pm \varepsilon_0 \sqrt{K_x^4 + K_y^2}$ in dimensionless…
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
In this article, we study a generalisation of the Seiberg-Witten equations, replacing the spinor representation with a hyperKahler manifold equipped with certain symmetries. Central to this is the construction of a (non-linear) Dirac…
We consider how the quasinormal spectrum for the conformal wave operator on the static patch of de Sitter changes in response to the addition of a small potential. Since the quasinormal modes and co-modes are explicitly known, we are able…
We revisit a construction principle of Fredholm operators using Hilbert complexes of densely defined, closed linear operators and apply this to particular choices of differential operators. The resulting index is then computed with the help…
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials $U(x)\sim x^m$, $m=2n \geq 2$. This is paralleled by a transformation of each…
The Lewis and Riesenfeld method has been investigated, by Ramos et al in Ref.[1], for quantum systems governed by time-dependent PT symmetric Hamiltonians and particularly where the quantum system is a particle submitted to action of a…
Interactions have strong effects in systems with flat bands. We examine the role of Coulomb interactions in two dimensional chiral anisotropic quasiparticles that disperse linearly in one direction and have relatively flat bands near the…
We study non-elliptic quadratic differential operators. Quadratic differential operators are non-selfadjoint operators defined in the Weyl quantization by complex-valued quadratic symbols. When the real part of their Weyl symbols is a…
An explicit formula for the wave operators associated with Schroedinger operators on the discrete half-line is deduced from their stationary expressions. The formula enables us to understand the wave operators as one dimensional…
We develop a microspectral theory for quasinilpotent linear operators $Q$ (i.e., those with $\sigma(Q) = \{0}$) in a Banach space. When such $Q$ is not compact, normal, or nilpotent, the classical spectral theory gives little information,…
We propose the use of the Dirac-Born-Infeld action in the phenomenological description of graphene sheet dynamics and interactions. Both the electronic properties of the Dirac fermions and the overall dynamics can be incorporated into this…
Let ${\bf R}$ denote any of the following classes: upper (lower) semi-Fredholm operators, Fredholm operators, upper (lower) semi-Weyl operators, Weyl operators, upper (lower) semi-Browder operators, Browder operators. For a bounded linear…
We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada. A main result in this paper is that the spectral density function of DMLs…
Graphene bilayers exhibit zero-energy flat bands at a discrete series of magic twist angles. In the absence of intra-sublattice inter-layer hopping, zero-energy states satisfy a Dirac equation with a non-abelian SU(2) gauge potential that…
The behavior of electrons in strained graphene is usually described using effective pseudomagnetic fields in a Dirac equation. Here we consider the particular case of a spatially constant strain. Our results indicate that lattice…
Starting from the free surface Euler equations, we derive a leading-order system in terms of surface variables, depending on the surface current and on the bathymetry through the depth-dependent Dirichlet-to-Neumann (DN) operator. The…