Related papers: Limiting absorption principle for long-range pertu…
Lepage's improvement scheme is a recent major progress in lattice $QCD$, allowing to obtain continuum physics on very coarse lattices. Here we discuss improvement in the Hamiltonian formulation, and we derive an improved Hamiltonian from a…
This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…
We model the low energy dynamics of graphene in the continuum in terms of a version of Reduced Quantum Electrodynamics restricting fermions to a (2+1)-dimensional brane, whilst photons remain within the (3+1)-dimensional bulk. For charge…
We show Rellich's theorem, the limiting absorption principle, and a Sommerfeld uniqueness result for a wide class of one-body Schr\"odinger operators with long-range potentials, extending and refining previously known results. Our general…
Lieb-Robinson-type bounds are reported for a large class of classical Hamiltonian lattice models. By a suitable rescaling of energy or time, such bounds can be constructed for interactions of arbitrarily long range. The bound quantifies the…
We establish a limiting absorption principle for Dirichlet Laplacians in quasi-cylindrical domains. Outside a bounded set these domains can be transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet Laplacians model quantum…
The main result of the article is validity of the limiting absorption principle and thus absence of the singular continuous spectrum for compact quantum graphs with several infinite leads attached. The technique used involves…
The unique terahertz properties of graphene has been identified for novel optoelectronic applications. In a graphene sample with bias voltage added, there is an enhanced absorption in the far infrared region and a diminished absorption in…
We investigate the absorption properties of graphene-based anisotropic metamaterial structures where the metamaterial layer possesses an electromagnetic response corresponding to a near-zero permittivity. We find that through analytical and…
We investigate a modified version of the $AB$ random sequential adsorption model. Specifically, this model involves the deposition of two distinct types of particles onto a lattice, with the constraint that different types cannot occupy…
We develop a microscopic theory of a strong electromagnetic field interaction with gated bilayer graphene. Quantum kinetic equations for density matrix are obtained using a tight binding approach within second quantized Hamiltonian in an…
Let H = -(1/m(x))L be the reduced wave operator defined on the N-dimensional Euclidean space, where \f L is the Laplacian. Here m(x) is a positive step function with possible countably infinte surfaces of discontinuity (separating surfaces)…
We reconsider the problem of finding all local symmetries of a Lagrangian. Our approach is completely Hamiltonian without any reference to the associated action. We present a simple algorithm for obtaining the restrictions on the gauge…
We propose a method to construct the ground state $\psi(\lambda)$ of local lattice hamiltonians with the generic form $H_0 + \lambda H_1$, where $\lambda$ is a coupling constant and $H_0$ is a hamiltonian with a non degenerate ground state…
The formalism for describing hadrons using a light-cone Hamiltonian of SU(N) gauge theory on a coarse transverse lattice is reviewed. Physical gauge degrees of freedom are represented by disordered flux fields on the links of the lattice. A…
In the context of loop quantum cosmology, we parametrise the lattice refinement by a parameter, $A$, and the matter Hamiltonian by a parameter, $\delta$. We then solve the Hamiltonian constraint for both a self-adjoint, and a…
We show that periodic optical lattices imprinted in cubic nonlinear media with strong two-photon absorption and localized linear gain landscapes support stable dissipative defect modes in both focusing and defocusing media. Their shapes and…
We study the connection between Lagrangian and Hamiltonian descriptions of closed/open dynamics, for a collection of particles with quadratic interaction (closed system) and a sub-collection of particles with linear damping (open system).…
We demonstrate that there exists a continuum Hamiltonian $H(\bf{r},\bf{p})$ that is formally the operator equivalent of the general tight-binding method, inheriting the associativity and Hermiticity of the latter operator. This provides a…
The generalized tight-binding model with exact diagonalization method is developed to calculate the optical properties of monolayer graphene in the presence of composite magnetic fields. The ratio of the uniform magnetic field and the…