Related papers: Kirchhoff's Rule for Quantum Wires
The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on the Euclidean plane which are homogeneous of degree zero…
We study the quantum propagator in the semiclassical limit with sharp confining potentials. Including the energy-dependent scattering phase due to sharp confining potential, the modified Van Vleck's formula is derived. We also discuss the…
It has been shown that, in the infinite length limit, the magnons of the gauge theory spin chain can form bound states carrying one finite and one strictly infinite R-charge. These bound states have been argued to be associated to simple…
Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's…
Entanglement is usually associated with compound systems. We first show that a one-dimensional (1D) completed scattering of a particle on a static potential barrier represents an entanglement of two alternative one-particle sub-processes,…
We analyze the scattering sector of the Hamiltonians for both gapless and gapped graphene in the presence of a charge impurity using the 2D Dirac equation, which is applicable in the long wavelength limit. We show that for certain range of…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The…
I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
We investigate the particle trapping and scattering properties in a tight-binding network which consists of several subgraphs. The particle trapping condition is proved under which particles can be trapped in a subgraph without leaking.…
In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground…
We generalized the 't Hooft-Veltman method of unitary regulators to put forward a path-integral framework for finite, alternative theories to a given quantum field theory. And we demonstrated that the proposed framework is feasible by…
Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary…
We study the spectral properties of the Laplace operator associated to a hyperbolic surface in the presence of a unitary representation of the fundamental group. Following the approach by Guillop\'e and Zworski, we establish a factorization…
We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity, and use the quantum Fisher…
We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz invariant formulation of baryon chiral perturbation theory. Using a symmetry preserving higher derivative form of the effective…
In this paper we study the scattering theory associated with the pseudofermion dynamical theory for the Hubbard chain. In terms of pseudofermions the spectral properties are controlled by zero-momentum forward scattering only. The…
A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected to the boundary, hence the…
In this work we present (and encourage the use of) the Williamson theorem and its consequences in several contexts in physics. We demonstrate this theorem using only basic concepts of linear algebra and symplectic matrices. As an immediate…
We consider mathematical models of the weak decay of the vector bosons $W^{\pm}$ into leptons. The free quantum field hamiltonian is perturbed by an interaction term from the standard model of particle physics. After the introduction of…