Related papers: Quantum confinement in $\alpha$-Grushin planes
With the help of a multi-configurational Green's function approach we simulate single-electron Coulomb charging effects in gated ultimately scaled nanostructures which are beyond the scope of a selfconsistent mean-field description. From…
We study measures on the real line and present various versions of what it means for such a measure to take only finitely many values. We then study perturbations of the Laplacian by such measures. Using Kotani-Remling theory, we show that…
A quark model with general Yang-Mills $SU_3$ symmetry leads to fourth-order field equations and linear confining potential. The confining gauge bosons (`confions') are treated as off-mass-shell particles and their indefinite energies are…
We consider Riemannian optimization problems with inequality and equality constraints and analyze a class of Riemannian interior point methods for solving them. The algorithm of interest consists of outer and inner iterations. We show that,…
We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the…
Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…
In a functional approach to QCD the infrared behaviour of Landau gauge Green functions is investigated. Positivity violation for, and thus confinement of, gluons is demonstrated, and the analytic structure of the gluon propagator is…
We introduce an entanglement entropy analysis to quantitatively identify the confinement and deconfinement of the spinons in the spin excitations of quantum magnets. Our proposal is implemented by the parton construction of a…
Light-front field theory offers a scenario in which a constituent picture of hadrons may arise, but only if cutoffs that violate explicit covariance and gauge invariance are used. The perturbative renormalization group can be used to…
Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic,…
We present a theory of graphene quantum rings designed to produce degenerate shells of single particle states close to the Fermi level. We show that populating these shells with carriers using a gate leads to correlated ground states with…
We develop a theoretical framework for the analysis of stabilized cut finite element methods for the Laplace-Beltrami operator on a manifold embedded in $\mathbb{R}^d$ of arbitrary codimension. The method is based on using continuous…
Quasidiagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed,…
The irreducible unitary representations of the Banach Lie group $U_0(\H)$ (which is the norm-closure of the inductive limit $\cup_k U(k)$) of unitary operators on a separable Hilbert space $\H$, which were found by Kirillov and Ol'shanskii,…
Quark confinement and the genesis of the constituent quark model are examined in nonperturbative QCD in Coulomb gauge. We employ a self-consistent method to construct a quasiparticle basis and to determine the quasiparticle interaction. The…
The Yang-Mills Schr\"odinger equation is variationally solved in Coulomb gauge for the vacuum sector using a trial wave functional, which is strongly peaked at the Gribov horizon. We find the absence of gluons in the infrared and also a…
A connection between a unitary quantization scheme and para-Fermi statistics of order 2 is considered. An appropriate extension of Green's ansatz is suggested. This extension allows one to transform bilinear and trilinear commutation…
In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…