Related papers: Dynamical Delocalization for the 1D Bernoulli Disc…
In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…
This paper studies a class of nonlinear massless Dirac equations in one dimension, which include the equations for massless Thirring model and massless Gross-Neveu model. Under the assumptions that the initial data has small charge and is…
We consider discrete one-dimensional Schr\"odinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical…
One dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the…
We study the $(1+1)$-dimensional Dirac oscillator within a class of doubly special relativity (DSR) models generated by linear-fractional (projective) transformations on momentum space that preserve both the invariant speed of light and a…
We consider a one-dimensional continuum Anderson model where the potential decays in average like $|x|^{-\alpha}$, $\alpha>0$. We show dynamical localization for $0<\alpha<\frac12$ and provide control on the decay of the eigenfunctions.
In this paper we extend previous results on convergent perturbative solutions of the Schroedinger equation of a class of periodically time-dependent two-level systems. The situation treated here is particularly suited for the investigation…
We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second order separated operators giving the resonances of the problem by complex dilation. The same operators have unique extensions as closed…
We investigate spectral properties of a discrete random displacement model, a Schr\"odinger operator on $\ell^2(\Z^d)$ with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of…
The discrete spectrum of the Dirac operator for a point electron in the maximal analytically extended Kerr--Newman spacetime is determined in the zero-$G$ limit (z$G$KN), under some restrictions on the electrical coupling constant and on…
We study the period doubling renormalization operator for dynamics which present two coupled laminar regimes with two weakly expanding fixed points. We focus our analysis on the potential point of view, meaning we want to solve…
The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac…
In this paper, we generalize a previous relativistic $1+1$-dimensional model for two mass-less Dirac particles with relativistic contact interactions to the $N$-particle case. Our model is based on the notion of a multi-time wave function…
We investigate the (1+1)-dimensional position-dependent mass Dirac equation within the confines of so(2,1) potential algebra by utilizing the character of a spatial varying Fermi velocity. We examine the combined effects of the two when the…
The relativistic ``no pair'' model of quantum electrodynamics uses the Dirac operator, D(A), for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A -- in the Coulomb gauge.…
We obtain for the attractive Dirac delta-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before…
We study the low-energy density of states of Dirac fermions in disordered d-wave superconductor. At zero energy, a finite density of states is obtained via the mechanism of dynamical mass generation in an effective (1+1)-dimensional…
The Two-Body Dirac equations of constraint theory are of special interest not only in view of applications for phenomenological calculations of mesonic spectra but also because they avoid no-go theorems about relativistic interactions.…
We consider static U(1) monopole in non-commutative space. Up to the second order in the non-commutativity scale $\theta$, we find no non-trivial corrections to the Dirac solution, the monopole mass remains infinite. We argue the same holds…
In this and subsequent papers, one dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the…