Related papers: T-matrix in discrete oscillator representation
I discuss particle content of the Ising field theory (the scaling limit of the Ising model in a magnetic field), in particular the evolution of its mass spectrum under the change of the scaling parameter. I consider both real and pure…
Using the results on the $1/n$-expansion of the Verblunsky coefficients for a class of polynomials orthogonal on the unit circle with $n$ varying weight, we prove that the local eigenvalue statistic for unitary matrix models is independent…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
The T-matrix method is widely used for the calculation of scattering by particles of sizes on the order of the illuminating wavelength. Although the extended boundary condition method (EBCM) is the most commonly used technique for…
Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…
We define a new scaling limit of matrix models which can be related to the method of causal dynamical triangulations (CDT) used when investigating two-dimensional quantum gravity. Surprisingly, the new scaling limit of the matrix models is…
In the first part of the paper, we discuss eigenvalue problems of the form -w"+Pw=Ew with complex potential P and zero boundary conditions at infinity on two rays in the complex plane. We give sufficient conditions for continuity of the…
A recently formulated conjecture of Gamayun, Iorgov and Lisovyy gives an asymptotic expansion of the Jimbo--Miwa--Ueno isomonodromic $\tau$-function for certain Painlev\'e transcendents. The coefficients in this expansion are given in terms…
We review the recent developments in the theory of normal, normal self-dual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large $N$ limit. The 1/N expansion…
Elastic ed scattering, with deuteron polarization, up to high momentum transfer provides detailed information on the deuteron wave function. This determines the range dependence of the orbital and spin components of the one- and two-body…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is…
I consider the problem of computing the mass of a charged, gravitating particle in quantum field theory. It is shown how solving for the first quantized propagator of a particle in the presence of its own potentials reproduces the gauge and…
We investigate the radiation from an inertial scalar particle evolving in a de Sitter expanding Universe. In the context of scalar QED the process is generated by the first order term in the perturbation theory expansion of the S-matrix.…
We examine harmonic oscillator defects coupled to a photon field in the environs of an optical fiber. Using techniques borrowed or extended from the theory of two dimensional quantum fields with boundaries and defects, we are able to…
The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other…
The nucleon-nucleon t-matrix is calculated directly as function of two vector momenta for different realistic NN potentials. The angular and momentum dependence of the full amplitude is studied and NN observables are calculated.
This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general…
In the extended (1 + 4) -dimensional space (T;X,Y,Z,S)-(time-space-interval) it is considered a model joining electromagnetic and gravitational fields. For the equations circumscribing these fields, the exact solutions appropriated to dot…
We adapt the transfer matrix ($\T$-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. In similarity to one-dimensional…