Related papers: T-matrix in discrete oscillator representation
We compare fits to piN elastic scattering data, based on a Chew-Mandelstam K-matrix formalism. Resonances, characterized by T-matrix poles, are compared in fits generated with and without explicit Chew-Mandelstam K-matrix poles.…
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and…
We show that a saturable single-frequency elastic T-matrix approach to scattering of light by atoms agrees remarkably well with a master equation description in the regime of unsaturated atoms, or for large separation between the atoms. If…
To any solution of a linear system of differential equations, we associate a kernel, correlators satisfying a set of loop equations, and in presence of isomonodromic parameters, a Tau function. We then study their semiclassical expansion…
The computation of light scattering by the superposition T-matrix scheme has been so far restricted to systems made of particles that are either sparsely distributed or of near-spherical shape. In this work, we extend the range of…
We study the spectrum of unbounded J-self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sufficient condition for the spectrum being real and derive variational principles for certain real…
We consider scalar Born-Infeld type theories with arbitrary potentials V(T) of a scalar field T. We find that for models with runaway potentials V(T) the generic inhomogeneous solutions after a short transient stage can be very well…
We bootstrap the S-matrix of massless particles in unitary, relativistic two dimensional quantum field theories. We find that the low energy expansion of such S-matrices is strongly constrained by the existence of a UV completion. In the…
The T-matrix is a powerful tool that provides the complete description of the linear interaction between the electromagnetic field and a given object. In here, we generalize the usual monochromatic formalism to the case of polychromatic…
We extend our previous results of solving the inverse problem of quantum scattering theory (Marchenko theory, fixed-$l$ inversion). In particular, we apply an isosceles triangular-pulse function set for the Marchenko equation input kernel…
We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this…
For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient…
We formulate an S-matrix theory in which localisation effects of the particle interactions involved in a scattering process are consistently taken into account. In the limit of an infinite spread of all interactions, the S-matrix assumes…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
In this article, we answer the following question: If the wave equation possesses bound states but it is exactly solvable for only a single non-zero energy, can we find all bound state solutions (energy spectrum and associated…
In this paper, by using the theory of circulant matrices we study some matrices over finite fields which involve the quadratic character and trinomial coefficients.
It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the…
We present a detailed study of the scattering system given by the Neumann Laplacian on the discrete half-space perturbed by a periodic potential at the boundary. We derive asymptotic resolvent expansions at thresholds and eigenvalues, we…
The propagator of linear molecules whose constituents interact through oscillator potentials can be obtained in a closed form for $N$ atoms as long as $N \leq 4$. We compute the propagator for arbitrary $N$ in the approximation $N \gg 1$.…
Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised…