Related papers: Resonances from Higher Order S-Matrix Poles with E…
We derive Gamow vectors from S-matrix poles of higher multiplicity in analogy to the Gamow vectors describing resonances from first-order poles. With these vectors we construct a density operator that describes resonances associated with…
In analogy to Gamow vectors that are obtained from first order resonance poles of the S-matrix, one can also define higher order Gamow vectors which are derived from higher order poles of the S-matrix. An S-matrix pole of r-th order at…
A state vector description for relativistic resonances is derived from the first order pole of the $j$-th partial $S$-matrix at the invariant square mass value $\sm_R=(m-i\Gamma/2)^2$ in the second sheet of the Riemann energy surface. To…
In the framework of the rigged Hilbert space, unstable quantum systems associated with first order poles of the analytically continued S-matrix can be described by Gamow vectors which are generalized vectors with exponential decay and a…
The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrodinger…
Whether one starts form the analytic S-matrix definition or the requirement of gauge parameter independence in renormalization theory, a relativistic resonance is given by a pole at a complex value s of energy squared. The complex number s…
The foundations of time asymmetric quantum theory are reviewed and are applied to the construction of relativistic Gamow vectors. Relativistic Gamow vectors are obtained from the resonance pole of the S-matrix and furnish an irreducible…
Decaying states can be represented by Gamow vectors with an exponential, asymmetric time evolution. This asymmetric evolution is a manifestation of irreversibility on the microphysical level. The Rigged Hilbert Space provides a mathematical…
Results from the Lax-Phillips Scattering Theory are used to analyze quantum mechanical scattering systems, in particular to obtain spectral properties of their resonances which are defined to be the poles of the scattering matrix. For this…
We study scattering from potentials that rise monotonically on one side; this is generally avoided. We report that resonant states are absent in such potentials when they are smooth and single-piece having less than three real turning…
Gamow's approach to exponential decay of meta-stable particles via complex 'eigenvalues' (resonances) of a Hamiltonian is scrutinized. We explain the sense in which the non-square-integrable 'eigenfunctions' that belong to these resonances…
The calculation of an amplitude involving resonance production is presented. This calculation employs for the resonance state a relativistic Gamow vector. It is used for investigating the question of compatibility of the relativistic Gamow…
We obtain the precise form of two Gamow functionals, representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing…
For an exponentially decaying potential, analytic structure of the $s$-wave S-matrix can be determined up to the slightest detail, including position of all its poles and their residues. Beautiful hidden structures can be revealed by its…
By means of expressing volumes in phase space in terms of traces of quantum operators, a relationship between the Hamiltonian poles and the Lyapunov exponents in a non Hermitian quantum dynamics, is presented. We illustrate the formalism by…
It is demonstrated that almost any S-matrix of quantum field theory in curved spaces posses an infinite set of complex poles (or branch cuts). These poles can be transformed into complex eigenvalues, the corresponding eigenvectors being…
The double pole singularity of the $S$-matrix, the so-called exceptional point, associated with the $5/2^-$ doublet of resonances in the spectrum of $^{7}$Be has been identified in the framework of the Gamow shell model. The exceptional…
In this article, we investigate systems of generalized Schr\"odinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matrices and then prove sharp upper and lower exponential decay…
A renewed version of the computer code GAMOW ~\cite{[Ve82]} is given in which the difficulties in calculating broad neutron resonances are amended. New types of phenomenological neutron potentials with strict finite range are built in.…
We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…