3,501 research outputs found
SUSY transformations with complex factorization constants. Application to spectral singularities
Supersymmetric (SUSY) transformation operators corresponding to complex
factorization constants are analyzed as operators acting in the Hilbert space
of functions square integrable on the positive semiaxis. Obtained results are
applied to Hamiltonians possessing spectral singularities which are
non-Hermitian SUSY partners of selfadjoint operators. A new regularization
procedure for the resolution of the identity operator in terms of continuous
biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed.
It is also shown that the continuous spectrum eigenfunction has zero binorm (in
the sense of distributions) at the singular point.Comment: Thanks to A. Sokolov a number of inaccuracies are correcte
SUSY transformation of the Green function and a trace formula
An integral relation is established between the Green functions corresponding
to two Hamiltonians which are supersymmetric (SUSY) partners and in general may
possess both discrete and continuous spectra. It is shown that when the
continuous spectrum is present the trace of the difference of the Green
functions for SUSY partners is a finite quantity which may or may not be equal
to zero despite the divergence of the traces of each Green function. Our
findings are illustrated by using the free particle example considered both on
the whole real line and on a half line
Binary Patterns in Binary Cube-Free Words: Avoidability and Growth
The avoidability of binary patterns by binary cube-free words is investigated
and the exact bound between unavoidable and avoidable patterns is found. All
avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the
growth rates of the avoiding languages are studied. All such languages, except
for the overlap-free language, are proved to have exponential growth. The exact
growth rates of languages avoiding minimal avoidable patterns are approximated
through computer-assisted upper bounds. Finally, a new example of a
pattern-avoiding language of polynomial growth is given.Comment: 18 pages, 2 tables; submitted to RAIRO TIA (Special issue of Mons
Days 2012
Electromagnetic form factors of the (rho) meson in light cone QCD sum rules
We investigate the electromagnetic form factors of the (rho) meson in light
cone QCD sum rules. We find that the ratio of the magnetic and charge form
factors is larger than two at all values of Q^2, (Q^2 >= 0.5 GeV^2). The values
of the individual form factors at fixed values of Q^2 predicted by the light
cone QCD sum rules are quite different compared to the results of other
approaches. These results can be checked in future, when more precise data on
(rho) meson form factors is available.Comment: 12 pages, 6 figures, LaTeX formatte
Initial-state nuclear effects in proton-nucleus collisions
Two important initial-state nuclear effects in hadron-nucleus collisions are
considered. The ratios of inclusive differential cross sections for Drell-Yan
dimuon production are calculated. The calculated results are compared to the
E866 data. It is shown that consideration of multiple soft rescatterings of
incident quarks in nuclei and initial-state quark energy loss effects allow to
get a good agreement between the calculated results and the experimental data.Comment: 6 pages, 6 figure
Is the CPT-norm always positive?
We give an explicit example of an exactly solvable PT-symmetric Hamiltonian
with the unbroken PT symmetry which has one eigenfunction with the zero
PT-norm. The set of its eigenfunctions is not complete in corresponding Hilbert
space and it is non-diagonalizable. In the case of a regular Sturm-Liouville
problem any diagonalizable PT-symmetric Hamiltonian with the unbroken PT
symmetry has a complete set of positive CPT-normalazable eigenfunctions. For
non-diagonalizable
Hamiltonians a complete set of CPT-normalazable functions is possible but the
functions belonging to the root subspace corresponding to multiple zeros of the
characteristic determinant are not eigenfunctions of the Hamiltonian anymore
On Abelian repetition threshold
We study the avoidance of Abelian powers of words and consider three reasonable generalizations of the notion of Abelian power to fractional powers. Our main goal is to find an Abelian analogue of the repetition threshold, i.e., a numerical value separating k-avoidable and k-unavoidable Abelian powers for each size k of the alphabet. We prove lower bounds for the Abelian repetition threshold for large alphabets and all definitions of Abelian fractional power. We develop a method estimating the exponential growth rate of Abelian-power-free languages. Using this method, we get non-trivial lower bounds for Abelian repetition threshold for small alphabets. We suggest that some of the obtained bounds are the exact values of Abelian repetition threshold. In addition, we provide upper bounds for the growth rates of some particular Abelian-power-free languages. © 2011 EDP Sciences
Eigenphase preserving two-channel SUSY transformations
We propose a new kind of supersymmetric (SUSY) transformation in the case of
the two-channel scattering problem with equal thresholds, for partial waves of
the same parity. This two-fold transformation is based on two imaginary
factorization energies with opposite signs and with mutually conjugated
factorization solutions. We call it an eigenphase preserving SUSY
transformation as it relates two Hamiltonians, the scattering matrices of which
have identical eigenphase shifts. In contrast to known phase-equivalent
transformations, the mixing parameter is modified by the eigenphase preserving
transformation.Comment: 16 pages, 1 figur
Exact propagators for SUSY partners
Pairs of SUSY partner Hamiltonians are studied which are interrelated by
usual (linear) or polynomial supersymmetry. Assuming the model of one of the
Hamiltonians as exactly solvable with known propagator, expressions for
propagators of partner models are derived. The corresponding general results
are applied to "a particle in a box", the Harmonic oscillator and a free
particle (i.e. to transparent potentials).Comment: 31 page
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