36 research outputs found
Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
When several inequivalent supercharges form a closed superalgebra in Quantum
Mechanics it entails the appearance of hidden symmetries of a
Super-Hamiltonian. We examine this problem in one-dimensional QM for the case
of periodic potentials and potentials with finite number of bound states. After
the survey of the results existing in the subject the algebraic and analytic
properties of hidden-symmetry differential operators are rigorously elaborated
in the Theorems and illuminated by several examples
Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
Resolutions of identity for certain non-Hermitian Hamiltonians constructed
from biorthogonal sets of their eigen- and associated functions are given for
the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under
consideration possess the continuous spectrum and the following peculiarities
are investigated: (1) the case when there is an exceptional point of arbitrary
multiplicity situated on a boundary of continuous spectrum; (2) the case when
there is an exceptional point situated inside of continuous spectrum. The
reductions of the derived resolutions of identity under narrowing of the
classes of employed test functions are revealed. It is shown that in the case
(1) some of associated functions included into the resolution of identity are
normalizable and some of them may be not and in the case (2) the bounded
associated function corresponding to the exceptional point does not belong to
the physical state space. Spectral properties of a SUSY partner Hamiltonian for
the Hamiltonian with an exceptional point are examined
Multi-criteria comparative evaluation of spallation reaction models
This paper presents an approach to a comparative evaluation of the predictive ability of spallation reaction models based on widely used, well-proven multiple-criteria decision analysis methods (MAVT/MAUT, AHP, TOPSIS, PROMETHEE) and the results of such a comparison for 17 spallation reaction models in the presence of the interaction of high-energy protons with natPb
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
Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
This is the third article in a series of three papers on the resonance energy
levels of anharmonic oscillators. Whereas the first two papers mainly dealt
with double-well potentials and modifications thereof [see J. Zinn-Justin and
U. D. Jentschura, Ann. Phys. (N.Y.) 313 (2004), pp. 197 and 269], we here focus
on simple even and odd anharmonic oscillators for arbitrary magnitude and
complex phase of the coupling parameter. A unification is achieved by the use
of PT-symmetry inspired dispersion relations and generalized quantization
conditions that include instanton configurations. Higher-order formulas are
provided for the oscillators of degrees 3 to 8, which lead to subleading
corrections to the leading factorial growth of the perturbative coefficients
describing the resonance energies. Numerical results are provided, and
higher-order terms are found to be numerically significant. The resonances are
described by generalized expansions involving intertwined non-analytic
exponentials, logarithmic terms and power series. Finally, we summarize
spectral properties and dispersion relations of anharmonic oscillators, and
their interconnections. The purpose is to look at one of the classic problems
of quantum theory from a new perspective, through which we gain systematic
access to the phenomenologically significant higher-order terms.Comment: 51 pages, LaTeX, Latin2 font
Single- and coupled-channel radial inverse scattering with supersymmetric transformations
The present status of the coupled-channel inverse-scattering method with
supersymmetric transformations is reviewed. We first revisit in a pedagogical
way the single-channel case, where the supersymmetric approach is shown to
provide a complete solution to the inverse-scattering problem. A special
emphasis is put on the differences between conservative and non-conservative
transformations. In particular, we show that for the zero initial potential, a
non-conservative transformation is always equivalent to a pair of conservative
transformations. These single-channel results are illustrated on the inversion
of the neutron-proton triplet eigenphase shifts for the S and D waves. We then
summarize and extend our previous works on the coupled-channel case and stress
remaining difficulties and open questions. We mostly concentrate on two-channel
examples to illustrate general principles while keeping mathematics as simple
as possible. In particular, we discuss the difference between the
equal-threshold and different-threshold problems. For equal thresholds,
conservative transformations can provide non-diagonal Jost and scattering
matrices. Iterations of such transformations are shown to lead to practical
algorithms for inversion. A convenient technique where the mixing parameter is
fitted independently of the eigenphases is developed with iterations of pairs
of conjugate transformations and applied to the neutron-proton triplet S-D
scattering matrix, for which exactly-solvable matrix potential models are
constructed. For different thresholds, conservative transformations do not seem
to be able to provide a non-trivial coupling between channels. In contrast, a
single non-conservative transformation can generate coupled-channel potentials
starting from the zero potential and is a promising first step towards a full
solution to the coupled-channel inverse problem with threshold differences.Comment: Topical review, 84 pages, 7 figures, 93 reference
Elaboration of approach to nuclear energy systems assessment by criterion of sustainable development
The paper describes the approach to the assessment of nuclear energy systems based on the integral indicator characterizing the level of their sustainability and results of comparative assessment of several nuclear energy system options incorporating different combinations of nuclear reactors and nuclear fuel cycle facilities. The nuclear energy systems are characterized by achievement of certain key events pertaining to the following six subject areas: economic performance, safety, availability of resources, waste handling, non-proliferation and public support. Achievement of certain key events is examined within the time interval until 2100, while the key events per se are assessed according to their contribution in the achievement of sustainable development goals. It was demonstrated that nuclear energy systems based on the once-through nuclear fuel cycle with thermal reactors and uranium oxide fuel do not score high according to the integral sustainable development indicator even in the case when the issue of isolation of spent nuclear fuel in geological formation is resolved. Gradual replacement of part of thermal reactors with fast reactors and closing the nuclear fuel cycle results in the achievement of evaluated characteristics in many subject areas, which are close to maximum requirements of sustainable development, and in the significant enhancement of the sustainability indicator
Control not quantum gate on the states of photon orbital angular momentum
The possibility of effectively creating quantum gates based on orbital angular momentum photon qubits using a Kerr nonlinear medium in a cavity is studied. It is shown how a quantum C-NOT gate can be produced with such qubits through four-wave mixing process. A theory of this gate operation is constructed using an input–output formalism. Parametric matching conditions are obtained for effective gate operation