19 research outputs found
Phase shift effective range expansion from supersymmetric quantum mechanics
Supersymmetric or Darboux transformations are used to construct local phase
equivalent deep and shallow potentials for partial waves. We
associate the value of the orbital angular momentum with the asymptotic form of
the potential at infinity which allows us to introduce adequate long-distance
transformations. The approach is shown to be effective in getting the correct
phase shift effective range expansion. Applications are considered for the
and partial waves of the neutron-proton scattering.Comment: 6 pages, 3 figures, Revtex4, version to be publised in Physical
Review
The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization
Using the convex optimization method and Helstrom family of ensembles
introduced in Ref. [1], we have discussed optimal ambiguous discrimination in
qubit systems. We have analyzed the problem of the optimal discrimination of N
known quantum states and have obtained maximum success probability and optimal
measurement for N known quantum states with equiprobable prior probabilities
and equidistant from center of the Bloch ball, not all of which are on the one
half of the Bloch ball and all of the conjugate states are pure. An exact
solution has also been given for arbitrary three known quantum states. The
given examples which use our method include: 1. Diagonal N mixed states; 2. N
equiprobable states and equidistant from center of the Bloch ball which their
corresponding Bloch vectors are inclined at the equal angle from z axis; 3.
Three mirror-symmetric states; 4. States that have been prepared with equal
prior probabilities on vertices of a Platonic solid.
Keywords: minimum-error discrimination, success probability, measurement,
POVM elements, Helstrom family of ensembles, convex optimization, conjugate
states PACS Nos: 03.67.Hk, 03.65.TaComment: 15 page
Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies
We study exact multi-soliton solutions of integrable hierarchies on
noncommutative space-times which are represented in terms of quasi-determinants
of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic
behavior of the multi-soliton solutions and found that the asymptotic
configurations in soliton scattering process can be all the same as commutative
ones, that is, the configuration of N-soliton solution has N isolated localized
energy densities and the each solitary wave-packet preserves its shape and
velocity in the scattering process. The phase shifts are also the same as
commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy
is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE
Lower bound of minimal time evolution in quantum mechanics
We show that the total time of evolution from the initial quantum state to
final quantum state and then back to the initial state, i.e., making a round
trip along the great circle over S^2, must have a lower bound in quantum
mechanics, if the difference between two eigenstates of the 2\times 2
Hamiltonian is kept fixed. Even the non-hermitian quantum mechanics can not
reduce it to arbitrarily small value. In fact, we show that whether one uses a
hermitian Hamiltonian or a non-hermitian, the required minimal total time of
evolution is same. It is argued that in hermitian quantum mechanics the
condition for minimal time evolution can be understood as a constraint coming
from the orthogonality of the polarization vector \bf P of the evolving quantum
state \rho={1/2}(\bf 1+ \bf{P}\cdot\boldsymbol{\sigma}) with the vector
\boldsymbol{\mathcal O}(\Theta) of the 2\times 2 hermitian Hamiltonians H
={1/2}({\mathcal O}_0\boldsymbol{1}+ \boldsymbol{\mathcal
O}(\Theta)\cdot\boldsymbol{\sigma}) and it is shown that the Hamiltonian H can
be parameterized by two independent parameters {\mathcal O}_0 and \Theta.Comment: 4 pages, no figure, revtex
Extended WKB method, resonances and supersymmetric radial barriers
Semiclassical approximations are implemented in the calculation of position
and width of low energy resonances for radial barriers. The numerical
integrations are delimited by t/T<<8, with t the period of a classical particle
in the barrier trap and T the resonance lifetime. These energies are used in
the construction of `haired' short range potentials as the supersymmetric
partners of a given radial barrier. The new potentials could be useful in the
study of the transient phenomena which give rise to the Moshinsky's diffraction
in time.Comment: 12 pages, 4 figures, 3 table
First-order intertwining operators with position dependent mass and - weak-psuedo-Hermiticity generators
A Hermitian and an anti-Hermitian first-order intertwining operators are
introduced and a class of -weak-pseudo-Hermitian position-dependent mass
(PDM) Hamiltonians are constructed. A corresponding reference-target
-weak-pseudo-Hermitian PDM -- Hamiltonians' map is suggested. Some
-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models
are used as illustrative examples. Energy-levels crossing and flown-away states
phenomena are reported for the resulting Scarf II spectrum. Some of the
corresponding -weak-pseudo-Hermitian Scarf II- and
periodic-type-isospectral models (PT -symmetric and non-PT -symmetric) are
given as products of the reference-target map.Comment: 11 pages, no figures, Revised/Expanded, more references added. To
appear in the Int.J. Theor. Phy
Superconformal mechanics and nonlinear supersymmetry
We show that a simple change of the classical boson-fermion coupling
constant, , , in the superconformal mechanics
model gives rise to a radical change of a symmetry: the modified classical and
quantum systems are characterized by the nonlinear superconformal symmetry. It
is generated by the four bosonic integrals which form the so(1,2) x u(1)
subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2
so(1,2)-representations and anticommuting for the order n polynomials of the
even generators. We find that the modified quantum system with an integer value
of the parameter is described simultaneously by the two nonlinear
superconformal symmetries of the orders relatively shifted in odd number. For
the original quantum model with , , this means the
presence of the order 2p nonlinear superconformal symmetry in addition to the
osp(2|2) supersymmetry.Comment: 16 pages; misprints corrected, note and ref added, to appear in JHE
(1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric
The effect of the built-in supersymmetric quantum mechanical language on the
spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and
complexified Lorentz scalar interactions, is re-emphasized. The signature of
the "quasi-parity" on the Dirac particles' spectra is also studied. A Dirac
particle with PDM and complexified scalar interactions of the form S(z)=S(x-ib)
(an inversely linear plus linear, leading to a PT-symmetric oscillator model),
and S(x)=S_{r}(x)+iS_{i}(x) (a PT-symmetric Scarf II model) are considered.
Moreover, a first-order intertwining differential operator and an
-weak-pseudo-Hermiticity generator are presented and a complexified
PT-symmetric periodic-type model is used as an illustrative example.Comment: 11 pages, no figures, revise
SU(1,1) Coherent States For Position-Dependent Mass Singular Oscillators
The Schroedinger equation for position-dependent mass singular oscillators is
solved by means of the factorization method and point transformations. These
systems share their spectrum with the conventional singular oscillator. Ladder
operators are constructed to close the su(1,1) Lie algebra and the involved
point transformations are shown to preserve the structure of the
Barut-Girardello and Perelomov coherent states.Comment: 11 pages, 5 figures. This shortened version (includes new references)
has been adapted for its publication in International Journal of Theoretical
Physic
Phase equivalent chains of Darboux transformations in scattering theory
We propose a procedure based on phase equivalent chains of Darboux transformations to generate local potentials satisfying the radial Schrodinger equation and sharing the same scattering data. For potentials related by a chain of transformations, an analytic expression is derived for the Jost function. It is shown how the same system of S-matrix poles can be differently distributed between poles and zeros of a Jost function that corresponds to different potentials with equal phase shifts. The concept of shallow and deep phase equivalent potentials is analyzed in connection with distinct distributions of poles. It is shown that phase equivalent chains do not violate the Levinson theorem. The method is applied to derive a shallow and a family of deep phase equivalent potentials describing the S-1(0) partial wave of the nucleon-nucleon scattering