1,171 research outputs found
Majorana spin-flip transitions in a magnetic trap
Atoms confined in a magnetic trap can escape by making spin-flip Majorana
transitions due to a breakdown of the adiabatic approximation. Several papers
have studied this process for atoms with spin or . The present
paper calculates the escape rate for atoms with spin . This problem has
new features because the perturbation which allows atoms to escape
satisfies a selection rule and multi-step
processes contribute in leading order. When the adiabatic approximation is
satisfied the leading order terms can be summed to yield a simple expression
for the escape rate.Comment: 16page
CONTINUITY OF CONDITION SPECTRUM AND ITS LEVEL SET IN BANACH ALGEBRA
For 0 < � < 1 and a Banach algebra element a, this thesis aims to establish
the results related to continuity of condition spectrum and its level set correspondence
at (�; a). Here we propose a method of study to achieve the continuity. We
first identify the Banach algebras at which the interior of the level set of condition
spectrum is empty and then we obtain the continuity results.
This thesis consists of four chapters. Chapter 1 contains all the prerequisites
which are crucial for the development of the thesis. In particular, this chapter
has a quick review of the basic properties of spectrum, condition spectrum, upper
and lower hemicontiuous correspondences. We also concentrate on analytic vector
valued maps and generalized maximum modulus theorem for them.
For an element a in A, Chapter 2 has the results related to interior of the level of
set of the condition spectrum of a. At first, we focus on
Second Order Darboux Displacements
The potentials for a one dimensional Schroedinger equation that are displaced
along the x axis under second order Darboux transformations, called 2-SUSY
invariant, are characterized in terms of a differential-difference equation.
The solutions of the Schroedinger equation with such potentials are given
analytically for any value of the energy. The method is illustrated by a
two-soliton potential. It is proven that a particular case of the periodic
Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the
corresponding Schroedinger equation equation are found for any value of the
energy. A simple analytic expression for a family of two-gap potentials is
derived
Connection between the Green functions of the supersymmetric pair of Dirac Hamiltonians
The Sukumar theorem about the connection between the Green functions of the
supersymmetric pair of the Schr\"odinger Hamiltonians is generalized to the
case of the supersymmetric pair of the Dirac Hamiltonians.Comment: 12 pages,Latex, no figure
Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States
We consider the multi-channel inverse scattering problem in one-dimension in
the presence of thresholds and bound states for a potential of finite support.
Utilizing the Levin representation, we derive the general Marchenko integral
equation for N-coupled channels and show that, unlike to the case of the radial
inverse scattering problem, the information on the bound state energies and
asymptotic normalization constants can be inferred from the reflection
coefficient matrix alone. Thus, given this matrix, the Marchenko inverse
scattering procedure can provide us with a unique multi-channel potential. The
relationship to supersymmetric partner potentials as well as possible
applications are discussed. The integral equation has been implemented
numerically and applied to several schematic examples showing the
characteristic features of multi-channel systems. A possible application of the
formalism to technological problems is briefly discussed.Comment: 19 pages, 5 figure
Toward a Spin- and Parity-Independent Nucleon-Nucleon Potential
A supersymmetric inversion method is applied to the singlet and
neutron-proton elastic phase shifts. The resulting central potential
has a one-pion-exchange (OPE) long-range behavior and a parity-independent
short-range part; it fits inverted data well. Adding a regularized OPE tensor
term also allows the reproduction of the triplet , and
phase shifts as well as of the deuteron binding energy. The potential is thus
also spin-independent (except for the OPE part) and contains no spin-orbit
term. These important simplifications of the neutron-proton interaction are
shown to be possible only if the potential possesses Pauli forbidden bound
states, as proposed in the Moscow nucleon-nucleon model.Comment: 9 pages, RevTeX, 5 ps figure
Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for Feshbach resonance
A new type of supersymmetric transformations of the coupled-channel radial
Schroedinger equation is introduced, which do not conserve the vanishing
behavior of solutions at the origin. Contrary to usual transformations, these
``non-conservative'' transformations allow, in the presence of thresholds, the
construction of potentials with coupled scattering matrices from uncoupled
potentials. As an example, an exactly-solvable potential matrix is obtained
which provides a very simple model of Feshbach-resonance phenomenon.Comment: 10 pages, 2 figure
Pseudospin, Spin, and Coulomb Dirac-Symmetries: Doublet Structure and Supersymmetric Patterns
Relativistic symmetries of the Dirac Hamiltonian with a mixture of
spherically symmetric Lorentz scalar and vector potentials, are examined from
the point of view of supersymmetric quantum mechanics. The cases considered
include the Coulomb, pseudospin and spin limits relevant, respectively, to
atoms, nuclei and hadrons.Comment: 8 pages, 1 figure, Proc. Int. Workshop on "Blueprints for the
Nucleus: From First Principles to Collective Motion", May 17-23, 2004, Feza
Gursey Institute, Istanbul, Turke
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