2,760 research outputs found
Semi-classical twists for sl(3) and sl(4) boundary r-matrices of Cremmer-Gervais type
We obtain explicit formulas for the semi-classical twists deforming the
coalgebraic structure of U(sl(3)) and U(sl(4)). In rank 2 and 3 the
corresponding universal R-matrices quantize the boundary r-matrices of
Cremmer-Gervais type defining Lie Frobenius structures on the maximal parabolic
subalgebras in sl(n)
Twists in U(sl(3)) and their quantizations
The solution of the Drinfeld equation corresponding to the full set of
different carrier subalgebras in sl(3) are explicitly constructed. The obtained
Hopf structures are studied. It is demonstrated that the presented twist
deformations can be considered as limits of the corresponding quantum analogues
(q-twists) defined for the q-quantized algebras.Comment: 31 pages, Latex 2e, to be published in Journ. Phys. A: Math. Ge
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
The loss of anisotropy in MgB2 with Sc substitution and its relationship with the critical temperature
The electrical conductivity anisotropy of the sigma-bands is calculated for
the (Mg,Sc)B2 system using a virtual crystal model. Our results reveal that
anisotropy drops with relatively little scandium content (< 30%); this
behaviour coincides with the lowering of Tc and the reduction of the Kohn
anomaly. This anisotropy loss is also found in the Al and C doped systems. In
this work it is argued that the anisotropy, or 2D character, of the sigma-bands
is an important parameter for the understanding of the high Tc found in MgB2
Darboux transformations of coherent states of the time-dependent singular oscillator
Darboux transformation of both Barut-Girardello and Perelomov coherent states
for the time-dependent singular oscillator is studied. In both cases the
measure that realizes the resolution of the identity operator in terms of
coherent states is found and corresponding holomorphic representation is
constructed. For the particular case of a free particle moving with a fixed
value of the angular momentum equal to two it is shown that Barut-Giriardello
coherent states are more localized at the initial time moment while the
Perelomov coherent states are more stable with respect to time evolution. It is
also illustrated that Darboux transformation may keep unchanged this different
time behavior.Comment: 13 page
Generalization of the Darboux transformation and generalized harmonic oscillators
The Darbroux transformation is generalized for time-dependent Hamiltonian
systems which include a term linear in momentum and a time-dependent mass. The
formalism for the -fold application of the transformation is also
established, and these formalisms are applied for a general quadratic system (a
generalized harmonic oscillator) and a quadratic system with an inverse-square
interaction up to N=2. Among the new features found, it is shown, for the
general quadratic system, that the shape of potential difference between the
original system and the transformed system could oscillate according to a
classical solution, which is related to the existence of coherent states in the
system
Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors
The displacement noise in the test mass mirrors of interferometric
gravitational wave detectors is proportional to their elastic dissipation at
the observation frequencies. In this paper, we analyze one fundamental source
of dissipation in thin coatings, thermoelastic damping associated with the
dissimilar thermal and elastic properties of the film and the substrate. We
obtain expressions for the thermoelastic dissipation factor necessary to
interpret resonant loss measurements, and for the spectral density of
displacement noise imposed on a Gaussian beam reflected from the face of a
coated mass. The predicted size of these effects is large enough to affect the
interpretation of loss measurements, and to influence design choices in
advanced gravitational wave detectors.Comment: 42 pages, 7 figures, uses REVTeX
Entangled Quantum State Discrimination using Pseudo-Hermitian System
We demonstrate how to discriminate two non-orthogonal, entangled quantum
state which are slightly different from each other by using pseudo-Hermitian
system. The positive definite metric operator which makes the pseudo-Hermitian
systems fully consistent quantum theory is used for such a state
discrimination. We further show that non-orthogonal states can evolve through a
suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such
evolution ceases at exceptional points of the pseudo-Hermitian system.Comment: Latex, 9 pages, 1 figur
Interactions of Hermitian and non-Hermitian Hamiltonians
The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian
Hamiltonians, each of which individually has a real energy spectrum, is
explored by means of a number of soluble models. It is found that in all cases
the energy remains real for small values of the coupling constant, but becomes
complex if the coupling becomes stronger than some critical value. For a
quadratic non-Hermitian PT-symmetric Hamiltonian coupled to an arbitrary real
Hermitian PT-symmetric Hamiltonian, the reality of the ground-state energy for
small enough coupling constant is established up to second order in
perturbation theory.Comment: 9 pages, 0 figure
Quadratic pseudosupersymmetry in two-level systems
Using the intertwining relation we construct a pseudosuperpartner for a
(non-Hermitian) Dirac-like Hamiltonian describing a two-level system
interacting in the rotating wave approximation with the electric component of
an electromagnetic field. The two pseudosuperpartners and pseudosupersymmetry
generators close a quadratic pseudosuperalgebra. A class of time dependent
electric fields for which the equation of motion for a two level system placed
in this field can be solved exactly is obtained. New interesting phenomenon is
observed. There exists such a time-dependent detuning of the field frequency
from the resonance value that the probability to populate the excited level
ceases to oscillate and becomes a monotonically growing function of time
tending to 3/4. It is shown that near this fixed excitation regime the
probability exhibits two kinds of oscillations. The oscillations with a small
amplitude and a frequency close to the Rabi frequency (fast oscillations) take
place at the background of the ones with a big amplitude and a small frequency
(slow oscillations). During the period of slow oscillations the minimal value
of the probability to populate the excited level may exceed 1/2 suggesting for
an ensemble of such two-level atoms the possibility to acquire the inverse
population and exhibit lasing properties.Comment: 5 figure
- …