126 research outputs found
Nonstandard coproducts and the Izergin-Korepin open spin chain
Corresponding to the Izergin-Korepin (A_2^(2)) R matrix, there are three
diagonal solutions (``K matrices'') of the boundary Yang-Baxter equation. Using
these R and K matrices, one can construct transfer matrices for open integrable
quantum spin chains. The transfer matrix corresponding to the identity matrix
K=1 is known to have U_q(o(3)) symmetry. We argue here that the transfer
matrices corresponding to the other two K matrices also have U_q(o(3))
symmetry, but with a nonstandard coproduct. We briefly explore some of the
consequences of this symmetry.Comment: 7 pages, LaTeX; v2 has one additional sentence on the degeneracy
patter
Analytical Bethe Ansatz for quantum-algebra-invariant open spin chains
We determine the eigenvalues of the transfer matrices for integrable open
quantum spin chains which are associated with the affine Lie algebras
, and which have the
quantum-algebra invariance U_q(C_n), U_q(B_n), U_q(C_n), U_q(D_n)$,
respectively.Comment: 14 pages, latex, no figures (a character causing latex problem is
removed
Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics
The continuity equation relating the change in time of the position
probability density to the gradient of the probability current density is
generalized to PT-symmetric quantum mechanics. The normalization condition of
eigenfunctions is modified in accordance with this new conservation law and
illustrated with some detailed examples.Comment: 16 pages, amssy
Generating Converging Bounds to the (Complex) Discrete States of the Hamiltonian
The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is
applied to the Hamiltonian, enabling
the algebraic/numerical generation of converging bounds to the complex energies
of the states, as argued (through asymptotic methods) by Delabaere and
Trinh (J. Phys. A: Math. Gen. {\bf 33} 8771 (2000)).Comment: Submitted to J. Phys.
Electron Wave Filters from Inverse Scattering Theory
Semiconductor heterostructures with prescribed energy dependence of the
transmittance can be designed by combining: {\em a)} Pad\'e approximant
reconstruction of the S-matrix; {\em b)} inverse scattering theory for
Schro\"dinger's equation; {\em c)} a unitary transformation which takes into
account the variable mass effects. The resultant continuous concentration
profile can be digitized into an easily realizable rectangular-wells structure.
For illustration, we give the specifications of a 2 narrow band-pass 12 layer
filter with the high energy peak more than {\em twice
narrower} than the other.Comment: 4 pages, Revtex with one eps figur
Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to
We show that a recently developed method for generating bounds for the
discrete energy states of the non-hermitian potential (Handy 2001) is
applicable to complex rotated versions of the Hamiltonian. This has important
implications for extension of the method in the analysis of resonant states,
Regge poles, and general bound states in the complex plane (Bender and
Boettcher (1998)).Comment: Submitted to J. Phys.
Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues
We analyze a set of three PT-symmetric complex potentials, namely harmonic
oscillator, generalized Poschl-Teller and Scarf II, all of which reveal a
double series of energy levels along with the corresponding superpotential.
Inspired by the fact that two superpotentials reside naturally in order-two
parasupersymmetry (PSUSY) and second-derivative supersymmetry (SSUSY) schemes,
we complexify their frameworks to successfully account for the three
potentials.Comment: LaTeX2e, 28 pages, no figure
Quantum Group Invariant Supersymmetric t-J Model with periodic boundary conditions
An integrable version of the supersymmetric t-J model which is quantum group
invariant as well as periodic is introduced and analysed in detail. The model
is solved through the algebraic nested Bethe ansatz method.Comment: 11 pages, LaTe
Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
We solve explicitly the two-dimensional harmonic oscillator and the harmonic
oscillator in a background magnetic field in noncommutative phase-space without
making use of any type of representation. A key observation that we make is
that for a specific choice of the noncommutative parameters, the time reversal
symmetry of the systems get restored since the energy spectrum becomes
degenerate. This is in contrast to the noncommutative configuration space where
the time reversal symmetry of the harmonic oscillator is always broken.Comment: 7 pages Late
Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries
The one-dimensional Hubbard model with open boundary conditions is exactly
solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer
matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.Comment: Only LaTex file; no figur
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