13,293 research outputs found
Symmetry restoration for odd-mass nuclei with a Skyrme energy density functional
In these proceedings, we report first results for particle-number and
angular-momentum projection of self-consistently blocked triaxial
one-quasiparticle HFB states for the description of odd-A nuclei in the context
of regularized multi-reference energy density functionals, using the entire
model space of occupied single-particle states. The SIII parameterization of
the Skyrme energy functional and a volume-type pairing interaction are used.Comment: 8 pages, 3 figures, workshop proceeding
Fractional statistics in some exactly solvable Calogero-like models with PT invariant interactions
Here we review a method for constructing exact eigenvalues and eigenfunctions
of a many-particle quantum system, which is obtained by adding some
nonhermitian but PT invariant (i.e., combined parity and time reversal
invariant) interaction to the Calogero model. It is shown that such extended
Calogero model leads to a real spectrum obeying generalised exclusion
statistics. It is also found that the corresponding exchange statistics
parameter differs from the exclusion statistics parameter and exhibits a
`reflection symmetry' provided the strength of the PT invariant interaction
exceeds a critical value.Comment: 8 pages, Latex, Talk given at Joint APCTP-Nankai Symposium, Tianjin
(China), Oct. 200
Model of supersymmetric quantum field theory with broken parity symmetry
Recently, it was observed that self-interacting scalar quantum field theories
having a non-Hermitian interaction term of the form ,
where is a real positive parameter, are physically acceptable in the
sense that the energy spectrum is real and bounded below. Such theories possess
PT invariance, but they are not symmetric under parity reflection or time
reversal separately. This broken parity symmetry is manifested in a nonzero
value for , even if is an even integer. This paper extends
this idea to a two-dimensional supersymmetric quantum field theory whose
superpotential is . The resulting quantum
field theory exhibits a broken parity symmetry for all . However,
supersymmetry remains unbroken, which is verified by showing that the
ground-state energy density vanishes and that the fermion-boson mass ratio is
unity.Comment: 20 pages, REVTeX, 11 postscript figure
PT-symmetric sextic potentials
The family of complex PT-symmetric sextic potentials is studied to show that
for various cases the system is essentially quasi-solvable and possesses real,
discrete energy eigenvalues. For a particular choice of parameters, we find
that under supersymmetric transformations the underlying potential picks up a
reflectionless part.Comment: 8 pages, LaTeX with amssym, no figure
Comment on `Supersymmetry, PT-symmetry and spectral bifurcation'
We demonstrate that the recent paper by Abhinav and Panigrahi entitled
`Supersymmetry, PT-symmetry and spectral bifurcation' [Ann.\ Phys.\ 325 (2010)
1198], which considers two different types of superpotentials for the
PT-symmetric complexified Scarf II potential, fails to take into account the
invariance under the exchange of its coupling parameters. As a result, they
miss the important point that for unbroken PT-symmetry this potential indeed
has two series of real energy eigenvalues, to which one can associate two
different superpotentials. This fact was first pointed out by the present
authors during the study of complex potentials having a complex
potential algebra.Comment: 6 pages, no figure, published versio
On an exactly solvable type Calogero model with nonhermitian PT invariant interaction
An exactly solvable many-particle quantum system is proposed by adding some
nonhermitian but PT invariant interactions to the Calogero model.
We have shown that such extended Calogero model leads to completely
real spectrum which obey generalised exclusion statistics. It is also found
that the corresponding exchange statistics parameter exhibit `reflection
symmetry' provided the strength of a PT invariant interaction exceeds a
critical value.Comment: Revtex, 13 pages, No figures, Minor changes, Version to appear in
Phys. Lett
Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model
For a specific exactly solvable 2 by 2 matrix model with a PT-symmetric
Hamiltonian possessing a real spectrum, we construct all the eligible physical
metrics and show that none of them admits a factorization CP in terms of an
involutive charge operator C. Alternative ways of restricting the physical
metric to a unique form are briefly discussed.Comment: 13 page
Multiple Meixner-Pollaczek polynomials and the six-vertex model
We study multiple orthogonal polynomials of Meixner-Pollaczek type with
respect to a symmetric system of two orthogonality measures. Our main result is
that the limiting distribution of the zeros of these polynomials is one
component of the solution to a constrained vector equilibrium problem. We also
provide a Rodrigues formula and closed expressions for the recurrence
coefficients. The proof of the main result follows from a connection with the
eigenvalues of block Toeplitz matrices, for which we provide some general
results of independent interest.
The motivation for this paper is the study of a model in statistical
mechanics, the so-called six-vertex model with domain wall boundary conditions,
in a particular regime known as the free fermion line. We show how the multiple
Meixner-Pollaczek polynomials arise in an inhomogeneous version of this model.Comment: 32 pages, 4 figures. References adde
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
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