11,410 research outputs found
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
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
Vector Casimir effect for a D-dimensional sphere
The Casimir energy or stress due to modes in a D-dimensional volume subject
to TM (mixed) boundary conditions on a bounding spherical surface is
calculated. Both interior and exterior modes are included. Together with
earlier results found for scalar modes (TE modes), this gives the Casimir
effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a
spherical shell. Known results for three dimensions, first found by Boyer, are
reproduced. Qualitatively, the results for TM modes are similar to those for
scalar modes: Poles occur in the stress at positive even dimensions, and cusps
(logarithmic singularities) occur for integer dimensions . Particular
attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe
Does the complex deformation of the Riemann equation exhibit shocks?
The Riemann equation , which describes a one-dimensional
accelerationless perfect fluid, possesses solutions that typically develop
shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter
\cP\cT-invariant complex deformation of this equation,
( real), is solved exactly using the
method of characteristic strips, and it is shown that for real initial
conditions, shocks cannot develop unless is an odd integer.Comment: latex, 8 page
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
On the eigenproblems of PT-symmetric oscillators
We consider the non-Hermitian Hamiltonian H=
-\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a
polynomial of degree at most n \geq 1 with all nonnegative real coefficients
(possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the
sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case
H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the
eigenfunction u and its derivative u^\prime and we find some other interesting
properties of eigenfunctions.Comment: 21pages, 9 figure
PT-symmetry breaking in complex nonlinear wave equations and their deformations
We investigate complex versions of the Korteweg-deVries equations and an Ito
type nonlinear system with two coupled nonlinear fields. We systematically
construct rational, trigonometric/hyperbolic, elliptic and soliton solutions
for these models and focus in particular on physically feasible systems, that
is those with real energies. The reality of the energy is usually attributed to
different realisations of an antilinear symmetry, as for instance PT-symmetry.
It is shown that the symmetry can be spontaneously broken in two alternative
ways either by specific choices of the domain or by manipulating the parameters
in the solutions of the model, thus leading to complex energies. Surprisingly
the reality of the energies can be regained in some cases by a further breaking
of the symmetry on the level of the Hamiltonian. In many examples some of the
fixed points in the complex solution for the field undergo a Hopf bifurcation
in the PT-symmetry breaking process. By employing several different variants of
the symmetries we propose many classes of new invariant extensions of these
models and study their properties. The reduction of some of these models yields
complex quantum mechanical models previously studied.Comment: 50 pages, 39 figures (compressed in order to comply with arXiv
policy; higher resolutions maybe obtained from the authors upon request
New Exactly Solvable Isospectral Partners for PT Symmetric Potentials
We examine in detail the possibilty of applying Darboux transformation to non
Hermitian hamiltonians. In particular we propose a simple method of
constructing exactly solvable PT symmetric potentials by applying Darboux
transformation to higher states of an exactly solvable PT symmetric potential.
It is shown that the resulting hamiltonian and the original one are pseudo
supersymmetric partners. We also discuss application of Darboux transformation
to hamiltonians with spontaneously broken PT symmetry.Comment: 11 pages, 2 figures, To be published in Journal of Physics A (2004
Entropy and Temperature of a Quantum Carnot Engine
It is possible to extract work from a quantum-mechanical system whose
dynamics is governed by a time-dependent cyclic Hamiltonian. An energy bath is
required to operate such a quantum engine in place of the heat bath used to run
a conventional classical thermodynamic heat engine. The effect of the energy
bath is to maintain the expectation value of the system Hamiltonian during an
isoenergetic expansion. It is shown that the existence of such a bath leads to
equilibrium quantum states that maximise the von Neumann entropy. Quantum
analogues of certain thermodynamic relations are obtained that allow one to
define the temperature of the energy bath.Comment: 4 pages, 1 figur
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