8,992 research outputs found
The Casimir Effect for Generalized Piston Geometries
In this paper we study the Casimir energy and force for generalized pistons
constructed from warped product manifolds of the type where
is an interval of the real line and is a smooth compact
Riemannian manifold either with or without boundary. The piston geometry is
obtained by dividing the warped product manifold into two regions separated by
the cross section positioned at . By exploiting zeta function
regularization techniques we provide formulas for the Casimir energy and force
involving the arbitrary warping function and base manifold .Comment: 16 pages, LaTeX. To appear in the proceedings of the Conference on
Quantum Field Theory Under the Influence of External Conditions (QFEXT11).
Benasque, Spain, September 18-24, 201
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
Prospects for direct detection of circular polarization of gravitational-wave background
We discussed prospects for directly detecting circular polarization signal of
gravitational wave background. We found it is generally difficult to probe the
monopole mode of the signal due to broad directivity of gravitational wave
detectors. But the dipole (l=1) and octupole (l=3) modes of the signal can be
measured in a simple manner by combining outputs of two unaligned detectors,
and we can dig them deeply under confusion and detector noises. Around f~0.1mHz
LISA will provide ideal data streams to detect these anisotropic components
whose magnitudes are as small as ~1 percent of the detector noise level in
terms of the non-dimensional energy density \Omega_{GW}(f).Comment: 5 pages, 1 figure, PRL in pres
An Efficient Data Structure for Dynamic Two-Dimensional Reconfiguration
In the presence of dynamic insertions and deletions into a partially
reconfigurable FPGA, fragmentation is unavoidable. This poses the challenge of
developing efficient approaches to dynamic defragmentation and reallocation.
One key aspect is to develop efficient algorithms and data structures that
exploit the two-dimensional geometry of a chip, instead of just one. We propose
a new method for this task, based on the fractal structure of a quadtree, which
allows dynamic segmentation of the chip area, along with dynamically adjusting
the necessary communication infrastructure. We describe a number of algorithmic
aspects, and present different solutions. We also provide a number of basic
simulations that indicate that the theoretical worst-case bound may be
pessimistic.Comment: 11 pages, 12 figures; full version of extended abstract that appeared
in ARCS 201
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
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
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
Ghost Busting: PT-Symmetric Interpretation of the Lee Model
The Lee model was introduced in the 1950s as an elementary quantum field
theory in which mass, wave function, and charge renormalization could be
carried out exactly. In early studies of this model it was found that there is
a critical value of g^2, the square of the renormalized coupling constant,
above which g_0^2, the square of the unrenormalized coupling constant, is
negative. Thus, for g^2 larger than this critical value, the Hamiltonian of the
Lee model becomes non-Hermitian. It was also discovered that in this
non-Hermitian regime a new state appears whose norm is negative. This state is
called a ghost state. It has always been assumed that in this ghost regime the
Lee model is an unacceptable quantum theory because unitarity appears to be
violated. However, in this regime while the Hamiltonian is not Hermitian, it
does possess PT symmetry. It has recently been discovered that a non-Hermitian
Hamiltonian having PT symmetry may define a quantum theory that is unitary. The
proof of unitarity requires the construction of a new time-independent operator
called C. In terms of C one can define a new inner product with respect to
which the norms of the states in the Hilbert space are positive. Furthermore,
it has been shown that time evolution in such a theory is unitary. In this
paper the C operator for the Lee model in the ghost regime is constructed
exactly in the V/N-theta sector. It is then shown that the ghost state has a
positive norm and that the Lee model is an acceptable unitary quantum field
theory for all values of g^2.Comment: 20 pages, 9 figure
Effects of the triaxial deformation and pairing correlation on the proton emitter 145Tm
The ground-state properties of the recent reported proton emitter 145Tm have
been studied within the axially or triaxially deformed relativistic mean field
(RMF) approaches, in which the pairing correlation is taken into account by the
BCS-method with a constant pairing gap. It is found that triaxiality and
pairing correlations play important roles in reproducing the experimental one
proton separation energy. The single-particle level, the proton emission orbit,
the deformation parameters beta = 0.22 and gamma = 28.98 and the corresponding
spectroscopic factor for 145Tm in the triaxial RMF calculation are given as
well.Comment: 17 pages, 7 figures and 1 table. accepted by Physical Review
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