12,801 research outputs found
Pairing correlations beyond the mean field
We discuss dynamical pairing correlations in the context of configuration
mixing of projected self-consistent mean-field states, and the origin of a
divergence that might appear when such calculations are done using an energy
functional in the spirit of a naive generalized density functional theory.Comment: Proceedings of the XIII Nuclear Physics Workshop ``Maria and Pierre
Curie'' on ``Pairing and beyond - 50 years of the BCS model'', held at
Kazimierz Dolny, Poland, September 27 - October 1, 2006. Int. J. Mod. Phys.
E, in prin
Configuration mixing within the energy density functional formalism: pathologies and cures
Configuration mixing calculations performed in terms of the Skyrme/Gogny
Energy Density Functional (EDF) rely on extending the Single-Reference energy
functional into non-diagonal EDF kernels. The standard way to do so, based on
an analogy with the pure Hamiltonian case and the use of the generalized Wick
theorem, is responsible for the recently observed divergences and steps in
Multi-Reference calculations. We summarize here the minimal solution to this
problem recently proposed [Lacroix et al, arXiv:0809.2041] and applied with
success to particle number restoration[Bender et al, arXiv:0809.2045]. Such a
regularization method provides suitable corrections of pathologies for EDF
depending on integer powers of the density. The specific case of fractional
powers of the density[Duguet et al, arXiv:0809.2049] is also discussed.Comment: 5 pages, Proceedings of the French-Japanese Symposium, September
2008. To be published in Int. J. of Mod. Phys.
Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable
In the quantization scheme which weakens the hermiticity of a Hamiltonian to
its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and
Coulomb potentials is defined at the purely imaginary effective charges
(Ze^2=if) and regularized by a purely imaginary shift of x. This model is
quasi-exactly solvable: We show that at each excited, (N+1)-st
harmonic-oscillator energy E=2N+3 there exists not only the well known harmonic
oscillator bound state (at the vanishing charge f=0) but also a normalizable
(N+1)-plet of the further elementary Sturmian eigenstates \psi_n(x) at
eigencharges f=f_n > 0, n = 0, 1, ..., N. Beyond the first few smallest
multiplicities N we recommend their perturbative construction.Comment: 13 pages, Latex file, to appear in J. Phys. A: Math. Ge
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
Spatially resolved spectroscopy of Coma cluster early-type galaxies IV. Completing the dataset
The long-slit spectra obtained along the minor axis, offset major axis and
diagonal axis are presented for 12 E and S0 galaxies of the Coma cluster drawn
from a magnitude-limited sample studied before. The rotation curves, velocity
dispersion profiles and the H_3 and H_4 coefficients of the Hermite
decomposition of the line of sight velocity distribution are derived. The
radial profiles of the Hbeta, Mg, and Fe line strength indices are measured
too. In addition, the surface photometry of the central regions of a subsample
of 4 galaxies recently obtained with Hubble Space Telescope is presented. The
data will be used to construct dynamical models of the galaxies and study their
stellar populations.Comment: 40 pages, 7 figures, 6 tables. Accepted for publication in ApJ
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
Chaotic systems in complex phase space
This paper examines numerically the complex classical trajectories of the
kicked rotor and the double pendulum. Both of these systems exhibit a
transition to chaos, and this feature is studied in complex phase space.
Additionally, it is shown that the short-time and long-time behaviors of these
two PT-symmetric dynamical models in complex phase space exhibit strong
qualitative similarities.Comment: 22 page, 16 figure
Spontaneous Symmetry Breaking of phi4(1+1) in Light Front Field Theory
We study spontaneous symmetry breaking in phi^4_(1+1) using the light-front
formulation of the field theory. Since the physical vacuum is always the same
as the perturbative vacuum in light-front field theory the fields must develop
a vacuum expectation value through the zero-mode components of the field. We
solve the nonlinear operator equation for the zero-mode in the one-mode
approximation. We find that spontaneous symmetry breaking occurs at
lambda_critical = 4 pi(3+sqrt 3), which is consistent with the value
lambda_critical = 54.27 obtained in the equal time theory. We calculate the
value of the vacuum expectation value as a function of the coupling constant in
the broken phase both numerically and analytically using the delta expansion.
We find two equivalent broken phases. Finally we show that the energy levels of
the system have the expected behavior within the broken phase.Comment: 17 pages, OHSTPY-HEP-TH-92-02
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
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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