12,427 research outputs found
Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
Conventional weak-coupling perturbation theory suffers from problems that
arise from resonant coupling of successive orders in the perturbation series.
Multiple-scale perturbation theory avoids such problems by implicitly
performing an infinite reordering and resummation of the conventional
perturbation series. Multiple-scale analysis provides a good description of the
classical anharmonic oscillator. Here, it is extended to study the Heisenberg
operator equations of motion for the quantum anharmonic oscillator. The
analysis yields a system of nonlinear operator differential equations, which is
solved exactly. The solution provides an operator mass renormalization of the
theory.Comment: 12 pages, Revtex, no figures, available through anonymous ftp from
ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at
http://euclid.tp.ph.ic.ac.uk/Papers/papers_95-6_.htm
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
Scalar Quantum Field Theory with Cubic Interaction
In this paper it is shown that an i phi^3 field theory is a physically
acceptable field theory model (the spectrum is positive and the theory is
unitary). The demonstration rests on the perturbative construction of a linear
operator C, which is needed to define the Hilbert space inner product. The C
operator is a new, time-independent observable in PT-symmetric quantum field
theory.Comment: Corrected expressions in equations (20) and (21
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 as a Generalization of Hermiticity
The Hilbert space in PT-symmetric quantum mechanics is formulated as a linear
vector space with a dynamic inner product. The most general PT-symmetric matrix
Hamiltonians are constructed for 2*2 and 3*3 cases. In the former case, the
PT-symmetric Hamiltonian represents the most general matrix Hamiltonian with a
real spectrum. In both cases, Hermitian matrices are shown to be special cases
of PT-symmetric matrices. This finding confirms and strengthens the early
belief that the PT-symmetric quantum mechanics is a generalization of the
conventional Hermitian quantum mechanics.Comment: 13 page
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
Fission modes of 256Fm and 258Fm in a microscopic approach
A static microscopic study of potential-energy surfaces within the
Skyrme-Hartree-Fock-plus-BCS model is carried out for the 256Fm and 258Fm
isotopes with the goal of deducing some properties of spontaneous fission. The
calculated fission modes are found to be in agreement with the experimentaly
observed asymmetric-to-symmetric transition in the fragment-mass distributions
and with the high- and low-total-kinetic-energy modes experimentally observed
in 258Fm. Most of the results are similar to those obtained in
macroscopic-microscopic models as well as in recent Hartree-Fock-Bogolyubov
calculations with the Gogny interaction, with a few differences in their
interpretations. In particular an alternative explanation is proposed for the
low-energy fission mode of 258Fm.Comment: 14 pages, 11 figures, 3 tables, submitted to Phys. Rev.
Properties of nuclei in the nobelium region studied within the covariant, Skyrme, and Gogny energy density functionals
We calculate properties of the ground and excited states of nuclei in the
nobelium region for proton and neutron numbers of 92 <= Z <= 104 and 144 <= N
<= 156, respectively. We use three different energy-density-functional (EDF)
approaches, based on covariant, Skyrme, and Gogny functionals, each within two
different parameter sets. A comparative analysis of the results obtained for
odd-even mass staggerings, quasiparticle spectra, and moments of inertia allows
us to identify single-particle and shell effects that are characteristic to
these different models and to illustrate possible systematic uncertainties
related to using the EDF modellingComment: 43 LaTeX pages, 14 figures, accepted in Nuclear Physics A, Special
Issue on Superheavy Element
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