4,864 research outputs found
Model tests of cluster separability in relativistic quantum mechanics
A relativistically invariant quantum theory first advanced by Bakamjian and
Thomas has proven very useful in modeling few-body systems. For three particles
or more, this approach is known formally to fail the constraint of cluster
separability, whereby symmetries and conservation laws that hold for a system
of particles also hold for isolated subsystems. Cluster separability can be
restored by means of a recursive construction using unitary transformations,
but implementation is difficult in practice, and the quantitative extent to
which the Bakamjian-Thomas approach violates cluster separability has never
been tested. This paper provides such a test by means of a model of a scalar
probe in a three-particle system for which (1) it is simple enough that there
is a straightforward solution that satisfies Poincar\'e invariance and cluster
separability, and (2) one can also apply the Bakamjian-Thomas approach. The
difference between these calculations provides a measure of the size of the
corrections from the Sokolov construction that are needed to restore cluster
properties. Our estimates suggest that, in models based on nucleon degrees of
freedom, the corrections that restore cluster properties are too small to
effect calculations of observables.Comment: 13 pages, 15 figure
Plasma dispersion of multisubband electron systems over liquid helium
Density-density response functions are evaluated for nondegenerate
multisubband electron systems in the random-phase approximation for arbitrary
wave number and subband index. We consider both quasi-two-dimensional and
quasi-one- dimensional systems for electrons confined to the surface of liquid
helium. The dispersion relations of longitudinal intrasubband and transverse
intersubband modes are calculated at low temperatures and for long wavelengths.
We discuss the effects of screening and two-subband occupancy on the plasmon
spectrum. The characteristic absorption edge of the intersubband modes is
shifted relatively to the single-particle intersubband separation and the
depolarization shift correction can be significant at high electron densities
Coupled phonon-ripplon modes in a single wire of electrons on the liquid-helium surface
The coupled phonon-ripplon modes of the quasi-one-dimensional electron chain
on the liquid helium sutface are studied. It is shown that the electron-ripplon
coupling leads to the splitting of the collective modes of the wire with the
appearance of low-frequency modes and high-frequency optical modes starting
from threshold frequencies. The effective masses of an electron plus the
associated dimple for low frequency modes are estimated and the values of the
threshold frequencies are calculated. The results obtained can be used in
experimental attempts to observe the phase transition of the electron wire into
a quasi-ordered phase.Comment: 5 pages, 1 figure, Physical Review (in press
Pseudo-epsilon expansion and the two-dimensional Ising model
Starting from the five-loop renormalization-group expansions for the
two-dimensional Euclidean scalar \phi^4 field theory (field-theoretical version
of two-dimensional Ising model), pseudo-\epsilon expansions for the Wilson
fixed point coordinate g*, critical exponents, and the sextic effective
coupling constant g_6 are obtained. Pseudo-\epsilon expansions for g*, inverse
susceptibility exponent \gamma, and g_6 are found to possess a remarkable
property - higher-order terms in these expansions turn out to be so small that
accurate enough numerical estimates can be obtained using simple Pade
approximants, i. e. without addressing resummation procedures based upon the
Borel transformation.Comment: 4 pages, 4 tables, few misprints avoide
Development of a Pulse Vacuum Arc Discharge in the Gap Containing an Insulator Sputtered with Electrode Material
The paper addresses a breakdown of a vacuum gap containing an insulator sputtered with electrode material. A mechanism for development of repeated discharges in the given electrode configuration is described
Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
We examine the completeness of bi-orthogonal sets of eigenfunctions for
non-Hermitian Hamiltonians possessing a spectral singularity. The correct
resolutions of identity are constructed for delta like and smooth potentials.
Their form and the contribution of a spectral singularity depend on the class
of functions employed for physical states. With this specification there is no
obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde
Interfering Doorway States and Giant Resonances. II: Transition Strengths
The mixing of the doorway components of a giant resonance (GR) due to the
interaction via common decay channels influences significantly the distribution
of the multipole strength and the energy spectrum of the decay products of the
GR. The concept of the partial widths of a GR becomes ambiguous when the mixing
is strong. In this case, the partial widths determined in terms of the - and
-matrices must be distinguished. The photoemission turns out to be most
sensitive to the overlapping of the doorway states. At high excitation
energies, the interference between the doorway states leads to a restructuring
towards lower energies and apparent quenching of the dipole strength.Comment: 17 pages, LaTeX, 5 figures as JPEG, to appear in PRC (July 1997
- …