pinecone/core-2020-05-10-deduplication huggingface dataset:
Quantization of Hyperbolic N-Sphere Scattering Systems in Three
  Dimensions

Most discussions of chaotic scattering systems are devoted to two-dimensional
systems. It is of considerable interest to extend these studies to the, in
general, more realistic case of three dimensions. In this context, it is
conceptually important to investigate the quality of semiclassical methods as a
function of the dimensionality. As a model system, we choose various three
dimensional generalizations of the famous three disk problem which played a
central role in the study of chaotic scattering in two dimensions. We present a
quantum-mechanical treatment of the hyperbolic scattering of a point particle
off a finite number of non-overlapping and non-touching hard spheres in three
dimensions. We derive expressions for the scattering matrix S and its
determinant. The determinant of S decomposes into two parts, the first one
contains the product of the determinants of the individual one-sphere
S-matrices and the second one is given by a ratio involving the determinants of
a characteristic KKR-type matrix and its conjugate. We justify our approach by
showing that all formal manipulations in these derivations are correct and that
all the determinants involved which are of infinite dimension exist. Moreover,
for all complex wave numbers, we conjecture a direct link between the
quantum-mechanical and semiclassical descriptions: The semiclassical limit of
the cumulant expansion of the KKR-type matrix is given by the Gutzwiller-Voros
zeta function plus diffractional corrections in the curvature expansion. This
connection is direct since it is not based on any kind of subtraction scheme
involving bounded reference systems. We present numerically computed resonances
and compare them with the corresponding data for the similar two-dimensional
N-disk systems and with semiclassical calculations.Comment: 35 pages, LaTeX plus 8 Postscript figures, uses epsf.sty, epsfig.sty
  and epsf.te
An Operational Approach to Quantum State Reduction

An operational approach to quantum state reduction, the state change of the
measured system caused by a measurement of an observable conditional upon the
outcome of measurement, is founded without assuming the projection postulate in
any stages of the measuring process. Whereas the conventional formula assumes
that the probe measurement satisfies the projection postulate, a new formula
for determining the state reduction shows that the state reduction does not
depend on how the probe observable is measured, or in particular does not
depend on whether the probe measurement satisfies the projection postulate or
not, contrary to the longstanding attempts in showing how the macroscopic
nature of probe detection provokes state reduction.Comment: 17 pages, LaTeX, no figures, to appear in Ann. Phys. (N.Y.
Conformal Invariance and Electrodynamics: Applications and General
  Formalism

The role of the conformal group in electrodynamics in four space-time
dimensions is re-examined. As a pedagogic example we use the application of
conformal transformations to find the electromagnetic field for a charged
particle moving with a constant relativistic acceleration from the Coulomb
electric field for the particle at rest. We also re-consider the reformulation
of Maxwell's equations on the projective cone, which is isomorphic to a
conformal compactification on Minkowski space, so that conformal
transformations, belonging to the group O(4,2), are realised linearly. The
resulting equations are different from those postulated previously and respect
additional gauge invariances which play an essential role in ensuring
consistency with conventional electrodynamics on Minkowski space. The solution
on the projective cone corresponding to a constantly accelerating charged
particle is discussed.Comment: 24 pages, 1 figure, plain tex, uses harvmac, eps
Local BRST cohomology in minimal D=4, N=1 supergravity

The local BRST cohomology is computed in old and new minimal supergravity,
including the coupling to Yang-Mills gauge multiplets. This covers the
determination of all gauge invariant local actions for these models, the
classification of all the possible counterterms that are invariant on-shell, of
all candidate gauge anomalies, and of the possible nontrivial (continuous)
deformations of the standard actions and gauge transformations. Among others it
is proved that in old minimal supergravity the most general gauge invariant
action can indeed be constructed from well-known superspace integrals, whereas
in new minimal supergravity there are only a few additional (but important)
contributions which cannot be constructed in this way without further ado.
Furthermore the results indicate that supersymmetry itself is not anomalous in
minimal supergravity and show that the gauge transformations are extremely
stable under consistent deformations of the models. There is however an unusual
deformation converting new into old minimal supergravity with local
R-invariance which is reminiscent of a duality transformation.Comment: 58 pages, latex 2.09, no figures; final version, minor corrections,
  Comment added in conclusions (footnote), refs. update
Reaction-Diffusion Processes from Equivalent Integrable Quantum Chains

One-dimensional reaction-diffusion systems are mapped through a similarity
transformation onto integrable (and a priori non-stochastic) quantum chains.
Time-dependent properties of these chemical models can then be found exactly.
The reaction-diffusion processes related to free fermion systems with
site-independent interactions are classified. The time-dependence of the mean
particle density is calculated. Furthermore new integrable stochastic processes
related to the Heisenberg XXZ chain are identified and the relaxation times for
the particle density and density correlation for these systems are found.Comment: 67 pages, Latex, 3 eps figures. (final version, typos corrected
Elliptic Quantum Billiard

The exact and semiclassical quantum mechanics of the elliptic billiard is
investigated. The classical system is integrable and exhibits a separatrix,
dividing the phasespace into regions of oscillatory and rotational motion. The
classical separability carries over to quantum mechanics, and the Schr\"odinger
equation is shown to be equivalent to the spheroidal wave equation. The quantum
eigenvalues show a clear pattern when transformed into the classical action
space. The implication of the separatrix on the wave functions is illustrated.
A uniform WKB quantization taking into account complex orbits is shown to be
adequate for the semiclassical quantization in the presence of a separatrix.
The pattern of states in classical action space is nicely explained by this
quantization procedure. We extract an effective Maslov phase varying smoothly
on the energy surface, which is used to modify the Berry-Tabor trace formula,
resulting in a summation over non-periodic orbits. This modified trace formula
produces the correct number of states, even close to the separatrix. The
Fourier transform of the density of states is explained in terms of classical
orbits, and the amplitude and form of the different kinds of peaks is
analytically calculated.Comment: 33 pages, Latex2e, 19 figures,macros: epsfig, amssymb, amstext,
  submitted to Annals of Physic
Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path
  Integrals

We investigate the usefulness of the "string-inspired technique" for gauge
theory calculations in a constant external field background. Our approach is
based on Strassler's worldline path integral approach to the Bern-Kosower
formalism, and on the construction of worldline (super--) Green's functions
incorporating external fields as well as internal propagators. The worldline
path integral representation of the gluon loop is reexamined in detail. We
calculate the two-loop effective actions induced for a constant external field
by a scalar and spinor loop, and the corresponding one-loop effective action in
the gluon loop case.Comment: 54 pages, no figures, Latex, uses dina4.sty, final version (minor
  corrections
Gaussian Time-Dependent Variational Principle for Bosons I - Uniform
  Case

We investigate the Dirac time-dependent variational method for a system of
non-ideal Bosons interacting through an arbitrary two body potential. The
method produces a set of non-linear time dependent equations for the
variational parameters. In particular we have considered small oscillations
about equilibrium. We obtain generalized RPA equations that can be understood
as interacting quasi-bosons, usually mentioned in the literature as having a
gap. The result of this interaction provides us with scattering properties of
these quasi-bosons including possible bound-states, which can include zero
modes. In fact the zero mode bound state can be interpreted as a new
quasi-boson with a gapless dispersion relation. Utilizing these results we
discuss a straightforward scheme for introducing temperature.Comment: 28 pages, 1 figure to appear in Annals of Physic
Applications of the Collective Field Theory for the Calogero-Sutherland
  Model

We use the collective field theory known for the Calogero-Sutherland model to
study a variety of low-energy properties. These include the ground state energy
in a confining potential upto the two leading orders in the particle number,
the dispersion relation of sound modes with a comparison to the two leading
terms in the low temperature specific heat, large amplitude waves, and single
soliton solutions. The two-point correlation function derived from the
dispersion relation of the sound mode only gives its nonoscillatory asymptotic
behavior correctly, demonstrating that the theory is applicable only for the
low-energy and long wavelength excitations of the system.Comment: LaTeX, 31 page
Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like
  Term and D=2 N oncommutative Geometry

We consider a new D=2 nonrelativistic classical mechanics model providing via
the Noether theorem the (2+1)-Galilean symmetry algebra with two central
charges: mass m and the coupling constant k of a Chern-Simons-like term. In
this way we provide the dynamical interpretation of the second central charge
of the (2+1)-dimensional Galilean algebra. We discuss also the interpretation
of k as describing the noncommutativity of D=2 space coordinates. The model is
quantized in two ways: using the Ostrogradski-Dirac formalism for higher order
Lagrangians with constraints and the Faddeev-Jackiw method which describes
constrained systems and produces nonstandard symplectic structures. We show
that our model describes the superposition of a free motion in noncommutative
D=2 space as well as the "internal" oscillator modes. We add a suitably chosen
class of velocity-dependent two-particle interactions, which is descrobed by
local potentials in D=2 noncommutative space. We treat, in detail, the
particular case of a harmonic oscillator and describe its quantization. It
appears that the indefinite metric due to the third order time derivative term
in the field equations, even in the presence of interactions, can be eliminated
by the imposition of a subsidiary condition.Comment: small changes to make the paper look identical to the published
  versio
A statistical theory of the mean field

A statistical theory of the mean field is developed. It is based on the
proposition that the mean field can be obtained as an energy average. Moreover,
it is assumed that the matrix elements of the residual interaction, obtained
after the average interaction is removed, are random with the average value of
zero. With these two assumptions one obtains explicit expressions for the mean
field and the fluctuation away from the average. The fluctuation is expanded in
terms of more and more complex excitations. Using the randomness of the matrix
elements one can then obtain formulas for the contribution to the error from
each class of complex excitations and a general condition for the convergence
of the expansion is derived. It is to be emphasized that no conditions on the
nature of the system being studied are made. Making some simplifying
assumptions a schematic model is developed. This model is applied to the
problem of nuclear matter. The model yields a measure of the strength of the
effective interaction. It turns out to be three orders of magnitude less than
that calculated using a potential which gives a binding energy of about -7
MeV/nucleon demonstrating the strong damping of the interaction strength
induced by the averaging process.Comment: 25 pages, REVTeX, 4 eps figure
Spin Observables in Coincidence Electron Scattering from Nuclei I:
  Reduced Response Functions

A theoretical description of nucleon knockout reactions initiated by
polarized electron scattering from polarized nuclei is presented. Explicit
expressions for the complete set of reduced response functions (independent of
the polarization angle) that can be experimentally obtained assuming plane
waves for the electron are given in a general multipole expansion. The
formalism is applied to the particular case of closed-shell-minus-one nuclei
using two models for the ejected nucleon, including the final-state interaction
phenomenologically with a complex optical potential and in the factorized
plane-wave impulse approximation. Relativistic effects in the kinematics and in
the electromagnetic current are incorporated throughout --- specifically a new
expansion of the electromagnetic current in powers only of the struck nucleon
momentum is employed. Results are presented for the nucleus 39K.Comment: 51 pages (LaTeX), 17 figures (postScript
The 2-Channel Kondo Model I: Review of Experimental Evidence for its
  Realization in Metal Nanoconstrictions

Certain zero-bias anomalies (ZBAs) in the voltage, temperature and magnetic
field dependence of the conductance $G(V,T,H)$ of quenched Cu point contacts
have previously been interpreted to be due to non-magnetic 2-channel Kondo
(2CK) scattering from near-degenerate atomic two-level tunneling systems (Ralph
and Buhrman, 1992; Ralph et al. 1994), and hence to represent an experimental
realization of the non-Fermi-liquid physics of the T=0 fixed point of the
2-channel Kondo model. In this, the first in a series of three papers
(I,II,III) devoted to 2-channel Kondo physics, we present a comprehensive
review of the quenched Cu ZBA experiments and their 2CK interpretation,
including new results on ZBAs in constrictions made from Ti or from metallic
glasses. We first review the evidence that the ZBAs are due to electron
scattering from stuctural defects that are not static, but possess internal
dynamics. In order to distinguish between several mechanisms proposed to
explain the experiments, we then analyze the scaling properties of the
conductance at low temperature and voltage and extract from the data a
universal scaling function $\Gamma(v)$. The theoretical calculation of the
corresponding scaling function within the 2CK model is the subject of papers II
and III. The main conclusion of our work is that the properties of the ZBAs,
and most notably their scaling behavior, are in good agreement with the 2CK
model and clearly different from several other proposed mechanisms.Comment: 35 pages RevTeX, 19 encapsulated postscript figures; this final
  published version features two additional authors, an additional section
  reviewing recent experiments on Ti nanoconstrictions that agree very well
  with the 2-channel Kondo model, 6 new figures (and is much shorter the
  previous 53 page version, due to reformatting
On the Poisson Structure of the Time-Dependent Mean-Field Equations for
  Systems of Bosons out of Equilibrium

We analyze the Poisson structure of the time-dependent mean-field equations
for bosons and construct the Lie-Poisson bracket associated to these equations.
The latter follow from the time-dependent variational principle of Balian and
Veneroni when a gaussian Ansatz is chosen for the density operator. We perform
a stability analysis of both the full and the linearized equations. We also
search for the canonically conjugate variables. In certain cases, the evolution
equations can indeed be cast in a Hamiltonian form.Comment: 21 pages. To appear in Annals of Physic
Propagator for spinless and spin-1/2 Aharonov-Bohm-Coulomb systems

The propagator of the spinless Aharonov-Bohm-Coulomb system is derived by
following the Duru-Kleinert method. We use this propagator to explore the
spin-1/2 Aharonov-Bohm-Coulomb system which contains a point interaction as a
Zeeman term. Incorporation of the self-adjoint extension method into the
Green's function formalism properly allows us to derive the finite propagator
of the spin-1/2 Aharonov-Bohm-Coulomb system. As a by-product, the relation
between the self-adjoint extension parameter and the bare coupling constant is
obtained. Bound-state energy spectra of both spinless and spin-1/2
Aharonov-Bohm-Coulomb systems are examined.Comment: Slightly changed, to appear in Annals of Physics. 18 pages, Late
Non-relativistic Maxwell-Chern-Simons Vortices

The non-relativistic Maxwell-Chern-Simons model recently introduced by Manton
is shown to admit self-dual vortex solutions with non-zero electric field. The
interrelated ``geometric'' and ``hidden'' symmetries are explained. The theory
is also extended to (non-relativistic) spinors. A relativistic, self-dual
model, whose non-relativistic limit is the Manton model is also presented. The
relation to previous work is discussed.Comment: 20 pages plain TeX. Revised: minor errors corrected and symmetries
  explained in a clearer way. Version as will appear in Ann. Phys. (N.Y.
Flavor Doubling and the Nature of Asymptopia

We consider the possibility that QCD with N flavors has a useful low-energy description with 2N flavors. Specifically, we investigate a free theory of 2N quarks. Although the free theory is U(N)_L X U(N)_R invariant, it admits a larger U(2N) invariance. However, when the axial anomaly is accounted for in the effective theory by a 't Hooft interaction, only SU(N)_L X SU(N)_R X U(1)_B not a symmetry of the QCD lagrangian. This S_2 subgroup of U(2N) has many interesting properties. For instance, when explicit chiral symmetry breaking effects are present, S_2 is broken unless \bar\theta=0 or pi. By expressing the free theory on the light-front, we show that flavor doubling implies several superconvergence relations in pion-hadron scattering. Implicit in the 2N-flavor effective theory is a Regge trajectory with vacuum quantum numbers and unit intercept whose behavior is constrained by S_2. In particular, S_2 implies that forward pion-hadron scattering becomes purely elastic at high-energies, in good agreement with experiment
Overtone spectra and intensities of tetrahedral molecules in
  boson-realization models

The stretching and bending vibrational spectrum and the intensities of
infrared transitions in a tetrahedral molecule are studied in two
boson-realization models, where the interactions between stretching and bending
vibrations are described by a quadratic cross term and by Fermi resonance
terms, called harmonically coupled and Fermi resonance boson-realization model,
respectively. The later is a development of our recent model. As an example,
the two models are applied to the overtone spectrum and the intensities of
silicon tetrafluorde. Those models provide fits to the published experimental
vibrational eigenvalues with standard deviations 1.956 cm$^{-1}$ and 0.908
cm$^{-1}$, respectively. The intensities of infrared transitions of its
complete vibrations are calculated in the two models, and results show a good
agreement with the observed data.Comment: 14 pages Revtex, no figure, to appear in Annals of Physic
Non-perturbative regularization and renormalization: simple examples
  from non-relativistic quantum mechanics

We examine several zero-range potentials in non-relativistic quantum
mechanics. The study of such potentials requires regularization and
renormalization. We contrast physical results obtained using dimensional
regularization and cutoff schemes and show explicitly that in certain cases
dimensional regularization fails to reproduce the results obtained using cutoff
regularization. First we consider a delta-function potential in arbitrary space
dimensions. Using cutoff regularization we show that for $d \ge 4$ the
renormalized scattering amplitude is trivial. In contrast, dimensional
regularization can yield a nontrivial scattering amplitude for odd dimensions
greater than or equal to five. We also consider a potential consisting of a
delta function plus the derivative-squared of a delta function in three
dimensions. We show that the renormalized scattering amplitudes obtained using
the two regularization schemes are different. Moreover we find that in the
cutoff-regulated calculation the effective range is necessarily negative in the
limit that the cutoff is taken to infinity. In contrast, in dimensional
regularization the effective range is unconstrained. We discuss how these
discrepancies arise from the dimensional regularization prescription that all
power-law divergences vanish. We argue that these results demonstrate that
dimensional regularization can fail in a non-perturbative setting.Comment: 19 pages, LaTeX, uses epsf.te
Linear and Nonlinear Theory of Eigenfunction Scars

The theory of scarring of eigenfunctions of classically chaotic systems by
short periodic orbits is extended in several ways. The influence of short-time
linear recurrences on correlations and fluctuations at long times is
emphasized. We include the contribution to scarring of nonlinear recurrences
associated with homoclinic orbits, and treat the different scenarios of random
and nonrandom long-time recurrences. The importance of the local classical
structure around the periodic orbit is emphasized, and it is shown for an
optimal choice of test basis in phase space, scars must persist in the
semiclassical limit. The crucial role of symmetry is also discussed, which
together with the nonlinear recurrences gives a much improved account of the
actual strength of scars for given classical orbits and in individual
wavefunctions. Quantitative measures of scarring are provided and comparisons
are made with numerical data.Comment: 20 pages, 11 figure
Quantal-Classical Duality and the Semiclassical Trace Formula

We consider Hamiltonian systems which can be described both classically and
quantum mechanically. Trace formulas establish links between the energy spectra
of the quantum description and the spectrum of actions of periodic orbits in
the classical description. This duality is investigated in the present paper.
The duality holds for chaotic as well as for integrable systems. For billiards
the quantal spectrum (eigenvalues of the Helmholtz equation) and the classical
spectrum (lengths of periodic orbits) are two manifestations of the billiard's
boundary. The trace formula expresses this link as a Fourier transform relation
between the corresponding spectral densities. It follows that the two-point
statistics are also simply related. The universal correlations of the quantal
spectrum are well known, consequently one can deduce the classical universal
correlations. An explicit expression for the scale of the classical
correlations is derived and interpreted. This allows a further extension of the
formalism to the case of complex billiard systems, and in particular to the
most interesting case of diffusive system. The concept of classical
correlations allows a better understanding of the so-called diagonal
approximation and its breakdown. It also paves the way towards a semiclassical
theory that is capable of global description of spectral statistics beyond the
breaktime. An illustrative application is the derivation of the
disorder-limited breaktime in case of a disordered chain, thus obtaining a
semiclassical theory for localization. A numerical study of classical
correlations in the case of the 3D Sinai billiard is presented. We gain a
direct understanding of specific statistical properties of the classical
spectrum, as well as their semiclassical manifestation in the quantal spectrum.Comment: 42 pages, 17 figure