48,034 research outputs found
Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States
We present the study of weakly bound, neutron-rich nuclei using the nuclear
shell model employing the complex Berggren ensemble representing the bound
single-particle states, unbound Gamow states, and the non-resonant continuum.
In the proposed Gamow Shell Model, the Hamiltonian consists of a one-body
finite depth (Woods-Saxon) potential and a residual two-body interaction. We
discuss the basic ingredients of the Gamow Shell Model. The formalism is
illustrated by calculations involving {\it several} valence neutrons outside
the double-magic core: He and O.Comment: 19 pages, 20 encapsulated PostScript figure
Bound states of dipolar molecules studied with the Berggren expansion method
Bound states of dipole-bound negative anions are studied by using a
non-adiabatic pseudopotential method and the Berggren expansion involving bound
states, decaying resonant states, and non-resonant scattering continuum. The
method is benchmarked by using the traditional technique of direct integration
of coupled channel equations. A good agreement between the two methods has been
found for well-bound states. For weakly-bound subthreshold states with binding
energies comparable with rotational energies of the anion, the direct
integration approach breaks down and the Berggren expansion method becomes the
tool of choice.Comment: 12 pages, 10 figure
Casimir Energy of a BEC: From Moderate Interactions to the Ideal Gas
Considering the Casimir effect due to phononic excitations of a weakly
interacting dilute {BEC}, we derive a re-normalized expression for the zero
temperature Casimir energy of a {BEC} confined to a parallel
plate geometry with periodic boundary conditions. Our expression is formally
equivalent to the free energy of a bosonic field at finite temperature, with a
nontrivial density of modes that we compute analytically. As a function of the
interaction strength, smoothly describes the transition from
the weakly interacting Bogoliubov regime to the non-interacting ideal {BEC}.
For the weakly interacting case, reduces to leading order to
the Casimir energy due to zero-point fluctuations of massless phonon modes. In
the limit of an ideal Bose gas, our result correctly describes the Casimir
energy going to zero.Comment: 12 pages, 3 figures, accepted for publication in JPA. New version
with corrected typos and an additional appendi
Low induction number, ground conductivity meters : a correction procedure in the absence of magnetic effects
Ground conductivity meters, comprising a variety of coilâcoil configurations, are intended to operate within the limits provided by a low induction number (LIN), electromagnetic condition. They are now routinely used across a wide range of application areas and the measured apparent conductivity data may be spatially assembled and examined/correlated alongside information obtained from many other earth science, environmental, soil and land use assessments. The theoretical behaviour of the common systems is examined in relation to both the prevailing level of subsurface conductivity and the instrument elevation. It is demonstrated that, given the inherent high level of accuracy of modern instruments, the prevailing LIN condition may require operation in environments restricted to very low (< 12 mS/m) conductivities. Beyond this limit, non-linear departures from the apparent conductivity that would be associated with a LIN condition occur and are a function of the coil configuration, the instrument height and the prevailing conductivity. Using both theory and experimental data, it is demonstrated that this has the potential to provide biased and spatially distorted measurements. A simple correction procedure that can be applied to the measured data obtained from any of the LIN instruments is developed. The correction procedure would, in the limit of a uniform subsurface, return the same (correct) conductivity, irrespective of the ground conductivity meter used, the prevailing conductivity or the measurement height
Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method I. General Theory
The present paper concerns the derivation of phase-integral quantization
conditions for the two-centre Coulomb problem under the assumption that the two
Coulomb centres are fixed. With this restriction we treat the general
two-centre Coulomb problem according to the phase-integral method, in which one
uses an {\it a priori} unspecified {\it base function}. We consider base
functions containing three unspecified parameters and .
When the absolute value of the magnetic quantum number is not too small, it
is most appropriate to choose . When, on the other hand,
is sufficiently small, it is most appropriate to choose .
Arbitrary-order phase-integral quantization conditions are obtained for these
choices of . The parameters and are determined from the
requirement that the results of the first and the third order of the
phase-integral approximation coincide, which makes the first-order
approximation as good as possible.
In order to make the paper to some extent self-contained, a short review of
the phase-integral method is given in the Appendix.Comment: 23 pages, RevTeX, 4 EPS figures, submitted to J. Math. Phy
Towards a Smart World: Hazard Levels for Monitoring of Autonomous Vehiclesâ Swarms
This work explores the creation of quantifiable indices to monitor the safe operations and movement of families of autonomous vehicles (AV) in restricted highway-like environments. Specifically, this work will explore the creation of ad-hoc rules for monitoring lateral and longitudinal movement of multiple AVs based on behavior that mimics swarm and flock movement (or particle swarm motion). This exploratory work is sponsored by the Emerging Leader Seed grant program of the Mineta Transportation Institute and aims at investigating feasibility of adaptation of particle swarm motion to control families of autonomous vehicles. Specifically, it explores how particle swarm approaches can be augmented by setting safety thresholds and fail-safe mechanisms to avoid collisions in off-nominal situations. This concept leverages the integration of the notion of hazard and danger levels (i.e., measures of the âclosenessâ to a given accident scenario, typically used in robotics) with the concept of safety distance and separation/collision avoidance for ground vehicles. A draft of implementation of four hazard level functions indicates that safety thresholds can be set up to autonomously trigger lateral and longitudinal motion control based on three main rules respectively based on speed, heading, and braking distance to steer the vehicle and maintain separation/avoid collisions in families of autonomous vehicles. The concepts here presented can be used to set up a high-level framework for developing artificial intelligence algorithms that can serve as back-up to standard machine learning approaches for control and steering of autonomous vehicles. Although there are no constraints on the conceptâs implementation, it is expected that this work would be most relevant for highly-automated Level 4 and Level 5 vehicles, capable of communicating with each other and in the presence of a monitoring ground control center for the operations of the swarm
Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
We find a massive simplification in the non-perturbative expression for the
structure constant of Wilson lines with 3 cusps when expressed in terms of the
key Quantum Spectral Curve quantities, namely Q-functions. Our calculation is
done for the configuration of 3 cusps lying in the same plane with arbitrary
angles in the ladders limit. This provides strong evidence that the Quantum
Spectral Curve is not only a highly efficient tool for finding the anomalous
dimensions but also encodes correlation functions with all wrapping corrections
taken into account to all orders in the `t Hooft coupling. We also show how to
study the insertions of scalars coupled to the Wilson lines and extend our
results for the spectrum and the structure constants to this case. We discuss
an OPE expansion of two cusps in terms of these states. Our results give
additional support to the Separation of Variables strategy in solving the
planar N=4 SYM theory.Comment: v1: 62 pages, lots of pictures; v2: section 9 expanded; v3: typos
fixe
Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
We consider specific quantum mechanical model problems for which perturbation
theory fails to explain physical properties like the eigenvalue spectrum even
qualitatively, even if the asymptotic perturbation series is augmented by
resummation prescriptions to "cure" the divergence in large orders of
perturbation theory. Generalizations of perturbation theory are necessary which
include instanton configurations, characterized by nonanalytic factors
exp(-a/g) where a is a constant and g is the coupling. In the case of
one-dimensional quantum mechanical potentials with two or more degenerate
minima, the energy levels may be represented as an infinite sum of terms each
of which involves a certain power of a nonanalytic factor and represents itself
an infinite divergent series. We attempt to provide a unified representation of
related derivations previously found scattered in the literature. For the
considered quantum mechanical problems, we discuss the derivation of the
instanton contributions from a semi-classical calculation of the corresponding
partition function in the path integral formalism. We also explain the relation
with the corresponding WKB expansion of the solutions of the Schroedinger
equation, or alternatively of the Fredholm determinant det(H-E) (and some
explicit calculations that verify this correspondence). We finally recall how
these conjectures naturally emerge from a leading-order summation of
multi-instanton contributions to the path integral representation of the
partition function. The same strategy could result in new conjectures for
problems where our present understanding is more limited.Comment: 66 pages, LaTeX; refs. to part II preprint update
On the Relationship between Large Order Graphs and Instantons for the Double Well Oscillator
The double well oscillator is used as a QCD-like model for studying the
relationship between large order graphs and the instanton-antiinstanton
solution. We derive an equation for the perturbative coefficients of the ground
state energy when the number of 3 and/or 4-vertices is fixed and large. These
coefficients are determined in terms of an exact``bounce'' solution. When the
number of 4-vertices is analytically continued to be near the negative of half
the number of 3-vertices the bounce solution approaches the
instanton-antiinstanton solution and detremines leading Borel singularity.Comment: 26 pages, Latex, 6 figures, 1 tabl
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