261 research outputs found
Completeness of the Coulomb scattering wave functions
Completeness of the eigenfunctions of a self-adjoint Hamiltonian, which is
the basic ingredient of quantum mechanics, plays an important role in nuclear
reaction and nuclear structure theory. However, until now, there was no a
formal proof of the completeness of the eigenfunctions of the two-body
Hamiltonian with the Coulomb interaction. Here we present the first formal
proof of the completeness of the two-body Coulomb scattering wave functions for
repulsive unscreened Coulomb potential. To prove the completeness we use the
Newton's method [R. Newton, J. Math Phys., 1, 319 (1960)]. The proof allows us
to claim that the eigenfunctions of the two-body Hamiltonian with the potential
given by the sum of the repulsive Coulomb plus short-range (nuclear) potentials
also form a complete set. It also allows one to extend the Berggren's approach
of modification of the complete set of the eigenfunctions by including the
resonances for charged particles. We also demonstrate that the resonant Gamow
functions with the Coulomb tail can be regularized using Zel'dovich's
regularization method.Comment: 12 pages and 1 figur
Tunneling times with covariant measurements
We consider the time delay of massive, non-relativistic, one-dimensional
particles due to a tunneling potential. In this setting the well-known Hartman
effect asserts that often the sub-ensemble of particles going through the
tunnel seems to cross the tunnel region instantaneously. An obstacle to the
utilization of this effect for getting faster signals is the exponential
damping by the tunnel, so there seems to be a trade-off between speedup and
intensity. In this paper we prove that this trade-off is never in favor of
faster signals: the probability for a signal to reach its destination before
some deadline is always reduced by the tunnel, for arbitrary incoming states,
arbitrary positive and compactly supported tunnel potentials, and arbitrary
detectors. More specifically, we show this for several different ways to define
``the same incoming state'' and ''the same detector'' when comparing the
settings with and without tunnel potential. The arrival time measurements are
expressed in the time-covariant approach, but we also allow the detection to be
a localization measurement at a later time.Comment: 12 pages, 2 figure
On the Global Existence of Bohmian Mechanics
We show that the particle motion in Bohmian mechanics, given by the solution
of an ordinary differential equation, exists globally: For a large class of
potentials the singularities of the velocity field and infinity will not be
reached in finite time for typical initial values. A substantial part of the
analysis is based on the probabilistic significance of the quantum flux. We
elucidate the connection between the conditions necessary for global existence
and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe
On time-dependent AdS/CFT
We clarify aspects of the holographic AdS/CFT correspondence that are typical
of Lorentzian signature, to lay the foundation for a treatment of
time-dependent gravity and conformal field theory phenomena. We provide a
derivation of bulk-to-boundary propagators associated to advanced, retarded and
Feynman bulk propagators, and provide a better understanding of the boundary
conditions satisfied by the bulk fields at the horizon. We interpret the
subleading behavior of the wavefunctions in terms of specific vacuum
expectation values, and compute two-point functions in our framework. We
connect our bulk methods to the closed time path formalism in the boundary
field theory.Comment: 19 pages, v2: added reference, JHEP versio
Order and Chaos in some Trigonometric Series: Curious Adventures of a Statistical Mechanic
This paper tells the story how a MAPLE-assisted quest for an interesting
undergraduate problem in trigonometric series led some "amateurs" to the
discovery that the one-parameter family of deterministic trigonometric series
\pzcS_p: t\mapsto \sum_{n\in\Nset}\sin(n^{-{p}}t), , exhibits both order
and apparent chaos, and how this has prompted some professionals to offer their
expert insights. It is proved that \pzcS_p(t) =
\alpha_p\rm{sign}(t)|t|^{1/{p}}+O(|t|^{1/{(p+1)}})\;\forall\;t\in\Rset, with
explicitly computed constant . Experts' commentaries are reproduced
stating the fluctuations of \pzcS_p(t) - \alpha_p{\rm{sign}}(t)|t|^{1/{p}}
are presumably not Gaussian. Inspired by a central limit type theorem of Marc
Kac, a well-motivated conjecture is formulated to the effect that the
fluctuations of the -th partial sum of \pzcS_p(t),
when properly scaled, do converge in distribution to a standard Gaussian when
, though --- provided that is chosen so that the frequencies
\{n^{-p}\}_{n\in\Nset} are rationally linear independent; no conjecture has
been forthcoming for rationally dependent \{n^{-p}\}_{n\in\Nset}. Moreover,
following other experts' tip-offs, the interesting relationship of the
asymptotics of \pzcS_p(t) to properties of the Riemann function is
exhibited using the Mellin transform.Comment: Based on the invited lecture with the same title delivered by the
author on Dec.19, 2011 at the 106th Statistical Mechanics Meeting at Rutgers
University in honor of Michael Fisher, Jerry Percus, and Ben Widom. (19
figures, colors online). Comments of three referees included. Conjecture 1
revised. Accepted for publication in J. Stat. Phy
The effects of cold working on sensitization and intergranular corrosion behavior of AISI 304 stainless steel
The effects of prior cold rolling of up to an 80 pct reduction in thickness on the sensitization-desensitization behavior of Type AISI 304 stainless steel and its susceptibility to intergranular corrosion have been studied by electrochemical potentiokinetic reactivation (EPR) and Strauss-test methods. The results indicate that the prior deformation accelerated the sensitization as compared to the undeformed stainless steel. The deformed Type 304 stainless steel experienced desensitization at higher temperatures and times, and it was found to be enhanced by increased cold deformation. This could be attributed to the increased long-range chromium diffusion, possibly brought on by increasing pipe diffusion and vacancies. The role of the deformation-induced martensite (DIM) and texture, introduced by uniaxial cold rolling, on the sensitization-desensitization kinetics has also been discussed. This study could not reveal any systematic relationship between texture and the degree of sensitization (DOS) obtained. The effect of DIM on DOS seems to be pronounced at 500 °C when the steel retained significant amounts of DIM; however, the retained DIM is insignificant at higher sensitization times and temperatures
- …