4,298 research outputs found
Levinson's Theorem for Dirac Particles
Levinson's theorem for Dirac particles constraints the sum of the phase
shifts at threshold by the total number of bound states of the Dirac equation.
Recently, a stronger version of Levinson's theorem has been proven in which the
value of the positive- and negative-energy phase shifts are separately
constrained by the number of bound states of an appropriate set of
Schr\"odinger-like equations. In this work we elaborate on these ideas and show
that the stronger form of Levinson's theorem relates the individual phase
shifts directly to the number of bound states of the Dirac equation having an
even or odd number of nodes. We use a mean-field approximation to Walecka's
scalar-vector model to illustrate this stronger form of Levinson's theorem. We
show that the assignment of bound states to a particular phase shift should be
done, not on the basis of the sign of the bound-state energy, but rather, in
terms of the nodal structure (even/odd number of nodes) of the bound state.Comment: Latex with Revtex, 7 postscript figures (available from the author),
SCRI-06109
Levinson's theorem for the Schr\"{o}dinger equation in two dimensions
Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically
symmetric potential in two dimensions is re-established by the Sturm-Liouville
theorem. The critical case, where the Schr\"{o}dinger equation has a finite
zero-energy solution, is analyzed in detail. It is shown that, in comparison
with Levinson's theorem in non-critical case, the half bound state for
wave, in which the wave function for the zero-energy solution does not decay
fast enough at infinity to be square integrable, will cause the phase shift of
wave at zero energy to increase an additional .Comment: Latex 11 pages, no figure and accepted by P.R.A (in August); Email:
[email protected], [email protected]
The Relativistic Levinson Theorem in Two Dimensions
In the light of the generalized Sturm-Liouville theorem, the Levinson theorem
for the Dirac equation in two dimensions is established as a relation between
the total number of the bound states and the sum of the phase shifts
of the scattering states with the angular momentum :
\noindent The critical case, where the Dirac equation has a finite
zero-momentum solution, is analyzed in detail. A zero-momentum solution is
called a half bound state if its wave function is finite but does not decay
fast enough at infinity to be square integrable.Comment: Latex 14 pages, no figure, submitted to Phys.Rev.A; Email:
[email protected], [email protected]
Comments on gluon scattering amplitudes via AdS/CFT
In this article we consider n gluon color ordered, planar amplitudes in N=4
super Yang Mills at strong 't Hooft coupling. These amplitudes are approximated
by classical surfaces in AdS_5 space. We compute the value of the amplitude for
a particular kinematic configuration for a large number of gluons and find that
the result disagrees with a recent guess for the exact value of the amplitude.
Our results are still compatible with a possible relation between amplitudes
and Wilson loops.
In addition, we also give a prescription for computing processes involving
local operators and asymptotic states with a fixed number of gluons. As a
byproduct, we also obtain a string theory prescription for computing the dual
of the ordinary Wilson loop, Tr P exp[ i\oint A ], with no couplings to the
scalars. We also evaluate the quark-antiquark potential at two loops.Comment: 27 pages, 9 figures,v3:minor correction
Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions
The two-dimensional Levinson theorem for the Klein-Gordon equation with a
cylindrically symmetric potential is established. It is shown that
, where denotes
the difference between the number of bound states of the particle
and the ones of antiparticle with a fixed angular momentum , and
the is named phase shifts. The constants and
are introduced to symbol the critical cases where the half bound
states occur at .Comment: Revtex file 14 pages, submitted to Phys. Rev.
Levinson's Theorem for Non-local Interactions in Two Dimensions
In the light of the Sturm-Liouville theorem, the Levinson theorem for the
Schr\"{o}dinger equation with both local and non-local cylindrically symmetric
potentials is studied. It is proved that the two-dimensional Levinson theorem
holds for the case with both local and non-local cylindrically symmetric cutoff
potentials, which is not necessarily separable. In addition, the problems
related to the positive-energy bound states and the physically redundant state
are also discussed in this paper.Comment: Latex 11 pages, no figure, submitted to J. Phys. A Email:
[email protected], [email protected]
Weakly Nonlinear AC Response: Theory and Application
We report a microscopic and general theoretical formalism for electrical
response which is appropriate for both DC and AC weakly nonlinear quantum
transport. The formalism emphasizes the electron-electron interaction and
maintains current conservation and gauge invariance. It makes a formal
connection between linear response and scattering matrix theory at the weakly
nonlinear level. We derive the dynamic conductance and predict the
nonlinear-nonequilibrium charge distribution. The definition of a nonlinear
capacitance leads to a remarkable scaling relation which can be measured to
give microscopic information about a conductor
The biological origin of linguistic diversity
In contrast with animal communication systems, diversity is characteristic of almost every aspect of human language. Languages variously employ tones, clicks, or manual signs to signal differences in meaning; some languages lack the noun-verb distinction (e.g., Straits Salish), whereas others have a proliferation of fine-grained syntactic categories (e.g., Tzeltal); and some languages do without morphology (e.g., Mandarin), while others pack a whole sentence into a single word (e.g., Cayuga). A challenge for evolutionary biology is to reconcile the diversity of languages with the high degree of biological uniformity of their speakers. Here, we model processes of language change and geographical dispersion and find a consistent pressure for flexible learning, irrespective of the language being spoken. This pressure arises because flexible learners can best cope with the observed high rates of linguistic change associated with divergent cultural evolution following human migration. Thus, rather than genetic adaptations for specific aspects of language, such as recursion, the coevolution of genes and fast-changing linguistic structure provides the biological basis for linguistic diversity. Only biological adaptations for flexible learning combined with cultural evolution can explain how each child has the potential to learn any human language
Runs of homozygosity implicate autozygosity as a schizophrenia risk factor
Autozygosity occurs when two chromosomal segments that are identical from a common ancestor are inherited from each parent. This occurs at high rates in the offspring of mates who are closely related (inbreeding), but also occurs at lower levels among the offspring of distantly related mates. Here, we use runs of homozygosity in genome-wide SNP data to estimate the proportion of the autosome that exists in autozygous tracts in 9,388 cases with schizophrenia and 12,456 controls. We estimate that the odds of schizophrenia increase by ~17% for every 1% increase in genome-wide autozygosity. This association is not due to one or a few regions, but results from many autozygous segments spread throughout the genome, and is consistent with a role for multiple recessive or partially recessive alleles in the etiology of schizophrenia. Such a bias towards recessivity suggests that alleles that increase the risk of schizophrenia have been selected against over evolutionary time
Candidate gene resequencing to identify rare, pedigree-specific variants influencing healthy aging phenotypes in the long life family study
Background: The Long Life Family Study (LLFS) is an international study to identify the genetic components of various healthy aging phenotypes. We hypothesized that pedigree-specific rare variants at longevity-associated genes could have a similar functional impact on healthy phenotypes. Methods: We performed custom hybridization capture sequencing to identify the functional variants in 464 candidate genes for longevity or the major diseases of aging in 615 pedigrees (4,953 individuals) from the LLFS, using a multiplexed, custom hybridization capture. Variants were analyzed individually or as a group across an entire gene for association to aging phenotypes using family based tests. Results: We found significant associations to three genes and nine single variants. Most notably, we found a novel variant significantly associated with exceptional survival in the 3' UTR OBFC1 in 13 individuals from six pedigrees. OBFC1 (chromosome 10) is involved in telomere maintenance, and falls within a linkage peak recently reported from an analysis of telomere length in LLFS families. Two different algorithms for single gene associations identified three genes with an enrichment of variation that was significantly associated with three phenotypes (GSK3B with the Healthy Aging Index, NOTCH1 with diastolic blood pressure and TP53 with serum HDL). Conclusions: Sequencing analysis of family-based associations for age-related phenotypes can identify rare or novel variants
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