Degenerate Limit Research Articles

Power loss of an energetic charged particle moving parallel to a graphene sheet

In this work we analyze the energy loss of a fast charged particle moving parallel to a two-dimensional (2 D) graphene sheet. The response dynamics of the 2 D graphene sheet are modeled using the random phase approximation in the degenerate limit (zero temperature). We determine the energy loss and stopping power for motion parallel to the graphene sheet as a function of the distance of the charged particle from the 2 D sheet and of its velocity.

Quasiparticle excitations in Bose-Fermi mixtures

We analyze the excitation spectrum of a three-dimensional Bose-Fermi mixture with tunable resonant interaction parameters and high hyperfine spin multiplets. We focus on a three-particle vertex describing fermionic and bosonic atoms which can scatter to create fermionic molecules or disassociate. For a single molecular level, in analogy to the single magnetic impurity problem we argue that the low-lying excitations of the mean-field theory are described by the Fermi-liquid picture with a quasiparticle weight and charge which is justified by a $1/{N}_{\ensuremath{\psi}}$ expansion, expected to be exact in the limit of infinite degeneracy (or very high fermionic spin) ${N}_{\ensuremath{\psi}}\ensuremath{\rightarrow}\ensuremath{\infty}$. Our emphasis is placed on the novel conditions for chemical equilibrium and how many-body chemical reactions renormalize the bosonic chemical potential, modifying condensation and superfluid-insulator transitions.

Graphene Stopping Power for a Fast Charged Particle: Parallel Case

In this paper, we analyze the energy loss and stopping power of a fast charged particle probe of a 2-D graphene sheet. The fast particle motion is taken to be parallel to the 2-D graphene sheet, and the system is considered at the degenerate limit (zero temperature). The 2-D graphene layer response dynamics are described in the random phase approximation. We determine the energy loss for motion parallel to the 2-D graphene layer as a function of the distance of the fast particle from the layer and its velocity, calculating the stopping power.

Constant mean curvature surfaces in AdS 3

We construct constant mean curvature surfaces of the general finite-gap type in AdS_3. The special case with zero mean curvature gives minimal surfaces relevant for the study of Wilson loops and gluon scattering amplitudes in N=4 super Yang-Mills. We also analyze properties of the finite-gap solutions including asymptotic behavior and the degenerate (soliton) limit, and discuss possible solutions with null boundaries.

Geometry of Weyl theory for Jacobi matrices with matrix entries

A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. The Weyl surface describing the dependence of Green’s matrix on the boundary conditions is interpreted as the set of maximally isotropic subspaces of a quadratic form given by the Wronskian. Analysis of the possibly degenerate limit quadratic form leads to the limit point/limit surface theory of maximal symmetric extensions for semi-infinite Jacobi matrices with matrix entries with arbitrary deficiency indices. The resolvent of the extensions is calculated explicitly.

Graphene energy loss spectroscopy: Perpendicular case

The energy loss of a fast charged particle probe incident on a two-dimensional graphene sheet is examined here. The fast particle motion is taken to be perpendicular to the 2D graphene sheet, which is considered to be in the degenerate limit of zero temperature. The response dynamics of the 2D graphene layer are described in the random phase approximation and the energy loss for particle motion perpendicular to the 2D graphene layer is calculated as a function of the velocity of the charged particle.

Addendum to “Pion mass effects on axion emission from neutron stars through NN bremsstrahlung processes” [Nucl. Phys. A 828 (2009) 439–449

The rates of axion emission by nucleon-nucleon bremsstrahlung are calculated with the inclusion of the full momentum contribution from a nuclear one pion exchange (OPE) potential. The contributions of the neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) processes in both the nondegenerate and degenerate limits are explicitly given. We find that the finite momentum corrections to the emissivities are quantitatively significant for the non-degenerate regime and temperature-dependent, and should affect the existing axion mass bounds. The trend of these nuclear effects is to diminish the emissivities.

A SPATIAL DYNAMIC PANEL DATA MODEL WITH BOTH TIME AND INDIVIDUAL FIXED EFFECTS

This paper establishes asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with both time and individual fixed effects when the number of individualsnand the number of time periodsTcan be large. We propose a data transformation approach to eliminate the time effects. Whenn / T→ 0, the estimators are$\root \of {nT}$consistent and asymptotically centered normal; whennis asymptotically proportional toT, they are$\root \of {nT}$consistent and asymptotically normal, but the limit distribution is not centered around 0; whenn / T→ ∞, the estimators are consistent with rateTand have a degenerate limit distribution. We also propose a bias correction for our estimators. When n1/3/T→ 0, the correction will asymptotically eliminate the bias and yield a centered confidence interval. The estimates from the transformation approach can be consistent whennis a fixed finite number.

Response of a relativistic quantum magnetized electron gas

The response 4-tensor is derived for a spin-independent, relativistic magnetized quantum electron gas. The sum over spins is carried out both directly and using a procedure due to Ritus. The 4-tensor components are written in terms of a sum over the two solutions of the resonance condition for the particle 4-momentum. It is shown that the dispersive properties may be described in terms of a single plasma dispersion function, for arbitrary occupation numbers for electrons and positrons in each Landau level. The plasma dispersion function is evaluated explicitly in the completely degenerate and nondegenerate thermal limits. The perpendicular wave number appears in the arguments of J-functions, which are proportional to generalized Laguerre polynomials, but not in the plasma dispersion function. The result generalizes a known form for the response tensor for parallel propagation (in the completely degenerate case), when the J-functions are either zero or unity, to arbitrary angles of propagation.

Pion mass effects on axion emission from neutron stars through NN bremsstrahlung processes

The rates of axion emission by nucleon–nucleon bremsstrahlung are calculated with the inclusion of the full momentum contribution from a nuclear one pion exchange (OPE) potential. The contributions of the neutron–neutron ( nn), proton–proton ( pp) and neutron–proton ( np) processes in both the non-degenerate and degenerate limits are explicitly given. We find that the finite-momentum corrections to the emissivities are quantitatively significant for the non-degenerate regime and temperature-dependent, and should affect the existing axion mass bounds. The trend of these nuclear effects is to diminish the emissivities.

Asymptotic Distributions of Order Statistics and Record Values Under the Marshall–Olkin Parametrization Operation

The Marshall and Olkin (1997) parametrization operation is given by where F 1 is a given distribution function and α > 0, = 1 − α. In this article, we show that both F α = 𝒫α(F 1) and the generating distribution F 1 belong to the same domain of maximal (minimal) (upper record value) (lower record value) attraction. Moreover, it is shown that the weak convergence of any non extreme order statistic (order statistic with variable rank) based on F 1, under given normalizing constants, to a non degenerate limit type implies that the same non extreme order statistic based on the family F α = 𝒫α(F 1), α≠1, under the same normalizing constants, does not converge to any non degenerate distribution and vice versa.

A note on binary choice duration models

We demonstrate that standard methods of asymptotic inference break down for a binary choice duration model in a time series setting. This is because the dependent variable has a degenerate limit distribution, which makes the asymptotic variance-covariance matrix singular.

Brane webs and 1/4-BPS geometries

We discuss brane webs preserving eight supercharges and derive geometries produced by them. Consistency conditions of supergravity are shown to impose certain requirements on the locations of the sources, and these restrictions are found to be in a perfect agreement with results of the probe analysis. In particular, solutions of IIB SUGRA describing (p,q) stings are inconsistent, unless the web consists of straight line segments whose orientation is correlated with charges of the string. The geometries produced by membranes and D3 branes are only consistent if brane profiles are holomorphic. Using perturbation theory, we show that a unique gravity solution exists for any allowed distribution of sources. We also revisit 1/4-BPS geometries with AdS_p x S^q asymptotics and derive the boundary conditions leading to regular geometries. All degenerate limits of regular solutions are shown to agree with expectations from the brane probe analysis.

Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large

This paper investigates the asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with …xed eects when both the number of individuals n and the number of time periods T are large. We consider the case where T is asymptotically large relative to n, the case where T is asymptotically proportional to n, and the case where n is asymptotically large relative to T. In the case where T is asymptotically large relative to n, the estimators are p nT consistent and asymptotically normal, with the limit distribution centered around 0. When n is asymptotically proportional to T, the estimators are p nT consistent and asymptotically normal, but the limit distribution is not centered around 0; and when n is large relative to T, the estimators are consistent with rate T, and have a degenerate limit distribution. The estimators of the …xed eects are p T consistent and asymptotically normal. We also propose a bias correction for our estimators. We show that when T grows faster than n 1=3 , the correction will asymptotically eliminate the bias and yield a centered con…dence interval.

Viability of Dirac phase leptogenesis

We discuss the conditions for a non-vanishing Dirac phaseδ and mixingangle θ13,sources of CP violation in neutrino oscillations, to be uniquely responsible for the observed matter–antimatterasymmetry of the Universe through leptogenesis. We show that this scenario, that we callδ-leptogenesis, is viable when the degenerate limit for the heavy right-handed(RH) neutrino spectrum is considered. We derive an interesting joint condition onsinθ13 and the absolute neutrino mass scale that can be tested in future neutrino oscillation experiments.In the limit of the hierarchical heavy RH neutrino spectrum, we strengthen the previous result thatδ-leptogenesis is only very marginally allowed, even when the production from the twoheavier RH neutrinos is taken into account. An improved experimental upper bound onsinθ13 and/oran account of quantum kinetic effects could completely rule out this option in the future. Therefore,δ-leptogenesis can be also regarded as motivation for models with degenerate heavy neutrinospectrum.

Enhancement and generation of sum squeezing in two-mode light in mixing with coherent light using a beam splitter

Recently, we showed [J. Phys. B: At. Mol. Opt. Phys. 38, 665 (2005)] that the `amplitude-squared squeezing', a non-classical feature, can be enhanced in mixing with a coherent light beam using a beam splitter. Here, we show that the sum squeezing in a two-uncorrelated-mode light beam (one mode is in Gaussian state and the other one is in coherent state), which is degenerate limit of amplitude-squared squeezing, may be generated or enhanced in mixing with a two-mode coherent light beam using a beam splitter.

Limits of discrete series with infinitesimal character zero

For a connected linear semisimple Lie group , this paper considers those nonzero limits of discrete series representations having infinitesimal character 0, calling them totally degenerate. Such representations exist if and only if has a compact Cartan subgroup, is quasisplit, and is acceptable in the sense of Harish-Chandra. Totally degenerate limits of discrete series are natural objects of study in the theory of automorphic forms: in fact, those automorphic representations of adelic groups that have totally degenerate limits of discrete series as archimedean components correspond conjecturally to complex continuous representations of Galois groups of number fields. The automorphic representations in question have important arithmetic significance, but very little has been proved up to now toward establishing this part of the Langlands conjectures. There is some hope of making progress in this area, and for that one needs to know in detail the representations of under consideration. The aim of this paper is to determine the classification parameters of all totally degenerate limits of discrete series in the Knapp-Zuckerman classification of irreducible tempered representations, i.e., to express these representations as induced representations with nondegenerate data. The paper uses a general argument, based on the finite abelian reducibility group attached to a specific unitary principal series representation of . First an easy result gives the aggregate of the classification parameters. Then a harder result uses the easy result to match the classification parameters with the representations of under consideration in representation-by-representation fashion. The paper includes tables of the classification parameters for all such groups

Asymptotics of the solution to the Neumann problem in a thin domain with sharp edge

An asymptotic expansion of the solution to the Neumann problem for a second-order equation in a thin domain with peak-like edge is constructed and justified. Owing to the sharpness of the edge, the procedure of dimension reduction leads to a degenerate limit equation on the longitudinal cross-section of the domain and a solution has irregular behavior near the boundary. Bibliography: 20 titles.

The space of doubly periodic minimal tori with parallel ends: Standard examples

We describe a 3-parametric family $\mathcal{K}$ of properly embedded minimal tori with four parallel ends in quotients of $\mathbb{R}^3$ by two independent translations, which we will call the \textit{Standard Examples.} These surfaces generalize the examples given by Karcher, Meeks and Rosenberg in \cite{ka4,ka6,mr3}. $\mathcal{K}$ can be endowed with a natural structure of a self-conjugated 3-dimensional real analytic manifold diffeomorphic to $\mathbb{R}\times(\mathbb{R}^2-\{(\pm 1,0)\})$ whose degenerate limits are the catenoid, the helicoid, the simply and doubly periodic Scherk minimal surfaces and the Riemann minimal examples. Perez, Rodriguez and Traizet \cite{PeRoTra1} characterize $\mathcal{K}$ in the following sense: If $M$ is a properly embedded minimal torus in a quotient of $\mathbb{R}^3$ by two independent translations with any number of parallel ends, then $M$ is a finite covering of a standard example.

Kinetic Flux Vector Splitting Schemes for Ideal Quantum Gas Dynamics

Novel quantum kinetic flux vector splitting schemes are presented for the computation of ideal quantum gas dynamical flows. The quantum Boltzmann equation approach is adopted and both Bose-Einstein and Fermi-Dirac gases are considered. Formulas for one spatial dimension are first derived, and the resulting kinetic flux vector splitting scheme is tested for shock tube flows. A modified flux vector splitting based on the BGK model is also presented to reduce the numerical diffusion. Implementation of the efficient weighted essentially nonoscillatory method to yield a class of high resolution methods is also devised. Both the classical limit and the nearly degenerate limit are computed. The flow structures can all be accurately captured by the present kinetic flux vector splitting schemes. Results for one-dimensional boson gas under external potential are also included.