Spectra Of He Research Articles

Excited Energy Spectra for He and Be Isotopes from Different Shell Model Interactions

Excited Energy Spectra for He and Be Isotopes from Different Shell Model Interactions

Unitary unfoldings of a Bose-Hubbard exceptional point with and without particle number conservation.

The conventional non-Hermitian but -symmetric three-parametric Bose-Hubbard Hamiltonian H(γ, v, c) represents a quantum system of N bosons, unitary only for parameters γ, v and c in a domain . Its boundary contains an exceptional point of order K (EPK; K = N + 1) at c = 0 and γ = v, but even at the smallest non-vanishing parameter c ≠ ~0 the spectrum of H(v, v, c) ceases to be real, i.e. the system ceases to be observable. In this paper, the question is inverted: all of the stable, unitary and observable Bose-Hubbard quantum systems are sought which would lie close to the phenomenologically most interesting EPK-related dynamical regime. Two different families of such systems are found. Both of them are characterized by the perturbed Hamiltonians for which the unitarity and stability of the system is guaranteed. In the first family the number N of bosons is assumed conserved while in the second family such an assumption is relaxed. Attention is paid mainly to an anisotropy of the physical Hilbert space near the EPK extreme. We show that it is reflected by a specific, operationally realizable structure of perturbations which can be considered small.

Lexicographic polynomials of graphs and their spectra

For a (simple) graph H and non-negative integers c0, c1,..., cd (cd ? 0), p(H) = ?dk=0 ck?Hk is the lexicographic polynomial in H of degree d, where the sum of two graphs is their join and ck?Hk is the join of ck copies of Hk. The graph Hk is the kth power of H with respect to the lexicographic product (H0 = K1). The spectrum (if H is connected and regular) and the Laplacian spectrum (in general case) of p(H) are determined in terms of the spectrum of H and ck's. Constructions of infinite families of cospectral or integral graphs are announced.

Infrared spectra of He–, Ne–, and Ar–C6D6

Spectra of He–, Ne– and Ar–C6D6 in the region of the ν12 fundamental of C6D6 are observed in a pulsed supersonic jet expansion using a tunable optical parametric oscillator laser source. These are the first reported infrared spectra of rare gas–benzene complexes and the first observation in any region for He– and Ne–C6D6. Two bands are studied for each complex: the ν12 fundamental itself (≈2289cm−1) and the ν2+ν13 combination band (≈2276cm−1) which are coupled by a Fermi resonance. Effective intermolecular separations of 3.593(1) and 3.455(1)Å are obtained for He– and Ne–C6D6, respectively, consistent with previous ultraviolet and microwave results for the analogous C6H6 complexes.

Comparative Study of Emission Spectra of He(3S)-He(2P) at 706 and 728 nm Due to the Triplet and Singlet Transitions

This study of the self-broadening of the 728 nm He line is performed in order to establish similarities and differences to the self-broadening of the triplet 3s-2p line at 706 nm. In a previous work we presented the first calculations of He-He collisional profiles at 706nm due to the triplet 3s-2p transition in a unified line shape semi-classical theory using ab-initio molecular potentials. The excellent agreement between experimental and theoretical determinations of the near wing of the line profiles established the accuracy of the interaction potentials. New ab-initio potentials for the singlet 3s-2p transitions allow us to extend our previous study to the line at 728 nm.

The HeII Lyman alpha forest and the thermal state of the IGM

Aims. Recent analyses of the intergalactic UV background by means of the Hell Lya forest assume that Hell and H absorption features have the same line widths. We omit this assumption to investigate possible effects of thermal line broadening on the inferred He II/HIratio η and to explore the potential of intergalactic Hell observations to constrain the thermal state of the intergalactic medium. Methods. Deriving a simple relation between the column density and the temperature of an absorber based on the temperature-density relation T T o (1+ δ) γ-1 we develop a procedure to fit To, y, and η simultaneously by modeling the observed spectra with Doppler profiles. In an alternative approach the temperature T of an absorber, the He II/HIratio η, and the redshift scale of η variations are estimated simultaneously by optimizing the Doppler parameters of He II Results. Testing our procedure with artificial data shows that well-constrained results can be obtained only if the signal-to-noise ratio in the Hell forest is S/N ≥ 20. Additionally, ambiguities in the line profile decomposition may result in significant systematic errors. Thus, it is impossible to give an estimate of the temperature-density relation with the He IIdata available at present (S/IN ∼ 5). However, we find that only 45% of the lines in our sample favor turbulent line widths while the remaining lines are probably affected by thermal broadening. Furthermore, the inferred η values are on average about 0.05 dex larger if a thermal component is taken into account, and their distribution is 46% narrower in comparison to a purely turbulent fit. Therefore, variations of η on a 10% level may be related to the presence of thermal line broadening. The apparent correlation between the strength of the H I absorption and the ηvalue, which has been found in former studies assuming turbulent line broadening, essentially disappears if thermal broadening is taken into account. In the redshift range 2.58 < z < 2.74 towards the quasars HE 2347-4342 and HS 1700+6416 we obtain η ≈100 and slightly larger. In the same redshift range the far-UV spectrum ofHS 1700+6416 is best and we estimate a mean value of log η2.11 ±0.32 taking into account combined thermal and turbulent broadening.

On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KDV potentials

We characterize the spectrum of one-dimensional Schrodinger operatorsH=−d2/dx2+V inL2(ℝdx) with quasi-periodic complex-valued algebro-geometric potentialsV, i.e., potentialsV which satisfy one (and hence infinitely many) equation(s) of the stationary Korteweg-de Vries (KdV) hierarchy, associated with nonsingular hyperelliptic curves. The spectrum ofH coincides with the conditional stability set ofH and can be described explicitly in terms of the mean value of the inverse of the diagonal Green’s function ofH.

On spectral properties of periodic polyharmonic matrix operators

We consider a matrix operatorH = (-Δ)l +V inRn, wheren ≥ 2,l ≥ 1, 4l > n + 1, andV is the operator of multiplication by a periodic inx matrixV(x). We study spectral properties ofH in the high energy region. Asymptotic formulae for Bloch eigenvalues and the corresponding spectral projections are constructed. The Bethe-Sommerfeld conjecture, stating that the spectrum ofH can have only a finite number of gaps, is proved.

Energetic ATI Spectra of He in Circularly Polarized Laser**The project supported by National High-Tech. ICF Committee in China and National Natural Science Foundation of China

A new analytic model for ATI spectra of He in circularly polarized laser is proposed. The model gives a way to describe the effects of the final state Coulomb interaction and the joint interaction of the atomic potential and laser field. The experimental spectra by Mohideen et al. can be quite well described. The peak intensity contradiction, which appeared in previous literatures, can be considerably eliminated.

Feeding habits of the Alaska greenlingHexagrammos octogrammus in the coastal waters of amurskii bay (sea of Japan)

Feeding habits of the Alaska greenlingHexagrammos octogrammus were studied in the coastal waters of Amurskii Bay in April–October 1997–1998. The greenling is characterized by a wide feeding spectrum of no less then 56 fish and invertebrate species. Decapods predominate in the diets of all fish age groups. The feeding spectrum ofH. octogrammus broadens as the fish grows. From spring to autumn, the stomach filling index of first-year fish rises, while that of the other age groups decreases, reaching minimum values in the spawning period.

On the spectrum of the Zhang-Zagier height

From recent work of Zhang and of Zagier, we know that their height H ( α ) \mathfrak {H}(\alpha ) is bounded away from 1 for every algebraic number α \alpha different from 0 , 1 , 1 / 2 ± − 3 / 2 0,1,1/2\pm \sqrt {-3}/2 . The study of the related spectrum is especially interesting, for it is linked to Lehmer’s problem and to a conjecture of Bogomolov. After recalling some definitions, we show an improvement of the so-called Zhang-Zagier inequality. To achieve this, we need some algebraic numbers of small height. So, in the third section, we describe an algorithm able to find them, and we give an algebraic number with height 1.2875274 … 1.2875274\ldots discovered in this way. This search up to degree 64 suggests that the spectrum of H ( α ) \mathfrak {H}(\alpha ) may have a limit point less than 1.292. We prove this fact in the fourth part.

Line Profile Variability in the Be Star α Eridani

AbstractWe present an analysis of line profile variability of the Be star α Eri (Achernar). Spectra of He I λ667.8nm were collected at Brazilian Laboratório Nacional de Astrofísica (LNA) during 10 observing runs covering 27 nights in 6 years. The presence of a 1.26 days period reported previously is confirmed and we report also the detection of other periods (0.73 and 0.53 days) and a possible 12.5 days modulation. A transient high-velocity absorption component with RV = −500 km/s, higher than −υsini (−220 km/s) has appeared at the end of 1993, near the presumed maximum of the Hα emission phase.

Above Threshold Ionization Spectra of He in a Circularly Polarized Laser Field

A new analytic model for the above threshold ionization spectrum of He in a circularly polarized laser field is proposed. The experimental spectrum obtained by Mohideen et al. can be quite well described by this model. The spectra predicted by our model agree with experiment better than those of Reiss when the spatiotemporal profile of the laser pulse is taken into account and better than those of the Keldysh-Faisal-Reiss theory when the profile is not taken into account. At the same time, we find that the experimental value of the peak laser intensity was overstated by a factor of about 5. This result supports the previous similar claim by Reiss.

Spectral deformations of one-dimensional Schrödinger operators

We provide a complete spectral characterization of a new method of constructing isospectral (in fact, unitary) deformations of general Schrödinger operatorsH=−d 2/dx 2+V in $$H = - d^2 /dx^2 + V in \mathcal{L}^2 (\mathbb{R})$$ . Our technique is connected to Dirichlet data, that is, the spectrum of the operatorH D onL 2((−∞,x 0)) ⊕L 2((x 0, ∞)) with a Dirichlet boundary condition atx 0. The transformation moves a single eigenvalue ofH D and perhaps flips which side ofx 0 the eigenvalue lives. On the remainder of the spectrum, the transformation is realized by a unitary operator. For cases such asV(x)→∞ as |x|→∞, whereV is uniquely determined by the spectrum ofH and the Dirichlet data, our result implies that the specific Dirichlet data allowed are determined only by the asymptotics asE→∞.

Upper bounds for the energy expectation in time-dependent quantum mechanics

We consider quantum systems driven by Hamiltonians of the formH+W(t), where the spectrum ofH consists of an infinite set of bands andW(t) depends arbitrarily on time. Let 〈H〈φ (t) denote the expectation value ofH with respect to the evolution at timet of an initial state φ. We prove upper bounds of the type 〈H〉φ (t)=O(t δ), δ>0, under conditions on the strength ofW(t) with respect toH. Neither growth of the gaps between the bands nor smoothness ofW(t) is required. Similar estimates are shown for the expectation value of functions ofH. Sufficient conditions to have uniformly bounded expectation values are made explicit and the consequences on other approaches to quantum stability are discussed.

Reaction-diffusion processes of hard-core particles

We study a 12-parameter stochastic process involving particles with two-site interaction and hard-core repulsion on ad-dimensional lattice. In this model, which includes the asymmetric exclusion process, contact processes, and other processes, the stochastic variables are particle occupation numbers taking valuesn x=0,1. We show that on a ten-parameter submanifold thek-point equal-time correlation functions 〈n x1...n xk〉 satisfy linear differential-difference equations involving no higher correlators. In particular, the average density 〈n x〉 satisfies an integrable diffusion-type equation. These properties are explained in terms of dual processes and various duality relations are derived. By defining the time evolution of the stochastic process in terms of a quantum HamiltonianH, the model becomes equivalent to a lattice model in thermal equilibrium ind+1 dimensions. We show that the spectrum ofH is identical to the spectrum of the quantum Hamiltonian of ad-dimensional anisotropic, spin-1/2 Heisenberg model. In one dimension our results hint at some new algebraic structure behind the integrability of the system.

Recent advances in gastritis

It is difficult to know where to begin an article on gastritis under the title of 'Recent advances'. Following the discovery of Helicobacter pylori in 1983, I our concepts of gastritis have had to be completely revised. Not only can we now recognize the major cause of 'chronic nonspecific gastritis', but the identification of H. pylori has also allowed us to delineate new forms like reflux 2 and lymphocytic gastritis) Furthermore we can now appreciate that acute 4 and atrophic gastritis s can be part of the spectrum ofH. pylori related inflammation. Given that this entire topic is in a state of flux, it seems reasonable that this article should concentrate on H. pylori gastritis and the two 'special' forms of gastritis, reflux (reactive) and lymphocytic gastritis. I shall examine the main histopathological aspects of these conditions, many of which have only recently been adequately explained.

Lipshitz continuity of gap boundaries for Hofstadter-like spectra

We consider an effective HamiltonianH representing the motion of a single-band-two-dimensional electron in a uniform magnetic field. ThenH belongs to the rotation algebra, namely the algebra of continuous functions over a non-commutative 2-torus. We define a non-commutative analog of smooth functions by mean of elements of classC l,n, wherel andn characterize respectively the degree of differentiability with respect to the magnetic field and the torus variables. We show that ifH is of classC 1,3+ε, the gap boundaries of the spectrum ofH are Lipshitz continuous functions of the magnetic field at each point for which the gap is open.

Localization at large disorder and at extreme energies: An elementary derivations

The work presents a short proof of localization under the conditions of either strong disorder (λ > λ0) or extreme energies for a wide class of self adjoint operators with random matrix elements, acting inl 2 spaces. A prototypical example is the discrete Schrodinger operatorH=−Δ+U 0(x)+λV x onZ d ,d≧1, withU 0(x) a specified background potential and {V x } generated as random variables. The general results apply to operators with −Δ replaced by a non-local self adjoint operatorT whose matrix elements satisfy: ∑ y |T x,y | S ≦Const., uniformly inx, for somes<1. Localization means here that within a specified energy range the spectrum ofH is of the pure-point type, or equivalently — the wave functions do not spread indefinitely under the unitary time evolution generated byH. The effect is produced by strong disorder in either the potential or in the off-diagonal matrix elementsT x, y . Under rapid decay ofT x, y , the corresponding eigenfunctions are also proven to decay exponentially. The method is based on resolvent techniques. The central technical ideas include the use of low moments of the resolvent kernel, i.e. <|G E (x, y)| s > withs small enough (<1) to avoid the divergence caused by the distribution's Cauchy tails, and an effective use of the simple form of the dependence ofG E (x, y) on the individual matrix elements ofH in elucidating the implications of the fundamental equation (H−E)G E (x,x 0)=δ x,x0 . This approach simplifies previous derivations of localization results, avoiding the small denominator difficulties which have been hitherto encountered in the subject. It also yields some new results which include localization under the following sets of conditions: i) potentials with an inhomogeneous non-random partU 0 (x), ii) the Bethe lattice, iii) operators with very slow decay in the off-diagonal terms (T x,y≈1/|x−y|(d+e)), and iv) localization produced by disordered boundary conditions.

Eigenvalue asymptotics for the Schr�dinger operator with perturbed periodic potential

We consider the Schrodinger operatorH=−Δ+W+V acting inL 2(ℝ m ),m≧2, with periodic potentialW perturbed by a potentialV which decays slowly at infinity. We study the asymptotic behaviour of the discrete spectrum ofH near any given boundary point of the essential spectrum.