Rummukainen-Gottlieb's formula on two-particle system with different mass

L\"uscher established a non-perturbative formula to extract the elastic scattering phases from two-particle energy spectrum in a torus using lattice simulations. Rummukainen and Gottlieb further extend it to the moving frame, which is devoted to the system of two identical particles. In this work, we generalize Rummukainen-Gottlieb's formula to the generic two-particle system where two particles are explicitly distinguishable, namely, the masses of the two particles are different. The finite size formula are achieved for both $C_{4v}$ and $C_{2v}$ symmetries. Our analytical results will be very helpful for the study of some resonances, such as kappa, vector kaon, and so on.Comment: matching its published paper and make it concise, and to remove text overlap with arXiv:hep-lat/9503028, arXiv:hep-lat/0404001 by other author

On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator

The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis, has an infinite symmetric tridiagonal form, also known as Jacobi matrix form. This Jacobi matrix structure involves a continued fraction representation for the inverse of the Green's matrix. The continued fraction can be transformed to a ratio of two $_{2}F_{1}$ hypergeometric functions. From this result we find an exact analytic formula for the matrix elements of the Green's operator of the Coulomb Hamiltonian.Comment: 8 page

Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states

If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Green's operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $\alpha$ particles.Comment: 7 pages, 4 ps figures, revised versio

Evidence for Weyl fermions in a canonical heavy-fermion semimetal YbPtBi

The manifestation of Weyl fermions in strongly correlated electron systems is of particular interest. We report evidence for Weyl fermions in the heavy fermion semimetal YbPtBi from electronic structure calculations, angle-resolved photoemission spectroscopy, magnetotransport and calorimetric measurements. At elevated temperatures where $4f$-electrons are localized, there are triply degenerate points, yielding Weyl nodes in applied magnetic fields. These are revealed by a contribution from the chiral anomaly in the magnetotransport, which at low temperatures becomes negligible due to the influence of electronic correlations. Instead, Weyl fermions are inferred from the topological Hall effect, which provides evidence for a Berry curvature, and a cubic temperature dependence of the specific heat, as expected from the linear dispersion near the Weyl nodes. The results suggest that YbPtBi is a Weyl heavy fermion semimetal, where the Kondo interaction renormalizes the bands hosting Weyl points. These findings open up an opportunity to explore the interplay between topology and strong electronic correlations.Comment: 19 pages, 5 figures, Supplementary Information available with open access at https://www.nature.com/articles/s41467-018-06782-

Three-potential formalism for the three-body scattering problem with attractive Coulomb interactions

A three-body scattering process in the presence of Coulomb interaction can be decomposed formally into a two-body single channel, a two-body multichannel and a genuine three-body scattering. The corresponding integral equations are coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve them by applying the Coulomb-Sturmian separable expansion method. We present elastic scattering and reaction cross sections of the $e^++H$ system both below and above the $H(n=2)$ threshold. We found excellent agreements with previous calculations in most cases.Comment: 12 pages, 3 figure

Faddeev approach to confined three-quark problems

We propose a method that allows for the efficient solution of the three-body Faddeev equations in the presence of infinitely rising confinement interactions. Such a method is useful in calculations of nonrelativistic and especially semirelativistic constituent quark models. The convergence of the partial wave series is accelerated and possible spurious contributions in the Faddeev components are avoided. We demonstrate how the method works with the example of the Goldstone-boson-exchange chiral quark model for baryons.Comment: 6 page

Fermi surface and quasiparticle dynamics of Na(x)CoO2 {x=0.7} investigated by Angle-Resolved Photoemission Spectroscopy

We present an angle-resolved photoemission study of Na0.7CoO2, the host cobaltate of the NaxCoO2.yH2O series. Our results show a large hexagonal-like hole-type Fermi surface, an extremely narrow strongly renormalized quasiparticle band and a small Fermi velocity. Along the Gamma to M high symmetry line, the quasiparticle band crosses the Fermi level from M toward Gamma consistent with a negative sign of effective single-particle hopping (t ): t is estimated to be about 8 meV which is on the order of exchange coupling J in this system. This suggests that t ~ J ~ 10 meV is an important energy scale in the system. Quasiparticles are well defined only in the T-linear resistivity regime. Small single particle hopping and unconventional quasiparticle dynamics may have implications for understanding the unusual behavior of this new class of compounds.Comment: Revised text, Added Figs, Submitted to PR

The frequency modulated auditory evoked response (FMAER), a technical advance for study of childhood language disorders: cortical source localization and selected case studies

Background: Language comprehension requires decoding of complex, rapidly changing speech streams. Detecting changes of frequency modulation (FM) within speech is hypothesized as essential for accurate phoneme detection, and thus, for spoken word comprehension. Despite past demonstration of FM auditory evoked response (FMAER) utility in language disorder investigations, it is seldom utilized clinically. This report's purpose is to facilitate clinical use by explaining analytic pitfalls, demonstrating sites of cortical origin, and illustrating potential utility. Results: FMAERs collected from children with language disorders, including Developmental Dysphasia, Landau-Kleffner syndrome (LKS), and autism spectrum disorder (ASD) and also normal controls - utilizing multi-channel reference-free recordings assisted by discrete source analysis - provided demonstratrions of cortical origin and examples of clinical utility. Recordings from inpatient epileptics with indwelling cortical electrodes provided direct assessment of FMAER origin. The FMAER is shown to normally arise from bilateral posterior superior temporal gyri and immediate temporal lobe surround. Childhood language disorders associated with prominent receptive deficits demonstrate absent left or bilateral FMAER temporal lobe responses. When receptive language is spared, the FMAER may remain present bilaterally. Analyses based upon mastoid or ear reference electrodes are shown to result in erroneous conclusions. Serial FMAER studies may dynamically track status of underlying language processing in LKS. FMAERs in ASD with language impairment may be normal or abnormal. Cortical FMAERs can locate language cortex when conventional cortical stimulation does not. Conclusion: The FMAER measures the processing by the superior temporal gyri and adjacent cortex of rapid frequency modulation within an auditory stream. Clinical disorders associated with receptive deficits are shown to demonstrate absent left or bilateral responses. Serial FMAERs may be useful for tracking language change in LKS. Cortical FMAERs may augment invasive cortical language testing in epilepsy surgical patients. The FMAER may be normal in ASD and other language disorders when pathology spares the superior temporal gyrus and surround but presumably involves other brain regions. Ear/mastoid reference electrodes should be avoided and multichannel, reference free recordings utilized. Source analysis may assist in better understanding of complex FMAER findings

Corticosteroid therapy in regressive autism: a retrospective study of effects on the Frequency Modulated Auditory Evoked Response (FMAER), language, and behavior

Background: Up to a third of children with Autism Spectrum Disorder (ASD) manifest regressive autism (R-ASD).They show normal early development followed by loss of language and social skills. Absent evidence-based therapies, anecdotal evidence suggests improvement following use of corticosteroids. This study examined the effects of corticosteroids for R-ASD children upon the 4 Hz frequency modulated evoked response (FMAER) arising from language cortex of the superior temporal gyrus (STG) and upon EEG background activity, language, and behavior. An untreated clinical convenience sample of ASD children served as control sample. Methods: Twenty steroid-treated R-ASD (STAR) and 24 not-treated ASD patients (NSA), aged 3 - 5 years, were retrospectively identified from a large database. All study participants had two sequential FMAER and EEG studies;Landau-Kleffner syndrome diagnosis was excluded. All subjects’ records contained clinical receptive and expressive language ratings based upon a priori developed metrics. The STAR group additionally was scored behaviorally regarding symptom severity as based on the Diagnostic and Statistical Manual IV (DSM-IV) ASD criteria list. EEGs were visually scored for abnormalities. FMAER responses were assessed quantitatively by spectral analysis. Treated and untreated group means and standard deviations for the FMAER, EEG, language, and behavior, were compared by paired t-test and Fisher’s exact tests. Results: The STAR group showed a significant increase in the 4 Hz FMAER spectral response and a significant reduction in response distortion compared to the NSA group. Star group subjects’ language ratings were significantly improved and more STAR than NSA group subjects showed significant language improvement. Most STAR group children showed significant behavioral improvement after treatment. STAR group language and behavior improvement was retained one year after treatment. Groups did not differ in terms of minor EEG abnormalities. Steroid treatment produced no lasting morbidity. Conclusions: Steroid treatment was associated with a significantly increased FMAER response magnitude, reduction of FMAER response distortion, and improvement in language and behavior scores. This was not observed in the non-treated group. These pilot findings warrant a prospective randomized validation trial of steroid treatment for R-ASD utilizing FMAER, EEG, and standardized ASD, language and behavior measures, and a longer follow-up period. Please see related article http://www.biomedcentral.com/1741-7015/12/7