Integrability and weak diffraction in a two-particle Bose-Hubbard model

A recently introduced one-dimensional two-particle Bose-Hubbard model with a single impurity is studied on finite lattices. The model possesses a discrete reflection symmetry and we demonstrate that all eigenstates odd under this symmetry can be obtained with a generalized Bethe ansatz if periodic boundary conditions are imposed. Furthermore, we provide numerical evidence that this holds true for open boundary conditions as well. The model exhibits backscattering at the impurity site -- which usually destroys integrability -- yet there exists an integrable subspace. We investigate the non-integrable even sector numerically and find a class of states which have almost the Bethe ansatz form. These weakly diffractive states correspond to a weak violation of the non-local Yang-Baxter relation which is satisfied in the odd sector. We bring up a method based on the Prony algorithm to check whether a numerically obtained wave function is in the Bethe form or not, and if so, to extract parameters from it. This technique is applicable to a wide variety of other lattice models.Comment: 13.5 pages, 11 figure

Bound states in the one-dimensional two-particle Hubbard model with an impurity

We investigate bound states in the one-dimensional two-particle Bose-Hubbard model with an attractive ($V> 0$) impurity potential. This is a one-dimensional, discrete analogy of the hydrogen negative ion H$^-$ problem. There are several different types of bound states in this system, each of which appears in a specific region. For given $V$, there exists a (positive) critical value $U_{c1}$ of $U$, below which the ground state is a bound state. Interestingly, close to the critical value ($U\lesssim U_{c1}$), the ground state can be described by the Chandrasekhar-type variational wave function, which was initially proposed for H$^-$. For $U>U_{c1}$, the ground state is no longer a bound state. However, there exists a second (larger) critical value $U_{c2}$ of $U$, above which a molecule-type bound state is established and stabilized by the repulsion. We have also tried to solve for the eigenstates of the model using the Bethe ansatz. The model possesses a global \Zz_2-symmetry (parity) which allows classification of all eigenstates into even and odd ones. It is found that all states with odd-parity have the Bethe form, but none of the states in the even-parity sector. This allows us to identify analytically two odd-parity bound states, which appear in the parameter regions $-2V<U<-V$ and $-V<U<0$, respectively. Remarkably, the latter one can be \textit{embedded} in the continuum spectrum with appropriate parameters. Moreover, in part of these regions, there exists an even-parity bound state accompanying the corresponding odd-parity bound state with almost the same energy.Comment: 18 pages, 18 figure

ADR and the Federal Government: Not Such Strange Bedfellows after All

These remarks focus on the Federal Government\u27s use of ADR. The Department of Justice, as the nation\u27s most prolific litigator, can benefit greatly from the effective use of ADR. What factors limit its use and how it has been implemented are discussed below

Bound States in the Continuum Realized in the One-Dimensional Two-Particle Hubbard Model with an Impurity

We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.Comment: A semi-exactly solvable model (half of the eigenstates are in the Bethe form

Cancer Stem Cells in Head and Neck Squamous Cell Carcinoma

Accumulating evidence suggests that self-renewal and differentiation capabilities reside only in a subpopulation of tumor cells, termed cancer stem cells (CSCs), whereas the remaining tumor cell population lacks the ability to initiate tumor development or support continued tumor growth. In head and neck squamous cell carcinoma (HNSCC), as with other malignancies, cancer stem cells have been increasingly shown to have an integral role in tumor initiation, disease progression, metastasis and treatment resistance. In this paper we summarize the current knowledge of the role of CSCs in HNSCC and discuss the therapeutic implications and future directions of this field

Adsorption of dibenzothiophenes from hydrocarbon and model diesel feeds

A process for adsorbing aromatic sulfur compounds, where an adsorbent is contacted with a C.sub.6-C.sub.20 aromatic and/or aliphatic stream which comprises a solution of (i) at least one benzothiophene compound, (ii) a solvent which comprises at least one C.sub.6-C.sub.16 aliphatic compound, and (iii) optionally at least one C.sub.6-C.sub.12 aromatic compound. In this process, the adsorbent is regenerated using an organic regenerant such as, but not limited to, toluene. Also disclosed is another process for adsorbing aromatic sulfur compounds. In this process, an adsorbent is contacted with a mixture comprising a model diesel feed comprising at least one benzothiophene compound. In this process, the adsorbent is regenerated using an organic regenerant such as, but not limited to, toluene

Acute stroke treatment and outcome in the oldest old (90 years and older) at a tertiary care medical centre in Germany-a retrospective study showing safety and efficacy in this particular patient population

Background Stroke is among the most common causes of death and disability worldwide. Despite the relevance of stroke-related disease burden, which is constantly increasing due to the demographic change in industrialized countries with an ageing population and consecutively an increase in age-associated diseases, there is sparse evidence concerning acute stroke treatment and treatment-related outcome in the elderly patient group. This retrospective study aimed at analysing patient characteristics, therapy-related complications and functional outcome in stroke patients aged 90 years or older who underwent acute stroke treatment (i.e. intravenous thrombolysis, mechanical thrombectomy, or both). Methods We identified files of all inpatient stays at the Department of Neurology at Saarland University Medical Center (tertiary care level with a comprehensive stroke unit) between June 2011 and December 2018 and filtered for subjects aged 90 years or older at the time of admission. We reviewed patient files for demographic data, symptoms upon admission, (main) diagnoses, comorbidities, and administered therapies. For patients admitted due to acute stroke we reviewed files for therapy-related complications and functional outcome. We compared the modified Rankin scale (mRS) scores upon admission and at discharge for these patients. Results We identified 566 inpatient stays of subjects aged 90 years or older. Three hundred sixty-seven of the 566 patients (64.8%) were admitted and discharged due to symptoms indicative of stroke. Two hundred eleven patients received a diagnosis of ischaemic stroke. These 211 patients were analysed subsequently. Sixty-four patients qualified for acute stroke treatment (intravenous thrombolysis n = 22, mechanical thrombectomy n = 26, intravenous thrombolysis followed by mechanical thrombectomy n = 16) and showed a significant improvement in their functional status as measured by change in mRS score (admission vs. discharge, p 0.001) with 7 (10.9%) observed potentially therapy-related complications (relevant drop in haemoglobin n = 2, subarachnoidal haemorrhage n = 1, cerebral haemorrhage n = 3, extracranial bleeding n = 1). One intravenous thrombolysis was stopped because of an uncontrollable hypertensive crisis. Patients who did not qualify for these treatments (including those declining acute treatment) did not show a change of their functional status between admission and discharge (p 0.064). Conclusion Our data indicate that acute stroke treatment is effective and safe in the oldest old. Age alone is no criterion to withhold an acute intervention even in oldest old stroke patients

Engineering Hybrid Epitaxial InAsSb/Al Nanowire Materials for Stronger Topological Protection

The combination of strong spin-orbit coupling, large $g$-factors, and the coupling to a superconductor can be used to create a topologically protected state in a semiconductor nanowire. Here we report on growth and characterization of hybrid epitaxial InAsSb/Al nanowires, with varying composition and crystal structure. We find the strongest spin-orbit interaction at intermediate compositions in zincblende InAs$_{1-x}$Sb$_{x}$ nanowires, exceeding that of both InAs and InSb materials, confirming recent theoretical studies \cite{winkler2016topological}. We show that the epitaxial InAsSb/Al interfaces allows for a hard induced superconducting gap and 2$e$ transport in Coulomb charging experiments, similar to experiments on InAs/Al and InSb/Al materials, and find measurements consistent with topological phase transitions at low magnetic fields due to large effective $g$-factors. Finally we present a method to grow pure wurtzite InAsSb nanowires which are predicted to exhibit even stronger spin-orbit coupling than the zincblende structure.Comment: 10 pages and 5 figure