Class of invariants for the 2D time-dependent Landau problem and harmonic oscillator in a magnetic field

We consider an isotropic two dimensional harmonic oscillator with arbitrarily time-dependent mass $M(t)$ and frequency $\Omega(t)$ in an arbitrarily time-dependent magnetic field $B(t)$. We determine two commuting invariant observables (in the sense of Lewis and Riesenfeld) $L,I$ in terms of some solution of an auxiliary ordinary differential equation and an orthonormal basis of the Hilbert space consisting of joint eigenvectors $\phi_\lambda$ of $L,I$. We then determine time-dependent phases $\alpha_\lambda(t)$ such that the $\psi_\lambda(t)=e^{i\alpha_\lambda}\phi_\lambda$ are solutions of the time-dependent Schr\"odinger equation and make up an orthonormal basis of the Hilbert space. These results apply, in particular to a two dimensional Landau problem with time-dependent $M,B$, which is obtained from the above just by setting $\Omega(t) \equiv 0$. By a mere redefinition of the parameters, these results can be applied also to the analogous models on the canonical non-commutative plane.Comment: 13 pages, 3 references adde

Stability of Impurities with Coulomb Potential in Graphene with Homogeneous Magnetic Field

Given a 2-dimensional no-pair Weyl operator with a point nucleus of charge Z, we show that a homogeneous magnetic field does not lower the critical charge beyond which it collapses.Comment: J. Math. Phys. (in press

Quasinormal modes and stability of the rotating acoustic black hole: numerical analysis

The study of the quasinormal modes (QNMs) of the 2+1 dimensional rotating draining bathtub acoustic black hole, the closest analogue found so far to the Kerr black hole, is performed. Both the real and imaginary parts of the quasinormal (QN) frequencies as a function of the rotation parameter B are found through a full non-linear numerical analysis. Since there is no change in sign in the imaginary part of the frequency as B is increased we conclude that the 2+1 dimensional rotating draining bathtub acoustic black hole is stable against small perturbations.Comment: 6 pages, ReVTeX4. v2. References adde

PD-1/PD-L1 inhibitor activity in patients with gene-rearrangement positive non-small cell lung cancer-an IMMUNOTARGET case series.

BACKGROUND Prior IMMUNOTARGET registry data had suggested that responses to immune [anti PD(L)1] monotherapy in gene-arranged non-small cell lung cancer (NSCLC) were rare or absent, depending on the specific oncogene. METHODS IMMUNOTARGET sites reporting prior registry data or new individual cases of gene rearranged NSCLC seeming to benefit from immune monotherapy were explored in detail looking to both validate their diagnosis of a functional gene rearrangement and to look for features potentially differentiating them from other such cases associated with low response rates. RESULTS Five cases of NSCLC with a gene rearrangement with reported responses or prolonged stabilization from immune monotherapy were identified in total. All had little or no prior smoking history and had programmed death-ligand 1 (PD-L1) values ranging from zero to 100%. A confirmed rearrangement partner was reported in only 2 of the cases (CD74-ROS1 and KIF5B-RET), however in one of the other three cases [analplastic lymophoma kinase (ALK)], significant benefit from a relevant prior targeted therapy was noted, also consistent with the rearrangement status being correctly assigned. CONCLUSIONS Not all driver oncogene subtypes of NSCLC are equally responsive to immune monotherapy, however even among patients with well-validated gene rearranged NSCLC which has traditionally been considered immune hyporesponsive, objective responses can occur. Additional explorations of the features associated with and underlying the immune hypo-responsiveness of most, but not all, cases of gene-rearranged NSCLC are required

On the Spectrum of Field Quadratures for a Finite Number of Photons

The spectrum and eigenstates of any field quadrature operator restricted to a finite number $N$ of photons are studied, in terms of the Hermite polynomials. By (naturally) defining \textit{approximate} eigenstates, which represent highly localized wavefunctions with up to $N$ photons, one can arrive at an appropriate notion of limit for the spectrum of the quadrature as $N$ goes to infinity, in the sense that the limit coincides with the spectrum of the infinite-dimensional quadrature operator. In particular, this notion allows the spectra of truncated phase operators to tend to the complete unit circle, as one would expect. A regular structure for the zeros of the Christoffel-Darboux kernel is also shown.Comment: 16 pages, 11 figure

Renal Fanconi Syndrome and Hypophosphatemic Rickets in the Absence of Xenotropic and Polytropic Retroviral Receptor in the Nephron.

Tight control of extracellular and intracellular inorganic phosphate (Pi) levels is critical to most biochemical and physiologic processes. Urinary Pi is freely filtered at the kidney glomerulus and is reabsorbed in the renal tubule by the action of the apical sodium-dependent phosphate transporters, NaPi-IIa/NaPi-IIc/Pit2. However, the molecular identity of the protein(s) participating in the basolateral Pi efflux remains unknown. Evidence has suggested that xenotropic and polytropic retroviral receptor 1 (XPR1) might be involved in this process. Here, we show that conditional inactivation of Xpr1 in the renal tubule in mice resulted in impaired renal Pi reabsorption. Analysis of Pi transport in primary cultures of proximal tubular cells or in freshly isolated renal tubules revealed that this Xpr1 deficiency significantly affected Pi efflux. Further, mice with conditional inactivation of Xpr1 in the renal tubule exhibited generalized proximal tubular dysfunction indicative of Fanconi syndrome, characterized by glycosuria, aminoaciduria, calciuria, and albuminuria. Dramatic alterations in the renal transcriptome, including a significant reduction in NaPi-IIa/NaPi-IIc expression, accompanied these functional changes. Additionally, Xpr1-deficient mice developed hypophosphatemic rickets secondary to renal dysfunction. These results identify XPR1 as a major regulator of Pi homeostasis and as a potential therapeutic target in bone and kidney disorders

A spectral method for elliptic equations: the Dirichlet problem

An elliptic partial differential equation Lu=f with a zero Dirichlet boundary condition is converted to an equivalent elliptic equation on the unit ball. A spectral Galerkin method is applied to the reformulated problem, using multivariate polynomials as the approximants. For a smooth boundary and smooth problem parameter functions, the method is proven to converge faster than any power of 1/n with n the degree of the approximate Galerkin solution. Examples in two and three variables are given as numerical illustrations. Empirically, the condition number of the associated linear system increases like O(N), with N the order of the linear system.Comment: This is latex with the standard article style, produced using Scientific Workplace in a portable format. The paper is 22 pages in length with 8 figure