Bound states and scattering in quantum waveguides coupled laterally through a boundary window

We consider a pair of parallel straight quantum waveguides coupled laterally through a window of a width $\ell$ in the common boundary. We show that such a system has at least one bound state for any $\ell>0$. We find the corresponding eigenvalues and eigenfunctions numerically using the mode--matching method, and discuss their behavior in several situations. We also discuss the scattering problem in this setup, in particular, the turbulent behavior of the probability flow associated with resonances. The level and phase--shift spacing statistics shows that in distinction to closed pseudo--integrable billiards, the present system is essentially non--chaotic. Finally, we illustrate time evolution of wave packets in the present model.Comment: LaTeX text file with 12 ps figure

Nuclear electron capture rate in stellar interiors and the case of 7Be

Nuclear electron capture rate from continuum in an astrophysical plasma environment (like solar core) is calculated using a modified Debye-Huckel screening potential and the related non-Gaussian q-distribution of electron momenta. For q=1 the well-known Debye-Huckel results are recovered. The value of q can be derived from the fluctuation of number of particles and temperature inside the Debye sphere. For 7Be continuum electron capture in solar core, we find an increase of 7 -- 10 percent over the rate calculated with standard Debye-Huckel potential. The consequence of this results is a reduction of the same percentage of the SSM 8B solar neutrino flux, leaving unchanged the SSM 7Be flux.Comment: 8 pages, 1 figure, IOP macro style, submitted to JP

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.Comment: version accepted for publication in J. Math. Phys.: criterion excluding basis property (Proposition 6) added, unbounded time-evolution discussed, new reference

Complex Calogero model with real energies

We show that and how PT symmetry (interpreted as a "weakened Hermiticity") can be extended to the exactly solvable two- and three-particle Calogero model.Comment: 16 pages, 3 figures, submitted to J. Phys.

Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Schroedinger equation H \psi=E \psi with PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of this non-variational construction is given. Our Taylor series form of \psi complements and completes the recent terminating solutions as obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appea

A single-mode quantum transport in serial-structure geometric scatterers

We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit $N\to\infty$. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. A detailed discussion is presented for a finite-periodic "comb"; we show how the resonance poles can be computed within the Krein formula approach. Another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads; we show that apart of the resonances coming from the decoupled-surface eigenvalues such scatterers exhibit the high-energy behavior typical for the delta' interaction for the physically interesting couplings.Comment: 36 pages, a LaTeX source file with 2 TeX drawings, 3 ps and 3 jpeg figures attache

CPT-symmetric discrete square well

A new version of an elementary PT-symmetric square well quantum model is proposed in which a certain Hermiticity-violating end-point interaction leaves the spectrum real in a large domain of couplings $\lambda\in (-1,1)$. Within this interval we employ the usual coupling-independent operator P of parity and construct, in a systematic Runge-Kutta discrete approximation, a coupling-dependent operator of charge C which enables us to classify our P-asymmetric model as CPT-symmetric or, equivalently, hiddenly Hermitian alias cryptohermitian.Comment: 12 pp., presented to conference PHHQP IX (http://www.math.zju.edu.cn/wjd/

The impact of diabetes on the pathogenesis of sepsis

Diabetes is associated with an increased susceptibility to infection and sepsis. Conflicting data exist on whether the mortality of patients with sepsis is influenced by the presence of diabetes, fuelling the ongoing debate on the benefit of tight glucose regulation in patients with sepsis. The main reason for which diabetes predisposes to infection appears to be abnormalities of the host response, particularly in neutrophil chemotaxis, adhesion and intracellular killing, defects that have been attributed to the effect of hyperglycaemia. There is also evidence for defects in humoral immunity, and this may play a larger role than previously recognised. We review the literature on the immune response in diabetes and its potential contribution to the pathogenesis of sepsis. In addition, the effect of diabetes treatment on the immune response is discussed, with specific reference to insulin, metformin, sulphonylureas and thiazolidinediones

Vasovagal tonus index (VVTI) as an indirect assessment of remission status in canine multicentric lymphoma undergoing multi-drug chemotherapy

Vasovagal tonus index (VVTI) is an indirect measure of heart rate variability and may serve as a marker of disease severity. Higher heart rate variability has predicted lower tumour burden and improved survival in humans with various tumour types. The purpose of this pilot study was to evaluate VVTI as a biomarker of remission status in canine lymphoma. The primary hypothesis was that VVTI would be increased in dogs in remission compared to dogs out of remission. Twenty-seven dogs were prospectively enrolled if they had a diagnosis of intermediate to high-grade lymphoma and underwent multidrug chemotherapy. Serial electrocardiogram data were collected under standard conditions and relationships between VVTI, remission status and other clinical variables were evaluated. VVTI from dogs in remission (partial or complete) did not differ from dogs with fulminant lymphoma (naive or at time of relapse). Dogs in partial remission had higher VVTI than dogs in complete remission (p = 0.021). Higher baseline VVTI was associated with higher subsequent scores (p < 0.001). VVTI also correlated with anxiety level (p = 0.03). Based on this pilot study, VVTI did not hold any obvious promise as a useful clinical biomarker of remission status. Further investigation may better elucidate the clinical and prognostic utility of VVTI in dogs with lymphoma