Evolution of a model quantum system under time periodic forcing: conditions for complete ionization

We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation $\eta(t)$. We show that for generic $\eta(t)$, which includes the sum of any finite number of harmonics, the system, started in a bound state will get fully ionized as $t\to\infty$. This is irrespective of the magnitude or frequency (resonant or not) of $\eta(t)$. There are however exceptional, very non-generic $\eta(t)$, that do not lead to full ionization, which include rather simple explicit periodic functions. For these $\eta(t)$ the system evolves to a nontrivial localized stationary state which is related to eigenfunctions of the Floquet operator

Resonance Theory for Schroedinger Operators

Resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods. A general theory is developed, with new and weaker conditions, allowing for perturbations of threshold eigenvalues and relaxed Fermi Golden rule. The exponential decay rate of resonances is addressed; its uniqueness in the time dependent picture is shown is certain cases. The relation to the existence of meromorphic continuation of the properly weighted Green's function to time dependent resonance is further elucidated, by giving an equivalent time dependent asymptotic expansion of the solutions of the Schr\"odinger equation. \keywords{Resonances; Time-dependent Schr\"odinger equation

Decay of a Bound State under a Time-Periodic Perturbation: a Toy Case

We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength'' (\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\alpha(t)), we prove complete ionization as (t \to \infty). We prove also that, under the same conditions, all the states of the system are scattering states.Comment: LaTeX2e, 15 page

Singular normal form for the Painlev\'e equation P1

We show that there exists a rational change of coordinates of Painlev\'e's P1 equation $y''=6y^2+x$ and of the elliptic equation $y''=6y^2$ after which these two equations become analytically equivalent in a region in the complex phase space where $y$ and $y'$ are unbounded. The region of equivalence comprises all singularities of solutions of P1 (i.e. outside the region of equivalence, solutions are analytic). The Painlev\'e property of P1 (that the only movable singularities are poles) follows as a corollary. Conversely, we argue that the Painlev\'e property is crucial in reducing P1, in a singular regime, to an equation integrable by quadratures

Some impressions of a visit to parts of the South Island, June 1962

In June, 1962, at the invitation of the Tussock Grasslands and Mountain Lands Institute of New Zealand, I inspected parts of the South Island (Appendix 1), to make comparisons between high mountain areas of Australia and tussock grassland and mountain areas of New Zealand (Appendix 2) and thereby gain a clearer understanding of New Zealand problems. The inspections were arranged and conducted by the Director of the Institute, Mr L. W. McCaskill, usually in conjunction with other workers, runholders and administrators concerned with high country problems. Despite the necessarily selective nature of the visit, both as regards places and people, a reasonable cross-section of country, problems and opinions was encountered which, with recollections of an earlier visit in 1951, permitted some impressions to be formed. What is the solution to the deteriorated condition of New Zealand tussock grasslands and mountain lands, as manifest in many ways such as soil erosion, stream aggradation, flooding, weed and pest invasion, and declining stock-carrying capacity? Since there is a common denominator to most of these areas-tussock grassland-universal solution is sometimes expected. But the environment is so diverse, especially as regards topography, altitude and associated climate that no one solution can be possible and the illusion is best forgotten. There are many problems and each may require a separate solution. There is little point is discussing the many day-to-day problems with which New Zealand workers are already fully familiar, such as the need for cheaper effective fencing, and feral animal and weed control. The basic question is the determination of correct land use and this is the issue which is considered here

When is a bottleneck a bottleneck?

Bottlenecks, i.e. local reductions of capacity, are one of the most relevant scenarios of traffic systems. The asymmetric simple exclusion process (ASEP) with a defect is a minimal model for such a bottleneck scenario. One crucial question is "What is the critical strength of the defect that is required to create global effects, i.e. traffic jams localized at the defect position". Intuitively one would expect that already an arbitrarily small bottleneck strength leads to global effects in the system, e.g. a reduction of the maximal current. Therefore it came as a surprise when, based on computer simulations, it was claimed that the reaction of the system depends in non-continuous way on the defect strength and weak defects do not have a global influence on the system. Here we reconcile intuition and simulations by showing that indeed the critical defect strength is zero. We discuss the implications for the analysis of empirical and numerical data.Comment: 8 pages, to appear in the proceedings of Traffic and Granular Flow '1

The Existence of Pair Potential Corresponding to Specified Density and Pair Correlation

Given a potential of pair interaction and a value of activity, one can consider the Gibbs distribution in a finite domain $\Lambda \subset \mathbb{Z}^d$. It is well known that for small values of activity there exist the infinite volume ($\Lambda \to \mathbb{Z}^d$) limiting Gibbs distribution and the infinite volume correlation functions. In this paper we consider the converse problem - we show that given $\rho_1$ and $\rho_2(x)$, where $\rho_1$ is a constant and $\rho_2(x)$ is a function on $\mathbb{Z}^d$, which are sufficiently small, there exist a pair potential and a value of activity, for which $\rho_1$ is the density and $\rho_2(x)$ is the pair correlation function

Extracellular free water and glutathione in first-episode psychosis-a multimodal investigation of an inflammatory model for psychosis.

Evidence has been accumulating for an immune-based component to the etiology of psychotic disorders. Advancements in diffusion magnetic resonance imaging (MRI) have enabled estimation of extracellular free water (FW), a putative biomarker of neuroinflammation. Furthermore, inflammatory processes may be associated with altered brain levels of metabolites, such as glutathione (GSH). Consequently, we sought to test the hypotheses that FW is increased and associated with decreased GSH in patients with first-episode schizophrenia (SZ) compared with healthy controls (HC). SZ (n = 36) and HC (n = 40) subjects underwent a multi-shell diffusion MRI scan on a Siemens 3T scanner. 1H-MR spectroscopy data were acquired using a GSH-optimized MEGA-PRESS editing sequence and GSH/creatine ratios were calculated for DLPFC (SZ: n = 33, HC: n = 37) and visual cortex (SZ: n = 29, HC: n = 35) voxels. Symptoms and functioning were measured using the SANS, SAPS, BPRS, and GSF/GRF. SZ demonstrated significantly elevated FW in whole-brain gray (p = .001) but not white matter (p = .060). There was no significant difference between groups in GSH in either voxel. However, there was a significant negative correlation between DLPFC GSH and both whole-brain and DLPFC-specific gray matter FW in SZ (r = -.48 and -.47, respectively; both p < .05), while this relationship was nonsignificant in HC and in both groups in the visual cortex. These data illustrate an important relationship between a metabolite known to be important for immune function-GSH-and the diffusion extracellular FW measure, which provides additional support for these measures as neuroinflammatory biomarkers that could potentially provide tractable treatment targets to guide pharmacological intervention