Sources of quantum waves

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the wave function in all space at a given instant. We compare this standard approach to "source boundary conditions'' that fix the wave at all times in a given region, in particular at a point in one dimension. In contrast to the well-known physical interpretation of the initial-value-problem approach, the interpretation of the source approach has remained unclear, since it introduces negative energy components, even for ``free motion'', and a time-dependent norm. This work provides physical meaning to the source method by finding the link with equivalent initial value problems.Comment: 12 pages, 7 inlined figures; typos correcte

Weak measurement of arrival time

The arrival time probability distribution is defined by analogy with the classical mechanics. The difficulty of requirement to have the values of non-commuting operators is circumvented using the concept of weak measurements. The proposed procedure is suitable to the free particles and to the particles subjected to an external potential, as well. It is shown that such an approach imposes an inherent limitation to the accuracy of the arrival time determination.Comment: 3 figure

Simulation of wavepacket tunneling of interacting identical particles

We demonstrate a new method of simulation of nonstationary quantum processes, considering the tunneling of two {\it interacting identical particles}, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum Wigner-Liouville equation. These classical trajectories obey Hamilton-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.Comment: 11 pages, 3 figure

Matter wave pulses characteristics

We study the properties of quantum single-particle wave pulses created by sharp-edged or apodized shutters with single or periodic openings. In particular, we examine the visibility of diffraction fringes depending on evolution time and temperature; the purity of the state depending on the opening-time window; the accuracy of a simplified description which uses ``source'' boundary conditions instead of solving an initial value problem; and the effects of apodization on the energy width.Comment: 11 pages, 11 figure

Time-of-arrival distributions from position-momentum and energy-time joint measurements

The position-momentum quasi-distribution obtained from an Arthurs and Kelly joint measurement model is used to obtain indirectly an ``operational'' time-of-arrival (TOA) distribution following a quantization procedure proposed by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA distribution is not time covariant. The procedure is generalized by using other phase-space quasi-distributions, and sufficient conditions are provided for time covariance that limit the possible phase-space quasi-distributions essentially to the Wigner function, which, however, provides a non-positive TOA quasi-distribution. These problems are remedied with a different quantization procedure which, on the other hand, does not guarantee normalization. Finally an Arthurs and Kelly measurement model for TOA and energy (valid also for arbitrary conjugate variables when one of the variables is bounded from below) is worked out. The marginal TOA distribution so obtained, a distorted version of Kijowski's distribution, is time covariant, positive, and normalized

Spin dependent observable effect for free particles using the arrival time distribution

The mean arrival time of free particles is computed using the quantum probability current. This is uniquely determined in the non-relativistic limit of Dirac equation, although the Schroedinger probability current has an inherent non-uniqueness. Since the Dirac probability current involves a spin-dependent term, an arrival time distribution based on the probability current shows an observable spin-dependent effect, even for free particles. This arises essentially from relativistic quantum dynamics, but persists even in the non-relativistic regime.Comment: 5 Latex pages, 2.eps figures; discussions sharpened and references added; accepted for publication in Physical Review

Study on administration of 1,5-anhydro-D-fructose in C57BL/6J mice challenged with high-fat diet

1,5-Anhydro-D-fructose (AF) is a mono-saccharide directly formed from starch and glycogen by the action of α-1,4-glucan lyase (EC 4.2.2.13). Our previous study has indicated that AF increases glucose tolerance and insulin secretion in NMRI mice after administration through a gastric gavage in a single dose at 150 mg per mouse. In this study, we used high-fat feeding of C57BL/6J mice to examine the influence of long-term administration of AF on glucose-stimulated insulin secretion in vivo and in vitro. We found that 8-weeks of high-fat feeding increased body weight, fasting blood glucose and insulin levels in C57BL/6J mice when compared to mice fed normal diet. Impaired glucose tolerance was also observed in mice receiving 8-weeks of high-fat diet. In contrast, AF (1.5 g/kg/day), administered through drinking water for 8-weeks, did not affect body weight or food and water intake in mice fed either the high-fat or normal diet. There was no difference in basal blood glucose or insulin levels between AF-treated and control group. Oral glucose tolerance test (OGTT) showed that AF did not affect glucose-stimulated insulin secretion in mice. In in vitro studies with isolated islets, AF did not influence glucose-stimulated insulin secretion in mice receiving either high-fat or normal diet. We therefore conclude that when given through drinking water for 8 weeks at 1.5 g/kg/day, AF has no effect on glucose-stimulated insulin secretion in C57BL/6J mice challenged with a high-fat diet

Small Corrections to the Tunneling Phase Time Formulation

After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for tunneling/reflecting particles in a particular colliding configuration where the idea of multiple peak decomposition is recovered. To partially overcome the analytical incongruities which frequently rise up when the stationary phase method is adopted for computing the (tunneling) phase time expressions, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and a unidimensional squared potential barrier where the scattered wave packets can be recomposed by summing the amplitudes of simultaneously reflected and transmitted wave components so that the conditions for applying the stationary phase principle are totally recovered. Lessons concerning the use of the stationary phase method are drawn.Comment: 14 pages, 3 figure

Pest population dynamics are related to a continental overwintering gradient

Overwintering success is an important determinant of arthropod populations that must be considered as climate change continues to influence the spatiotemporal population dynamics of agricultural pests. Using a long-term monitoring database and biologically relevant overwintering zones, we modeled the annual and seasonal population dynamics of a common pest, Helicoverpa zea (Boddie), based on three overwintering suitability zones throughout North America using four decades of soil temperatures: the southern range (able to persist through winter), transitional zone (uncertain overwintering survivorship), and northern limits (unable to survive winter). Our model indicates H. zea population dynamics are hierarchically structured with continental-level effects that are partitioned into three geographic zones. Seasonal populations were initially detected in the southern range, where they experienced multiple large population peaks. All three zones experienced a final peak between late July (southern range) and mid-August to mid-September (transitional zone and northern limits). The southern range expanded by 3% since 1981 and is projected to increase by twofold by 2099 but the areas of other zones are expected to decrease in the future. These changes suggest larger populations may persist at higher latitudes in the future due to reduced low-temperature lethal events during winter. Because H. zea is a highly migratory pest, predicting when populations accumulate in one region can inform synchronous or lagged population development in other regions. We show the value of combining long-term datasets, remotely sensed data, and laboratory findings to inform forecasting of insect pests