Quantum Goos-H\"{a}nchen shift and tunneling transmission at a curved step potential

We study the quantum Goos-H\"{a}nchen (GH) shift and the tunneling transmission at a curved step potential by investigating the time evolution of a wave packet. An initial wave packet is expanded in terms of the eigenmodes of a circular step potential. Its time evolution is then given by the interference of their simple eigenmode oscillations. We show that the GH shift along the step boundary can be explained by the energy-dependent phase loss upon reflection, which is defined by modifying the one-dimensional (1D) effective potential derived from the 2D circular system. We also demonstrate that the tunneling transmission of the wave packet is characterized by a free-space image distant from the boundary. The tunneling transmission exhibits a rather wide angle divergence and the direction of maximum tunneling is slightly rotated from the tangent at the incident point, which is consistent with the time delay of the tunneling wave packet computed in the 1D modified effective potential

Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models

International audienceResonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunneling-induced level splittings which is found to be in very good agreement with the exact splittings obtained through numerical diagonalisation

Patterns of Development and Nitrogen Reserves Mobilization during Regrowth of Defoliated Clover

Contribution of nitrogen reserves to regrowth following defoliation was studied in white clover plants (Trifolium repens) according to the morphological pattern of differentiation of the aerial parts during the same period. Low temperature and short day lengths were used as a pre-treatment in order to increase branching and enhance new sites of leaf production during a further 25 d period of regrowth. Pre-treated plants exhibited a large reduction in leaf area largely counterbalanced with a high increase in leaf pool size during the first 10 d of regrowth. The mobilization of nitrogen reserves during regrowth of defoliated clover was intimately linked to the pattern of differentiation of the newly developed organs. It thus appeared that regrowth of pretreated plants was less supported by endogenous N during the first 10 d as compared to control plants continously grown in standard conditions. It is assumed that regrowth of dwarf plants is less dependent upon the mobilization rate of soluble proteins previously accumulated in roots and uncut stolons

Modelling Nitrogen Uptake in Winter Oilseed Rape by Using Influx Kinetics of Nitrate Transport Systems

A mechanistic model was proposed in order to predict nitrogen uptake by a culture of oilseed rape (Brassica napus L.), using independently measured characteristics of plants growing in hydroponic or under field conditions. Uptake kinetics of the different components (Constitutive and Inducible) of the Low and High Affinity Transport Systems of nitrate (CLATS, ILATS, CHATS and IHATS, respectively) were determined by 15NO3- labelling in controlled conditions. The use of kinetic equations of transport systems and the experimental field data from the INRA-Châlons rape databank allowed to model NO3- uptake during the plant growth cycle. The study of different factors such as root temperature, day/night cycle and ontogenetic stages on NO3- uptake rate has been undertaken in order to improve the model prediction. Model outputs show that the high affinity transport system (HATS) accounted for about 90 % of total NO3- uptake (20 and 70 % for CHATS and IHATS without fertilization, respectively). The low affinity transport system (LATS) accounted for a minor proportion of total N uptake, and its activity was restricted to the early phase of the growth cycle. However, N autumnal fertilization increased the duration of its contribution (from 67 to 100 days) to total N uptake

Instantons revisited: dynamical tunnelling and resonant tunnelling

Starting from trace formulae for the tunnelling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate complex-time paths. We show how this instanton-like approach, which takes advantage of an incomplete Wick rotation, accurately reproduces tunnelling effects not only in the usual double-well potential but also in situations where a pure Wick rotation is insufficient, for instance dynamical tunnelling or resonant tunnelling. Even though only one-dimensional autonomous Hamiltonian systems are quantitatively studied, we discuss the relevance of our method for multidimensional and/or chaotic tunnelling

A primer for resonant tunnelling

Resonant tunnelling is studied numerically and analytically with the help of a three-well quantum one-dimensional time-independent model. The simplest cases are considered where the three-well potential is polynomial or piecewise constant.Comment: accepted to EJP, 19 pages, 8 figure

Tunneling dynamics in exactly-solvable models with triple-well potentials

Inspired by new trends in atomtronics, cold atoms devices and Bose-Einstein condensate dynamics, we apply a general technique of N=4 extended Supersymmetric Quantum Mechanics to isospectral Hamiltonians with triple-well potentials, i.e. symmetric and asymmetric. Expressions of quantum-mechanical propagators, which take into account all states of the spectrum, are obtained, within the N = 4 SQM approach, in the closed form. For the initial Hamiltonian of a harmonic oscillator, we obtain the explicit expressions of potentials, wavefunctions and propagators. The obtained results are applied to tunneling dynamics of localized states in triple-well potentials and for studying its features. In particular, we observe a Josephson-type tunneling transition of a wave packet, the effect of its partial trapping and a non-monotonic dependence of tunneling dynamics on the shape of a three-well potential. We investigate, among others, the possibility of controlling tunneling transport by changing parameters of the central well, and we briefly discuss potential applications of this aspect to atomtronic devices.Comment: Latex, 28 pages, 7 Figs, 2 Tables; minor presentation changes, journal versio

Regulation of two germin-like protein genes during plum fruit development

Germin-like proteins (GLPs) have several proposed roles in plant development and defence. Two novel genes (Ps-GLP1 and 2) encoding germin-like protein were isolated from plum (Prunus salicina). Their regulation was studied throughout fruit development and during ripening of early and late cultivars. These two genes exhibited similar expression patterns throughout the various stages of fruit development excluding two important stages, pit hardening (S2) and fruit ripening (S4). During fruit development until the ripening phase, the accumulation of both Ps-GLPs is related to the evolution of auxin. However, during the S2 stage only Ps-GLP1 is induced and this could putatively be in a H2O2-dependent manner. On the other hand, the diversity in the Ps-GLPs accumulation profile during the ripening process seems to be putatively due to the variability of endogenous auxin levels among the two plum cultivars, which consequently change the levels of autocatalytic ethylene available for the fruit to co-ordinate ripening. The effect of auxin on stimulating ethylene production and in regulating Ps-GLPs transcripts was also investigated. These data, supported by their localization in the extracellular matrix, suggest that auxin is somehow involved in the regulation of both transcripts throughout fruit development and ripening