Equations in Dual Variables for Whittaker Functions

It is known that the Whittaker functions w(q) associated with the group GL(N) are eigenfunctions of the Hamiltonians of the open Toda chain, hence satisfy a set of differential equations in the Toda variables q _i . Using the expression of the q _i for the closed Toda chain in terms of Sklyanin variables _i , and the known relations between the open and the closed Toda chains, we show that Whittaker functions also satisfy a set of new difference equations in _i .     

Localization-delocalization transition in chains with long-range correlated disorder

We investigated numerically localization properties of electron eigenstates in a chain with long-range correlated diagonal disorder. A tight-binding one-dimensional model with on-site energies exhibiting long-range correlated disorder (LCD) was used with various disorder strength W. LCD was defined so that it gave a power-law spectral density of the form S(k)αk^-p, where p determines the roughness of the potential landscape. Numerical results on the correlation length ξ of eigenstates shows the existence of the localization-delocalization transition at p=2. It is found that the critical values for disorder strength W_c and also the critical exponent ν for localization length change with the values of p.     

Freezing Transitions in Non-Fellerian Particle Systems

Non-Fellerian particle systems are characterized by nonlocal interactions, somewhat analogous to non-Gibbsian distributions. They exhibit new phenomena that are unseen in standard interacting particle systems. We consider freezing transitions in one-dimensional non-Fellerian processes which are built from the abelian sandpile additions to which in one case, spin flips are added, and in another case, so called anti-sandpile subtractions. In the first case and as a function of the sandpile addition rate, there is a sharp transition from a non-trivial invariant measure to the trivial invariant measure of the sandpile process. For the combination sandpile plus anti-sandpile, there is a sharp transition from one frozen state to the other anti-state.     

Combination of two basic types of synchronization in a coupled semiconductor laser system

Combination of two basic types of synchronization, anticipatory synchronization and lagged synchronization, is investigated numerically between two coupled semiconductor lasers. It is found that lagged synchronization produced by a backward coupling with a suitable delay can combine with the originally hidden anticipatory synchronization and produce a type of synchronization overcoming the original lagged synchronization produced by a forward coupling. We study the combination synchronization phenomenon when the delay of the backward coupling is different from that of the original anticipatory synchronization. Our results suggest that the synchronization combination phenomenon might allow an interpretation of an experimental observation by Sivaprakasam et al. [Phys. Rev. Lett. 87, 154101 (2001)] that the anticipating time is irrespective of the external-cavity round trip time, which to date remains to be understood.     

Controllable π junction in a Josephson quantum-dot device with molecular spin

We consider a model for a single molecule with a large frozen spin sandwiched in between two BCS superconductors at equilibrium, and show that this system has a π junction behavior at low temperature. The π shift can be reversed by varying the other parameters of the system, e.g., temperature or the position of the quantum dot level, implying a controllable π junction with novel application as a Josephson current switch. We show that the mechanism leading to the π shift can be explained simply in terms of the contributions of the Andreev bound states and of the continuum of states above the superconducting gap. The free energy for certain configuration of parameters shows a bistable nature, which is a necessary pre-condition for achievement of a qubit.     

Anisotropic ferromagnetism induced in rutile single crystals by Co implantation

The magnetic and electrical properties of Co-implanted single crystalline TiO₂ rutile are presented. For fluences of the order of 10¹⁷ cm^-2 and implantation energy of 150 keV the maximum atomic concentration of cobalt is 13 at% at a depth of 65 nm from the surface. The as implanted single crystals exhibit superparamagnetic behaviour attributed to the formation of nanosized cobalt clusters. After annealing at 1073 K an anisotropic ferromagnetic behaviour emerges with the easy magnetization axis lying in the (001) plane of rutile. The ferromagnetic behaviour is associated with oriented cobalt aggregates. Electrical conductivity of the implanted samples annealed in vacuum also exhibits anisotropic behaviour at low temperatures, but no magnetoresistive effects were detected.     

Shot noise in a quantum dot coupled to carbon nanotube terminals applied with a microwave field

We have investigated the spectral density of shot noise for the system of a quantum dot (QD) coupled to two single-wall carbon nanotube terminals irradiated with a microwave field on the QD. The terminal features are involved in the shot noise through modifying the self-energy of QD. The contributions of carbon nanotube terminals to the shot noise exhibit obvious behaviors. The novel side peaks are associated with the photon absorption and emission procedure accompanying the suppression of shot noise. The shot noise in balanced absorption belongs to sub-Poissonian, and it is symmetric with respect to the gate voltage. The differential shot noise displays intimate relation with the nature of carbon nanotubes and the applied microwave field. It exhibits asymmetric behavior for the unbalanced absorption case versus gate voltage. The Fano factor of the system exhibits the deviation of shot noise from the Schottky formula, and the structures of terminals obviously contribute to it. The super-Poissonian and sub-Poissonian shot noise can be achieved in the unbalanced absorption in different regime of source-drain bias.