Thermoelectric effects in superconducting nanostructures

We study thermoelectric effects in superconducting nanobridges and demonstrate that the magnitude of these effects can be comparable or even larger than that for a macroscopic circuit. It is shown that a large gradient of the electron temperature can be realistically created on a nanoscale and the masking effects due to spurious magnetic fields can be minimised in nanostructures. For these reasons, nanodevices can provide an interesting possibility to study the thermoelectric effect in superconductors.     

Hausdorff Dimension of the Set of Generic Points for Gibbs Measures

For a Gibbs measure on the configuration space of a finite spin lattice system, we find (in terms of entropy) the Hausdorff dimension of the set of generic points. Using this result, we evaluate the Hausdorff dimension of level sets for Birkhoff ergodic averages of some continuous functions on the configuration space.     

A statistical limit in the solution of the nonlinear Schrödinger equation under deterministic initial conditions

We investigate the semiclassical limit for the nonlinear Schrödinger equation in the case of a defocusing medium under oscillating nonperiodic initial conditions specified on the entire x axis. We formulate a system of integral conservation laws in terms of an infinite number of spatially averaged densities explicitly calculated from the initial conditions. We study the direct scattering problem and show that the scattering phase is a uniformly distributed random variable. The evolution of this system leads to the development of nonlinear oscillations, which become statistical in nature on long time scales. A modified inverse scattering method based on constructing a maximizer of the N-soliton solution in the continuum limit for N → is used to obtain an asymptotic solution. Using the maximizer, we found an infinite set of conserved averaged densities in the statistical state. This allowed us to couple the initial state with the limiting statistical steady (for t → ∞) state and, thus, to unambiguously determine the level spectrum in the statistical limit.     

Silicon nanocluster formation under electron-beam-induced modification of a silicate matrix

A cathodoluminescence band in the green spectral region is observed in silicate matrices when the excitation density exceeds a certain threshold value. This band is due to the formation of silicon nanoclusters 4–5 nm in size and becomes manifest at SiO₂/Si interfaces when impurities are introduced into the silicate matrix, as well as under electron-beam irradiation.     

Drag of ballistic electrons by an ion beam

Drag of electrons of a one-dimensional ballistic nanowire by a nearby one-dimensional beam of ions is considered. We assume that the ion beam is represented by an ensemble of heavy ions of the same velocity V. The ratio of the drag current to the primary current carried by the ion beam is calculated. The drag current turns out to be a nonmonotonic function of velocity V. It has a sharp maximum for V near v _nF/2, where n is the number of the uppermost electron miniband (channel) taking part in conduction and v _nF is the corresponding Fermi velocity. This means that the phenomenon of ion beam drag can be used for investigation of the electron spectra of ballistic nanostructures. We note that whereas observation of the Coulomb drag between two parallel quantum wires may in general be complicated by phenomena such as tunneling and phonon drag, the Coulomb drag of electrons of a one-dimensional ballistic nanowire by an ion beam is free of such spurious effects.     

Dember effect: Problems and solutions

In the existing theory of Dember effect research community understands that the photo-electromotive force is the voltage difference arising between the illuminated and dark surfaces of a semiconductor. In this work it is shown that the latter is incorrect. A new formulation of the linear theory of Dember effect is presented. Conclusions of this new theory are essentially different from the ones of conventional theory. Proposed theory is applied to both open- and closed-circuit conditions.     

Low temperature thermal magnetoconductance of metals

A low temperature transverse thermal magnetoconductance of metals and semimetals is treated theoretically. It is shown that its high magnetic field behavior is determined by the characteristic time τ_ɛ of jumps from one cyclotron circle to another due to electron-phonon collisions rather than by the transport time τ_tr that determines the conductance. The phonon-electron drag contribution to the magnetoconductance is also discussed.     

A study of lithium insertion into electrodes with thin gold films

The process of lithium insertion into thin gold films is studied. It is found that lithium is reversibly inserted with the formation of compounds, which are close to Li_1.5Au in their average composition. The long-term cycling leads to the breakdown of gold layer (and corresponding decrease in the electrode capacity), which is associated with considerable volume changes due to lithium insertion.     

Primality testing through algebraic groups

We propose a deterministic primality test based on a section of a group scheme. Pépin’s test and the tests of Lucas–Lehmer type are special cases of our construction, provided the group scheme is taken to be the multiplicative group and the Waterhouse–Weisfeiler group scheme, respectively. Besides, we suggest a test involving formal completions of these schemes.