Abstract: The nonlinear Schrodinger equation is solved on an infinitesimal thin ring or circle. We obtained the exact real wave functions with their corresponding energies for the ground state and the excited states. Critical values of the circle perimeter are found at which the ground state changes its structure and additional higher excited states appear. Also, the complex wave functions that correspond to energy levels with finite angular momentum are studied.

Abstract: When floating on a two-dimensional surface of superfluid He-4, electrons arrange themselves in two-dimensional crystalline structure known as Wigner crystal. In channels, the boundaries interfere the crystalline order and in case of very narrow channels one observes a quasi-one-dimensional (quasi-1D) Wigner crystal formed by just a few rows of electrons and, ultimately, one row in the “quantum wire” regime. Recently, the “quantum wire” regime was accessed experimentally [D.G. Rees, H. Totsuji, K. Kono, Phys. Rev. Lett. 108, 176801 (2012)] resulting in unusual transport phenomena such as, e.g., oscillations in the electron conductance. Using molecular dynamics simulations, we study the nonlinear transport of electrons in channels with various types of constrictions: single and multiple symmetric and asymmetric geometrical constrictions with varying width and length, and saddle-point-type potentials with varying gate voltage. In particular, we analyze the average particle velocity of the particles and the corresponding electron current versus the driving force or the gate voltage. We have revealed a significant difference in the dynamics for long and short constrictions: The oscillations of the average velocity of the particles for the systems with short constrictions exhibit a clear correlation with the transitions between the states with different numbers of rows of particles; on the other hand, for the systems with longer constrictions these oscillations are suppressed. The obtained results qualitatively agree with the experimental observations. Next, we propose a FET-like structure that consists of a channel with asymmetric constrictions. We show that applying a transverse bias results either in increase of the average particle velocity or in its suppression thus allowing a flexible control tool over the electron transport. The advantage of the asymmetric FET is that it does not have a gate and it allows an easy control of relatively large electron flow. Furthermore, the asymmetric device can be used for rectification of an ac-driven electron flow. Our results bring important insights into the dynamics of electrons floating on the surface of superfluid He-4 in channels with constrictions and allow the effective control over the electron transport.

Abstract: We consider magnetic flux moving in superconductors with periodic pinning arrays. We show that sample heating by moving vortices produces negative differential resistivity (NDR) of both N and S type (i.e., N- and S-shaped) in the voltage-current characteristic (VI curve). The uniform flux flow state is unstable in the NDR region of the VI curve. Domain structures appear during the NDR part of the VI curve of an N type, while a filamentary instability is observed for the NDR of an S type. The simultaneous existence of the NDR of both types gives rise to the appearance of striking self-organized (both stationary and nonstationary) two-dimensional dynamical structures.

Abstract: The electro-phonon resonance effect is a consequence of a resonant interaction between two electric subbands mediated by an optical phonon. It occurs in a quasi-two-dimensional electron system each time the energy difference between two electric subbands equals the energy of a Lo phonon. We study the influence of this effect on the electron mobility by using the momentum balance equation. The temperature and electron density dependences of the resonances are studied in the linear and non-linear response regimes.

Abstract: We studied equally charged particles, suspended in a complex plasma, which move in a plane and interact with a screened Coulomb potential (Yukawa type) and with an additional external confining parabolic potential in one direction, which makes the system quasi-one-dimensional (Q1D). The normal modes of the system are studied in the presence of dissipation. We also investigated how a perpendicular magnetic field couples the phonon modes with each other. Two different ways of exciting the normal modes are discussed: (1) a uniform excitation of the Q1D lattice, and (2) a local forced excitation of the system in which one particle is driven by, e.g., a laser. Our results are in very good agreement with recent experimental findings on a finite single chain system [Liu , Phys. Rev. Lett. 91, 255003 (2003)]. Predictions are made for the normal modes of multichain structures in the presence of damping.

Abstract: Patients with sleep related breathing disorders (SRBD) can be treated with nasal continuous positive airway pressure (nCPAP) or with several upper airway (UA) interventions. While nCPAP is almost always effective when clinically well tolerated, the therapeutic outcome of UA surgery and UA devices is difficult to predict. The improvement of our capability to perform the latter predictions more accurately is of great clinical importance since it will prevent patients to be treated with ineffective, sometimes irreversible, techniques. In this review we describe the importance of new imaging methods in this respect. We first refer to the most important pathophysiological mechanisms known so far to play a role in SRBD, indicating that functional imaging could elucidate these mechanisms in a patient specific manner. Then we describe the new technologies that make UA imaging more functional referring to the data as they are presently available. Finally we summarise the studies that do indicate that the use of functional imaging of the UA in SRBD patients may significantly help to predict the clinical outcome after UA interventions.

Abstract: In this paper we study two cold atmospheric pressure plasma jets, operating in Ar + 2% air, with a different electrode geometry but with the same power dissipated in the plasma. The density profiles of the biomedically active NO and O species throughout the plasma jet, previously obtained by laser diagnostics, are calculated by means of a zero-dimensional semi-empirical reaction kinetics model. A good agreement between the calculated and measured data is demonstrated. Furthermore, the most probable spatial power distribution in an RF driven plasma jet is obtained for the first time by comparing measured and calculated species density profiles. This was possible due to the strong effect of the power distribution on the NO and O density profiles. In addition the dominant reaction pathways for both the NO and the O species are identified. The model allows us to obtain key information on the reactive species production inside the jet, which is difficult to access by laser diagnostics in a coaxial geometry. Finally, we demonstrate that water impurities in the order of 100 ppm in the gas feed can have a significant effect on the spatial distribution of the NO and O density.