Enhancement of persistent current on multichannel ring

We describe a "train" effect which may exist in small metallic and semiconductor rings and might be associated with the long-standing problem of the persistent current enhancement. The current is associated with the cooperative motion of N electrons constituing the N-electron "train". The train arises via an excitation or a backflow of spin waves or of interchannel charge density sound modes. The impurities and defects have a little effect on the "train" current. The reason is that the "train" current is associated with a small momentum transfer, which is much smaller than the momentum transfer of the free electron current equal to 2 pi/L. For an illustration of the "train" effect we have calculated the persistent current in the framework of the Bethe ansatz solutions for Hubbard model. The fractional M/N periodicities of the persistent current serve as an indication of the electron "train"

Duality and exact results for conductivity of 2D isotropic heterophase systems in magnetic field

Using a fact that the effective conductivity sigma_{e} of 2D random heterophase systems in the orthogonal magnetic field is transformed under some subgroup of the linear fractional group, connected with a group of linear transformations of two conserved currents, the exact values for sigma_{e} of isotropic heterophase systems are found. As known, for binary (N=2) systems a determination of exact values of both conductivities (diagonal sigma_{ed} and transverse Hall sigma_{et}) is possible only at equal phase concentrations and arbitrary values of partial conductivities. For heterophase (N > 2) systems this method gives exact values of effective conductivities, when their partial conductivities belong to some hypersurfaces in the space of these partial conductivities and the phase concentrations are pairwise equal. In all these cases sigma_e does not depend on phase concentrations. The complete, 3-parametric, explicit transformation, connecting sigma_e in binary systems with a magnetic field and without it, is constructe

Phase transitions to dipolar clusters and charge density waves in high Tc superconductors

We show that doping of hole charge carriers leads to formation of electric dipolar clusters in cuprates. They are created by many body interactions between the dopant ion outside and holes inside the CuO planes. Because of the two-fold degeneracy holes in the CuO plane cluster into four-particles resonance valence bond plaquettes bound with dopant ions. Such dipoles may order into charge-density waves (CDW) or stripes or form a disordered state depending on doping and temperature. The lowest energy of the ordered system corresponds to a local anti-ferroelectric ordering. The mobility of individual disordered dipoles is very low at low temperatures and they prefer first to bind into dipole-dipole pairs. Electromagnetic radiation interacts strongly with electric dipoles and when the sample is subjected to it the mobility changes significantly. This leads to a fractal growth of dipolar clusters. The existence of electric dipoles and CDW induce two phase transitions with increasing temperature, melting of the ordered state and disappearance of the dipolar state. Ferroelectricity at low doping is a natural consequence of such dipole moments. We develop a theory based on two-level systems and dipole-dipole interaction to explain the behavior of the polarization as a function of temperature and electric field

Gravitational vortices and clump formation in Saturn's F ring during an encounter with Prometheus

Saturn rings are most beautiful and dynamic places in the solar system, consisting of ice particles in a constant battle between the gravitational forces of Saturn and its many moons. Fan, spiral, propellers, moonlets and streamer-channels observed by CASSINI in the F-ring have been attributed to encounters by Prometheus on the F ring, with investigations of optical thickness revealing large populations of transient moonlets. Taking into account gravitational interaction between particles and a multi-stranded F-ring structure we show that Prometheus' encounters create rotational flows, like atmospheric vortices and the self-gravity enhances the accelerated growth and size of moonlets. Vortex patches form caustics, which is a primary cause of the transient particle density clumps of 20 km width and 100 km length, and they are elongated to cover an area of 1600 km by 150 km, which may eventually combine into a vortex sheet

Phase transitions to dipolar clusters and charge density waves in high Tc superconductors

We show that doping of hole charge carriers leads to formation of electric dipolar clusters in cuprates. They are created by many body interactions between the dopant ion outside and holes inside the CuO planes. Because of the two-fold degeneracy holes in the CuO plane cluster into four-particles resonance valence bond plaquettes bound with dopant ions. Such dipoles may order into charge-density waves (CDW) or stripes or form a disordered state depending on doping and temperature. The lowest energy of the ordered system corresponds to a local anti-ferroelectric ordering. The mobility of individual disordered dipoles is very low at low temperatures and they prefer first to bind into dipole-dipole pairs. Electromagnetic radiation interacts strongly with electric dipoles and when the sample is subjected to it the mobility changes significantly. This leads to a fractal growth of dipolar clusters. The existence of electric dipoles and CDW induce two phase transitions with increasing temperature, melting of the ordered state and disappearance of the dipolar state. Ferroelectricity at low doping is a natural consequence of such dipole moments. We develop a theory based on two-level systems and dipole-dipole interaction to explain the behavior of the polarization as a function of temperature and electric field

Intersite elastic coupling and invar effect

The invar phenomenon (very small thermal expansion in some iron alloys or compounds) is usually explained by the thermally-induced transitions between different spin states of Fe, having different atomic volumes. We consider these processes taking into account elastic interaction between Fe atoms in different spin states. Inclusion of these interactions explains why thermal expansion may be close to zero in a broad temperature interval and thus gives rise to the invar effect

Dipolar clusters and ferroelectricity in high Tc superconductors

In this paper, we show that doping of hole charge carriers induces formation of resonance plaquettes (RPs) having electric dipolar moments and fluctuating stripes in cuprates. A single RP is created by many-body interactions between the dopant ion or a charge fluctuation outside and holes inside the CuO plane. In such a process, Coulomb interacting holes in the CuO plane are self-organized into four-particles resonance valence bond plaquettes bound with dopants or polarons located in the spacer layer between CuO planes. Such RPs have ordered and disordered phases. They are ordered into charge density waves (CDW) or stripes only at certain conditions. The lowest energy of the ordered phase corresponds to a local antiferroelectric ordering. The RPs mobility is very low at low temperatures and they are bound into dipole–dipole pairs. Electromagnetic radiation interacts strongly with RPs electric dipoles and when the sample is subjected to it, the mobility changes significantly. This leads to a fractal growth of dipolar RP clusters. The existence of electric dipoles and CDW reveal a series of new phenomena such as ferroelectricity, strong light and microwave absorption and the field induced superconductivity

Suppression of superconductivity in mesoscopic superconductors

We propose a new boundary-driven phase transition associated with vortex nucleation in mesoscopic superconductors (of size of the order of, or larger than, the penetration depth). We derive the rescaling equations and we show that boundary effects associated with vortex nucleation lowers the conventional transition temperature in mesoscopic superconductors by an amount which is a function of the size of the superconductor. This result explains recent experiments in small superconductors where it was found that the transition temperature depends on the size of the system and is lower than the critical Berezinsk\u{i}-Kosterlitz-Thouless temperature

Black holes in economics

The economics is one of the most complex systems in nature. There is still no united view on all processes happen there. Here we would like to present a geometrical approach to economics, where we introduce a new concept of economic metric space. We show that there may exist black holes, the objects, which may play a crucial role in the economics dynamics. We argue that the existence of black holes in such system from one side may stimulate economics while from other side may originate financial crisis

Graphene levitons and anti-levitons in magnetic fields

The leviton is an electron or hole wavepacket that rides the surface of the Fermi sea. When a series of Lorentzian or Gaussian time dependent pulses are applied to an ultracold system a soliton-like excitation with only one electron and no localised hole emerges. Graphene is a unique system where the Fermi surface may arise from a Dirac point and therewith the levitons character may display many interesting features. For example, the leviton formation may be associated with a chiral anomaly, and inside a single potential step an anti-leviton forms. We show that the application of weak magnetic fields may switch on and off the leviton Klein tunnelling. Also, in a moderate field negative refraction arises along a curved trajectory, whereas with a stronger field a new elementary excitation – the levity vortex – in the reflected wavefunction occurs. Herein we describe these phenomena in detail along with a complete explanation of the transmission of graphene levitons at a step potential in terms of the probability densities and a series of phase diagrams and the tunnelling times