Abstract:
Magnetic ratchets -- two-dimensional systems with superimposed non-centrosymmetric ferromagnetic gratings -- are considered theoretically. It is demonstrated that excitation by radiation results in a directed motion of two-dimensional carriers due to pure orbital effect of the periodic magnetic field. Magnetic ratchets based on various two-dimensional systems like topological insulators, graphene and semiconductor heterostructures are investigated. The mechanisms of the electric current generation caused by both radiation-induced heating of carriers and by acceleration in the radiation electric field in the presence of space-oscillating Lorentz force are studied in detail. The electric currents sensitive to the linear polarization plane orientation as well as to the radiation helicity are calculated. It is demonstrated that the frequency dependence of the magnetic ratchet currents is determined by the dominant elastic scattering mechanism of two-dimensional carriers and differs for the systems with linear and parabolic energy dispersions.

Abstract:
The driving of charge carriers confined in a quantum well lacking the center of space inversion by an alternating electric field leads to the formation of a direct electric current. We develop a microscopic theory of such a quantum ratchet effect for quantum wells subjected to a static magnetic field. We show that the ratchet current emerges for a linearly polarized alternating electric field as well as a rotating electric field and drastically increases at the cyclotron resonance conditions. For the magnetic field tilted with respect to the quantum well normal, the ratchet current contains an additional resonance at the first subharmonic of the cyclotron resonance.

Abstract:
We report on the observation of the cyclotron-resonance-assisted photon drag effect. Resonant photocurrent is detected in InSb/InAlSb quantum wells structures subjected to a static magnetic field and excited by terahertz radiation at oblique incidence. The developed theory based on Boltzmann's kinetic equation is in a good agreement with the experimental findings. We show that the resonant photocurrent originates from the transfer of photon momentum to free electrons drastically enhanced at cyclotron resonance.

Abstract:
We report on the observation of cyclotron resonance induced photocurrents, excited by continuous wave terahertz radiation, in a 3D topological insulator (TI) based on an 80 nm strained HgTe film. The analysis of the photocurrent formation is supported by complimentary measurements of magneto-transport and radiation transmission. We demonstrate that the photocurrent is generated in the topologically protected surface states. Studying the resonance response in a gated sample we examined the behavior of the photocurrent, which enables us to extract the mobility and the cyclotron mass as a function of the Fermi energy. For high gate voltages we also detected cyclotron resonance (CR) of bulk carriers, with a mass about two times larger than that obtained for the surface states. The origin of the CR assisted photocurrent is discussed in terms of asymmetric scattering of TI surface carriers in the momentum space. Furthermore, we show that studying the photocurrent in gated samples provides a sensitive method to probe the effective masses and the mobility of 2D Dirac surface states, when the Fermi level lies in the bulk energy gap or even in the conduction band.

Abstract:
We report on the observation of the giant spin-polarized photocurrent in HgTe/HgCdTe quantum well (QW) of critical thickness at which a Dirac spectrum emerges. Exciting QW of 6.6 nm width by terahertz (THz) radiation and sweeping magnetic field we detected a resonant photocurrent. Remarkably, the position of the resonance can be tuned from negative (-0.4 T) to positive (up to 1.2 T) magnetic fields by means of optical gating. The photocurent data, accompanied by measurements of radiation transmission as well as Shubnikov-de Haas and quantum Hall effects, give an evidence that the enhancement of the photocurrent is caused by cyclotron resonance in a Dirac fermion system. The developed theory shows that the current is spin polarized and originates from the spin dependent scattering of charge carriers heated by the radiation.

Abstract:
The Hamiltonian associated to the mass variable system is constructed from first principles through finding a constant of motion of the system. A comparison is made of the classical motion of a body with its mass position depending in the (x,v) space and (x,p) space which are defined by the constant of motion and the Hamiltonian, for a particular model of mass variation. As one could expected, these motion looks different on these spaces. The quantization of the harmonic oscillator with this mass variation is done, and a comparison is made by using the usual Hamiltonian approach with the proposed quantization of the constant of motion approach. This comparison is done at first order in perturbation theory, and one sees a difference between both approaches which can, in principle, be measured.

Abstract:
It is demonstrated that the universally accepted system of gas-dynamic (hydrodynamic) equations is applicable only to homogeneous (isentropic) media and requires advancement to get applicable to non-homogeneous media. A generalized equation of gravitational wave for adiabatic and ideal media is obtained from advanced system. From this equation, in turn, is obtained an equation of acoustic wave, which is plane and different form the known equation in that the phase speed of the wave in the Earth atmosphere obviously depends on altitude, i.e. C = C (z, T) instead of accepted C = C (T). Thus, acoustic wave is a short-period gravitational wave in which gravitational effects are revealed at altitudes z > 2.3 × 10^{3} m, which leads to amplification of refraction of sound. The sphere of applicability of the equation is determined and it is demonstrated that it is true only up to the upper boundary of the troposphere ( z ≤ 11 - 12km.) above which anomalous processes develop in the atmosphere.

Abstract:
Processes of formation and destruction of submicrostructure under friction loading are being discussed from the point of view of dislocation representations. Semi-uniform distribution of dislocation clusters of nano- and submicroscopic sizes in surface layers of nickel has been determined. Synergetic aspects of this phenomenon are being discussed.

The shortest k-dimension paths (k-paths)
between vertices of n-cube are considered on the basis a bijective mapping of
k-faces into words over a finite alphabet. The presentation of such paths is
proposed as (n － k + 1)×n matrix of characters from the same alphabet. A
classification of the paths is founded on numerical invariant as special
partition. The partition consists of n parts, which correspond to columns of the
matrix.

By removing a ^{12}C atom from the tetrahedral
configuration of the diamond, replacing it by a ^{13}C atom, and repeating
this in a linear direction, it is possible to have a linear chain of nuclear
spins one half and to build a solid state quantum computer. One qubit rotation,
controlled-not (CNOT) and controlled-controlled-not (CCNOT) quantum gates are
obtained immediately from this configuration. CNOT and CCNOT quantum gates are
used to determined the design parameters of this quantum computer.