Volume 1, Issue 4

We present an overview of two models of quantum random walk. In the first model, the discrete quantum random walk, we present the explicit solution for the recurring amplitude of the quantum random walk on a one-dimensional lattice. We also introduce a new method of solving the problem of random walk in the most general case and use it to derive the hitting amplitude for quantum random walk on the hypercube. The second is a special model based on a local interaction between neighboring spin-1/2 particles on a one-dimensional lattice. We present explicit results for the relevant quantities and obtain an upper bound on the speed of convergence to limiting probability distribution.

In this paper detailed theoretical study and experimental results concerning acoustic surface and undersurface propagation modes in multilayered Co/Cu superlattices are provided. The theoretical approach was adopted from that of Adler and Farnel. Experimental results were obtained in Brillouin light-scattering measurements. The Sezawa and Love acoustic modes were observed as a result of boundary conditions at the interface between hexagonal and cubic structures.

We consider the complex problem of how to calculate particle motions taking into account multiparticle collisions. Multiparticle contacts occur when a particle collides with neighbouring particles, so that those contacts have a direct influence on each other. We will focus on the molecular dynamics method. Particularly, we will analyse what happens in cohesive materials during multiparticle contacts. We investigated the expression of repulsive force formulated under fractional calculus which is able to control dynamically the transfer and dissipation of energy in granular media. Such approach allows to perform simulations of arbitrary multiparticle collisions and also granular cohesion dynamics.

We discuss a procedure to transfer the description of a fermion system from a subspace of the full shell model space built in terms of collective pairs onto a space of corresponding bosons. We apply the procedure to systems of six nucleons in the 1s0d major shell. We perform exact shell model calculations and compare them with calculations in the collective pair and boson approximations. The effects of the truncation of the boson Hamiltonian and of the consequent violation of the Pauli principle are examined.

The results of the detailed scanning electron microscopy study of PrBa2Cu3O7-δ single crystals after the long-lasting high-temperature post-growth treatment are reported. The presence of the unstable decomposition products on the crystal surface indicates that the onset of superconductivity must be related to the structural transformations in the bulk (approximately 20% of the total volume of the examined crystals). The time-dependent character of the superconductivity in the Pr-123 crystals could be attributed to the migration of defects in the Pr−Ba sublattice from the bulk toward the surface.

The formation of Saturn and its disk is simulated using a new N-body self-gravitational model. It is demonstrated that the formation of the disk and the planet is the result of gravitational contraction of a slowly rotated particle cloud that have a shape of slightly deformed sphere. The sphere was flattened by a coefficient of 0.8 along the axis of rotation. During the gravitational contraction, the major part of the cloud transformed into a planet and a minor part transformed into a disk. The thin structured disk is a result of the electromagnetic interaction in which the magnetic forces acting on charged particles of the cloud originate in the core of the planet. The simulation program gives such parameters of Saturn as the escape velocity of about 35 km/s at the surface, density, rotational velocities of the rings and temperature distribution.

The three dimensional electron density in momentum space ρ(p) and in wave vector space n(k) was reconstructed for cadmium (Cd). The measurements were performed using the two dimensional angular correlation of annihilation radiation (2D-ACAR) technique. Enhanced contributions in the spectra were observed around 5.5 mrad, discussed in terms of a Kahana-like enhancement effect. From another viewpoint, Fermi radii were analyzed in the (λM K), (ALM) and (AHK) planes, and they showed a maximum deviation of about 4% from the free electron Fermi radius. Moreover, comparisons to a radio-frequency size effect (RFSE) experiment and theoretical band structure calculations (using augmented plane wave (APW), linear combination of atomic orbital (LCAO) and linear muffin tin orbital (LMTO) methods) were examined. The results showed a qualitative agreement with both APW and LCAO calculations. However, a favorable agreement with the APW method was determined via Fermi surface dimensions. The differences of bands' occupation of n(k) between the current work and the APW method were argued in view of positron wave function in Cd.

The notions of centrifugal (centripetal) and Coriolis' velocities and accelerations are introduced and considered in spaces with affine connections and metrics [ $$ (\bar L_n ,g) $$ -spaces] as velocities and accelerations of flows of mass elements (particles) moving in space-time. It is shown that these types of velocities and accelerations are generated by the relative motions between the mass elements. They are closely related to the kinematic characteristics of the relative velocity and relative acceleration. The centrifugal (centripetal) velocity is found to be in connection with the Hubble law. The centrifugal (centripetal) acceleration could be interpreted as gravitational acceleration as has been done in the Einstein theory of gravitation. This fact could be used as a basis for workingout new gravitational theories in spaces with affine connections and metrics.

We consider the problem of invariance of distillable entanglement D and quantum capacities Q under erasure of information about single copy of quantum state or channel respectively. We argue that any 2 ⊗N two-way distillable state is still two-way distillable after erasure of single copy information. For some known distillation protocols the obtained two-way distillation rate is the same as if Alice and Bob knew the state from the very beginning. The isomorphism between quantum states and quantum channels is also investigated. In particular it is pointed out that any transmission rate down the channel is equal to distillation rate with formal LOCC-like superoperator that uses in general nonphysical Alice actions. This allows to we prove that if given channel Λ has nonzero capacity (Q → or Q ⟺) then the corresponding quantum state ϱ(Λ) has nonzero distillable entanglement (D → or D ⟺). Follwoing the latter arguments are provided that any channel mapping single qubit into N level system allows for reliable two-way transmission after erasure of information about single copy. Some open problems are discussed.

An investigation was made of the characteristics of the formation of a selfcontroled volume discharge for the pumping of CO2 lasers, i.e. self-sustained volume discharge (SSVD), which involved a preliminary filling of a discharge gap by an electron flux from an auxiliary-discharge plasma. We have found that this method was suitable for large interelectrode gaps, that distortion of the electric field in the gap by the space charge of the electron flux played an important role in the formation of the discharge and that the electrodes could be profiled dynamically during propagation of an electron flux through the discharge gap and a SSVD could form in systems with a strongly inhomogeneous field. High power SSVD based CO2 laser systems have been created and investigated. Another type of self-controled volume discharge without pre-ionization, i.e. a selfinitiated volume discharge (SIVD), in nonchain HF lasers with SF6−C2H6 mixtures was investigated as well in our review. We have established that, after the primary local electrical breakdown of the discharge gap, the SIVD spreads along the gap in directions perpendicular to that of the electric field by means of the successive formation of overlapping diffuse channels under a discharge voltage close to its quasi-steady state value. It is shown that, as new channels appear, the current flowing through the channels formed earlier decreases. The volume occupied by the SIVD increases with increase in the energy deposited in the plasma and, when the discharge volume is confined by a dielectric surface, the discharge voltage increases simultaneously with increase in the current. The possible mechanisms which explain the observed phenomena, namely the dissociation of SF6 molecules and electron attachment SF6 molecules, are examined. A simple analytical model, which makes it possible to describe these mechanisms at a qualitative level, was developed. High power SIVD based HF(DF) lasers have been developed and tested.