Spinor fields at spacelike infinity

The concept of a spinor structure at spacelike infinity is introduced for space-times which are asymptotically flat. It is shown how zero-rest-mass fields on space-time acquire smooth limits on this structure and that these limits satisfy certain differential equations characterized by the helicity and regularity of the field. The geometry of the limits of twistor fields is also discussed, and it seems possible that one can define the momentum and angular momentum of an asymptotically flat space-time in terms of a twistor space at spacelike infinity.     

Conformal invariance of quantum fields in two-dimensional space-time

Our investigations of conformal invariance are based on the theory of analytic representations of the conformal group and its universal covering group. With its help the action of the conformal group on free massless fields, Greenberg fields, Wick products of these fields, and the Thirring fields is studied. In this context we find an infinite set of new operator solutions for the Thirring model that are all equivalent to each other. Explicit constructions of the nonlocal special conformal transformations of all these fields are given.     

On the space of quantum fields in massive two-dimensional theories

For a large class of integrable quantum field theories we show that the S-matrix determines a space of fields which decomposes into subspaces labeled, besides the charge and spin indices, by an integer k. For scalar fields k   is non-negative and is naturally identified as an off-critical extension of the conformal level. To each particle we associate an operator acting in the space of fields whose eigenvectors are primary (k=0$k=0$) fields of the massive theory. We discuss how the existing results for models as different as Zn$Z_n$, sine-Gordon or Ising with magnetic field fit into this classification.     

Perfect fluid solution of Einstein equations with two spacelike killing fields

We present a perfect fluid solution of Einstein's equations, admitting a Killing tensor with Segre characteristics [(11)(11)] and two commuting spacelike Killing fields. The Equation of state has no physical meaning but is the same as that of the Wahlquist solution,e+3p=constant, which admits the same Killing tensor, as our solution, although the two Killing fields are timelike and spacelike, respectively.     

A quantum pseudodot system with two-dimensional pseudoharmonic oscillator in external magnetic and Aharonov-Bohm fields

Using the Nikiforov–Uvarov (NU) method, the energy levels and the wave functions of an electron confined in a two-dimensional (2D) pseudoharmonic quantum dot are calculated under the influence of temperature and an external magnetic field inside dot and Aharonov–Bohm (AB) field inside a pseudodot. The exact solutions for energy eigenvalues and wave functions are computed as functions of the chemical potential parameters, applied magnetic field strength, AB flux field, magnetic quantum number and temperature. Analytical expression for the light interband absorption coefficient and absorption threshold frequency are found as functions of applied magnetic field and geometrical size of quantum pseudodot. The temperature dependence energy levels for GaAs semiconductor are also calculated.     

Nonexistence of massless zero-spin particles in relativistic quantum mechanics

The Klein-Gordon equation is cast, using its two-components version, into a form which exactly parallels the Dirac equation and which is used to discuss the Klein-Gordon analogs of the unitary and nonunitary transformations of physical interest appearing in the latter. In particular, it is found that massless zero-spin particles do not exist within the framework of this theory.     

Quantum computation with two-dimensional graphene quantum dots

We study an array of graphene nano sheets that form a two-dimensional S=1/2 Kagome spin lattice used for quantum computation. The edge states of the graphene nano sheets are used to form quantum dots to confine electrons and perform the computation. We propose two schemes of bang-bang control to combat decoherence and realize gate operations on this array of quantum dots. It is shown that both schemes contain a great amount of information for quantum computation. The corresponding gate operations are also proposed.     

Quantum computation with two-dimensional graphene quantum dots

We study an array of graphene nano sheets that form a two-dimensional S=1/2 Kagome spin lattice used for quantum computation.The edge states of the graphene nano sheets are used to form quantum dots to confine electrons and perform the computation.We propose two schemes of bang-bang control to combat decoherence and realize gate operations on this array of quantum dots.It is shown that both schemes contain a great amount of information for quantum computation.The corresponding gate operations are also proposed.     

Control of nanoparticles with arbitrary two-dimensional force fields

An anti-Brownian electrophoretic trap is used to create arbitrary two-dimensional force fields for individual nanoscale objects in solution. The trap couples fluorescence microscopy with digital particle tracking and real-time feedback to generate a position-dependent electrophoretic force on a single nanoparticle. The force may vary over nanometer distances and millisecond times and need not be the gradient of a potential. As illustrations of this technique, I study Brownian motion in harmonic, power-law, and double-well potentials.     

Influence of twinning planes on upper critical fields

Within the framework of a Ginzburg-Landau theory for a scalar order parameter, we discuss the effect of the presence of twinning planes on the behavior of the upper critical field as function of the temperature. In particular we study the case of a finite array of planes in the region of weak magnetic field, both from the analytical and the numerical point of view.     

Rotating quantum cosmological models with wave fields

The quantum evolution of homogeneous rotating cosmological models of the Gödel type with spinor and scalar fields is considered within the framework of the formalism of superspace quantization. De Witt's equation for a rotating cosmological model is shown to take the form of a Schrödinger equation in which the role of time is played by the phase of the spinor field, and it becomes possible to determine correctly the probability that rotating models lacking an initial singularity exist.K. D. Ushinskii Yaroslav Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 41–44, January, 1993.     

Fock representations of quantum fields with generalized statistics

We develop a rigorous framework for constructing Fock representations of quantum fields obeying generalized statistics. The main features of these representations are investigated. Various aspects of the underlying mathematical structure are illustrated by means of explicit examples.     

On fermi quantum fields constructed from bose quantum fields and their applications

In former papers a representation of the quantum Fermi and para-Fermi fields was proposed. This representation is such that the only basic quantum entities are Bose quantum fields. In this paper we show several possibilities of application: (i) to lower the number of elementary particles; (ii) to describe as separate states of a fundamental particle other particles that presently are considered as different, and to induce an ordering among them; (iii) to obtain relations among the quantum numbers of those particles; (iv) to obtain a physical picture of some unstable particles. This article is concerned with the physical interpretation of the formalism, and some of the statements that are contained here have a conjectural character.     

The equilibrium shape of a two-dimensional crystal between parallel planes

By applying rather standard techniques for equilibrium crystal shapes (Wulff construction), we derive a construction for the equilibrium shape of a 2D crystal grown between two parallel plane substrates. The critical distance of the substrates at which this crystal splits into two parts is computed as a function of the wall free energy of the substrates. This may open new perspectives for the measurement of wall free energies.     

Nonexistence of spatially bounded force-free magnetic fields: ascaling point of view

Force-free magnetic fields obey the vector differential equation ∇xB=αB. In the absence of any displacement current, the magnetic force on the conduction current is then zero. A previous proof of the nonexistence of spatially bounded force-free fields is simplified and is shown to be purely mathematical in nature, with no need to introduce non-magnetic stresses. A new nonexistence proof, based only on the scaling properties of the differential equation, is presented     

The two-dimensional quantum Euclidean algebra

The algebra dual to Woronowicz's deformation of the two-dimensional Euclidean group is constructed. The same algebra is obtained from SU _q (2) via contraction on both the group and algebra levels.