Entropy of Spin Fields in Schwarzschild Spacetime

By using the Teukolsky master equation, we consider the gravitational,electromagnetic, and neutrino fields in Schwarzschild spacetime. The free energyand entropy of the spin fields are obtained in terms of the brick-wall model. Itis shown that the entropy of all the spin fields due to the presence of the eventhorizon is proportional to the surface area of the event horizon, and the entropyof the neutrino field is the absolute minimum.     

Relativistic Neutrino Spin Precession in Magnetic Fields

The spin rotation formula of a relativistic neutrino propagating in a constant magnetic field is derived. Contrary to a recent assertion, we find that in the ultrarelativistic limit, the formula actually reduces to the standard Larmor result.     

Random Multi-Overlap Structures and Cavity Fields in Diluted Spin Glasses

We introduce the concept of Random Multi-Overlap Structure (RaMOSt) as a generalization of the one introduced by Aizenman, Sims and Starr for non-diluted spin glasses. We use such concept to find generalized bounds for the free energy of the Viana-Bray model of diluted spin glasses and to formulate and prove the Extended Variational Principle that implicitly provides the free energy of the model. Then we exhibit a theorem for the limiting RaMOSt, analogous to the one found by F. Guerra for the Sherrington–Kirkpatrick model, that describes some stability properties of the model. Last, we show how our technique can be used to prove the existence of thermodynamic limit of the free energy. The present work paves the way to a revisited Parisi theory for diluted spin systems.     

<Emphasis Type="Italic">CPT</Emphasis> Groups of Higher Spin Fields

CPT groups of higher spin fields are defined in the framework of automorphism groups of Clifford algebras associated with the complex representations of the proper orthochronous Lorentz group. Higher spin fields are understood as the fields on the Poincaré group which describe orientable (extended) objects. A general method for construction of CPT groups of the fields of any spin is given. CPT groups of the fields of spin-1/2, spin-1 and spin-3/2 are considered in detail. CPT groups of the fields of tensor type are discussed. It is shown that tensor fields correspond to particles of the same spin with different masses.     

The Hawking Effect for Spin 1/2 Fields

We prove the Hawking effect, for a gravitational collapse of charged star in the case of a charged massive Dirac field.     

Spin 1 Fields in Riemann-Cartan Space-Times via Duffin-Kemmer-Petiau Theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.     

Interacting Spin 0 Fields with Torsion via Duffin-Kemmer-Petiau Theory

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KG field, a result that breaks the usual equivalence between the DKP and the KG fields.Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenböck manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed.On leave from     

Manipulation of Persistent Spin Helix States by Weak External Magnetic Fields

We study theoretically the effect of weak external magnetic fields on persistent spin helix states in semi- conductor two-dimensional electron gases with both Rashba and linear-in-momentum Dresselhaus spin-orbit coupling. We show that in the presence of weak external magnetic fields, some basic properties of a persistent spin helix state, including the dispersion relation between the decay time and the magnitude of the wavevector, the maximum decay time and the value of the characteristic magnitude of the wavevector at which the maximum decay time occurs, will all depend sensitively on the directions of applied external magnetic fields.     

Entropy in Kerr–de Sitter Black Holes with Spin Fields

Generalized master equations due to spin fields are given. We obtain the entropy of electromagnetic, gravitational, Dirac, and scalar fields in a unified form by using the improved brick-wall method—membrane model. The results show that, as the cutoff is properly chosen, the entropy in the black hole satisfies the Bekenstein–Hawking area formula.     

Higher Spin Quaternion Waves in the Klein-Gordon Theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d’Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories.     

Temperley-Lieb-Jones Algebraic Structures in Higher Spin Chain Models

We investigate the Temperley-Lieb-Jones algebraic structures in isomorphic higher spin chain modgls with nearest neighbour interactions and SU(2) symmetry. The Ternperley-Lieb-Jones algebraic constructions for such chains of spins from 1 to 7/2 are presented. For the case of spin-1 we also give the Temperley-Lieb-Jones algebraic representations related to the anisomorphic spin chain with q-deformed SU_q(2) symmetry. Their related spin chain Harniltonians with SU(2) and SU_q(2) symmetries as well as the corresponding solutions of Yang-Baxter equation are also discussed.     

Stochastic Higher Spin Vertex Models on the Line

We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain Markov dualities. Using this, for the systems started in step initial data, we write down nested contour integral formulas for moments and Fredholm determinant formulas for Laplace-type transforms. Taking various choices or limits of parameters, this family degenerates to many of the known exactly solvable models in the Kardar–Parisi–Zhang universality class, as well as leads to many new examples of such models. In particular, asymmetric simple exclusion process, the stochastic six-vertex model, q-totally asymmetric simple exclusion process and various directed polymer models all arise in this manner. Our systems are constructed from stochastic versions of the R-matrix related to the six-vertex model. One of the key tools used here is the fusion of R-matrices and we provide a probabilistic proof of this procedure.     

Spin Transport in a Rashba Ring-Quantum Dot System Pumped by Microwave Fields

We report a theoretical study on producing electrically spin-polarized current in the Rashba ring with parallel double dots embedded, which are subject to two time-dependent microwave fields. By means of the Keldysh Green's function method, we present an analytic result of the pumped current at adiabatic limit and demonstrate that the interplay between the quantum pumping effectand spin-dependent quantum interference can lead to an arbitrarily controllable spin-polarized current in the device. The magnitude and direction of the charge and spin current can be effectively modulated by system parameters such as the pumping phase difference, Rashba precession phase, and the dynamic phase difference of electron traveling in two arms of ring; moreover, thespin-polarization degree of the charge current can also be tuned in the range [-∞, +∞]. Our findings may shed light on the all-electric way to produce the controllable spin-polarized charge current in the field of spintronics.     

The Entropy of Spherically Symmetric Black Holes Due to Arbitrary Spin Fields

Using the membrane model which is based on brick-wall model, we calculated the free energy and entropy of spherically symmetric black holes due to arbitrary spin. The result shows that the entropy of a scalar field and the entropy of a Fermionic field have similar formulas. There is only a coefficient between them.     

Higher Harmonics and Transport Coefficients of Plasmas in Circulary Polarized Magnetic Fields and Additional Electromagnetic Fields

With the methods of kinetic theory on the basis of the Boltzmann and Fokker-Planck kinetic equations the behaviour of a Lorentz plasma in a circularly polarized (rotating) magnetic field (rotation frequency ω), an alternating electric field (frequency ω′) and additional constant electromagnetic fields is investigated. By means of a generalized Fourier expansion it is shown that the above fields create in the plasma currents of the frequencies 0, ω′, ω–ω′,ω, ω+ω′, 2ω–ω′, 2ω, and 2ω+ω′. Transport coefficients are calculated explicitly and the validity of Onsager reciprocity relations and that of Kronig-Kramers relations is discussed. The special case of the electric field induced by the rotating magnetic field is treated separately. Finally, problems of plasma containment are discussed.     

Entropy of Gibbons—Maeda Dilaton Black Hole Due to Arbitrary Spin Fields

Using the membrane model which is based on brick-wall model, we calculated the free energy and entropy of Gibbons—Maeda dilation black hole due to arbitrary spin fields. The result shows that the entropy of a scalar field and the entropy of a fermion field have similar formulas. There is only a coefficient difference between them. Furthermore, both entropies depend on the degeneracy of the field.     

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schrödinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schrödinger equation and some special and limiting cases are outlined.