Narrow Results

Path integral representations for generalized Schrödinger operators obtained under a class of Bernstein functions of the Laplacian are established. The one-to-one correspondence of Bernstein functions with Lévy subordinators is used, thereby the role of Brownian motion entering the standard Feynman–Kac formula is taken here by subordinate Brownian motion. As specific examples, fractional and relativistic Schrödinger operators with magnetic field and spin are covered. Results on self-adjointness of these operators are obtained under conditions allowing for singular magnetic fields and singular external potentials as well as arbitrary integer and half-integer spin values. This approach also allows to propose a notion of generalized Kato class for which an L^p-L^q bound of the associated generalized Schrödinger semigroup is shown. As a consequence, diamagnetic and energy comparison inequalities are also derived.

This paper presents of development of quantum transport equations for barrier devices with both electron and hole transport in dilute magnetic semiconductor (DMS) structures. The equations are developed from the time dependent equation of motion of the density matrix equation in the coordinate representation, from which both the spin drift and diffusion and transient Wigner equations are obtained, for a system in which high 'g' factor materials result in significant spin-splitting of the valence and conduction bands. Then for a structure in which the DMS layer is confined to the first barrier solutions to the coupled Poisson's and spin dependent Wigner equations yield the IV and carrier distributions. Negative differential conductance as well as the significant unequal spinup and spin down charge distributions are obtained.

We review the results of our current research on quantum engineering which include the theory, modeling and simulations of quantum devices for potential applications to threat reduction and homeland security. In particular, we discuss: (i) scalable solid-state quantum computation with qubits based on (a) nuclear spins of impurity atoms in solids, (b) superconducting junctions, and (c) unpaired electron spins of spin radicals in self-assembled organic materials; (ii) quantum neural devices; (iii) quantum annealing; (iv) novel magnetic memory devices based on magnetic tunneling junctions with large tunneling magnetoresistance; (v) terahertz detectors based on microcantilever as a light pressure sensor; (vi) BEC based interferometers; (vii) quantum microscopes with a single-spin resolution based on (a) a magnetic resonant force microscopy and (b) an optically detected magnetic resonance; and (viii) novel approach for suppression of fluctuations in free space high-speed optical communication. Finally, we describe the similarities between the behavior of cross sections in reactions with heavy nuclei in the regions of strongly overlapped resonances and electron conductivity in semiconductor heterostructures.

Two terminal devices have traditionally provided band-structure based high frequency operation. Third terminal control often involves hybrid design approaches. The presence of diluted magnetic semiconductor layers in device fabrication should permit the magnetic field to function as a pseudothird terminal. This is discussed for single barrier, double barrier and superlattice structures, where control is demonstrated. The limits of high frequency operation are discussed in general terms with application to barrier devices and superlattices containing DMS layers.

Recent advances in successful operation of silicon-based devices where transport is dependent on electron magnetic moment, or "spin", could provide a future alternative to CMOS for logic processing. The basics of this spin electronics (Spintronics) technology are discussed and the specific methods necessary for application to silicon are described. Fundamental measurements of spin polarization and spin precession are demonstrated.

In the weak field limit of Einstein gravity, there are gravitational analogues of the vector potential and the magnetic field. The equivalence principle guides us to a magnetic-like interaction arising from inertial acceleration. The spin precession due to this accelero-magnetic field is identified as the Thomas precession. Hence the torque that is responsible for the precession of the spin is identified as resulting from a physical interaction with a magnetic-like inertial-field. Once the equivalence principle is assumed to some accuracy, well supported by precision tests, this implies that the average effect of the accelero-magnetic field on a classical or quantum gyroscope is the same as that of the gravito-magnetic field on a gyroscope. Precision spectroscopy of spin-orbit doublets in atoms is hence an indirect high precision test of the existence and properties of the gravito-magnetic field. This also implies that the planned and current experiments will not see any deviations from the predictions of general relativity. This line of thought is extended to a brief discussion on the possibility of formulating an independent equivalence principle for the spin.

The production asymmetry of both π and ρ mesons in the reaction p↑p→hX is calculated in a two-component model in which hadrons are produced by a nonperturbative recombination process and by fragmentation of quarks in the final state. Thomas precession in the recombination mechanism seems to be responsible of the single spin asymmetry. We obtain a good description of experimental data. Predictions of single spin asymmetries for ρ production at RHIC energies are presented.

The nucleon has been used as a laboratory to investigate its own spin structure and quantum chromodynamics. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture of the transition region from the confinement regime of the theory to its asymptotic freedom regime. Insight for some aspects of the theory is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Gerasimov–Drell–Hearn, Bjorken and Burkhardt–Cottingham). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The sum rules are verified to good accuracy assuming that no singular behavior of the structure functions is present at very high excitation energies. The higher-twist contributions have been examined through the moments evolution as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g₁ at momentum transfer of 0.1 GeV² but fail to reproduce the neutron data in the case of the generalized polarizability δ_LT.

The personal view on some recent aspects of average spin and orbital momenta of partons in nucleon is discussed and compared with the previous understanding. The special attention is payed to the strangeness polarization mediated by gluon anomaly and treatment of the strange quarks in a heavy ones in a multiscale nucleon. The crucial role in the orbital structure of nucleon is played by relocalization (Belinfante) invariance and Equivalence Principle (EP). The new manifestation of EP for spin 1 particles is suggested and discussed.

We examine the large-x QCD evolution of the twist-three gluonic-pole strength defining an effective T-odd Sivers function, where evolution of the T-even transverse-spin DIS structure function g₂ is multiplicative. The result corresponds to a colour-factor modified spin-averaged twist-two evolution.

As two generalizations of Einstein's general relativity, the nontrivial spacetime torsion and the compact extra dimensions have been largely studied in the literature. In this paper, by combining a torsioned Kaluza–Klein scheme and the field-theory cosmic string theory, we discuss that a higher-dimensional torsion component can be expressed in terms of the usual four-dimensional field strength two-form, and this torsion form can then get trapped into the cores of the cosmic strings and further relate to the intrinsic spins of the strings.

We investigate a squark cascade decay, i.e. . It is shown that some information on the mass and spin of the supersymmetric particles might be obtained from the cascade decay chain at the Large Hadron Collider at CERN.

We calculate the twist-three distribution f_⊥(x, k^⊥) contributing to Cahn effect in unpolarized semi-inclusive deep inelastic scattering. We use light-front Hamiltonian technique and take the state to be a dressed quark at one-loop in perturbation theory. The "genuine twist-three" contribution comes from the quark–gluon interaction part in the operator and is explicitly calculated. f_⊥(x, k^⊥) is compared with f₁(x, k^⊥).

The Fierz transformations (Ft) for SU(2) and SU(3) operators in eighth-order fermion interactions are derived. These terms appear in expansions in terms of fermion currents of the following form: I₁ I₂ I₃ I₄ and also the composite , where Γ⁽ⁱ⁾ are either the SU(2) Pauli matrices or SU(3) Gell-Mann matrices. The calculation is carried out using the exchange projector operators.

Recently the ATLAS and CMS experiments at the LHC have found a Higgs-like boson h with a mass around 125 GeV from several decay modes. The decay mode h →γγ is one of the most important modes in studying whether h is actually the Standard Model (SM) Higgs boson. Current data indicate that h→γγ has a branching ratio larger than the SM prediction for h being identified as the SM Higgs boson. To decide whether the h discovered at the LHC is the SM Higgs boson, more data are needed. We study how γγ collider can help to provide some of the most important information about the Higgs boson properties. We show that a γγ collider can easily verify whether the enhanced h →γγ observed at the LHC hold. Different models can be tested by studying Higgs boson decay to γZ. Studying angular distribution of the γγ through on-shell production of h and its subsequent decays into a γγ pair can decide whether the Higgs-like boson h at the LHC is a spin-0 or a spin-2 boson.

We consider a homogeneous and isotropic Universe, described by the minisuperspace Lagrangian with the scale factor as a generalized coordinate. We show that the energy of a closed Universe is zero. We apply the uncertainty principle to this Lagrangian and propose that the quantum uncertainty of the scale factor causes the primordial fluctuations of the matter density. We use the dynamics of the early Universe in the Einstein–Cartan theory of gravity with spin and torsion, which eliminates the big-bang singularity and replaces it with a nonsingular bounce. Quantum particle production in highly curved spacetime generates a finite period of cosmic inflation that is consistent with the Planck satellite data. From the inflated primordial fluctuations we determine the magnitude of the temperature fluctuations in the cosmic microwave background, as a function of the numbers of the thermal degrees of freedom of elementary particles and the particle production coefficient which is the only unknown parameter.

We show that a scalar field without a kinetic term in the Lagrangian density, coupled to the covariant divergence of the torsion vector in the Einstein–Cartan theory of gravity, becomes kinetic in its general-relativistic equivalent formulation. The resulting kinetic term is negative: such a scalar field could be a source of phantom dark energy.

We define a 3-generator algebra obtained by replacing the commutators with anticommutators in the defining relations of the angular momentum algebra. We show that integer spin representations are in one to one correspondence with those of the angular momentum algebra. The half-integer spin representations, on the other hand, split into two representations of dimension . The anticommutator spin algebra is invariant under the action of the quantum group SO_q(3) with q=-1.

The gravitational effects in the relativistic quantum mechanics are investigated in a relativistically derived version of Heaviside's speculative gravity (in flat space–time) named here as "Maxwellian gravity." The standard Dirac's approach to the intrinsic spin in the fields of Maxwellian gravity yields the gravitomagnetic moment of a Dirac (spin ½) particle exactly equal to its intrinsic spin. Violation of the Equivalence Principle (both at classical and quantum-mechanical level) in the relativistic domain has also been reported in this work.

Unification ideas motivate the formulation of field equations on an extended matrix-spin space. Demanding that the Poincaré symmetry be maintained, one derives scalar symmetries that are associated with flavor and gauge groups. Boson and fermion solutions are obtained with a fixed representation. A field theory can be equivalently written and interpreted in terms of elements of such a space and is similarly constrained. At 5+1 dimensions, one obtains isospin and hypercharge SU(2)_L×U(1) symmetries, their vector carriers, two-flavor charged and chargeless leptons, and scalar particles. Mass terms produce breaking of the symmetry to an electromagnetic U(1), a Weinberg's angle with sin²(θ_W)=0.25, and additional information on the respective coupling constants. The particles' underlying spin symmetry gives information on their masses; one reproduces the Standard Model ratio M_Z/M_W, and predicts possible Higgs masses of M_H≈114 and M_H≈161 GeV, at tree level.