Super Universality of the Quantum Hall Effect and the?“Large N Picture” of the ? Angle

It is shown that the “massless chiral edge excitations” are an integral and universal aspect of the low energy dynamics of the ϑ vacuum that has historically gone unnoticed. Within the SU(M+N)/S(U(M)×U(N)) non-linear sigma model we introduce an effective theory of “edge excitations” that fundamentally explains the quantum Hall effect. In sharp contrast to the common beliefs in the field our results indicate that this macroscopic quantization phenomenon is, in fact, a super universal strong coupling feature of the ϑ angle with the replica limit M=N=0 only playing a role of secondary importance. To demonstrate super universality we revisit the large N expansion of the CP ^N−1 model. We obtain, for the first time, explicit scaling results for the quantum Hall effect including quantum criticality of the quantum Hall plateau transition. Consequently a scaling diagram is obtained describing the cross-over between the weak coupling “instanton phase” and the strong coupling “quantum Hall phase” of the large N theory. Our results are in accordance with the “instanton picture” of the ϑ angle but fundamentally invalidate all the ideas, expectations and conjectures that are based on the historical “large N picture.”     

Examples of gauged Laplacians on noncommutative spaces

We present two (classes of) examples of gauged Laplacian operators. The first one is a model of spin-Hall effect on a noncommutative four-sphere S _ϑ ⁴ with isospin degrees of freedom, coming from a noncommutative instanton, and invariant under the quantum group SO _ϑ (5). The second one, a Hall effect on a quantum 2-dimensional sphere S _q ², describes ‘excitations moving on the quantum sphere’ in the field of a magnetic monopole with symmetry coming from the quantum group SU _q (2). For both models, ample symmetries provide a complete diagonalization.     

Quantum corrections to thermodynamics of polar hard sphere fluids

The quantum corrections to the thermodynamic properties of polar hard sphere fluids and fluid mixtures are estimated taking into account the influence of dipole and quadrupole moments. Expressions are given for the second virial coefficient, free energy and pressure and results are given for different values ofμ* andϑ*. The first order quantum correction arises due to the translational contribution only. The quantum effect increases with density,μ* andϑ*. Numerical results are also estimated for binary mixtures of (i) hard spheres and dipole hard spheres and (ii) hard spheres and quadrupole hard spheres. The ‘excess’ free energy for dipole hard sphere binary mixture is also reported. It is found that the ‘excess’ quantum effect depends on the concentration and the particle diameter ratio and increases with increase ofμ* andϑ*.     

On the theory of the integral quantized Hall effect

Summary In the present paper the integral quantum Hall effect is studied using the Schrauben functions which are suitable eigenfunctions to describe the quantum transport in uniform electric and magnetic fields. The effect of Landau band structure on the Hall quantization is investigated. A model calculation of the conductivities σ_xy and σ_yy is presented and the onset of a Hall current dissipation is discussed. Also, the quantum oscillations of a free-electron gas into the quantum Hall regime are studied, including the electric-field effect.     

Dendritic and eutectic growth in Sb<Subscript>60</Subscript>Ag<Subscript>20</Subscript>Cu<Subscript>20</Subscript> ternary alloy

The rapid solidification of Sb60Ag20Cu20 ternary alloy was realized by high undercooling method, and the maximum undercooling is up to 142 K (0.18TL). Within the wide undercooling range of 40-142 K, the solidified microstructures are composed of (Sb), θand ε phases. High undercooling enlarges the solute solubility of (Sb) phase, which causes its crystal lattice to expand and its crystal lattice constants to increase. Primary (Sb) phase grows in two modes at small undercoolings non-faceted dendrite growth is the main growth form; whereas at large undercoolings faceted dendrite growth takes the dominant place. The remarkable difference of crystal structures between (Sb) and θphases leads to (θ Sb) pseudobinary eutectic hard to form, whereas strips of θform when the alloy melt reaches the (θ Sb) pseudobinary eutectic line. The cooperative growth of θand ε phases contributes to the formation of (ε θ) pseudobinary eutectic easily. In addition, the crystallization route has been determined via microstructural characteristic analysis and DSC experiment.     

A unified theory of weak interactions

A gauge model for the weak interactions of the leptons (v _e, e, μ, ν_μ) and the quarks (q _p, q_n,qλ,q _p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW ^±) and two neutrals are necessarily heavier than the third (W ⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless. The dominant charged weak currents coupling toW ^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions. The Cabibbo angleϑ _c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ _c = ±π/8, | tanϑ _c | = √2 − 1 (an alternative solution | tanϑ _c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ _c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ _c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ _c | = 0.4.     

Fedosov Deformation Quantization as a BRST Theory

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold ℳ is presented as a second class constrained surface in the fibre bundle ?^* _ρℳ which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The second class system is converted into the first class one by continuation of the constraints into the extended manifold, being a direct sum of ?^* _ρℳ and the tangent bundle Tℳ. This extended manifold is equipped with a nontrivial Poisson bracket which naturally involves two basic ingredients of Fedosov geometry: the symplectic structure and the symplectic connection. The constructed first class constrained theory, being equivalent to the original symplectic manifold, is quantized through the BFV-BRST procedure. The existence theorem is proven for the quantum BRST charge and the quantum BRST invariant observables. The adjoint action of the quantum BRST charge is identified with the Abelian Fedosov connection while any observable, being proven to be a unique BRST invariant continuation for the values defined in the original symplectic manifold, is identified with the Fedosov flat section of the Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized as a conventional product of the quantum BRST invariant observables. Received: 28 April 2000 / Accepted: 6 December 2000     

Charged particle orbits in the field of two charges placed symmetrically near a schwarzschild black hole

From the Copson and Linet solution for the electrostatic field due to a point charge near a Schwarzschild black hole, we have deduced the field due to two equal charges placed symmetrically (diametrically opposite) about the hole. It turns out that the motion of a test-charged particle is completely solvable only in the equatorial plane, because theϑ-equation does not yield the first integral forϑ ≠π/2. We have however considered circular orbits about the axis forϑ=constant ≠π/2 by requiring bothϑ andr to remain fixed all through the motion. Forϑ ≠π/2 orbits, in contrast to the similar classical situation, there occur forbiddenϑ-ranges. This seems to be a relativistic effect.     

Kinetics of the diffusion of an impurity atom on a square lattice

An analytical study of the migration of an embedded impurity atom over a solid surface under the influence of the diffusion of vacancies is presented. The case of small surface coverages of both vacancies ϑ _v and impurity atoms ϑ _i , with ϑ _i ≪ ϑ _v ≪ 1, is considered. It is shown that the realization of multiple collisions of a single impurity atom with vacancies imparts a Brownian character to its motion. At long times, the dependence of the mean square displacement on the time differs little from the linear, whereas the spatial density distribution is close to the Gaussian, features that makes it possible to introduce a diffusion coefficient. For the latter, an analytical expression is derived, which differs from the product of the diffusion coefficient of vacancies and their relative concentration only by a numerical factor η. The dependence of the diffusion coefficient of an impurity atom on the ratio of the frequency of its jumps to the frequency of jumps of vacancies is analyzed. In the kinetic mode, at ω ≪ 1, the diffusion coefficient of impurity atoms depends linearly on ω, whereas at ω ≫ 1, a saturation is observed; i.e., the dependence on the frequency of jumps of the impurity atom disappears. Nevertheless, the value of η remains less than unity, and no total entrainment of impurity atoms with vacancies occurs.     

A Locally Compact Quantum Group Analogue of the Normalizer of SU(1,1) in SL(2, ℂ)

 S.L. Woronowicz proved in 1991 that quantum SU(1,1) does not exist as a locally compact quantum group. Results by L.I. Korogodsky in 1994 and more recently by Woronowicz gave strong indications that the normalizer of SU(1,1) in SL(2,ℂ) is a much better quantization candidate than SU(1,1) itself. In this paper we show that this is indeed the case by constructing , a new example of a unimodular locally compact quantum group (depending on a parameter 0<q<1) that is a deformation of . After defining the underlying von Neumann algebra of we use a certain class of q-hypergeometric functions and their orthogonality relations to construct the comultiplication. The coassociativity of this comultiplication is the hardest result to establish. We define the Haar weight and obtain simple formulas for the antipode and its polar decomposition. As a final result we produce the underlying C ^* -algebra of . The proofs of all these results depend on various properties of q-hypergeometric ₁ϕ₁ functions. Received: 28 June 2001 / Accepted: 25 July 2002 Published online: 10 December 2002 RID="*" ID="*" Post-doctoral researcher of the Fund for Scientific Research – Flanders (Belgium) (F.W.O.) Communicated by L. Takhtajan     

Probing the neutrino mass matrix in next-generation neutrino oscillation experiments

We review the current status of the neutrino mass and mixing parameters needed to reconstruct the neutrino mass matrix. A comparative study of the precision in the measurement of oscillation parameters expected from the next-generation solar, atmospheric, reactor-and accelerator-based neutrino experiments is presented. We discuss the potential of 0νββ experiments in determining the neutrino mass hierarchy and the importance of a better ϑ ₁₂ measurement for it. The text was submitted by the author in English.     

Quantization of a nonlinear oscillator as a model of the harmonic oscillator on spaces of constant curvature: One- and two-dimensional systems

The quantum version of a nonlinear oscillator, previously analyzed at the classical level, is studied first in one dimension and then in two dimensions. This is a problem of quantization of a system with position-dependent mass of the form m = (1 + λx ²)⁻¹ and with a λ-dependent nonpolynomial rational potential. The quantization procedure analyzes the existence of Killing vectors and makes use of an invariant measure. It is proved that this system can be considered as a model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature. The text was submitted by the authors in English.     

Magneto-intersubband zener tunneling in a wide GaAs quantum well at high filling factors

The dependence of the differential resistance r _xx on the dc current density J _dc in a wide GaAs quantum well with two occupied size quantization subbands has been investigated at the temperature T = 4.2 K in the magnetic fields B < 1 T. A peak, whose position is given by the relation 2R _c eE _H = ħω_c/2, where R _c is the cyclotron radius, E _H is the Hall electric field, and ω_c is the cyclotron frequency, has been observed in the r _xx (J _dc) curves at high filling factors. The experimental results are attributed to Zener tunneling of electrons between the Landau levels of different subbands.     

Dynamics of the superconducting mixed state in YBa2Cu3O7-δ/PrBa2Cu3O7-δ superlattices in radio frequency regime

Epitaxial multilayers of YBa₂Cu₃O_7-δ and P₁Ba₂Cu₃O_7-δ have been deposited on (100) cut SrTiO₃ substrates using the technique of pulsed laser deposition. Standard ϑ-2ϑ X-ray diffraction measurements on the films showed excellent superlattice reflections. The mixed state of these superlattices has been probed through measurements of radio frequency penetration depth (λ) as a function of temperature (T), magnetic field (H) and it’s orientation (ϑ) with respect to the planes of the superlattices. These data reflect the two-dimensional nature of the mixed state in these systems.     

The estimation of the Z′ gauge boson mass in E 6 models

The aim of this study is to estimate the Z′ boson mass by using the calculations of the decay width of Z′(ϑ) boson. So, the decay width of the extra Z boson is calculated numerically in effective rank 5 models for different mixing angles ϑ of the model and for different mass values of the extra Z boson. The decay width of Z′ boson to the Standard Model (SM) fermions is found to be between 4.42 and 19.36 GeV and the full decay width of Z′ boson to all particles is found to be between 20.88 and 37.15 GeV. We calculated the full decay width at the angle ϑ ≊ 0 for Z′ and Z ₂ → Z′. The full decay width of Z′ boson is written in a single equation according to our calculations. By using these calculations and the previous works the mass of Z′ boson and the number of generations of the exotic particles are estimated. The article is published in the original.     

Magnetic breakdown and quantum magnetotransport with a constant pseudospin under tilted magnetic fields in an n -In x Ga1? x As/GaAs double quantum well

A procedure is proposed for precise scanning of the (B _⊥, B _‖) plane between the magnetic field projections that are perpendicular and parallel to (quasi-)two-dimensional layers when measuring their longitudinal and Hall magnetoresistances. Investigations of a n-In _x Ga_1−x As/GaAs double quantum well (x ≈ 0.2) performed using this procedure make it possible to reveal a number of the features of the magnetoresistance, which appear due to a complex energy spectrum of the double quantum well in a parallel field, and to separate them from the structures associated with the magnetic breakdown. The trajectories representing the features of the magnetoresistance in the (B _⊥, B _‖) plane are described by the semiclassical calculations of the quantization of the energy spectrum of the double quantum well under the action of the perpendicular field component. The structures appearing due to the magnetic breakdown are amplified with increasing the total magnetic field magnitude and, in the samples with low mobility, completely suppress the features caused by the motion of an electron with a constant pseudospin component. The peaks corresponding to the magnetic breakdown are split in a strong parallel field due to the spin splitting of the Landau levels. These splittings correspond to the effective Landé factor |g*| ≈ 3. Original Russian Text ? M.V. Yakunin, S.M. Podgornykh, V.N. Neverov, 2007, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 132, No. 1, pp. 241–249.     

Constant-cutoff approach to Λ (1405) resonance in the bound-state soliton model

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB = 1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study strong and electromagnetic properties of the Λ(1405) hyperon in the bound-state approach to theSU(3)-soliton model for the hyperons, withSU(3)-symmetry breaking. We calculate the strong coupling constantg _Λ*NK; , the magnetic moment of Λ*, the mean square radii, and the radiative decay amplitudes. Finally we compare the present results with those obtained using other models and with the available empirical data. We show that there is a general qualitative agreement between our results and the results of other models and available empirical data, except for the Λ*πΣ coupling, which, as in the case of the complete Skyrme model, vanishes in the second-order approximation of the kaon fluctuations used in this work.     

Influence of quantization of band states on the effective electron mass in quaternary alloys

Summary An attempt is made to study the effective electron mass in quaternary alloys, taking a In_1−x Ga _x As _y P_1−y lattice matched to InP, by using the three-band Kane model under different physical conditions,e.g. bulk specimens, magnetic quantization, cross-field configuration, quantum well, electric-field-aided quantum well, magnetic-field-aided quantum well, quantum well under cross fields, quantum well wires, electric-field-aided quantum well wires, magnetic-field-aided quantum well wires and quantum well wires under cross fields by formulating the respective expressions. We have plotted the effective Fermi level mass with various physical variables under different conditions. In the presence of a quantizing magnetic field the effective mass depends on the spin splitting of Landau levels due to the spin-orbit splitting parameter of the valence bands. Under cross-field configuration and the various quantum confined low-dimensional systems, the effective masses depend on the respective quantum numbers in addition to the Fermi energies even for parabolic models because of the inherent features of such systems. In addition, the corresponding results for relatively wide-gap materials have also been obtained from our generalized formulations under certain limiting conditions.     

Quantization of gauge fields through fibre bundle multiconnectivity

A geometric model for the quantum nature of interaction fields is proposed. We utilize a trivial fibre bundle whose typical fibre has a multiconnectivity characterized by a discrete group Γ. By seeing Γ as a gauge group with global action on each fibre, we show that the corresponding field strength is non-zero only on the future part of the light cone whose vertex is at the interaction point. When the interaction is submitted to the symmetries of a Lie group G, we consider the gauge group G x Γ. The field strength of the gauge having this group includes a term expressing the quantization of the interaction field described by G. This geometric interpretation of quantization makes use of topological arguments similar to those applied to explain the Aharonov-Bohm effect. Two examples show how this interpretation applies to the cases of electromagnetic and gravitational fields.      

Condition of strong magnetic field in the mode of quantum reluctance oscillations

The volume (3D), quasi-two-dimentional (Q2D), and two-dimentional (2D) oscillations of degenerated electrons of the Shubnikov-de Haase reluctance reveal common properties. The region of quantum oscillations is bounded (in the magnetic field) from below by the weak field condition (ω_cτ_t≤1) and from above by the quantum limit condition (ξ_F≥ħω_c/2). The monotonic oscillation component is saturated for the occupied main conduction E_m-subband and excitation E_p-subband of dimensional quantization for the Q2D and 2D electron systems in strong magnetic fields. The reluctance of the Q2D system in the quantum limit changes according to a law ∼B ^α with α ≈ 2.6–2.8. The oscillation amplitude is described by an exponential dependence on the magnetic field strength and temperature, similarly to the 3D case. This is caused by the identity of physical conditions and the topology of resonant escape of the Landau levels out of the Fermi surface. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 33–39, March, 2006.