Gauge theories in the many-gluon limit

We argue that the idea that the dynamics of a gauge theory simplifies in the limit N → ∞, where N is the number of colors, can be invoked even if the gauge group is an exceptional Lie group, rather than one of the classical groups. We also point out that quantum tunneling phenomena can in some cases survive in the N → ∞ limit, contrary to the usual claim that the N → ∞ limit is “classical.”     

Rashba splitting of kinetically bound states in gated HgCdTe surface quantum wells

The Rashba spin–orbit splitting of 2D electron gas in gated HgCdTe surface quantum wells on n-HgCdTe is studied experimentally (by the magneto-capacitance spectroscopy of Landau level method) and theoretically with emphasis on the peculiarities of spectrum at surface densities N_s corresponding to the onset of 2D subbands occupancy, where the regime of kinetic binding is realized. Although the spin–orbit splitting in kinetic confinement regime is small, the “Rashba polarization” Δn/n can achieve 100% because of strong difference in values of cutoff wave vector k_c for different spin-split sub-subbands.     

Compositionally asymmetrical multiquantum wells: “Pseudo-molecules” for giant optical nonlinearities in the infrared (9–11 μm)

Intersubband transitions in quantum well have extremely large oscillator strengths and induce strong nonlinear effects in structures where inversion symmetry is broken, realized by growing AlGaAs quantum wells with asymmetrical A1 gradients. These compositionally asymmetrical multiquantum wells may thus be viewed as giant “quasimolecules” optimized for optimal nonlinearities in the mid infrared. Optical rectification as well as second harmonic generation have been measured in those structures using a continuous CO₂ laser. At 10.6 μm the nonlinear coefficients are more than 3 orders of magnitude higher in these samples than for bulk GaAs (i.e. χ₀⁽²⁾ = 5.3 × 10⁻⁶m/V, χ_2ω⁽²⁾ = 7.2 × 10⁻⁷ m/V) and are in good agreement with theoretical predictions. We present more complex “pseudo-molecules” involving weakly coupled quantum wells. The optical rectification effects in these devices are so large χ₀⁽²⁾ = 1.6 × 10⁻³ m/V) that application to infrared detection may be envisioned.     

Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

Quantum mechanics with difference operators

A formulation of quantum mechanics with additive and multiplicative (q-) difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding quantisation method. After a short discussion this method is translated step-by-step to a framework based on difference operators. To restrict the resulting plethora of possible quantisations additional assumptions motivated by simplicity and plausibility are required. Multiplicative difference operators and the corresponding q-Borel kinematics are given on the circle and its N-point discretisation; the connection to q-deformations of the Witt algebra is discussed. For a “natural” choice of the q-kinematics a corresponding q-difference evolution equation is obtained. This study shows general difficulties for a generalisation of a physical theory from a known one to a “new” framework.     

Photoexcited carrier dynamics in aligned InAs/GaAs quantum dots grown on strain-relaxed InGaAs layers

Carrier dynamics in aligned InAs/GaAs quantum dots (QDs) grown on cross-hatched patterns induced by metastable In_xGa_1−xAs layers have been studied by time-resolved photoluminescence. The low-temperature carrier lifetimes were found to be of the order of 100–200 ps and determined by carrier trapping and nonradiative recombination. Comparisons with control “nonaligned” InAs QDs show remarkable differences in dependence of peak PL intensities on excitation power, and in PL decay times dependences on both temperature and excitation intensities. Possible origin of traps, which determine the carrier lifetimes, is discussed.     

Double-dielectric-mirror InGaN/GaN microcavities formed using selective removal of an AlInN layer

We describe the fabrication and optical properties of a 3λ/2 InGaN/GaN-based microcavity using “upper” and “lower” silica/zirconia mirrors. The fabrication of this structure involved selective removal of an AlInN layer following multistep thinning of a free-standing GaN substrate. Photoluminescence spectra show a narrowing of the excitonic emission from InGaN/GaN quantum wells in the microcavity, giving a cavity quality factor Q exceeding 400.     

Dynamical behavior of the phase transition of strained from atomistic simulations

Using an atomistic shell model we study the temperature dependence of the ferroelectric properties of BaTiO₃ under biaxial compressive strain applicable to growth on perovskites substrate. Molecular dynamics simulations show a “r→c→p” sequence of phase transitions when temperature is increased, and the absence of an “ac phase”. The first-order paraelectric-to-ferroelectric phase transition presents in bulk changes to a second-order one as a consequence of the in-plane constraint imposed by the mechanical boundary conditions. From the tetragonal ferroelectric c phase, the transition takes place in a finite range of temperature where the lattice parameter normal to the plane keeps approximately constant until T_c is reached. Analysis of the local polarization behavior reveals an order–disorder dynamics as the dominant mechanism of the transition.     

The Multidimensional Filter Diagonalization Method: I. Theory and Numerical Implementation

The theory and numerical aspects of the recently developed multidimensional version of the filter diagonalization method (FDM) are described in detail. FDM can construct various “ersatz” or “hybrid” spectra from multidimensional time signals. Spectral resolution is not limited by the time-frequency uncertainty principle in each separate frequency dimension, but rather by the total joint information content of the signal, i.e., N_total = N₁ × N₂ × × N_D, where some of the interferometric dimensions do not have to be represented by more than a few (e.g., two) time increments. It is shown that FDM can be used to compute various reduced-dimensionality projections of a high-dimensional spectrum directly, i.e., avoiding construction of the latter. A subsequent paper (J. Magn. Reson. 144, 357–366 (2000)) is concerned with applications of the method to 2D, 3D, and 4D NMR experiments.     

On the theory of temporal aberrations for cathode lenses

A new approach to the theory of temporal aberration for cathode lenses is given in the present paper. A definition of temporal aberration is given in which a certain initial energy of electron emission along the axial direction ε_z1 (0ε_z1ε_0max) is considered. A new method to calculate the temporal aberration coefficients of cathode lenses named “direct integral method” is also presented. The “direct integral method” gives new expressions of the temporal aberration coefficients which are expressed in integral forms. The difference between “direct integral method” and “τ-variation method” is that the “τ-variation method” needs to solve the differential equations for the three of temporal geometrical aberration coefficients of second order, while the “direct integral method” only needs to carry out the integral calculation for all of these temporal aberration coefficients of second order.All of the formulae of the temporal aberration coefficients deduced from “direct integral method” and “τ-variation method” have been verified by an electrostatic concentric spherical system model, and contrasted with the analytical solutions. Results show that these two methods have got identical solutions and the solutions of temporal aberration coefficients of the first and second order are the same as with the analytical solutions. Although some forms of the results seem different, but they can be transformed into the same form. Thus, it can be concluded these two methods given by us are equivalent and correct, but the “direct integral method” is related to solve integral equations, which is more convenient for computation and could be suggested for use in practical design.     

Central elements of the elliptic monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the R-matrix are studied. When the crossing parameter w takes a special rational value , where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the “quantum determinant” provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo.     

Noncommutative Dynamics of Random Operators

We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra А on a transformation groupoid Γ = E × G where E is the total space of a principal fibre bundle over spacetime, and G a suitable group acting on Γ . We show that every a ∊ А defines a random operator, and we study the dynamics of such operators. In the noncommutative regime, there is no usual time but, on the strength of the Tomita–Takesaki theorem, there exists a one-parameter group of automorphisms of the algebra А which can be used to define a state dependent dynamics; i.e., the pair (А, ϕ), where ϕ is a state on А, is a “dynamic object.” Only if certain additional conditions are satisfied, the Connes–Nikodym–Radon theorem can be applied and the dependence on ϕ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair (А, ϕ) defines the so-called free probability calculus, as developed by Voiculescu and others, with the state ϕ playing the role of the noncommutative probability measure. This shows that in the noncommutative regime dynamics and probability are unified. This also explains probabilistic properties of the usual quantum mechanics.     

Quantization as Selection Problem

Quantum systems exhibit a smaller number of energetic states than classical systems (A. Einstein, 1907, Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme, Ann. Phys. 22, 180ff). We take up the selection criterion for this in two parts. (1) The selection problem between classical and nonclassical mechanical systems is formulated in terms of possible and impossible configurations (among others, this overcomes the difficulties occurring when discussing the behavior of quantum particles in terms of paths). (2) The (nonclassical) selection of the quantum states is formulated, using recurrence relations and the energy law. The reformulation of “quantization as eigenvalue problem” in terms of “quantization as selection problem” allows one to derive Schrödinger’s stationary equation from classical mechanics through a straightforward and unique procedure; the nonstationary and multibody equations are subsequently acquired within the same frame. In contrast to the (classical) eigenvalue problem, the (nonclassical) selection problem can be formulated and solved without any reference to additional a priori assumptions on the nature of the quantum system, such as the wave-corpuscle dualism or an underlying wave equation or the existence of Planck’s finite action parameter. The existence of such an additional parameter—as the only additional one—is inherent in the procedure. Within our axiomatic-deductive approach, we modify classical mechanics only where it itself indicates an inherent limitation.     

The Distance Between Classical and Quantum Systems

In a recent paper, a “distance” function, , was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a “distance”, D, which measures the distance between either pure or impure classical and quantum states. We also compare the new distance formula with the previous formula, when the latter is applicable. To illustrate these distances, we have used 2 × 2 matrix examples and two-dimensional vectors for simplicity and clarity. Several specific examples are calculated.     

Phase modulation in dipolar-coupled A2 spin systems: effect of maximum state mixing in H NMR in vivo

Coupling constants of nuclear spin systems can be determined from phase modulation of multiplet resonances. Strongly coupled systems such as citrate in prostatic tissue exhibit a more complex modulation than AX connectivities, because of substantial mixing of quantum states. An extreme limit is the coupling of n isochronous spins (A_n system). It is observable only for directly connected spins like the methylene protons of creatine and phosphocreatine which experience residual dipolar coupling in intact muscle tissue in vivo. We will demonstrate that phase modulation of this “pseudo-strong” system is quite simple compared to those of AB systems. Theory predicts that the spin-echo experiment yields conditions as in the case of weak interactions, in particular, the phase modulation depends linearly on the line splitting and the echo time.     

Effective spin susceptibility, electron mass and Landé factor in two-dimensional (2D) Si inversion layers

We have studied the silicon (Si) band-structure, electron–electron and electron-ionized donor interaction effects on our accurate and approximate results (AcR and ApR) for renormalized effective spin susceptibitity (RESS), electron mass (EEM), Landé factor and spin polarization in the impure 2D Si (electron system), showing that:(i) our ApR, being strongly deviated from our AcR, reproduces approximately all the data obtained recently by Pudalov et al. (Phys. Rev. Lett. 88 (2002) 196404) [in particular, RESS =4.7 at the critical value of Wigner–Seitz radius r_s: r_s=r_c≈8.5 at which occur the “apparent” metal–insulator transition (MIT)] and can also be compared with other ApRs found in the recent literature,(ii) both the RESS and EEM produce physical singularities at the same critical value: r_s=r_c11.05661 (weakly disordered samples) at which occurs the “true” MIT; the existence of such two “apparent and true” critical values in this impure system agrees with a recent discussion by Abrahams et al. (Rev. Mod. Phys. 73 (2001) 251), and(iii) at r_s=r_c=8.5, at which occurs the “apparent” MIT, our AcR for effective spin polarization and the corresponding result, obtained using a disordered Hubbard model and a determinant quantum Monte Carlo method by Denteneer and Scalettar (Phys. Rev. Lett. 90 (2003) 246401), both give the same result: ξ_eff.=ξ_c0.31 at B0.4 T, which is found to be lower than the critical parallel magnetic field for full spin polarization, B_c=1.29 T, supporting thus the existence of such an “apparent” MIT.     

Magnetooptical studies of Cd1−xMnxTe quantum wells with parabolic confining potential

We report on magnetooptical studies of II–VI semiconductor quantum wells with a parabolic shape of the potential grown on the basis of Cd_1−xMn_xTe. Photoluminescence excitation measurements revealed a series of peaks equidistant in energy associated with interband optical transitions between “harmonic oscillator states”. We observed the Zeeman splitting for heavy-hole excitons up to the subband index n=5. From the comparison of the experimental data with numerical calculations for the Zeeman splitting it was possible to determine the correct shape of the potential.     

Noncommutative theories, the axial anomaly, Fujikawa's method and the Atiyah–Singer index

Fujikawa's method is employed to compute at first order in the noncommutative parameter the U(1)_A anomaly for noncommutative SU(N). We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θ^μν, which is of “magnetic” type. Our results for SU(N) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.     

A new method for increasing the laser damage threshold of metal mirrors

In order to increase the damage threshold of metal mirrors we propose to create a special structure on the surface of the mirrors (“photonic surface”). This structure must have the period about λ/2 and will suppress propagation of surface plasmons with the frequency ω₀=2πc/λ along the surface. This structure will also slightly increase the heat removal from the mirror’s surface by the excitation of the thermostimulated plasmon emission from the surface. The heat removal from the surface is estimated and possible implementation of this approach for use with CO₂-lasers (λ=10.6 μm) and Nd-YAG-lasers (λ=1.06 μm) is analyzed.