Wave Node Dynamics and Revival Symmetry in Quantum Rotors

Symmetries and dynamics of wave nodes in space and time expose principles of quantum theory and its relativistic underpinning. Among these are key principles behind recently discovered dephasing and rephasing phenomena known as revivals. A reexamination of basic Eberly revivals, Berry “quantum fractal” landscapes, and the “quantum carpets” of Schleich and co-workers reveals a simple Farey arithmetic and C_n-group revival structure in one of the earliest quantum wave models, the Bohr rotor. These principles may be useful for interpreting modern time-dependent rovibrational spectra. The nodal dynamics of the Bohr rotor is seen to have a quasi-fractal structure similar to that of earlier systems involving chaotic circle maps. The fractal structure is an overlay of discrete versions of Bohr's rotor model. Each N-point Bohr rotor acts like a base-N quantum “odometer” which performs rational fraction arithmetic. Such systems may have applications for optical information technology and quantum computing.     

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.     

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.     

Quantum interference rectifier

Electron transport in bent quantum wire in the presence of a magnetic field which is orthogonal to the system plane is considered. Possible constructions of “quantum interference switch” and “quantum interference rectifier” are suggested.     

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.     

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.     

Physics versus Semantics: A Puzzling Case of the Missing Quantum Theory

A case for the project of excising of confusion and obfuscation in the contemporary quantum theory initiated and promoted by David Deutsch has been made. It has been argued that at least some theoretical entities which are conventionally labelled as “interpretations” of quantum mechanics are in fact full-blooded physical theories in their own right, and as such are falsifiable, at least in principle. The most pertinent case is the one of the so-called “Many-Worlds Interpretation” (MWI) of Everett and others. This set of idea differs from other “interpretations” since it does not accept reality of the collapse of Schrödinger’s wavefunction. A survey of several important proposals for discrimination between quantum theories with and without wavefunction collapse appearing from time to time in the literature has been made, and the possibilities discussed in the framework of a wider taxonomy.     

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.     

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.     

Investigations of backscattering peaks and of the nature of the confining potential in open quantum dots

The properties of open quantum dots are examined in magneto-transport. The quantum dots are prepared from a two-dimensional electron system (2DES) in AlGaAs/GaAs by lateral gate structures. These quantum dots are open, i.e. they are still connected to the surrounding 2DES regions. The low magnetic field magnetoresistance shows peak structures. These structures can be related to semi-classical ballistic trajectories in the confining potential of a dot. The calculations of different confining potentials (abrupt “hard-wall” and parabolic “soft-wall”) are compared with the experimental results. The experiments are better described by a soft-wall potential.     

A Note on the Characterization of Gravitation

In this note we start with the Planck scale or the quantum of area which is of importance in recent quantum gravity approaches. We then deduce the gravitational constant from the theory. It turns out that gravitation has the Sakharov character of being an “excess” of energy. In the process we obtain an elegant rationale for the quantum of area and an alternative expression for the Bekenstein radiation time. All results are in agreement with observation (in the order of magnitude sense).     

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.”     

K–K excitations on as “primary” superfields

We show that the K–K spectrum of IIB string on is described by “twisted chiral” superfields, naturally described in “harmonic superspace”, obtained by taking suitable gauge singlets polynomials of the D3-brane boundary superconformal field theory.To each p-order polynomial is associated a massive K–K short representation with states. The quadratic polynomial corresponds to the “supercurrent multiplet” describing the “massless” bulk graviton multiplet.     

Adiabatic Theorems and Reversible Isothermal Processes

Isothermal processes of a finitely extended, driven quantum system in contact with an infinite heat bath are studied from the point of view of quantum statistical mechanics. Notions like heat flux, work and entropy are defined for trajectories of states close to, but distinct from states of joint thermal equilibrium. A theorem characterizing reversible isothermal processes as quasi-static processes (“isothermal theorem”) is described. Corollaries concerning the changes of entropy and free energy in reversible isothermal processes and on the 0th law of thermodynamics are outlined.*Supported by the Swiss National Foundation.     

Randomized Acquisition for the Suppression of Systematic F1 Artifacts in Two-Dimensional NMR Spectroscopy

2D spectra, particularly for homonuclear correlation, can show a variety of artifactual signals in the F₁ domain. Common sources include carry-over of signal modulation from one transient to the next (“rapid pulsing artifacts”) and systematic variations in room temperature (“parallel diagonals”). In both cases there is one very simple expedient which can greatly reduce the impact of these sources of error. Multidimensional data sets are almost invariably recorded by simply incrementing or decrementing evolution periods, largely for reasons of convenience and historical precedent. If instead the sampling of the evolution periods is carried out in random order, the perturbations responsible for the sharp F₁ signals in the conventional experiment manifest themselves as t₁ noise. Since the randomized acquisition redistributes coherent artifactual signals randomly in F₁, the maximum artifactual signal is substantially reduced in the randomized experiment and no longer appears in the form of misleading distinct peaks.     

What the inflaton might tell us about RHIC/LHC

Topical phenomena in high-energy physics related to collision experiments of heavy nuclei (“Little Bang”) and early universe cosmology (“Big Bang”) involve far-from-equilibrium dynamics described by quantum field theory. One example concerns the role of plasma instabilities for the process of thermalization in heavy-ion collisions. The reheating of the early universe after inflation may exhibit rather similar phenomena following a tachyonic or parametric resonance instability. Certain universal aspects associated to nonthermal fixed points even quantitatively agree, and considering these phenomena from a common perspective can be fruitful.     

Vertical magneto-tunneling through a quantum dot and the density of states of small electronic systems

One-electron tunneling through a quantum dot with a strong magnetic field in the direction of the current is studied. The linear magneto-conductance is computed for a model parabolic dot with seven electrons in the intermediate states and for different values of the magnetic field. It is shown that the dot density of states at low excitation energies can be extracted from a precise measurement of the conductance at the upper edge of the Coulomb blockade diamond. We parametrized the density of states with a single “temperature” parameter (in the so called “constant temperature approximation”), and found that this parameter depends very weakly on the magnetic field.     

A general derivation of the density of states function for quantum wells and superlattices

The intent of this paper is to provide the reader with a detailed summary of the development of the density of states (DOS) functions for two-dimensional systems. Specifically, the DOS is derived for an infinite quantum well, a finite well, and a periodic array of coupled wells (a superlattice). Many authors state that the DOS is “simply …” without references, yet many who are new to the subject of two-dimensional systems may not see the “simplicity,” for instance, of the derivation of the DOS for a superlattice. We also show the relationships between the expressions for each case when the appropriate limits are taken. This comparison shows the consistency that such a general derivation furnishes to each expression.     

Nanostructuring-induced modification of optical properties of p-GaAs (1 0 0)

A pulsed anodic etching method has been utilized for nanostructuring of p-type GaAs (1 0 0) surface, using HCl-based solution as electrolyte. The resulting porous GaAs layer is characterized by atomic force microscopy (AFM), room temperature photoluminescence (PL), Raman spectroscopy and optical reflectance measurements. AFM imaging reveals that the porous GaAs layer is consisted of a pillar-like of few nm in width distributed between more-reduced size nanostructures. In addition to the “infrared” PL band of un-etched GaAs, a strong “green” PL band is observed in the etched sample. The broad visible PL band of a high-energy (3.82 eV) excitation is found to compose of two PL band attributed to excitons confinement in two different sizes distribution of GaAs nanocrystals. The quantum confinement effects in GaAs nanocrystallites is also evidenced from Raman spectroscopy through the pronounced appearance of the transverse optical (TO) phonon line in the spectra of the porous sample. Porosity-induced a significant reduction of the specular reflection, in the spectral range (400–800 nm), is also demonstrated.