The simplified Fermi accelerator in classical and quantum mechanics

We review the simplified classical Fermi acceleration mechanism and construct a quantum counterpart by imposing time-dependent boundary conditions on solutions of the free Schrödinger equation at the unit interval. We find similiar dynamical features in the sense that limiting KAM curves, respectively purely singular quasienergy spectrum, exist(s) for sufficiently smooth wall oscillations (typically ofC ² type). In addition, we investigate quantum analogs to local approximations of the Fermi map both in its quasiperiodic and irregular phase space regions. In particular, we find pure point q.e. spectrum in the former case and conjecture that random boundary conditions are necessary to model a quantum analog to the chaotic regime of the classical accelerator.     

Vorticity intensification and transition to turbulence in three-dimensional euler equations

The evolution of a perturbed vortex tube is studied by means of a second-order projection method for the incompressible Euler equations. We observe, to the limits of grid resolution, a nonintegrable blowup in vorticity. The onset of the intensification is accompanied by a decay in the mean kinetic energy. Locally, the intensification is characterized by tightly curved regions of alternating-sign vorticity in a 2n-pole structure. After the firstL peak, the enstrophy and entropy continue to increase, and we observe reconnection events, continued decay of the mean kinetic energy, and the emergence of a Kolmogorov (k ^–5/3) range in the energy spectrum.     

Nanoparticle Microreactor: Application to Synthesis Of Titania by Thermal Decomposition of Titanium Tetraisopropoxide

The nanoparticle microreactor (NPMR) is a new concept that we have introduced to describe a very small-scale system capable of converting an aerosol precursor to solid particles. The liquid precursor of about 1 µl is injected by a syringe through a septum into a tubular evaporator of 1.0 cm³ in volume with stopcocks at both ends. The evaporator has been preheated by a heating tape to a temperature sufficiently high for vaporization to occur in half a minute. By opening the stopcocks, the vaporized precursor is transported by a carrier gas stream into a quartz tube which is mounted along the axis of a tubular furnace. The nanoparticle aggregates produced in the reactor are sampled by deposition on an electron micrograph grid at the reactor exit. The NPMR was applied first to the synthesis of TiO₂ particles by thermal decomposition of titanium tetraisopropoxide (TTIP) in a nitrogen carrier gas, with TTIP concentrations varying from 1.0 to 7.0 mol% or 2.35×10^–6 to 1.65×10^–5 in TiO₂ volume loading, and decomposition temperatures from 300°C to 1000°C. Studies were made with a 2 mm reaction tube and a 4 mm tube with sheath gas. With the 2 mm tube, a considerable fraction of the TTIP precursor was consumed at the wall by surface reaction, resulting in very small particles. With the 4 mm tube, the primary particle size was comparable to that reported in the literature for steady flow experiments using a 22.2 mm tube. Primary particle sizes ranged from 200 to 400 nm. Depending on TTIP concentration and reactor temperature, the particles exhibited a bimodal size distribution, probably due to a two-stage nucleation. A fourfold increase in the gas flow rate had little effect on particle size, indicating that particle growth ended early, within one-fourth the tube length. Residence time in the reactor was between 0.35 and 1.4 s, and total run time about 1 min. The NPMR has potential for rapid assembly of large databases and is adaptable to combinatorial discovery of nanoparticles with novel properties. Design requirements for an ideal aerosol microreactor are discussed briefly.     

The effect of external visible light on the breakdown voltage of a long discharge tube

The breakdown characteristics of a discharge tube with a configuration typical of gas-discharge light sources and electric-discharge lasers (a so-called “long discharge tube”) filled with argon or helium at a pressure of 1 Torr have been investigated. A breakdown has been implemented using positive and negative voltage pulses with a linear leading edge having a slope dU/dt ~ 10–10⁷ V/s. Visible light from an external source (halogen incandescent lamp) is found to affect the breakdown characteristics. The dependences of the dynamic breakdown voltage of the tube on dU/dt and on the incident light intensity are measured. The breakdown voltage is found to decrease under irradiation of the high-voltage anode of the tube in a wide range of dU/dt. A dependence of the effect magnitude on the light intensity and spectrum is obtained. Possible physical mechanisms of this phenomenon are discussed.     

Localization for random potentials supported on a subspace

We consider the lattice Schrödinger operator acting onl ² ( ^d ) with random potential (independent, identically distributed random variables), supported on a subspace of dimension 1 v <d. We use the multiscale analyses scheme to prove that this operator exhibits exponential localization at the edges of the spectrum for any disorder or outside the interval [-2d, 2d] for sufficiently high disorder.     

Conductance of a single-wall carbon nanotube in a one-parameter tight-binding model

The dependence of current-voltage characteristics of single-wall nanotubes on their radius and chirality is studied theoretically. It is shown that the conductance of a single-wall nanotube at low voltages can assume discrete values equal to zero for a dielectric tube and 4(e²/h) for a conducting tube (e is the electron charge, h is the Planck constant). The current-voltage characteristic of a nanotube exhibits kinks related to the discreteness of the electron spectrum. The behavior of the conductance of the nanotube at zero temperature is analyzed in a quantizing longitudinal magnetic field that changes the type of tube conduction. In a magnetic field, the conductance of a dielectric tube at low voltages can assume a value of 2(e²/h) in the region where the tube becomes conducting. In a weak magnetic field, a conducting tube becomes dielectric with an energy gap depending on the magnitude of the magnetic field. The conductance of a carbon nanotube is calculated as a function of the temperature and longitudinal magnetic field.     

Localization phenomenon in gaps of the spectrum of random lattice operators

We consider a class of random lattice operators including Schrödinger operators of the formH=–+w+gv, wherew(x) is a real-valued periodic function,g is a positive constant, andv(x),x ^d , are independent, identically distributed real random variables. We prove that if the operator –+w has gaps in the spectrum andg is sufficiently small, then the operatorH develops pure point spectrum with exponentially decaying eigenfunctions in a vicinity of the gaps.     

A generalized spectral duality theorem

We establish a version of the spectral duality theorem relating the point spectrum of a family of^*-representations of a certain covariance algebra to the continuous spectrum of an associated family of^*-representations. Using that version, we prove that almost all the images of any element of a certain space of fixed points of some^*-automorphism of an irrational rotation algebra via standard^*-representations of the algebra inl ² do not have pure point spectrum over any non-empty open subset of the common spectrum of those images. As another application of the spectral duality theorem, we prove that if almost all the Bloch operators associated with a real almost periodic function on have pure point spectrum over a Borel subset of , then almost all the Schrödinger operators with potentials belonging to the compact hull of the translates of this function have, over the same set, purely continuous spectrum.Dedicated to Professor Marek Burnat     

Globally noncausal space-times. II. Naked singularities and curvature conditions

In this paper we prove that if there is a naked singularity, then there will be some null geodesic, reaching ⁺ from the singularity, which does not satisfy the strong curvature condition regardless of whether causality is violated or not. Assuming that a naked singularity is a strong curvature singularity only sufficiently far to the future, we prove that strong causality is violated arbitrarily close to ⁺.Work partially supported by the Nuffield Foundation and by the Consiglio Nazionale delle Ricerche of Italy under contract N.CT 81.00532.02.     

Laser-induced fluorescence decay lifetimes of shock-heated NO (A 2Σ+)

Radiative emission in the NO -band system occurs when air at a few Torr initial pressure is shock-heated at sufficiently high temperatures of 3500–7000 K. Emission spectra of this system in shocks indicate that collisional quenching of the emitting A ²⁺ state is a critical quantity controlling the intensity. Quenching of excited NO by NO itself has been measured using direct time decay of laser-induced fluorescence in the shock tube at 3500 K. The cross section (2– error) is 59±20 Ų, compared to the room temperature value 37±8 Ų. At 3500 K, N₂ also quenches NO with a cross section 2 Ų, much larger than the value at 300 K.Sabbatical visitor, on leave from DLR Stuttgart, Fed. Rep. Germany     

On separation of phases in one-dimensional gases

We prove that in a one-dimensional gas in the canonical ensemble with pair interactionA/r –B/r ², >2, we have a separation of phases at sufficiently low temperatures. The same combinatorial framework can be used for both lattice and continuous models. A rather precise bound on the critical temperature in a 1/r ² lattice gas is obtained when the nearest neighbour coupling is large. The interface between the two phases is defined and investigated.     

The sign of the magnetic moment of191Pt(g.s.) determined by Mössbauer effect on oriented nuclei

Radioactive¹⁹¹Pt(3/2^–) alloyed to iron has been oriented at low temperature in a dilution refrigerator. The resonance absorption spectrum of the 82.4 keV transition of the polarized split source has been registered at high ( 1 K) and low ( 15 mK) temperatures. From the high temperature spectrum (E2/M1; 82.4) < 0 is established. From the positive-to-negative speed asymmetry of the low tempe rature spectrum we determined [191-Pt(g.s.)] > 0. This result is in agreement with deformed Hartree-Fock calculation predictions.     

Correlation functionals of infinite volume quantum spin systems

The existence and analyticity of the correlation functionals of a quantum lattice in the infinite volume limit is proved. The result is valid at sufficiently high temperatures and for a large class of interactions. Our method estimates the kernelK for a set of Kirkwood-Salzburg equations. While a naive estimate would indicate that K =, we take into account cancellations between different contributions toK in order to show that for sufficiently high temperatures K <1, and this estimate is independent of the volume of the system.Supported in part by the Air Force Office of Scientific Research.     

Global validity of the Boltzmann equation for a three-dimensional rare gas in vacuum

We consider a system ofN hard spheres in the Boltzmann-Grad limit (i.e.d0,N,Nd ^2–1>0, whered is the diameter of the spheres). If is sufficiently large, and if the joint distribution densities factorize at time zero, with the one particle distribution decaying sufficiently rapidly in space and velocities, we prove that the time evolved one-particle distribution converges for all times to the solution of the Boltzmann equation with the same initial datum. This result improves and is based on a previous paper [1], valid only in two dimensions.Partially supported by MPI and GNFM (CNR)     

Algebraic Rate of Decay for the Excess Free Energy and Stability of Fronts for a Nonlocal Phase Kinetics Equation with a Conservation Law. I

This is the first of two papers devoted to the study of a nonlocal evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki dynamics and Kac potentials. We consider subcritical temperatures, for which there are two local equilibria, and begin the proof of a local nonlinear stability result for the minimum free energy profiles for the magnetization at the interface between regions of these two different local equilibria; i.e., the fronts. We shall show in the second paper that an initial perturbation v ₀ of a front that is sufficiently small in L ² norm, and sufficiently localized that x ² v ₀(x)² dx<, yields a solution that relaxes to another front, selected by a conservation law, in the L ¹ norm at an algebraic rate that we explicitly estimate. There we also obtain rates for the relaxation in the L ² norm and the rate of decrease of the excess free energy. Here we prove a number of estimates essential for this result. Moreover, the estimates proved here suffice to establish the main result in an important special case.on leave from     

Quasiparticle energies,excitonic effects and optical absorption spectra of small-diameter single-walled carbon nanotubes

We present a first-principles study of the effects of many-electron interactions on the optical properties of single-walled carbon nanotubes. Motivated by recent experiments, we have carried out ab initio calculations on the single-walled carbon nanotubes (3, 3), (5, 0) and (8, 0). The calculations are based on a many-body Greens function approach in which both the quasiparticle (single-particle) excitation spectrum and the optical (electron–hole excitation) spectrum are determined. We show that the optical spectrum of both the semiconducting and metallic nanotubes studied exhibits important excitonic effects due to their quasi-one-dimensional nature. Binding energies for excitonic states range from zero for the metallic (5, 0) tube to nearly 1 eV for the semiconducting (8, 0) tube. Moreover, the metallic (3, 3) tube possesses exciton states bound by nearly 100 meV. Our calculated spectra explain quantitatively the observed features found in the measured spectra. PACS 78.67.Ch; 71.35.Cc; 73.22.-f     

Hidden variables and Bell's theorem in quantum mechanics

In the present paper we give a precise definition of a hidden-variable theory for quantum mechanics, whereby we adopt the weakest possible definition of a hidden-variable theory, which is compatible with the assumption that the bounded observables of a quantum mechanical system are represented by the elements of the real part A_r of a W^*-algebra A (of the most general type) and the states are represented by the normal states (in the mathematical sense) of A. We then go on to show that an example put forward by Bell in 1966 satisfies our definition (Sec. 2). Finally we make use of Bell's famous theorem to show that for a sufficiently non-commutative W^*-algebra A no hidden-variable theory in our sense exists (Theorem 3.3 and its corollaries).     

Spectral properties of inviscid solutions of the burgers equation with random initial conditions

The Burgers equation with random self-similar initial conditions is investigated numerically in the inviscid limit by a parallel fast Legendre transform algorithm, using Connection Machine CM-200. The use of this equation for solving the problem of nervous impulse propagation through axons is discussed. An attempt is made to simulate recent experiments where the form of the density of propagated nerve impulses, which initially had a power spectrum close to a white noise distribution, appeared similar to the triangular pulses that arise in the inviscid Burgers equation and where the 1/f power law was observed on scales larger than the typical time interval between pulses. It is shown that in the inviscid Burgers equation model the power spectra for different types of initial conditions in the developed Burgers turbulence regime (i.e., at a sufficiently large time) consists of two parts with a rather sharp transition between them: The spectrum virtually coincides with the initial spectra for low wavenumbers, and the 1/f² law holds for high wavenumbers. There is no interval with an intermediate power law dependence such as 1/f. It is inferred that the true 1/f spectrum of nerve impulses propagating through axons cannot be explained in terms of the Burgers equation model and that other mechanisms must be taken into account.The Stockholm University, Sweden, and the Institute for Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, Perm', Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 225–231, March–April, 1995.     

On the spectrum of the Rayleigh piston

We make a rigorous study of the spectrum of the Rayleigh piston. Our main results are that one is dealing with a trace-class perturbation for all values of the mass ratio y between test particles and heat bath particles and that apart from the ground state the discrete spectrum is empty for y sufficiently near 1. We also show that the so-called Lorentz limit ( ) is mathematically well defined and derive a qualitative statement on the discrete spectrum of the scattering operator for 1.     

The geometry of generalized quantum logics

Let II be a quantum logic; by this we mean an orthocomplemented, orthomodular, partially ordered set. We assume that II carries a sufficiently large collection of states (probability measures). Then, is embedded as a base for the cone of a partially ordered normed spaceL and II is also embedded in the dual order-unit Banach spaceL ^*. We consider conditions on the pairs (, II) and (L,L ^*) that guarantee that II is a dense subset of the extreme points of the positive part of the unit ball ofL ^*. We demonstrate a connection of these conditions in noncommutative measure theory. The assumptions made here are far weaker than the assumptions of the traditional quantum mechanical formalisms and also apply to situations quite different from quantum mechanics. Finally, we show the connections of this theory to the well-known models of quantum mechanics and classical measure theory.