Photochemical Studies in Flash Photolysis. II. Photolysis of Acetone with Filtered Light

Flash photolysis was studied in the absence of wavelengths below 200 mμ. Effects of acetone pressure, light intensity, added biacetyl, temperature, and wavelength were investigated. The results are consistent with primary acts postulated previously on the basis of low‐intensity studies, but with the absence of complicating first‐order secondary reactions at these high radical concentrations. Deactivation of excited molecules explains the pressure effect on the C_2H_6/CO ratio, for wall effects are absent under flash conditions. A hot radical mechanism is suggested by the data for methane formation. The effect of wavelength on C_2H_6/CO ratio in regions centered near 260, 280, and 295 mμ is rather striking, and the results are compared with trends in low‐intensity studies in the same pressure region

Bimolecular Recombination Reactions: Low Pressure Rates in Terms of Time-Dependent Survival Probabilities, Total J Phase Space Sampling of Trajectories, and Comparison with RRKM Theory

We consider the bimolecular formation and redissociation of complexes using classical trajectories and the survival probability distribution function P(E,J,t) of the intermediate complexes at time t as a function of the energy E and total angular momentum quantum number J. The P(E,J,t) and its deviation from single exponential behavior is a main focus of the present set of studies. Together with weak deactivating collisions, the P(E,J,t) and a cumulative reaction probability at the given E and J can also be used to obtain the recombination rate constant k at low pressures of third bodies. Both classical and quantum expressions are given for k in terms of P(E,J,t). The initial conditions for the classical trajectories are sampled for atom−diatom reactions for various (E,J)’s using action-angle variables. A canonical transformation to a total J representation reduces the sampling space by permitting analytic integration over several of the variables. A similar remark applies for the calculation of the density of states of the intermediate complex ρ and for the number of states N* of the transition state as a function of E and J. The present approach complements the usual approach based on the rate of the reverse reaction, unimolecular dissociation, and the equilibrium constant. It provides results not necessarily accessible from the unimolecular studies. The formalism is applied elsewhere to the study of nonstatistical aspects of the recombination and redissociation of the resulting ozone molecules and comparison with RRKM theory

Exact on-event expressions for discrete potential systems

The properties of systems composed of atoms interacting though discrete potentials are dictated by a series of events which occur between pairs of atoms. There are only four basic event types for pairwise discrete potentials and the square-well/shoulder systems studied here exhibit them all. Closed analytical expressions are derived for the on-event kinetic energy distribution functions for an atom, which are distinct from the Maxwell-Boltzmann distribution function. Exact expressions are derived that directly relate the pressure and temperature of equilibrium discrete potential systems to the rates of each type of event. The pressure can be determined from knowledge of only the rate of core and bounce events. The temperature is given by the ratio of the number of bounce events to the number of disassociation/association events. All these expressions are validated with event-driven molecular dynamics simulations and agree with the data within the statistical precision of the simulations

Inverse Symmetry Breaking in Multi-Scalar Field Theories

We review how the phenomena of inverse symmetry breaking (and symmetry nonrestoration) may arise in the context of relativistic as well as nonrelativistic multi-scalar field theories. We discuss how the consideration of thermal effects on the couplings produce different transition patterns for both theories. For the relativistic case, these effects allow the appearance of inverse symmetry breaking (and symmetry nonrestoration) at arbitrarily large temperatures. On the other hand, the same phenomena are suppressed in the nonrelativistic case, which is relevant for condensed matter physics. In this case, symmetry nonrestoration does not happen while inverse symmetry is allowed only to be followed by symmetry restoration characterizing a reentrant phase. The aim of this paper is to give more insight concerning the, qualitatively correct, results obtained by using one loop perturbation theory in the evaluation of thermal masses and couplings.Comment: 7 pages, 3 figures, talk given at the workshop on Quantum Fields Under the Influence of External Conditions, QFEXT05, Barcelona, sep-200

Fourier Transforms of Lorentz Invariant Functions

Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail, and the results for 1+n dimensions are given.Comment: 15 pages, 1 figur

Observation of correlations up to the micrometer scale in sliding charge-density waves

High-resolution coherent x-ray diffraction experiment has been performed on the charge density wave (CDW) system K$_{0.3}$MoO$_3$. The $2k_F$ satellite reflection associated with the CDW has been measured with respect to external dc currents. In the sliding regime, the $2k_F$ satellite reflection displays secondary satellites along the chain axis which corresponds to correlations up to the micrometer scale. This super long range order is 1500 times larger than the CDW period itself. This new type of electronic correlation seems inherent to the collective dynamics of electrons in charge density wave systems. Several scenarios are discussed.Comment: 4 pages, 3 figures Typos added, references remove

Theory of Semiclassical Transition Probabilities for Inelastic and Reactive Collisions. II Asymptotic Evaluation of the S Matrix

The asymptotic evaluation of the integral representation for an S matrix element in a previously developed semiclassical theory of molecular collisions is considered. The integral representation is evaluated asymptotically by the method of Chester, Friedman, and Ursell to give a uniform approximation for the S matrix element which is valid for classically accessible and classically inaccessible transitions. The results unify and extend those previously derived, which were restricted to the simple semiclassical and Airy function cases. A comparison is made with the simple, Airy, and uniform semiclassical approximations that occur in Miller's semiclassical theory of molecular collisions. Although the starting point of the two theories is different, it is concluded that their asymptotic results are essentially identical. In addition, a simpler derivation of the integral representation for an S matrix element from the semiclassical wavefunction is given, one which avoids the use of Green's theorem

Theory of Reactive Collisions: Conformal Transformation

Conformal mapping techniques are applied to the Schrödinger equation for a bimolecular exchange reaction, with all three atoms lying on a line. For the case of a very heavy central mass, the extension of the theory to three dimensions is indicated. An angle-shaped region of the potential-energy surface is mapped onto an infinite strip in order to simplify the theoretical treatment of the boundary conditions. The mapping function is determined with the help of the Schwarz–Christoffel formula, and its properties described. The transformed Schrödinger equation is converted into an integral equation using the method of Green's functions, and integral representations for the reflection and transmission coefficients are obtained

Statistical Properties of Level Widths and Conductance Peaks in a Quantum Dot

We study the statistics of level widths of a quantum dot with extended contacts in the absence of time-reversal symmetry. The widths are determined by the amplitude of the wavefunction averaged over the contact area. The distribution function of level widths for a two-point contact is evaluated exactly. The distribution resembles closely the result obtained when the wavefunction fluctuates independently at each point, but differs from the one-point case. Analytical calculations and numerical simulations show that the distribution for many-point contacts has a power-law behavior at small level widths. The exponent is given by the number of points in the lead and diverges in the continuous limit. The distribution of level widths is used to determine the distribution of conductance peaks in the resonance regime. At intermediate temperatures, we find that the distribution tends to normal and fluctuations in the height of the peaks are suppressed as the lead size is increased.Comment: 13 pages, RevTeX 3, six uuencoded postscript figures, CMT-ERM-940

Geometric flux formula for the gravitational Wilson loop

Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at the Planck scale is essential for making progress in quantum gravity. The holonomy and Wilson loop of the Levi-Civita connection are potentially interesting ingredients in the construction of quantum curvature observables. Motivated by recent developments in nonperturbative quantum gravity, we establish new relations in three and four dimensions between the holonomy of a finite loop and certain curvature integrals over the surface spanned by the loop. They are much simpler than a gravitational version of the nonabelian Stokes' theorem, but require the presence of totally geodesic surfaces in the manifold, which follows from the existence of suitable Killing vectors. We show that the relations are invariant under smooth surface deformations, due to the presence of a conserved geometric flux.Comment: 36 pages, 5 figures; minor text changes, clarifying the role of diffeomorphism invariance; agrees with published versio