Computations and application of classical phase space integrals in reactive molecular collisions

Classical treatment of the evaluation of prior distribution functions (PDF) of product state and recoil energy distributions in reactive collisions is presented. It is shown that for any diatomic potential a single one dimensional numerical (or often analytical) integration suffices to determine the relevant PDF. The conservation of total angular momentum leads to an explicit dependence of the resulting distributions on the maximal total angular momentum of the reactants. The evaluation of prior cross section and branching ratios in collision induced dissociation necessitates the estimation of the radius of the interaction zone. A method for the estimation of the interaction radius and the evaluation of the priors is presented.     

Translational energy disposal in molecular collisions: The transfer of momentum constraint

A Franck—Condon type argument, which requires the least transfer of momenta to the nuclei during a collision is outlined and applied to the analysis of translational energy disposal and its dependence on the initial translational energy. Using the maximal entropy procedure of information theory we are able to proceed directly from the assumed (model) constraint to the product state distribution.     

Minimal energy losses in light polarization and brightness considerations

We studied the possibility to obtain linear-polarized light from a partially polarized beam, subject to the requirement of minimal energy losses. In the case when the two components of the beam carry equal amounts of energy and are fully time-correlated, an ideal polarizer will cause energy losses of at least 41%. In any other situation the losses of such a polarizer will range from this value down to zero. This results from brightness conservation considerations. The analysis was carried out for quasi zero entropy light sources.     

Why is the DNA denaturation transition first order?

We study a model for the denaturation transition of DNA in which the molecules are considered as being composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d = 2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.     

Melting and unzipping of DNA

Existing experimental studies of the thermal denaturation of DNA yield sharp steps in the melting curve suggesting that the melting transition is first order. This transition has been theoretically studied since the early sixties, mostly within an approach in which the microscopic configurations of a DNA molecule consist of an alternating sequence of non-interacting bound segments and denaturated loops. Studies of these models neglect the repulsive, self-avoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. In the present study we take into account in an approximate way the excluded-volume interaction between denaturated loops and the rest of the chain. This is done by exploiting recent results on scaling properties of polymer networks of arbitrary topology. We also ignore the heterogeneity of the polymer. We obtain a first-order melting transition in d = 2 dimensions and above, consistent with the experimental results. We also consider within our approach the unzipping transition, which takes place when the two DNA strands are pulled apart by an external force acting on one end. We find that the under equilibrium condition the unzipping transition is also first order. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. For instance, the loop size distribution decays algebraically at the transition and the length of the denaturated end segment diverges as the transition is approached. We evaluate these critical properties within our approach. Received 21 August 2001 and Received in final form 26 January 2002     

Moiré deflectometry—ray tracing interferometry

A method for ray deflection mapping, moiré deflectometry, which is fully compatible with interferometry, is described and demonstrated by numerous examples, including testing of optical components, visualization of flow, study of transient phenomena, and modulation transfer function analysis. Unlike interferometry, moiré deflectometry is a pure ray tracing technique and, therefore, the analysis of three- dimensional objects is greatly simplified. Although the ray tracing approach to optical systems is much older than wave theory, moiré deflectometry seems to be the first attempt to apply ray tracing methods systematically to optical metrology. Moiré deflectometry is fully quantitative, interferometry-compatible in accuracy and has the additional advantage of tunable sensitivity.     

DNA unzipping and the unbinding of directed polymers in a random media

We consider the unbinding of a directed polymer in a random media from a wall in d=1+1 dimensions and a simple one-dimensional model for DNA unzipping. Using the replica trick we show that the restricted partition functions of these problems are identical up to an overall normalization factor. Our finding gives an example of a generalization of the stochastic matrix form decomposition to disordered systems, a method which allows us to reduce the dimensionality of the problem. The equivalence between the two problems, for example, allows us to derive the probability distribution for finding the directed polymer a distance z from the wall. We discuss implications of these results for the related Kardar-Parisi-Zhang equation and the asymmetric exclusion process.     

Cusp Singularities in Boundary-Driven Diffusive Systems

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be non-differentiable, a phenomenon that is unique to non-equilibrium systems, and discuss the types of models which display such singularities. The structure of these singularities is found to generically be a cusp, which can be described by a Landau free energy or, equivalently, by catastrophe theory. Connections with analogous results in systems with finite-dimensional phase spaces are drawn.     

Quantum interface between an electrical circuit and a single atom

We show how to bridge the divide between atomic systems and electronic devices by engineering a coupling between the motion of a single ion and the quantized electric field of a resonant circuit. Our method can be used to couple the internal state of an ion to the quantized circuit with the same speed as the internal-state coupling between two ions. All the well-known quantum information protocols linking ion internal and motional states can be converted to protocols between circuit photons and ion internal states. Our results enable quantum interfaces between solid state qubits, atomic qubits, and light, and lay the groundwork for a direct quantum connection between electrical and atomic metrology standards.