Uniform semiclassical approximations on a topologically non-trivial configuration space: The hydrogen atom in an electric field

Semiclassical periodic-orbit theory and closed-orbit theory represent a quantum spectrum as a superposition of contributions from individual classical orbits. Close to a bifurcation, these contributions diverge and have to be replaced with a uniform approximation. Its construction requires a normal form that provides a local description of the bifurcation scenario. Usually, the normal form is constructed in flat space. We present an example taken from the hydrogen atom in an electric field where the normal form must be chosen to be defined on a sphere instead of a Euclidean plane. In the example, the necessity to base the normal form on a topologically non-trivial configuration space reveals a subtle interplay between local and global aspects of the phase space structure. We show that a uniform approximation for a bifurcation scenario with non-trivial topology can be constructed using the established uniformization techniques. Semiclassical photo-absorption spectra of the hydrogen atom in an electric field are significantly improved when based on the extended uniform approximations

Persistence of transition state structure in chemical reactions driven by fields oscillating in time

Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition state barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving, barrier top also fails to be recrossing-free. We construct a moving dividing surface in phase space over a transition state trajectory. This surface is recrossing-free for both Hamiltonian and dissipative dynamics. This is confirmed even for strongly anharmonic barriers using simulation. The power of transition state theory is thereby applicable to chemical reactions and other activated processes even when the bottlenecks are time-dependent and move across space

Chemical reactions induced by oscillating external fields in weak thermal environments

Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally varying external field, the transition state that the reaction must pass through during the transformation from reactant to product is no longer a fixed geometric structure, but is instead time-dependent. For a periodically forced model reaction, we develop a recrossing-free dividing surface that is attached to a transition state trajectory [T. Bartsch, R. Hernandez, and T. Uzer, Phys. Rev. Lett. 95, 058301 (2005)]. We have previously shown that for single-mode sinusoidal driving, the stability of the time-varying transition state directly determines the reaction rate [G. T. Craven, T. Bartsch, and R. Hernandez, J. Chem. Phys. 141, 041106 (2014)]. Here, we extend our previous work to the case of multi-mode driving waveforms. Excellent agreement is observed between the rates predicted by stability analysis and rates obtained through numerical calculation of the reactive flux. We also show that the optimal dividing surface and the resulting reaction rate for a reactive system driven by weak thermal noise can be approximated well using the transition state geometry of the underlying deterministic system. This agreement persists as long as the thermal driving strength is less than the order of that of the periodic driving. The power of this result is its simplicity. The surprising accuracy of the time-dependent noise-free geometry for obtaining transition state theory rates in chemical reactions driven by periodic fields reveals the dynamics without requiring the cost of brute-force calculations

Reentrant glass transition in a colloid-polymer mixture with depletion attractions

Performing light scattering experiments we show that introducing short-ranged attraction to a colloidal suspension of nearly hard spheres by addition of free polymer produces new glass transition phenomena. We observe a dramatic acceleration of the density fluctuations amounting to the melting of a colloidal glass. Increasing the strength of the attractions the system freezes into another nonergodic state sharing some qualitative features with gel states occurring at lower colloid packing fractions. This reentrant glass transition is in qualitative agreement with recent theoretical predictions.Comment: 14 pages, 3 figure

Boltzmann-type approach to transport in weakly interacting one-dimensional fermionic systems

We investigate transport properties of one-dimensional fermionic tight binding models featuring nearest and next-nearest neighbor hopping, where the fermions are additionally subject to a weak short range mutual interaction. To this end we employ a pertinent approach which allows for a mapping of the underlying Schr\"odinger dynamics onto an adequate linear quantum Boltzmann equation. This approach is based on a suitable projection operator method. From this Boltzmann equation we are able to numerically obtain diffusion coefficients in the case of non-vanishing next-nearest neighbor hopping, i.e., the non-integrable case, whereas the diffusion coefficient diverges without next-nearest neighbor hopping. For the latter case we analytically investigate the decay behavior of the current with the result that arbitrarily small parts of the current relax arbitrarily slowly which suggests anomalous diffusive transport behavior within the scope of our approach.Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev.