Semiclassical Propagation of Wavepackets with Real and Complex Trajectories

We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield three different semiclassical formulae involving different real trajectories. One of these formulae is Heller's thawed gaussian approximation. The other approximations are non-gaussian and may involve several trajectories determined by mixed initial-final conditions. These different formulae are tested for the cases of scattering by a hard wall, scattering by an attractive gaussian potential, and bound motion in a quartic oscillator. The formula with complex trajectories gives good results in all cases. The non-gaussian approximations with real trajectories work well in some cases, whereas the thawed gaussian works only in very simple situations.Comment: revised text, 24 pages, 6 figure

Signatures of Classical Periodic Orbits on a Smooth Quantum System

Gutzwiller's trace formula and Bogomolny's formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a large spatial and energy range.Comment: 12 pages, uuencoded postscript file (1526 kb

Interfaces within graphene nanoribbons

We study the conductance through two types of graphene nanostructures: nanoribbon junctions in which the width changes from wide to narrow, and curved nanoribbons. In the wide-narrow structures, substantial reflection occurs from the wide-narrow interface, in contrast to the behavior of the much studied electron gas waveguides. In the curved nanoribbons, the conductance is very sensitive to details such as whether regions of a semiconducting armchair nanoribbon are included in the curved structure -- such regions strongly suppress the conductance. Surprisingly, this suppression is not due to the band gap of the semiconducting nanoribbon, but is linked to the valley degree of freedom. Though we study these effects in the simplest contexts, they can be expected to occur for more complicated structures, and we show results for rings as well. We conclude that experience from electron gas waveguides does not carry over to graphene nanostructures. The interior interfaces causing extra scattering result from the extra effective degrees of freedom of the graphene structure, namely the valley and sublattice pseudospins

Weak-Localization in Chaotic Versus Non-Chaotic Cavities: A Striking Difference in the Line Shape

We report experimental evidence that chaotic and non-chaotic scattering through ballistic cavities display distinct signatures in quantum transport. In the case of non-chaotic cavities, we observe a linear decrease in the average resistance with magnetic field which contrasts markedly with a Lorentzian behavior for a chaotic cavity. This difference in line-shape of the weak-localization peak is related to the differing distribution of areas enclosed by electron trajectories. In addition, periodic oscillations are observed which are probably associated with the Aharonov-Bohm effect through a periodic orbit within the cavities.Comment: 4 pages revtex + 4 figures on request; amc.hub.94.

Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators

We discuss some basic tools for an analysis of one-dimensionalquantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi distributions are discussed, in particular their zeros.Furthermore, the use of the complexifier coherent states for a semiclassical analysis is demonstrated by deriving a semiclassical coherent state propagator in phase space.Comment: 29 page

Reflection Symmetric Ballistic Microstructures: Quantum Transport Properties

We show that reflection symmetry has a strong influence on quantum transport properties. Using a random S-matrix theory approach, we derive the weak-localization correction, the magnitude of the conductance fluctuations, and the distribution of the conductance for three classes of reflection symmetry relevant for experimental ballistic microstructures. The S-matrix ensembles used fall within the general classification scheme introduced by Dyson, but because the conductance couples blocks of the S-matrix of different parity, the resulting conductance properties are highly non-trivial.Comment: 4 pages, includes 3 postscript figs, uses revte

Recognition of essential purines by the U1A protein

<p>Abstract</p> <p>Background</p> <p>The RNA recognition motif (RRM) is one of the largest families of RNA binding domains. The RRM is modulated so that individual proteins containing RRMs can specifically recognize RNA targets with diverse sequences and structures. Understanding the principles governing this specificity will be important for the rational modification and design of RRM-RNA complexes.</p> <p>Results</p> <p>In this paper we have investigated the origins of specificity of the N terminal RRM of the U1A protein for stem loop 2 (SL2) of U1 snRNA by substituting modified bases for essential purines in SL2 RNA. In one series of modified bases, hydrogen bond donors and acceptors were replaced by aliphatic groups to probe the importance of these functional groups to binding. In a second series of modified bases, hydrogen bond donors and acceptors were incorrectly placed on the purine bases to analyze the origins of discrimination between cognate and non-cognate RNA. The results of these experiments show that three different approaches are used by the U1A protein to gain specificity for purines. Specificity for the first base in the loop, A1, is based primarily on discrimination against RNA containing the incorrect base, specificity for the fourth base in the loop, G4, is based largely on recognition of the donors and acceptors of G4, while specificity for the sixth base in the loop, A6, results from a combination of direct recognition of the base and discrimination against incorrectly placed functional groups.</p> <p>Conclusion</p> <p>These investigations identify different roles that hydrogen bond donors and acceptors on bases in both cognate and non-cognate RNA play in the specific recognition of RNA by the U1A protein. Taken together with investigations of other RNA-RRM complexes, the results contribute to a general understanding of the origins of RNA-RRM specificity and highlight, in particular, the contribution of steric and electrostatic repulsion to binding specificity.</p

Interfaces Within Graphene Nanoribbons

We study the conductance through two types of graphene nanostructures: nanoribbon junctions in which the width changes from wide to narrow, and curved nanoribbons. In the wide-narrow structures, substantial reflection occurs from the wide-narrow interface, in contrast to the behavior of the much studied electron gas waveguides. In the curved nanoribbons, the conductance is very sensitive to details such as whether regions of a semiconducting armchair nanoribbon are included in the curved structure -- such regions strongly suppress the conductance. Surprisingly, this suppression is not due to the band gap of the semiconducting nanoribbon, but is linked to the valley degree of freedom. Though we study these effects in the simplest contexts, they can be expected to occur for more complicated structures, and we show results for rings as well. We conclude that experience from electron gas waveguides does not carry over to graphene nanostructures. The interior interfaces causing extra scattering result from the extra effective degrees of freedom of the graphene structure, namely the valley and sublattice pseudospins.Comment: 19 pages, published version, several references added, small changes to conclusion

How Phase-Breaking Affects Quantum Transport Through Chaotic Cavities

We investigate the effects of phase-breaking events on electronic transport through ballistic chaotic cavities. We simulate phase-breaking by a fictitious lead connecting the cavity to a phase-randomizing reservoir and introduce a statistical description for the total scattering matrix, including the additional lead. For strong phase-breaking, the average and variance of the conductance are calculated analytically. Combining these results with those in the absence of phase-breaking, we propose an interpolation formula, show that it is an excellent description of random-matrix numerical calculations, and obtain good agreement with several recent experiments.Comment: 4 pages, revtex, 3 figures: uuencoded tar-compressed postscrip