Semiclassical Treatment of Diffraction in Billiard Systems with a Flux Line

In billiard systems with a flux line semiclassical approximations for the density of states contain contributions from periodic orbits as well as from diffractive orbits that are scattered on the flux line. We derive a semiclassical approximation for diffractive orbits that are scattered once on a flux line. This approximation is uniformly valid for all scattering angles. The diffractive contributions are necessary in order that semiclassical approximations are continuous if the position of the flux line is changed.Comment: LaTeX, 17 pages, 4 figure

On the connection between gamma and radio radiation spectra in pulsars

The model of pulsar radio emission is discussed in which a coherent radio emis-sion is excited in a vacuum gap above polar cap of neutron star. Pulsar X and gamma radiation are considered as the result of low-frequency radio emission inverse Comp-ton scattering on ultra relativistic electrons accelerated in the gap. The influence of the pulsar magnetic field on Compton scattering is taken into account. The relation of radio and gamma radiation spectra has been found in the framework of the model.Comment: 15 pages, 3 figures, Russian version accepted to JETP, partly published in JETP Letters, Vol. 85, #6 (2007

Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions

Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier space. The uniform approximation used here relies upon the fact that by passing into Fourier space the Mathieu equation can be mapped onto the simpler problem of a double well potential. The resulting eigenfunctions (Bloch waves), which are uniformly valid for all angles, are then used to describe the semiclassical scattering of waves by potentials varying sinusoidally in one direction. In such situations, for instance in the diffraction of atoms by gratings made of light, it is common to make the Raman-Nath approximation which ignores the motion of the atoms inside the grating. When using the eigenfunctions no such approximation is made so that the dynamical diffraction regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important references to existing work on uniform approximations, such as Olver's method applied to the modified Mathieu equation. It is emphasised that the paper presented here pertains to Fourier space uniform approximation

Spectral Statistics and Dynamical Localization: sharp transition in a generalized Sinai billiard

We consider a Sinai billiard where the usual hard disk scatterer is replaced by a repulsive potential with $V(r)\sim\lambda r^{-\alpha}$ close to the origin. Using periodic orbit theory and numerical evidence we show that its spectral statistics tends to Poisson statistics for large energies when $\alpha2$, while for $\alpha=2$ it is independent of energy, but depends on $\lambda$. We apply the approach of Altshuler and Levitov [Phys. Rep. {\bf 288}, 487 (1997)] to show that the transition in the spectral statistics is accompanied by a dynamical localization-delocalization transition. This behaviour is reminiscent of a metal-insulator transition in disordered electronic systems.Comment: 8 pages, 2 figures, accepted for publication in Phys. Rev. Let

Spontaneous annihilation of high-density matter in the electroweak theory

In the presence of fermionic matter the topologically distinct vacua of the standard model are metastable and can decay by tunneling through the sphaleron barrier. This process annihilates one fermion per doublet due to the anomalous non-conservation of baryon and lepton currents and is accompanied by a production of gauge and Higgs bosons. We present a numerical method to obtain local bounce solutions which minimize the Euclidean action in the space of all configurations connecting two adjacent topological sectors. These solutions determine the decay rate and the configuration of the fields after the tunneling. We also follow the real time evolution of this configuration and analyze the spectrum of the created bosons. If the matter density exceeds some critical value, the exponentially suppressed tunneling triggers off an avalanche producing an enormous amount of bosons.Comment: 38 pages, 6 Postscript figure

A Structural View on the Stereospecificity of Plant Borneol‐Type Dehydrogenases

The development of sustainable processes for the valorization of byproducts and other waste streams remains an ongoing challenge in the field of catalysis. Racemic borneol, isoborneol and camphor are currently produced from alpha-pinene, a side product from the production of cellulose. The pure enantiomers of these monoterpenoids have numerous applications in cosmetics and act as reagents for asymmetric synthesis, making an enzymatic route for their separation into optically pure enantiomers a desirable goal. Known short-chain borneol-type dehydrogenases (BDHs) from plants and bacteria lack the required specificity, stability or activity for industrial utilization. Prompted by reports on the presence of pure (-)-borneol and (-)-camphor in essential oils from rosemary, we set out to investigate dehydrogenases from the genus Salvia and discovered a dehydrogenase with high specificity (E>120) and high specific activity (>0.02 U mg(-1)) for borneol and isoborneol. Compared to other specific dehydrogenases, the one reported here shows remarkably higher stability, which was exploited to obtain the first three-dimensional structure of an enantiospecific borneol-type short-chain dehydrogenase. This, together with docking studies, led to the identification of a hydrophobic pocket in the enzyme that plays a crucial role in the stereo discrimination of bornane-type monoterpenoids. The kinetic resolution of borneol and isoborneol can be easily integrated into the existing synthetic route from alpha-pinene to camphor thereby allowing the facile synthesis of optically pure monoterpenols from an abundant renewable source

Field Theory Approach to Quantum Interference in Chaotic Systems

We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor. Far-reaching structural parallels, as well as a number of differences, to recent semiclassical approaches to the problem are discussed.Comment: 18 pages, 4 figures, revised version, accepted for publication in J. Phys A (Math. Gen.

Wavefunctions, Green's functions and expectation values in terms of spectral determinants

We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The wavefunctions, Green's functions and expectation values of the unperturbed Hamiltonian are expressed in terms of the spectral determinant of the perturbed Hamiltonian. Semiclassical resummation methods for spectral determinants are applied and yield approximations in terms of a finite number of classical trajectories. The final formulas have a simple form. In contrast to Poincare surface of section methods, the resummation is done in terms of the periods of the trajectories.Comment: 18 pages, no figure

How Chaotic is the Stadium Billiard? A Semiclassical Analysis

The impression gained from the literature published to date is that the spectrum of the stadium billiard can be adequately described, semiclassically, by the Gutzwiller periodic orbit trace formula together with a modified treatment of the marginally stable family of bouncing ball orbits. I show that this belief is erroneous. The Gutzwiller trace formula is not applicable for the phase space dynamics near the bouncing ball orbits. Unstable periodic orbits close to the marginally stable family in phase space cannot be treated as isolated stationary phase points when approximating the trace of the Green function. Semiclassical contributions to the trace show an $\hbar$ - dependent transition from hard chaos to integrable behavior for trajectories approaching the bouncing ball orbits. A whole region in phase space surrounding the marginal stable family acts, semiclassically, like a stable island with boundaries being explicitly $\hbar$-dependent. The localized bouncing ball states found in the billiard derive from this semiclassically stable island. The bouncing ball orbits themselves, however, do not contribute to individual eigenvalues in the spectrum. An EBK-like quantization of the regular bouncing ball eigenstates in the stadium can be derived. The stadium billiard is thus an ideal model for studying the influence of almost regular dynamics near marginally stable boundaries on quantum mechanics.Comment: 27 pages, 6 figures, submitted to J. Phys.

Near integrable systems

A two-dimensional circular quantum billiard with unusual boundary conditions introduced by Berry and Dennis (\emph{J Phys A} {\bf 41} (2008) 135203) is considered in detail. It is demonstrated that most of its eigenfunctions are strongly localized and the corresponding eigenvalues are close to eigenvalues of the circular billiard with Neumann boundary conditions. Deviations from strong localization are also discussed. These results agree well with numerical calculations.Comment: 27 pages, 10 figure