Shuffling cards, factoring numbers, and the quantum baker's map

It is pointed out that an exactly solvable permutation operator, viewed as the quantization of cyclic shifts, is useful in constructing a basis in which to study the quantum baker's map, a paradigm system of quantum chaos. In the basis of this operator the eigenfunctions of the quantum baker's map are compressed by factors of around five or more. We show explicitly its connection to an operator that is closely related to the usual quantum baker's map. This permutation operator has interesting connections to the art of shuffling cards as well as to the quantum factoring algorithm of Shor via the quantum order finding one. Hence we point out that this well-known quantum algorithm makes crucial use of a quantum chaotic operator, or at least one that is close to the quantization of the left-shift, a closeness that we also explore quantitatively.Comment: 12 pgs. Substantially elaborated version, including a new route to the quantum bakers map. To appear in J. Phys.

Multifractal eigenstates of quantum chaos and the Thue-Morse sequence

We analyze certain eigenstates of the quantum baker's map and demonstrate, using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse sequence, a simple sequence that is at the border between quasi-periodicity and chaos, and hence is a good paradigm for quantum chaotic states. We show a family of states that are also simply related to Thue-Morse sequence, and are strongly scarred by short periodic orbits and their homoclinic excursions. We give approximate expressions for these states and provide evidence that these and other generic states are multifractal.Comment: Substantially modified from the original, worth a second download. To appear in Phys. Rev. E as a Rapid Communicatio

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

Laser cooling of a diatomic molecule

It has been roughly three decades since laser cooling techniques produced ultracold atoms, leading to rapid advances in a vast array of fields. Unfortunately laser cooling has not yet been extended to molecules because of their complex internal structure. However, this complexity makes molecules potentially useful for many applications. For example, heteronuclear molecules possess permanent electric dipole moments which lead to long-range, tunable, anisotropic dipole-dipole interactions. The combination of the dipole-dipole interaction and the precise control over molecular degrees of freedom possible at ultracold temperatures make ultracold molecules attractive candidates for use in quantum simulation of condensed matter systems and quantum computation. Also ultracold molecules may provide unique opportunities for studying chemical dynamics and for tests of fundamental symmetries. Here we experimentally demonstrate laser cooling of the molecule strontium monofluoride (SrF). Using an optical cycling scheme requiring only three lasers, we have observed both Sisyphus and Doppler cooling forces which have substantially reduced the transverse temperature of a SrF molecular beam. Currently the only technique for producing ultracold molecules is by binding together ultracold alkali atoms through Feshbach resonance or photoassociation. By contrast, different proposed applications for ultracold molecules require a variety of molecular energy-level structures. Our method provides a new route to ultracold temperatures for molecules. In particular it bridges the gap between ultracold temperatures and the ~1 K temperatures attainable with directly cooled molecules (e.g. cryogenic buffer gas cooling or decelerated supersonic beams). Ultimately our technique should enable the production of large samples of molecules at ultracold temperatures for species that are chemically distinct from bialkalis.Comment: 10 pages, 7 figure

Calculations of collisions between cold alkaline earth atoms in a weak laser field

We calculate the light-induced collisional loss of laser-cooled and trapped magnesium atoms for detunings up to 50 atomic linewidths to the red of the ^1S_0-^1P_1 cooling transition. We evaluate loss rate coefficients due to both radiative and nonradiative state-changing mechanisms for temperatures at and below the Doppler cooling temperature. We solve the Schrodinger equation with a complex potential to represent spontaneous decay, but also give analytic models for various limits. Vibrational structure due to molecular photoassociation is present in the trap loss spectrum. Relatively broad structure due to absorption to the Mg_2 ^1Sigma_u state occurs for detunings larger than about 10 atomic linewidths. Much sharper structure, especially evident at low temperature, occurs even at smaller detunings due to of Mg_2 ^1Pi_g absorption, which is weakly allowed due to relativistic retardation corrections to the forbidden dipole transition strength. We also perform model studies for the other alkaline earth species Ca, Sr, and Ba and for Yb, and find similar qualitative behavior as for Mg.Comment: 20 pages, RevTex, 13 eps figures embedde

Comparing nuclear power trajectories in Germany and the UK: from ‘regimes' to ‘democracies’ in sociotechnical transitions and Discontinuities

This paper focuses on arguably the single most striking contrast in contemporary major energy politics in Europe (and even the developed world as a whole): the starkly differing civil nuclear policies of Germany and the UK. Germany is seeking entirely to phase out nuclear power by 2022. Yet the UK advocates a ‘nuclear renaissance’, promoting the most ambitious new nuclear construction programme in Western Europe.Here,this paper poses a simple yet quite fundamental question: what are the particular divergent conditions most strongly implicated in the contrasting developments in these two countries. With nuclear playing such an iconic role in historical discussions over technological continuity and transformation, answering this may assist in wider understandings of sociotechnical incumbency and discontinuity in the burgeoning field of‘sustainability transitions’. To this end, an ‘abductive’ approach is taken: deploying nine potentially relevant criteria for understanding the different directions pursued in Germany and the UK. Together constituted by 30 parameters spanning literatures related to socio-technical regimes in general as well as nuclear technology in particular, the criteria are divided into those that are ‘internal’ and ‘external’ to the ‘focal regime configuration’ of nuclear power and associated ‘challenger technologies’ like renewables. It is ‘internal’ criteria that are emphasised in conventional sociotechnical regime theory, with ‘external’ criteria relatively less well explored. Asking under each criterion whether attempted discontinuation of nuclear power would be more likely in Germany or the UK, a clear picture emerges. ‘Internal’ criteria suggest attempted nuclear discontinuation should be more likely in the UK than in Germany– the reverse of what is occurring. ‘External’ criteria are more aligned with observed dynamics –especially those relating to military nuclear commitments and broader ‘qualities of democracy’. Despite many differences of framing concerning exactly what constitutes ‘democracy’, a rich political science literature on this point is unanimous in characterising Germany more positively than the UK. Although based only on a single case,a potentially important question is nonetheless raised as to whether sociotechnical regime theory might usefully give greater attention to the general importance of various aspects of democracy in constituting conditions for significant technological discontinuities and transformations. If so, the policy implications are significant. A number of important areas are identified for future research, including the roles of diverse understandings and specific aspects of democracy and the particular relevance of military nuclear commitments– whose under-discussion in civil nuclear policy literatures raises its own questions of democratic accountability

Ab initio simulations of the kinetic properties of the hydrogen monomer on graphene

The understanding of the kinetic properties of hydrogen (isotopes) adatoms on graphene is important in many fields. The kinetic properties of hydrogen-isotope (H, D and T) monomers were simulated using a composite method consisting of density functional theory, density functional perturbation theory and harmonic transition state theory. The kinetic changes of the magnetic property and the aromatic $\pi$ bond of the hydrogenated graphene during the desorption and diffusion of the hydrogen monomer was discussed. The vibrational zero-point energy corrections in the activation energies were found to be significant, ranging from 0.072 to 0.205 eV. The results obtained from quantum-mechanically modified harmonic transition state theory were compared with the ones obtained from classical-limit harmonic transition state theory over a wide temperature range. The phonon spectra of hydrogenated graphene were used to closely explain the (reversed) isotope effects in the prefactor, activation energy and jump frequency of the hydrogen monomer. The kinetic properties of the hydrogen-isotope monomers were simulated under conditions of annealing for 10 minutes and of heating at a constant rate (1.0 K/s). The isotope effect was observed; that is, a hydrogen monomer of lower mass is desorbed and diffuses more easily (with lower activation energies). The results presented herein are very similar to other reported experimental observations. This study of the kinetic properties of the hydrogen monomer and many other involved implicit mechanisms provides a better understanding of the interaction between hydrogen and graphene.Comment: Accepted by J. Phys. Chem.

BioMAJ: a flexible framework for databanks synchronization and processing

Large- and medium-scale computational molecular biology projects require accurate bioinformatics software and numerous heterogeneous biological databanks, which are distributed around the world. BioMAJ provides a flexible, robust, fully automated environment for managing such massive amounts of data. The JAVA application enables automation of the data update cycle process and supervision of the locally mirrored data repository. We have developed workflows that handle some of the most commonly used bioinformatics databases. A set of scripts is also available for post-synchronization data treatment consisting of indexation or format conversion (for NCBI blast, SRS, EMBOSS, GCG, etc.). BioMAJ can be easily extended by personal homemade processing scripts. Source history can be kept via html reports containing statements of locally managed databanks

Projected Range Contractions of European Protected Oceanic Montane Plant Communities: Focus on Climate Change Impacts Is Essential for Their Future Conservation

Global climate is rapidly changing and while many studies have investigated the potential impacts of this on the distribution of montane plant species and communities, few have focused on those with oceanic montane affinities. In Europe, highly sensitive bryophyte species reach their optimum occurrence, highest diversity and abundance in the northwest hyperoceanic regions, while a number of montane vascular plant species occur here at the edge of their range. This study evaluates the potential impact of climate change on the distribution of these species and assesses the implications for EU Habitats Directive-protected oceanic montane plant communities. We applied an ensemble of species distribution modelling techniques, using atlas data of 30 vascular plant and bryophyte species, to calculate range changes under projected future climate change. The future effectiveness of the protected area network to conserve these species was evaluated using gap analysis. We found that the majority of these montane species are projected to lose suitable climate space, primarily at lower altitudes, or that areas of suitable climate will principally shift northwards. In particular, rare oceanic montane bryophytes have poor dispersal capacity and are likely to be especially vulnerable to contractions in their current climate space. Significantly different projected range change responses were found between 1) oceanic montane bryophytes and vascular plants; 2) species belonging to different montane plant communities; 3) species categorised according to different biomes and eastern limit classifications. The inclusion of topographical variables in addition to climate, significantly improved the statistical and spatial performance of models. The current protected area network is projected to become less effective, especially for specialised arctic-montane species, posing a challenge to conserving oceanic montane plant communities. Conservation management plans need significantly greater focus on potential climate change impacts, including models with higher-resolution species distribution and environmental data, to aid these communities’ long-term survival