Topological aspects of quantum chaos

Quantized classically chaotic maps on a toroidal two-dimensional phase space are studied. A discrete, topological criterion for phase-space localization is presented. To each eigenfunction is associated an integer, analogous to a quantized Hall conductivity, which tests the way the eigenfunction explores the phase space as some boundary conditions are changed. The correspondence between delocalization and chaotic classical dynamics is discussed, as well as the role of degeneracies of the eigenspectrum in the transition from localized to delocalized states. The general results are illustrated with a particular model.     

Thinking Transport as a Twist

The determination of the conductivity of a deterministic or stochastic classical system coupled to reservoirs at its ends can in general be mapped onto the problem of computing the stiffness (the ‘energy’ cost of twisting the boundaries) of a quantum-like system. The nature of the coupling to the reservoirs determines the details of the mechanical coupling of the torque at the ends.     

Duality and Hidden Symmetries in Interacting Particle Systems

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the “hidden” symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.     

Strong Soret Effect in One Dimension

We consider a one-dimensional gas of two kinds of particles with different masses interacting through short range interactions. The system exhibits an extreme form of the Soret effect: when the ends of the system are in contact with thermal baths of different temperatures, there is complete separation of the species. We show how this separation can be well described in the Boltzmann approximation and discuss the origin of this odd behavior.     

Gallavotti–Cohen Theorem,Chaotic Hypothesis and the Zero-Noise Limit

The Fluctuation Relation for a stationary state, kept at constant energy by a deterministic thermostat—the Gallavotti–Cohen Theorem— relies on the ergodic properties of the system considered. We show that when perturbed by an energy-conserving random noise, the relation follows trivially for any system at finite noise amplitude. The time needed to achieve stationarity may stay finite as the noise tends to zero, or it may diverge. In the former case the Gallavotti–Cohen result is recovered, while in the latter case, the crossover time may be computed from the action of ‘instanton’ orbits that bridge attractors and repellors. We suggest that the ‘Chaotic Hypothesis’ of Gallavotti, Cohen and Ruelle can thus be reformulated as a matter of stochastic stability of the measure in trajectory space. In this form this hypothesis may be directly tested.     

Constraint optimisation and landscapes

We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses such problems in the more familiar terms of optimisation in rugged energy landscapes. In particular, it allows one to understand the puzzling fact that unsophisticated programs are successful well beyond what was considered to be the `hard’ transition, and suggests an algorithm defining a new, higher, easy-hard frontier.     

A Model with Darwinian Dynamics on a Rugged Landscape

We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase diagram in terms of the size of the population and the diffusion rate, with a glass phase inside which the dynamics keeps searching for better configurations, and outside which deleterious ‘mutations’ spoil the performance. The phase diagram is analogous to that of dense active matter in terms of temperature and drive.

     

Release and report: a new photolabile caging system with a two-photon fluorescence reporting function

A new efficient photocaging system with a fluorescence reporting function has been developed. The photolabile latch is based on adducts of C-nucleophiles with aromatic ketones, such as thioxanthones and xanthones. The system is designed to quantify the release of biological effectors and to monitor their spatial distribution and localization by single- and two-photon fluorescence microscopy. In the armed state the ketone's conjugation is disrupted by nucleophilic addition, resulting in a blue shift of the absorption maxima and a dramatic decrease in fluorescence intensity. The mechanism of the photoinduced uncaging involves homolytic C-C bond fragmentation followed by radical disproportionation, regenerating the carbonyl moiety and restoring fluorescence. The uncaging can be initiated via either a one- or two-photon process, offering a new powerful tool for molecular life sciences. The synthesis and uncaging of dendrimer- and polymeric bead-based model systems are described.