Rigidity of compact Riemannian spin Manifolds with Boundary

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy

Self-organized critical neural networks

A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable at the single synapse level. This principle is studied in a two-dimensional neural network with randomly wired asymmetric weights. In this class of networks, network connectivity is closely related to a phase transition between ordered and disordered dynamics. A slow topology change is imposed on the network through a local rewiring rule motivated by activity-dependent synaptic development: Neighbor neurons whose activity is correlated, on average develop a new connection while uncorrelated neighbors tend to disconnect. As a result, robust self-organization of the network towards the order disorder transition occurs. Convergence is independent of initial conditions, robust against thermal noise, and does not require fine tuning of parameters.Comment: 5 pages RevTeX, 7 figures PostScrip

Quantum Thermodynamic Cycles and quantum heat engines

In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwell's demon in quantum thermodynamic cycles. We find that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine.Comment: 17 pages, 9 figures, 4 table

Variance of transmitted power in multichannel dissipative ergodic structures invariant under time reversal

We use random matrix theory (RMT) to study the first two moments of the wave power transmitted in time reversal invariant systems having ergodic motion. Dissipation is modeled by a number of loss channels of variable coupling strength. To make a connection with ultrasonic experiments on ergodic elastodynamic billiards, the channels injecting and collecting the waves are assumed to be negligibly coupled to the medium, and to contribute essentially no dissipation. Within the RMT model we calculate the quantities of interest exactly, employing the supersymmetry technique. This approach is found to be more accurate than another method based on simplifying naive assumptions for the statistics of the eigenfrequencies and the eigenfunctions. The results of the supersymmetric method are confirmed by Monte Carlo numerical simulation and are used to reveal a possible source of the disagreement between the predictions of the naive theory and ultrasonic measurements.Comment: 10 pages, 2 figure

Laser beam coupling with capillary discharge plasma for laser wakefield acceleration applications

One of the most robust methods, demonstrated up to date, of accelerating electron beams by laser-plasma sources is the utilization of plasma channels generated by the capillary discharges. These channels, i.e., plasma columns with a minimum density along the laser pulse propagation axis, may optically guide short laser pulses, thereby increasing the acceleration length, leading to a more efficient electron acceleration. Although the spatial structure of the installation is simple in principle, there may be some important effects caused by the open ends of the capillary, by the supplying channels etc., which require a detailed 3D modeling of the processes taking place in order to get a detailed understanding and improve the operation. However, the discharge plasma, being one of the most crucial components of the laser-plasma accelerator, is not simulated with the accuracy and resolution required to advance this promising technology. In the present work, such simulations are performed using the code MARPLE. First, the process of the capillary filling with a cold hydrogen before the discharge is fired, through the side supply channels is simulated. The main goal of this simulation is to get a spatial distribution of the filling gas in the region near the open ends of the capillary. A realistic geometry is used for this and the next stage simulations, including the insulators, the supplying channels as well as the electrodes. Second, the simulation of the capillary discharge is performed with the goal to obtain a time-dependent spatial distribution of the electron density near the open ends of the capillary as well as inside the capillary. Finally, to evaluate effectiveness of the beam coupling with the channeling plasma wave guide and electron acceleration, modeling of laser-plasma interaction was performed with the code INF&RNOComment: 11 pages, 9 figure

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.

On production and asymmetric focusing of flat electron beams using rectangular capillary discharge plasmas

A method for the asymmetric focusing of electron bunches, based on the active plasma lensing technique is proposed. This method takes advantage of the strong inhomogeneous magnetic field generated inside the capillary discharge plasma to focus the ultrarelativistic electrons. The plasma and magnetic field parameters inside the capillary discharge are described theoretically and modeled with dissipative magnetohydrodynamic computer simulations enabling analysis of the capillaries of rectangle cross-sections. Large aspect ratio rectangular capillaries might be used to transport electron beams with high emittance asymmetries, as well as assist in forming spatially flat electron bunches for final focusing before the interaction point.Comment: 16 pages, 7 figures, 1 tabl

Effect of the frequency chirp on laser wakefield acceleration

The role of laser frequency chirps in the laser wakefield accelerator is examined. We show that in the linear regime, the evolution of the laser pulse length is affected by the frequency chirp, and that positive (negative) chirp compresses (stretches) the laser pulse, thereby increasing (decreasing) the peak vector potential and wakefield amplitude. In the blowout regime, the frequency chirp can be used to fine tune the localized etching rates at the front of the laser. In our simulations, chirped laser pulses can lead to 15% higher self-trapped electrons, and 10% higher peak energies as compare to the transform-limited pulse. Chirps may be used to control the phase velocity of the wake, and to relax the self-guiding conditions at the front of the laser. Our predictions are confirmed by multi-dimensional particle-in-cell simulations with OSIRIS.Comment: Submitted in NJP, 4 figure

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