Suppression of synchrotron radiation due to beam crystallization

With respect to a "hot", non-crystallized beam the synchrotron radiation of a cold crystallized beam is considerably modified. We predict suppression of synchrotron radiation emitted by a crystallized beam in a storage ring. We also propose experiments to detect this effect.Comment: LaTeX, 3 pages, 1 figure, To be published in Eur. Phys. J. A, December 199

Synchrotron radiation of crystallized beams

We study the modifications of synchrotron radiation of charges in a storage ring as they are cooled. The pair correlation lengths between the charges are manifest in the synchrotron radiation and coherence effects exist for wavelengths longer than the coherence lengths between the charges. Therefore the synchrotron radiation can be used as a diagnostic tool to determine the state (gas, liquid, crystal) of the charged plasma in the storage ring. We show also that the total power of the synchrotron radiation is enormously reduced for crystallized beams. This opens the possibility of accelerating particles to ultra-relativistic energies using small-sized cyclic accelerators.Comment: REVTeX, 27 pages, 6 figures, submitted to Phys. Rev.

Quantal-Classical Duality and the Semiclassical Trace Formula

We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the classical description. This duality is investigated in the present paper. The duality holds for chaotic as well as for integrable systems. For billiards the quantal spectrum (eigenvalues of the Helmholtz equation) and the classical spectrum (lengths of periodic orbits) are two manifestations of the billiard's boundary. The trace formula expresses this link as a Fourier transform relation between the corresponding spectral densities. It follows that the two-point statistics are also simply related. The universal correlations of the quantal spectrum are well known, consequently one can deduce the classical universal correlations. An explicit expression for the scale of the classical correlations is derived and interpreted. This allows a further extension of the formalism to the case of complex billiard systems, and in particular to the most interesting case of diffusive system. The concept of classical correlations allows a better understanding of the so-called diagonal approximation and its breakdown. It also paves the way towards a semiclassical theory that is capable of global description of spectral statistics beyond the breaktime. An illustrative application is the derivation of the disorder-limited breaktime in case of a disordered chain, thus obtaining a semiclassical theory for localization. A numerical study of classical correlations in the case of the 3D Sinai billiard is presented. We gain a direct understanding of specific statistical properties of the classical spectrum, as well as their semiclassical manifestation in the quantal spectrum.Comment: 42 pages, 17 figure

Lightsolver challenges a leading deep learning solver for Max-2-SAT problems

Maximum 2-satisfiability (MAX-2-SAT) is a type of combinatorial decision problem that is known to be NP-hard. In this paper, we compare LightSolver's quantum-inspired algorithm to a leading deep-learning solver for the MAX-2-SAT problem. Experiments on benchmark data sets show that LightSolver achieves significantly smaller time-to-optimal-solution compared to a state-of-the-art deep-learning algorithm, where the gain in performance tends to increase with the problem size

On the Accuracy of the Semiclassical Trace Formula

The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system increases, the mean level spacing decreases as $\hbar^d$, while the semiclassical approximation is commonly believed to provide an accuracy of order $\hbar^2$, independently of d. If this were true, the semiclassical trace formula would be limited to systems in d <= 2 only. In the present work we set about to define proper measures of the semiclassical spectral accuracy, and to propose theoretical and numerical evidence to the effect that the semiclassical accuracy, measured in units of the mean level spacing, depends only weakly (if at all) on the dimensionality. Detailed and thorough numerical tests were performed for the Sinai billiard in 2 and 3 dimensions, substantiating the theoretical arguments.Comment: LaTeX, 31 pages, 14 figures, final version (minor changes

Diagnostic criterion for crystallized beams

Small ion crystals in a Paul trap are stable even in the absence of laser cooling. Based on this theoretically and experimentally well-established fact we propose the following diagnostic criterion for establishing the presence of a crystallized beam: Absence of heating following the shut-down of all cooling devices. The validity of the criterion is checked with the help of detailed numerical simulations.Comment: REVTeX, 11 pages, 4 figures; submitted to PR

Impulse response measurement of nonlinear systems:properties of existing techniques and wide noise sequences

Various impulse response measurement methods are accurate for Hammerstein systems but when a linear filter precedes a static non-linearity, as in a Wiener-Hammerstein system, intermodulation distortion results in undesirable artifacts. In this paper the advantages of the wide maximum length sequence and multiple noise sequences methods are combined to create a method of measuring the diagonal Volterra series expansion of the impulse response of general nonlinear systems that may be seen as an alternative to the existing dynamic convolution method