Kinetics and scaling in ballistic annihilation

We study the simplest irreversible ballistically-controlled reaction, whereby particles having an initial continuous velocity distribution annihilate upon colliding. In the framework of the Boltzmann equation, expressions for the exponents characterizing the density and typical velocity decay are explicitly worked out in arbitrary dimension. These predictions are in excellent agreement with the complementary results of extensive Monte Carlo and Molecular Dynamics simulations. We finally discuss the definition of universality classes indexed by a continuous parameter for this far from equilibrium dynamics with no conservation laws

Ballistic Annihilation

Ballistic annihilation with continuous initial velocity distributions is investigated in the framework of Boltzmann equation. The particle density and the rms velocity decay as $c=t^{-\alpha}$ and $=t^{-\beta}$, with the exponents depending on the initial velocity distribution and the spatial dimension. For instance, in one dimension for the uniform initial velocity distribution we find $\beta=0.230472...$. We also solve the Boltzmann equation for Maxwell particles and very hard particles in arbitrary spatial dimension. These solvable cases provide bounds for the decay exponents of the hard sphere gas.Comment: 4 RevTeX pages and 1 Eps figure; submitted to Phys. Rev. Let

Stochastic Ballistic Annihilation and Coalescence

We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic density decay. By universal we mean that all models in the class are described by a single phase diagram spanned by two reduced parameters. The phase diagram reveals four regimes, two of which contain the previously studied cases of ballistic annihilation. The two new phases are a direct consequence of the stochasticity. The solution is obtained through a matrix product approach and builds on properties of a q-deformed harmonic oscillator algebra.Comment: 4 pages RevTeX, 3 figures; revised version with some corrections, additional discussion and in RevTeX forma

Ionization via Chaos Assisted Tunneling

A simple example of quantum transport in a classically chaotic system is studied. It consists in a single state lying on a regular island (a stable primary resonance island) which may tunnel into a chaotic sea and further escape to infinity via chaotic diffusion. The specific system is realistic : it is the hydrogen atom exposed to either linearly or circularly polarized microwaves. We show that the combination of tunneling followed by chaotic diffusion leads to peculiar statistical fluctuation properties of the energy and the ionization rate, especially to enhanced fluctuations compared to the purely chaotic case. An appropriate random matrix model, whose predictions are analytically derived, describes accurately these statistical properties.Comment: 30 pages, 11 figures, RevTeX and postscript, Physical Review E in pres

Traffic and Related Self-Driven Many-Particle Systems

Since the subject of traffic dynamics has captured the interest of physicists, many astonishing effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by so-called ``phantom traffic jams'', although they all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction of the traffic volume cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize in lanes, while similar systems are ``freezing by heating''? Why do self-organizing systems tend to reach an optimal state? Why do panicking pedestrians produce dangerous deadlocks? All these questions have been answered by applying and extending methods from statistical physics and non-linear dynamics to self-driven many-particle systems. This review article on traffic introduces (i) empirically data, facts, and observations, (ii) the main approaches to pedestrian, highway, and city traffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts like a general modelling framework for self-driven many-particle systems, including spin systems. Subjects such as the optimization of traffic flows and relations to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are discussed as well.Comment: A shortened version of this article will appear in Reviews of Modern Physics, an extended one as a book. The 63 figures were omitted because of storage capacity. For related work see http://www.helbing.org

Semiclassical Spectra from Periodic-Orbit Clusters in a Mixed Phase Space.

We calculate complete quasienergy spectra (rather than partial information thereon) from classical periodic orbits for the kicked top, throughout the transition from integrability to well-developed chaos. The standard error incurred for the quasienergies is a small percentage of their mean spacing, even though the effective Planck constant is not pushed to small values. The price paid is the inclusion of collective contributions of clusters of periodic orbits near bifurcations into Gutzwiller's trace formula