We investigate the $O\left(N\right)$ symmetric linear $\sigma$ model in two dimensions by means of an exact nonperturbative evolution equation. The perturbative infrared divergences are absent in this formulation. We use a simple approximative solution of the flow equation which corresponds to a derivative expansion for the effective action. For $N=2\mathrm{}$ this gives a good picture of the Kosterlitz-Thouless phase transition.

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, $T(x,v)$, of a free inertial process driven by Gaussian white noise from a region $(0,L)$ in space. We obtain a completely explicit expression for $T(x,0\mathrm{})$ and discuss the dependence of $T(x,v)$ as a function of the size $L$ of the region. We develop a new method that may be used to solve other exit time problems.

A histogram Monte Carlo method is used to evaluate the existence probability $E_p$ and the percolation probability $P$ of bond and site percolation on finite square, plane triangular, and honeycomb lattices. We find that, by choosing a very small number of nonuniversal metric factors, all scaled data of $E_p$ and $P$ may fall on the same universal scaling functions. We also find that free and periodic boundary conditions share the same nonuniversal metric factors. This study may be extended to many critical systems.

The classical Lorentz model for charged noninteracting point particles in a perpendicular magnetic field is reconsidered in 2D. We show that the standard Boltzmann equation is not valid for this model, even in the Grad limit. We construct a generalized Boltzmann equation which is, and solve the corresponding initial value problem exactly. The diffusion tensor follows. Away from the Grad limit a percolation problem arises. We study numerically its critical properties.

A Comment on the Letter by Wojciech Hubert Zurek and Juan Pablo Paz, Phys. Rev. Lett. 72, 2508 (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by Giulio Casati and B. V. Chirikov.

A Comment on the Letter by M. V. N. Murthy and R. Shankar, Phys. Rev. Lett. 73, 3331 (94). The authors of the Letter offer a Reply.

A Reply to the Comment by Alain Dasnières de Veigy and StéphaneOuvry.

We enhance the response of a “stochastic resonator” by coupling it into a chain of identical resonators. Specifically, we show via numerical simulation that local linear coupling of overdamped nonlinear oscillators significantly enhances the signal-to-noise ratio of the response of a single oscillator to a time-periodic signal and noise. We relate this array enhanced stochastic resonance to the global spatiotemporal dynamics of the array and show how noise, coupling, and bistable potential cooperate to organize spatial order, temporal periodicity, and peak signal-to-noise ratio.

We examine a collection of particles interacting with inverse-square two-body potentials in the thermodynamic limit. We find explicit large-amplitude density waves and soliton solutions for the motion of the system. Waves can be constructed as coherent states of either solitons or phonons. Therefore, either solitons or phonons can be considered as the fundamental excitations. The generic wave is shown to correspond to a two-band state in the quantum description of the system, while the limiting cases of solitons and phonons correspond to particle and hole excitations.

The wave field defined by the Korteweg–de Vries equation and stimulated by a source moving at nonstationary, transcritical speeds is described. Pairwise interactions of solitons are common in the upstream-propagating packet. The number of solitons generated for various trajectories of the source speed through the transcritical band is quantified in terms of a simple resonant action.

We consider the problem of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature $T$. In the classical limit it reduces to a well-known “toy” model for an interface in a random medium. It is also related to the problem of electron localization in a disordered medium. We find a transition temperature into a glassy phase characterized by replica symmetry breaking. The quantum fluctuations play a role of enhancing the effects of the quenched disorder. The location of the de Almeida–Thouless line is obtained for different values of the particle mass.

We study properties of decay of the correlations for a class of smooth observables and mutual mixing for a class of subsets, with various rates ranging from the power-law to the exponential rate, in simple deterministic nonstrongly chaotic dynamical systems on the torus $T^2$. In fact, these systems are ergodic, have zero $K-S$ entropy and an absolutely continuous part in their spectrum, and display divergence of trajectories with a power-law rate. We show that they generate time series which are unpredictable in the sense of the statistical theory of prediction.

We discuss the statistical mechanics of a two-dimensional gas of non-Abelian Chern-Simons particles which obey the non-Abelian braid statistics. The second virial coefficient is evaluated in the framework of the non-Abelian Chern-Simons quantum mechanics.

Cesium atoms prepared in a state of well-defined total energy have been reflected from a vibrating mirror, causing the matter waves to be phase modulated. The mirror is an evanescent light wave whose intensity is modulated in time at a frequency $\nu$ in the range 0 to 2 MHz; the atoms are reflected at normal incidence. The resulting beam consists of a “carrier” plus various sidebands corresponding to de Broglie waves propagating at different velocities. The precision and flexibility of this technique make it a promising tool in atom optics.

We show that one can ascertain the presence of an object in some sense without interacting with it. One repeatedly, but weakly, tests for the presence of the object, which would inhibit an otherwise coherent evolution of the interrogating photon. The fraction of “interaction-free” measurements can be arbitrarily close to 1. Using single photons in a Michelson interferometer, we have performed a preliminary demonstration of some of these ideas.

A Comment on the Letter by Rosario N. Mantegna and H. Eugene Stanley Phys. Rev. Lett. 73, 2946 (1994)

The wave-action conservation laws for three-wave interactions are of fundamental importance. These laws, known as Manley-Rowe relations, are usually obtained with great difficulty from nonlinear evolution equations. Here, we derive them directly from a Noether symmetry of the appropriate Lagrangian. As an example, the Lagrangian formulation for stimulated Raman scattering is presented, and local Manley-Rowe relations, valid even for noneikonal wave fields, are derived by the Noether method.

If a physical system contains a single particle, and if two distant detectors test the presence of linear superpositions of one-particle and vacuum states, a violation of classical locality can occur, due to the creation of a two-particle component by the detecting process itself.

Renormalization group equations for the physical $t$ matrix are written for quantum scattering with some potentials singular at the origin in two and three dimensions. The momentum-space perturbative treatment of these scattering problems exhibits ultraviolet divergences and permits renormalization leading to a scale. These equations yield the correct asymptotic behavior and some low-energy properties of the $t$ matrix. Illustrations are made for the Dirac delta potential in two and three dimensions.