A gedanken experiment is described in which the noninvasive determination of joint probability densities for the magnetic flux linking a superconducting quantum-interference device is determined using variable threshold superconducting switches followed by superconducting magnetometers. As a result, it is demonstrated that an important prediction of quantum mechanics can be tested in principle against those of macrorealistic theories using superconducting circuits.

The eigenfrequencies of resonance cavities shaped as stadium or Sinai billiards are determined by microwave absorption. In the applied frequency range 0–18.74 GHz the used cavities can be considered as two dimensional. For this case quantum-mechanical and electromagnetic boundary conditions are equivalent, and the resonance spectrum of the cavity is, if properly normalized, identical with the quantum-mechanical eigenvalue spectrum. Spectra, containing up to a thousand eigenfrequencies, are obtained within minutes. Statistical properties of the spectra as well as their correlation with classical periodic orbits are discussed.

We show that the time evolution of a space curve is associated with a geometric phase. This phase arises from the path dependence of the rotation of the natural Frenet-Serret triad with respect to a nonrotating (Fermi-Walker) frame. We derive a general expression in 1+1 dimension for the phase and the associated gauge potential, and discuss the application of this formalism to the classical, continuous, antiferromagnetic Heisenberg spin chain.

A Maxwell demon gathers and uses information to extract work from heat. Limits derived here suggest that a Maxwell demon can extract work only by waiting for rare thermal fluctuations.

It is shown that fractional statistics on a torus are consistent only with multicomponent wave functions. This is expected to be generally true for all 2D, closed, multiply connected, orientable manifolds. The fractional quantum Hall effect with periodic boundary conditions is seen to fit into this new picture, where the quasiholes may be interpreted as a kind of generalized anyons.

It is shown on the basis of numerical data that the normalized localization length of eigenvectors of band random matrices follows a scaling law. The scaling parameter is ${\mathit{b}}^2$/N, where b measures the bandwidth and N is the size of the matrix.

We present a solvable singular quantum billiard which displays fully developed wave chaos. Its level statistics is investigated and proved to coincide with predictions of the Gaussian orthogonal ensemble of random matrices. The corresponding wave functions are shown to be well approximated by a Gaussian ransom variable.

We investigate the order-parameter distribution P(q) of the Ising spin glass with nearest-neighbor interactions in four dimensions using Monte Carlo simulations on lattices of linear dimension up to L=6. We find that, below the transition temperature ${\mathit{T}}_{\mathit{c}}$, the weight at small q seems to saturate to a nonzero value as the size increases, similar to the infinite-range Sherrington-Kirkpatrick model. We discuss our results in the light of recent theoretical predictions for the nature of the spin-glass phase.

We show that for fermions interacting with potentials with a momentum cutoff the Hamiltonian is stable and defines a time evolution in the Heisenberg representation. A mixing property of these systems is derived.

The scattering of a nonlinear wave packet as an envelope soliton by a one-dimensional disordered system is studied. It is well known that in the linear limit the transmission coefficient decays exponentially with a characteristic localization length. We predict, using a simple independent scattering approach and soliton perturbation theory in the framework of the nonlinear Schrödinger equation, that strong nonlinearity above certain threshold allows undistorted propagation of wave packets.

We have carried out a modern version of the Kennedy-Thorndike experiment by searching for sidereal variations between the frequency of a laser locked to an ${\mathit{l}}_2$ reference line and a laser locked to the resonance frequency of a highly stable cavity. No variations were found at the level of 2×${10}^{\mathrm{-}13}$. This represents a 300-fold improvement over the original Kennedy-Thorndike experiment and allows the Lorentz transformations to be deduced entirely from experiment at an accuracy level of 70 ppm.

Sharp-energy S-matrix elements have been successfully extracted from a wave-packet description of three-boson and quartet-spin, neutron-deuteron scattering at energies well above the breakup threshold. Essential to the success of this procedure is use of an expansion basis comprising functions from each of the three two-cluster arrangements.

A hierarchical approach to complexity of infinite stationary strings of symbols is introduced by investigating the scaling behavior of suitable quantities. The topological entropy, which estimates the growth rate of the number of admissible words, corresponds to the first-order indicator ${\mathit{C}}^{\mathrm{}\left(1\right)\mathrm{}}$. At the second level, a novel indicator ${\mathit{C}}^{\mathrm{}\left(2\right)\mathrm{}}$ is introduced which measures the growth rate of the number of irreducible forbidden words. Finally, a detailed analysis of 2D maps reveals that ${\mathit{C}}^{\mathrm{}\left(2\right)\mathrm{}}$ can be expressed in terms of the Lyapunov exponents.

We study a general Bak-Tang-Wiesenfeld–type automaton model of self-organized criticality in which the toppling conditions depend on local height, but not on its gradient. We characterize the critical state, and determine its entropy for an arbitrary finite lattice in any dimension. The two-point correlation function is shown to satisfy a linear equation. The spectrum of relaxation times describing the approach to the critical state is also determined exactly.

It is pointed out that scaling (multifractal) properties of chaotic repellers underlying irregular scattering in two-degrees-of-freedom systems can be deduced by measuring simple length scales generated hierarchically along a straight line taken far away from the interaction region, or on the Poincaré plane, and analyzing them in the spirit of the thermodynamic formalism. The method is easier to apply than a periodic orbit analysis.

We incorporate linear mode conversion in wave-kinetic theory when the incoming waves are incoherent, as occurs when the wave sources are turbulent processes or thermal emission. Mode conversion takes place when the rays of either wave mode cross the mode conversion manifold in the ray phase space. Jump conditions are derived which match the incoming and outgoing wave actions across the mode-conversion manifold, leading to a pair of coupled wave-kinetic equations. We also discuss how incoherent linear mode conversion acts as a source of wave entropy.

Dynamical quasidegeneracies may arise in the spectrum of systems having discrete symmetries. They are semiclassically interpreted as quantized congruent but distinct tori in phase space. With them the separation of regular and irregular states in the quantum spectrum of some mixed phase-space systems may be performed in a simple yet clear fashion. At finite energies (h finite), the frontier between regular and irregular states is not sharp. This is illustrated by the study of two coupled quartic oscillators.

We carry out Monte Carlo simulations of the two-dimensional classical neutral Coulomb gas of integer charges on a square lattice, as a function of temperature and chemical potential, and find new critical behavior. At low temperature, as density increases, the system has a first-order transition to an ordered-charge lattice. As temperature increases, this dense phase has a Kosterlitz-Thouless transition followed by an Ising transition. The first-order line joins the line of Ising transitions at a new tricritical point.

In two space dimensions we generalize the boson-vortex duality picture for spinless particles to boson-vortex-Skyrmion duality for spin-1/2 particles. The spin-singlet fractional quantum Hall effect and spin-singlet anyon superconductivity can be understood as the condensation of vortices and Skyrmions into various fractional quantum Hall states.

Tracing the neutron spin on its passage through a magnetic field which rotates at various frequencies it was possible to observe geometrically induced phase shifts of a quantum-mechanical state even for incomplete revolutions of this field. The experiments show that we can extract such purely geometric effects also from nonadiabatic evolutions.