The parametric motion of eigenvalues of two chaotic quantum systems, a stadium billiard and a kicked rotator, is studied to investigate the curvature distribution introduced by Gaspard et al. [Phys. Rev. A 42, 4015 (1990)]. By using an average of a statistical quantity over the parameter values along the motion, we obtain the curvature distribution and confirm the predicted universality of its tail behavior. We also show a nonuniversal characteristic at small curvatures, which is attributed to the existence of solitonlike structures.

Bond-energy correlation functions are calculated exactly for a planar Ising model in finite-size strip geometry for subcritical temperatures with surface fields of either equal or opposite sign applied to opposite edges. We show that the Wulff construction (surface free-energy minimization) applied to the bubble model for the 2-point energy correlation function gives exact results and demonstrates the significance of wetting phenomena.

A direct test for deterministic dynamics can be established by measurement of average directional vectors in a coarse-grained d-dimensional embedding of a time series. Theoretical analysis of the statistical properties of a random time series using the same embedding technique is possible by consideration of classical results concerning random walks in d dimensions. Examples are given to show the clear differences between deterministic dynamics, such as may be generated by chaotic systems, and stochastic dynamics.

A new adiabatic theory permits the understanding of one-dimensional dynamics of particles interacting with a large-amplitude wave packet for bounce time short compared with the transit time. This theory differs from previous ones in that the Hamiltonian varies slowly not with the time, but with the coordinate. The resulting adiabatic invariant is not equal, even in lowest order, to the usual action. This theory predicts the basic features of the interaction observed in previous numerical studies.

Delay times relative to a beat envelope are deduced from a path-integral solution of the telegrapher equation, analytically continued to imaginary time when the square of the effective velocity becomes negative. The results are approximately described by a semiclassical model translated in frequency from the nominal to an effective cutoff, thus improving the agreement with experimental results.

The Ott-Grebogi-Yorke control method is analyzed in the case that the attractor is reconstructed from a time series using time delay coordinates. It turns out that the control formula of Ott, Grebogi, and Yorke should be modified in order to apply to experimental systems if time delay coordinates are used. We reveal that the experimental surface of section map depends not only on the actual parameter but also on the preceding one. In order to meet this dependence two modifications are introduced which lead to a better performance of the control. To compare their control abilities they are applied to simulations of a Duffing oscillator.

It was proposed that the mass of a particle be defined by its de Broglie frequency, measured as ${\mathit{c}}^2$/λ/γv, where λ/ is the mean de Broglie wavelength of the particle when it has mean speed v and Lorentz factor γ; the masses of systems too large to have a measurable λ/ are then to be derived by specifying the usual inertial and additive properties of mass. This avoids the use of an arbitrary macroscopic standard such as the prototype kilogram, and does not even require the choice of a specific particle as a mass standard. Suggestions are made as to how this absolute mass can be realized and measured at the macroscopic level and comments are made on the effect of the new definition on the form of the equations of physics.

Relying on the recent proposed multicanonical algorithm, we present a numerical simulation of the first-order phase transition in the 2D 10-state Potts model on lattices up to sizes 100×100. It is demonstrated that the new algorithm lacks an exponentially fast increase of the tunneling time between metastable states as a function of the linear size L of the system. Instead, the tunneling time diverges approximately proportional to ${\mathit{L}}^{2.65}$. On our largest lattice we gain more than 2 orders of magnitude as compared to a standard heat-bath algorithm. As a first physical application we report a high-precision computation of the interfacial free energy per unit area.

Universal amplitude relations associated with hyperscaling are obtained exactly for several integrable perturbations of two-dimensional (multi)critical points described by minimal models. The results are confirmed numerically and it is discussed how they can be verified by experiment.

We study how a Cantor spectrum, its level statistics, and corresponding dynamics are affected by the onset of classical chaos. While the spectrum undergoes visible changes, its level spacing distribution follows an inverse power law p(s)∼${\mathit{s}}^{\mathrm{-}3/2}$ on small scales. We find a crossover which is manifested in the time domain by two diffusive regimes characterized by a classical and a quantum-mechanical diffusion coefficient. In the strong quantum limit we show by means of a transformation that the spectrum is governed by the IintegrableP Harper equation, even if the classical phase space is strongly chaotic.

The spin-orbit interaction is shown to arise as a Berry phase term in the adiabatic effective Hamiltonian for the orbital motion of a Dirac electron. This approach makes explicit the intimate connection of the spin-orbit interaction and Thomas precession.

The Korteweg–de Vries, modified Korteweg–de Vries, and Harry Dym hierarchies of integrable systems are shown to be equivalent to a hierarchy of chiral shape dynamics of closed curves in the plane. These purely local dynamics conserve an infinite number of global geometric properties of the curves, such as perimeter and enclosed area. Several techniques used to study these integrable systems are shown to have simple differential-geometric interpretations. Connections with incompressible, inviscid fluid flow in two dimensions are suggested.

The fluctuations of the advancing interface observed in experiments on two-phase fluid flow in porous media are investigated using several evaluation techniques. We find that the amplitudes η of these fluctuations are distributed according to a power law of the form P(η)∼${\mathrm{\eta }}^{\mathrm{-}(\mathrm{\mu }+1)}$, with μ≊2.7. Our results together with a recent model of anomalous roughening suggest a plausible explanation for the nonuniversal values of the exponents observed in the experiment on two-phase flow.

We study nonequilibrium steady states produced by a competition between anomalous diffusion (random Levy-flight exchanges) and local dynamics satisfying detailed balance for the equilibrium state of either the Ising chain or the spherical model. The phase transitions occurring in these systems are investigated via simulations and an exact solution. The results show that the steady-state properties are dominated by effective long-range interactions decaying with distance as ${\mathit{r}}^{\mathrm{-}\mathit{d}\mathrm{-}\mathrm{\sigma }}$, where d is the spatial dimension while σ is the dimension of the Levy flight.

A quantity related to the elastic enhancement in nuclear reactions is introduced to analyze how the transition from integrable to chaotic behavior is a classical system is reflected in the eigenstates of the corresponding quantum system. Its behavior is first studied for random matrix models believed to represent such a transition, namely, a band matrix ensemble as well as a Poisson ensemble perturbed by a Gaussian orthogonal ensemble. Both of these display similar behavior. We then show that the same characteristics may be found in a more realistic system showing such a transition, namely, molecular Rydberg states calculated for high angular momenta.

The random-matrix-theory approach to the avoided-crossings probability distribution for quantum chaotic systems is proposed. Analytical results are obtained for all three (orthogonal, unitary, and symplectic) universality classes of physical systems as well as for systems with partially broken time-reversal invariance. The numerical experiments on the kicked-top model give results in excellent agreement with the theoretical predictions.

We analyze the dynamic behavior of large two-dimensional systems of limit-cycle oscillators with random intrinsic frequencies that interact via time-delayed nearest-neighbor coupling. We find that even small delay times lead to a novel form of frequency depression where the system decays to stable states which oscillate at a delay and interaction-dependent reduced collective frequency. For greater delay or tighter coupling between oscillators we find metastable synchronized states that we describe analytically and numerically.

Results for d=2 percolation allow one to determine exactly the critical exponents for a polymer undergoing the special surface transition, while its bulk is at the FTHETA’ point. ${\gamma }_1$=8/7 and ${\mathrm{\phi }}_{\mathit{s}}$=8/21 are the entropic and the crossover surface exponents, respectively. On the other hand, exact enumerations analysis leads to conjecture ${\gamma }_1$=4/7 at an ordinary FTHETA’ point. This strongly supports universality of FTHETA and FTHETA’ points. Similar exact results are obtained for a multicritical walk in the presence of correlated percolation vacancies.

For multiparticle systems we formulate the notions of signal locality (i.e., absence of faster-than-light signaling) and Einstein-Bell locality (or local realism) and obtain inequalities between experimental correlation functions to test them. Quantum theory obeys signal locality but violates Einstein-Bell locality by a factor $2^{\left(\mathit{n}\mathrm{-}1\right)/2}$ for n-particle systems.

We study the Hamiltonian of a two-level system interacting with a one-mode radiation field by means of the Wigner method and without using the rotating-wave approximation. We show that a phenomenon of collapses and revival, reminiscent of that exhibited by the Jaynes-Cumming model, takes place in the high coupling limit. This process appears as irreversible or virtually reversible, according to whether the semiclassical regime is chaotic or not. Thus we find a new mechanism for dissipation in the quantum domain.