In this paper we propose and test a possible varitaional principle for nonequilibrium steady states far from equilibrium where local thermodynamic equilibrium has broken down. We propose that subject to the externally imposed constraints, the rate of decrease of the volume of phase space which is accessible to the system, is a local minimum. This hypothesis reduces to the familiar principle of minimum entropy production for systems in local thermodynamic equilibrium. We provide computer-simulation data in support of our hypothesis.

A recently proposed phase-space representation for quantum mechanics provides a formal means for investigating the correspondence between classical and quantum mechanics. To explore the implications of this new representation, we introduce a numerical method for propagating an initial wave function directly in phase space. We illustrate the usefulness of the proposed method by analyzing two simple quantum-mechanical systems in phase space.

We reduce a random-band-matrix (RBM) problem to a one-dimensional, nonlinear, supersymmetric, σ model. This reduction becomes exact in the limit b→∞, b being the effective bandwidth. We prove that ${\mathit{b}}^2$/N, N being the matrix size, is the relevant scaling parameter. When the mean value of diagonal elements increases linearly along the diagonal an extra scaling parameter arises. These conclusions are in agreement with recent numerical results.

We combine the cycle-expansion method with a functional equation to obtain highly excited semiclassical energy eigenvalues for chaotic Hamiltonian systems. Applications to the anisotropic Kepler problem and to a bounded billiard demonstrate the power of the method. The agreement with quantum results is surprisingly good even for highly excited states.

Experimental evidence of ultrasonic emission from volcanic rocks has been produced for the first time by a survey of the Strombolian activity. The statistical analysis of the recorded acoustic wave bursts show that the notion of self-organized criticality applies well to the mechanism responsible for the observed emission phenomenon.

It is shown that the conventional Bloch-Kirchhoff description of NMR-laser activity needs the inclusion of a nonlinear relaxation term for the transverse magnetization in order to account for the experimental observation. The validity of the modified equations is demonstrated by comparing in a two-parameter space the Poincaré sections and periodic-orbit structures of model and experiment. All unstable orbits up to order nine have been extracted and employed to obtain an approximation to a generating partition.

We consider wandering of a nonrelativistic particle in a time-dependent random potential in d spatial dimensions. Its root-mean-square displacement from the initial position increases superdiffusively with time t as ${\mathit{t}}^{9/8}$ for d>1, and as ${\mathit{t}}^{6/5}$ in d=1. Its kinetic energy increases as ${\mathit{t}}^{1/2}$ for d>1, and as ${\mathit{t}}^{2/5}$ in d=1. These scaling behaviors hold for both the classical and the corresponding quantum-mechanical problem in continuous space-time and differ from those of lattice models.

We study a rule for quantizing chaos based on the dynamical zeta function defined by a Euler product over the classical periodic orbits as suggested by Gutzwiller’s semiclassical trace formula. A test of our approximate quantization formula is carried out for the planar hyperbold billiard, which shows that at least the first 150 quantum energy levels can be generated.

Localization in the quantum-kicked-rotator problem leads to nontrivial dynamical correlations that are absent in the classical limit. Consequently, both coherence and diffusion in the presence of colored noise depend on its long-range autocorrelations. This implies that a Markovian treatment of the dynamics for a system that is coupled to a low-temperature heat bath is not valid even if the system is classically chaotic.

The close relations between statistical properties of quantum dissipative systems and scattering systems is discussed. It is conjectured that for quantum chaotic scattering the distribution of the resonance poles of the S matrix is generic and follows the predictions of the Ginibre ensemble of random non-Hermitian matrices. This phenomenon has been demosntrated on a simple example of a single particle scattered by eight randomly distributed point obstacles in three dimensions.

The chaotic dynamics found in the diode resonator has been converted into stable orbits with periods up to 23 drive cycles long. The method used is a modification of that of Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)]. In addition to stabilizing existing low-period orbits, the method allows making small alterations in the attractor permitting previously nonexistent periodic orbits to be stabilized. It is an analog technique and therefore can be very fast, making it applicable to a wide variety of systems.

The demonstrations of Wigner and others, that observables which do not commute with additive conserved quantities cannot be measured precisely, are reexamined. A proposed new formulation of the claim is shown to be valid for observables with a continuous spectrum whenever the conserved quantities are bounded. However, a countermodel is constructed, and it suggests that the position can be measured as precisely as the momentum even though the measuring interaction conserves the total linear momentum.

We propose a new model for studying dissipation in quantum-mechanical systems. The mechanism of dissipation is solely due to the scattering of the environment excitations by the particle of interest. We treat the problem via the functional integral formalism. It is shown that the model gives a damping parameter which is temperature dependent.

The asymptotic spectrum of the wave-height autocorrelation is of power-law form for surface gravity waves in deep water. Physical oceanographers have utilized Kolmogorov-type scaling arguments within transport theory in order to predict the exponent of the power law once the wave statistics become stationary. I advance the hypothesis that the asymptotics can be achieved using Hamilton’s equations correct to third order with an arbitrary nonsingular interaction term which has the symmetry, degree of homogeneity, and quasilocality in k space of the full Hasselmann interaction term. Examples which support the hypothesis are presented, and its further implications are discussed.

A theorem which describes the Newtonian dynamics of the center of mass (as defined with respect to the energy density) of nonlinear Klein-Gordon-type solitary waves is proved. It appears as a generalization of Ehrenfest’s theorem in quantum mechanics, which describes the Newtonian dynamics of the center of mass (as defined with respect to the probability density) of the linear wave functions. As an example, the interaction of recently discovered two-dimensional pulsons [cf. E. M. Maslov, Phys. Lett. A 151, 47 (1990)] is considered.

Spin-1/2 xxz and q-Potts quantum chains with translation-invariant boundary conditions are analyzed as representations of the periodic Temperley-Lieb-Jones algebra. A connection with the affine Hecke algebra is established and used to find the irreducible content. This analysis provides an explanation for both the degeneracies and the overlap in the spectra of these models.

Using the Faddeev equations in configuration space, we solve numerically the problem of three anyons interacting via harmonic forces. The relevance of our results to the many-anyon problem is discussed.

The low-lying quantum states of three anyons confined in a harmonic-oscillator well are obtained numerically. The interpolation of these states between the limits of noninteracting bosons to noninteracting fermions in the well is established. Particular attention is paid to the transformation of the fermionic ground state to an excited Bosonic state, and its overlap with Laughlin-Wu-type correlated states.

An exact analysis of the Ising model with infinite-range interactions in a random field and a local mean-field theory in three dimensions is carried out leading to a phase diagram with several coexistence surfaces and lines of critical points. Our results show that the phase diagram depends crucially on whether the distribution of random fields is symmetric or not. Thus, Ising-like phase transitions in a porous medium (the asymmetric case) are in a different universality class from the conventional random-field model (symmetric case).

We present an integrability criterion for discrete-time systems that is the equivalent of the Painlevé property for systems of a continuous variable. It is based on the observation that for integrable mappings the singularities that may appear are confined, i.e., they do not propagate indefinitely when one iterates the mapping. Using this novel criterion we show that there exists a family of nonautonomous integrable mappings which includes the discrete Painlevé equations by ${\mathit{P}}_{\mathrm{I}}$, recently derived in a model of two-dimensional quantum gravity, and ${\mathit{P}}_{\mathrm{II}}$, obtained as a similarity reduction of the integrable modified Korteweg–de Vries lattice. These systems possess Lax pairs, a well-known integrability feature.