The rate at which pure initial states deteriorate into mixtures is computed for a harmonic oscillator interacting with an environment in thermal equilibrium. The decoherence process resulting from this interaction selects a set of states characterized by maximal stability (or minimal loss of predictive power) which can be quantified by the rate of increase in either linear or statistical entropy. In the weak coupling limit, coherent states are shown to produce the least entropy, thus becoming the natural counterparts of classical points in phase space.

A class of models of deposition and evaporation of dimers, trimers,..., k-mers is studied analytically and by simulation. Correlation functions decay as power laws in time, related to broken symmetries in associated spin Hamiltonians. For k≥3, the number of jammed and evolving steady states increases exponentially with size. Finite size scaling studies support a phenomenological diffusive picture for dynamics and indicate universality over k in many subspaces.

We present a new type of cluster algorithm that strongly reduces critical slowing down in simulations of vertex models. Since the clusters are closed paths of bonds, we call it the loop algorithm. The basic steps in constructing a cluster are the breakup and the freezing of vertices. We concentrate on the case of the F model, which is a subset of the six-vertex model exhibiting a Kosterlitz-Thouless transition. The loop algorithm is also applicable to simulations of other vertex models and of one- and two-dimensional quantum spin systems.

We bring out the connection between Berry’s geometric phase and a gauge invariant expression introduced by Bargmann. We exploit this relationship to show that the Güoy effect, which referes to the phase jump experienced by a focused beam as it crosses the caustic, is the geometric phase associated with the underlying Lobachevskian hyperbolic geometry.

The linearized Vlasov-Maxwell system and ideal magnetohydrodynamics are examples of systems with a pseudo-Hermitian structure with respect to an indefinite inner product on the space of complex representations of real fields [J. Larsson, Phys. Rev. Lett. 66, 1466 (1991)]. This structure leads to variational principles, whose variation with respect to local wave phase yields new wave-action conservation laws, which generalize previous eikonal versions.

The possible amount of information transfer between any source and any user via a quantum system is bounded through the quantum entropy function. In contrast to the classical case, this shows that infinite information transfer implies infinite entropy. The entropy bound is also applied to obtain the ultimate quantum information transmission capacity of the free electromagnetic field under a power and a bandwidth constraint.

We report on a a new measurement of the relativistic Doppler shift in neon. We measured the frequency difference between a two-photon transition in a fast beam and a slow beam. The result is compared to the prediction of special relativity. The experiment represents a more than tenfold improvement over other Doppler shift measurements and verifies the time dilation effect at an accuracy level of 2.3 ppm.

We propose a new method to estimate the quenched free energy in disordered systems. It uses generalized thermodynamic potentials, given by annealed averages of the partition function with appropriate constraints realized by the aid of Lagrange multipliers. The method is applied to Ising models with random magnetic fields. In that particular case, the constraints correspond to average only over the disorder configurations where the sum of the random variables has the correct mean value and variance.

Finite-size scaling allows the extraction of a dimension from scaling ${\mathit{d}}_{\mathit{s}}$, as well as critical exponents for systems with a second-order phase transition. The calculation of ${\mathit{d}}_{\mathit{s}}$ allows comparisons to be made with other expansions in dimension, in which ${\mathit{d}}_{\mathit{s}}$ plays the role of the physical dimension. This is demonstrated by a numerical transfer-matrix study of the pure ferromagnetic Ising model in two and three dimensions, as well as for quenched random bonds in the two-dimensional Ising ferromagnet.

A model Hamiltonian describing an energy-exhange process between an ultrarelativistic particle and a one-dimensional spin array is proposed and solved exactly. Interesting relations with the quantum measurement problem are discussed.

We propose a systematic perturbative method for calculating the binding energy of threshold bound states—states which exist for arbitrary small coupling. The starting point is a (regularized) free theory. Explicit calculations are performed for quantum mechanics with arbitrary short-range potential in 1D and various (1+1)-dimensional quantum field theories. We check the method by comparing the results with exact formulas available in solvable models.

Classical transition-rate theory provides analytic techniques for computing the asymptotics of a weakly perturbed particle’s mean residence time in the basin of attraction of a metastable state. If the dynamics of the particle are derivable from a potential, it typically escapes over a saddle point. In the nonpotential case exit may take place over an unstable point instead, leading to unexpected phenomena. These may include an anomalous pre-exponential factor, with a continuously varying exponent, in the residence time asymptotics. Moreover, the most probable escape trajectories may eventually deviate from the least-action escape path.

We develop a novel fragmentation model in which the fragmentation cascade is randomly inactivated according to the homogeneous inactivation probability function. For the multiplicative breakup kernel ${\mathit{scrF}}_{\mathit{i},}$j=(ij${)}^{\mathrm{\alpha }}$, we discuss the existence of scaling solutions as t→∞ in different regions of the phase diagram. We also study fluctuations in the cluster-size distribution and find an intermittent behavior in the infinite-cluster phase and at the transition line. Finally, we discuss the relevance of this model for nuclear multifragmentation.

We consider the dynamics of a particle carrying a magnetic moment in a strong magnetic field whose direction varies slowly in space. In particular, we discuss the geometric Lorentz-type and electric-type forces that were discovered in studies of Berry’s phase. We show that the Lorentz-type force felt by the particle is caused by a small misalignment of the magnetic moment with respect to the magnetic field while the electric-type force is the time average of a strong oscillatory force induced by the precession of the magnetic moment.

We investigate the quantum mechanical bound to how precisely we can determine a phase shift given only a constraint on the mean total number of photons available. By considering how quickly one can gain information from data analysis, we derive the sensitivity achievable (in principle) for measurements involving even highly non-Gaussian noise. Using these results we calculate the sensitivity of several recent proposals for precision phase measurement, and show that no proposal to date beats the sensitivity believed achievable by squeezed state interferometry.

Coupled Hénon maps are introduced to model in a more appropriate way chaos in extended systems. An effective technique allows the extraction of spatiotemporal periodic orbits, which are then used to approximate the invariant measure. A further implementation of the ζ-function formalism reveals the extensive character of entropies and dimensions, and allows the computation of the associated multifractal spectra. Finally, the analysis of short chains indicates the existence of distinct phases in the invariant measure, characterized by a different number of positive Lyapunov exponents.

Landau level mixing by external potentials is considered in a Born-Oppenheimer expansion which separates the dynamics of the fast velocities of cyclotron rotation and the slow coordinates of the guiding centers. Level mixing is present already in the extreme adiabatic limit and in transitions at avoided crossings. Nonvanishing Berry’s phase adds effective magnetic field depending on external potential. Explicit results are given for weakly inhomogeneous potentials. The projection on a single Landau level appears as an extreme limit of the formalism.

We report the first quantitative measurements of spontaneous temperature fluctuations in a physical system well modeled by a canonical ensemble. Using superconducting magnetometers and a carefully controlled thermal environment, we have measured the noise spectra of paramagnetic salt thermometers that were coupled to thermal reservoirs at 2 K. The noise spectra were found to be in very good agreement with the predictions of the fluctuation-dissipation theorem. Our observations are at variance with some interpretations of fluctuations in the canonical ensemble.

As is well known, operations on one particle of an Einstein-Podolsky-Rosen (EPR) pair cannot influence the marginal statistics of measurements on the other particle. We characterize the set of states accessible from an initial EPR state by one-particle operations and show that in a sense they allow two bits to be encoded reliably in one spin-1/2 particle: One party, ‘‘Alice,’’ prepares an EPR pair and sends one of the particles to another party, ‘‘Bob,’’ who applies one of four unitary operators to the particle, and then returns it to Alice. By measuring the two particles jointly, Alice can now reliably learn which operator Bob used.

Based on the subgraph expansions for phase transition models, we present a histogram Monte Carlo method to calculate the free energy and other physical quantities for such models as continuous functions of the system parameter. The method does not have any critical slowing down. We then use physical quantities thus obtained in a percolation renormalization group method to calculate critical point, critical exponents, and thermodynamic order parameter. Our method gives quite accurate results and may be applied to many phase transition models.