We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in one dimension and belong to the 1/${\mathit{r}}^2$ family of interactions. The algebra consists of the commutation between a ‘‘super-Hamiltonian’’ and two other operators, in an enlarged Hilbert space. These reduce to quantal Ordered Lax equations when projected onto the original subspace, and to a statement about the ‘‘Harmonic Lattice Potential’’ structure of the Lax operator, leading to a highly automatic proof of the integrability of these models and to an interesting hierarchy of new models.

With CPT-invariant initial conditions that commute with CPT-invariant final conditions, the respective probabilities (when defined) of a set of histories and its CPT reverse are equal, giving a CPT-symmetric universe. This leads me to question whether the asymmetry of the Gell-Mann–Hartle decoherence functional for ordinary quantum mechanics should be interpreted as an asymmetry of time.

Point masses moving in 2+1 dimensions draw out braids in space-time. If they move under the influence of some pairwise potential, what braid types are possible? By starting with fictional paths of the desired topology and ‘‘relaxing’’ them by minimizing the action, we explore the braid types of potentials of the form V∝${\mathit{r}}^{\mathrm{\alpha }}$ from α≤-2, where all braid types occur, to α=2, where the system is integrable. We also discuss issues of symmetry and stability. We propose this kind of topological classification as a tool for extending the ‘‘symbolic dynamics’’ approach to many-body dynamics.

A nonperturbative method for solving differential equations and for finding limit cycles is proposed and is illustrated on the anharmonic oscillator and on the Van der Pol equation. It is shown to give the amplitude, period, and equation of the limit cycle with a better accuracy than any perturbative results so far obtained.

Lower and upper bounds are derived for the decay and transitions of quantum states, evolving under a time-dependent Hamiltonian, in terms of the energy uncertainty of the initial and final state. The bounds are simultaneously a rigorous version of Fermi’s golden rule and of the time-energy uncertainty relation. They are sharp, refer to short times, and are compared with recent long-time results for time-independent Hamiltonians. Illustrations for tunneling systems, laser-driven processes, and neutron interferometry in time-dependent magnetic fields are given.

It is shown that joint measurements of certain commuting operators, performed on pre- and postselected quantum systems, invariably disturb each other. This result is applied to recent assertions that quantum theory has no realistic Lorentz-invariant interpretation (even without requiring locality).

We show that kink solitons may exist on top of a rotating background as localized objects if the background dynamics is phase locked to a rapidly oscillating ac force. The result is demonstrated analytically for the sine-Gordon model, showing excellent agreement with numerical simulations. In the context of long Josephson junctions this phenomenon means that the well known Shapiro steps in the current-voltage characteristics change into a set of the zero-field steps according to the number of propagating fluxons.

Frequency analysis is a numerical technique for studying the long-time dynamics of nearly integrable Hamiltonian systems or symplectic maps over large regions of phase space. This technique may be especially useful because of its inherent simplicity, and we demonstrate its effectiveness in studying long-time diffusion of orbits in a simplified but nontrivial accelerator model.

We discuss a model of repeated measurements of position in a quantum system which is monitored for a finite amount of time with a finite instrumental error. In this framework we recover the optimum monitoring of a harmonic oscillator proposed in the case of an instantaneous collapse of the wave function into an infinite-accuracy measurement result. We also establish numerically the existence of an optimal measurement strategy in the case of a nonlinear system. This optimal strategy is completely defined by the spectral properties of the nonlinear system.

Levinson’s theorem for the Dirac equation is known in the form of a sum of positive and negative energy phase shifts at zero momentum related to the total number of bound states. In this Letter we prove a stronger version of Levinson’s theorem valid for positive and negative energy phase shifts separately. The surprising result is that, in general, the phase shifts for each sign of the energy do not give the number of bound states with the same sign of the energy (in units of π), but instead are related to the number of bound states of a certain Schrödinger equation, which coincides with the Dirac equation at zero momentum.

We report the first observation of interference effects in the light scattered from two trapped atoms. The visibility of the fringes can be explained in the framework of Bragg scattering by a harmonic crystal and simple ‘‘which path’’ considerations of the scattered photons. If the light scattered by the atoms is detected in a polarization-sensitive way, then it is possible to selectively demonstrate either the particle nature or the wave nature of the scattered light.

We consider particle oscillations and their damping in second-quantized form. We find that the damping or ‘‘decoherence’’ may be described by a Boltzmann-like collision integral with ‘‘non-Abelian blocking factors’’ (fermions). Earlier results are generalized in that the momentum degrees of freedom are included and that the mixing equations become intrinsically nonlinear at high densities.

The probabilistic element of quantum theory can be combined with the unitary time evolution of Schrödinger’s equation in a natural and consistent way using the idea of a quantum trajectory, the quantum analog of the trajectory traced out in phase space as a function of time by a point representing the state of a closed classical system. A family of quantum trajectories can be defined using bases for the quantum Hilbert space at different times chosen so that an appropriate noninterference condition, related to the Gell-Mann and Hartle notion of medium decoherence, is satisfied. The result is a generalization of the consistent histories approach to quantum mechanics.

We consider a model of a D-dimensional tethered manifold interacting by excluded volume in ${\mathit{openR}}^{\mathit{d}}$ with a single point. By use of intrinsic distance geometry, we first provide a rigorous definition of the analytic continuation of its perturbative expansion for arbitrary D, 0<D<2. We then construct explicitly a renormalization operation ssR, ensuring renormalizability to all orders. This is the first example of mathematical construction and renormalization for an interacting extended object with continuous internal dimension, encompassing field theory.

We study the Lorentz gas in small external electric and magnetic fields, with the particle kinetic energy held fixed by a Gaussian ‘‘thermostat.’’ Starting from any smooth initial density, a unique stationary, ergodic measure is approached for times t→∞. The steady-state electric current J(B,E) is given by a Kawasaki formula and the entropy production J⋅E/T, with T the ‘‘temperature,’’ is equal to both the asymptotic decay rate of the Gibbs entropy and minus the sum of the Lyapunov exponents. The Einstein and Kubo formulas hold, i.e., J(B,E)=σ(B)⋅E + higher order terms, with the diffusion matrix D(B) at E=0 given by ${\mathit{k}}_{\mathit{B}}$T times the symmetric part σ̃(B) of the conductivity matrix.

An unknown quantum state ‖φ〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender, ‘‘Alice,’’ and the receiver, ‘‘Bob,’’ must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state ‖φ〉 which Alice destroyed.

Solutions to the time-dependent Schrödinger equation for a particle in a spatially uniform time-dependent field and some potentials of arbitrary form are proved to be like the time-independent eigenfunctions for an identical static potential. The field phase modulates the wave function and translates its envelope. This work applies directly to constant, linear, and parabolic static potentials and is self-consistent. Results for the modulation by a time-dependent field of the current through a rectangular barrier are relevant to the traversal time for tunneling and associated device limitations.

The conformal invariant charcter of n-multicomponent integrable systems is described from the point of veiw of the response to the curvature of the two-dimensional space. The ν×ν dressed-charge matrix, which determines the dimensions of the primary fields, is shown to be a representation of the momentum Fourier components of the diagonal generators of ν independent Kac-Moody algebras in the basis of the ground state and gapless excitations of momentum k→$0^{\pm }$. The dynamical decoupling which occurs in these systems is characterized in terms of the conductivities associated with the diagonal generators.

A new application of finite size scaling to Monte Carlo simulations is introduced. Using this technique, critical behavior can be investigated at temperatures arbitrarily close to the critical point without large lattice sizes. Applying this method to the two-dimensional standard O(3) model it is shown that for the correlation length asymptotic scaling holds for β≥2.25; the magnetic susceptibility converges to the asymptotic scaling very slowly. In the scaling region, it is observed that the specific heat decreases with β, which implies no singular behavior of the specific heat for this model.

By an exact calculation on the planar Ising model we show that for all subcritical temperatures, the bubble model predicts the correct average distribution of matter contributing to the pair-spin correlation function in the two-particle sector. This considerably substantiates the bubble model which is generalized to higher dimensions with an external field h and then used to show that the free energy has an essential singularity in h of Andreev-Fisher form at all points along the phase boundary. We argue that such a singularity would also occur in the Baxter model.