Long-term experiments on spiral interaction carried out in the framework of the Belousov- Zhabotinsky reaction have revealed the influence of the initial pattern symmetry on further pattern evolution. This symmetry is characterized by the different distance from each spiral tip to the boundary where the emitted wave fronts collide. The spiral initially closer to the shock line is observed to rotate with a lower mean frequency and to be dominated by the other one. Besides, both spiral tips are observed to drift. Different relationships between tangential and normal drift velocities of both tips have been found depending on whether domination is total or partial.

The Duru-Kleinert method of solving unknown path integrals of quantum mechanical systems by relating them to known ones does not apply to Markov processes since the Duru-Kleinert transform of a Fokker-Planck equation is, in general, not a Fokker-Planck equation. In this Letter, we present a significant modification of the method, based again on a combination of path-dependent time and coordinate transformations, to obtain such relations after all. As an application we express unknown Green functions for a one-parameter family of Markov processes in terms of the known one for the Schenzle-Brand process.

A method to obtain a new class of discrete eigenfunctions and associated real, nonsingular, decaying, “reflectionless” potentials to the time dependent Schrödinger equation is presented. Using the inverse scattering transform, related solutions of the Kadomtsev-Petviashvili equation are found. The eigenfunctions have poles of order $m$, $m>\mathrm{}1\mathrm{}$ in the complex plane and are also characterized by an index, or “charge,” which is obtained as a constraint in the theory.

A quantum system is called inseparable if its density matrix cannot be written as a mixture of product states. In this Letter we apply the separability criterion, local filtering, and Bennett et al. distillation protocol [Phys. Rev. Lett. 76, 722 (1996)] to show that any inseparable $2\times 2$ system represents the entanglement which, however small, can be distilled to a singlet form.

A semiclassical approach is presented that allows us to extend the usual Van Vleck–Gutzwiller formulation to the description of nonadiabatic quantum dynamics on coupled potential-energy surfaces. Based on Schwinger's theory of angular momentum, the formulation employs an exact mapping of the discrete quantum variables onto continuous degrees of freedom. The resulting dynamical problem is evaluated through a semiclassical initial-value representation of the time-dependent propagator. As a first application we have performed semiclassical simulations for a spin-boson model, which reproduce the exact quantum-mechanical results quite accurately.

We have demonstrated an output coupler for Bose condensed atoms in a magnetic trap. Short pulses of rf radiation were used to create Bose condensates in a superposition of trapped and untrapped hyperfine states. The fraction of out-coupled atoms was adjusted between 0% and 100% by varying the amplitude of the rf radiation. This configuration produces output pulses of coherent atoms and can be regarded as a pulsed “atom laser.”

A new apparatus featuring a double magneto-optic trap and an Ioffe-type magnetic trap was used to create condensates of $2\times {10}^6$ atoms in either of the $|F=2,m=2\mathrm{}〉$ or $|F=1,m=-1\mathrm{}〉$ spin states of ${}^{87}$Rb. Overlapping condensates of the two states were also created using nearly lossless sympathetic cooling of one state via thermal contact with the other evaporatively cooled state. We observed that (i) the scattering length of the $|1,-1〉$ state is positive, (ii) the rate constant for binary inelastic collisions between the two states is $2.2\left(9\right)\times {10}^{-14\mathrm{}}{\mathrm{cm}}^3/\mathrm{s}$, and (iii) there is a repulsive interaction between the two condensates. Similarities and differences between the behaviors of the two spin states are observed.

This paper extends work done to date on quantum computation by association of potentials with different types of steps. Quantum Turing machine Hamiltonians, generalized to include potentials, correspond to sums over tight binding Hamiltonians each with a different potential distribution. Which distribution applies is determined by the initial state. An example, which enumerates the integers in succession as binary strings, is analyzed. It is seen that for some initial states, the potential distributions have quasicrystalline properties and are similar to a substitution sequence.

An explicit expression for the vortex velocity field as a function of the order parameter field is derived for the case of point defects in the $O\left(n\right)$ symmetric time-dependent Ginzburg-Landau model. This expression is used to find the vortex velocity probability distribution in the Gaussian closure approximation in the case of phase ordering kinetics for a nonconserved order parameter. The velocity scales as $L^{-1\mathrm{}}$ in scaling regime where $L\approx t^{1/2}$ and $t$ is the time after the quench.

A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.

We present the exact solution of a three-dimensional lattice-statistical model consisting of layers of vertex models coupled with interlayer interactions. For a particular nontrivial interlayer interaction between charge-conserving vertex models and using a transfer matrix approach, we show that the eigenvalues and eigenvectors of the transfer matrix are related to those of the two-dimensional vertex model. As an illustration of the general solution, we analyze the phase transitions in a realistic three-dimensional dimer system and determine its phase diagram and nature of transitions.

We show that the singularity of the free energy of Ising models in the absence of a magnetic field on the triangular, square, and honeycomb lattices is related to zeros of the pseudopartition function on an elementary cycle. Using the Griffiths' smoothness postulate, we extend these results to the case in a magnetic field and derive a formula of the critical line of an Ising antiferromagnet, which is in good agreement with the numerical results.

We introduce a “prepotential” $F$ in quantum mechanics and show that the coordinate $x$ is proportional to the Legendre transform of $F$ with respect to the probability density. Inversion of the Schrödinger equation leads us to consider an $x$– $\psi$ duality related to a modular symmetry. The scaling of $x$ is determined by the “beta function,” suggesting that in quantum mechanics the space coordinate is a macroscopic variable of a statistical system with $ħ$ playing the role of scale. The formalism is extended to higher dimensions and to the Klein-Gordon equation.

We study the nonequilibrium steady states of an Ising chain in a transverse field $h$ by investigating the effect of a field $\lambda$, which drives the current of energy. The zero-temperature, $h$- $\lambda$ phase diagram is determined exactly, and it is found that the energy current appears continuously above a threshold $\lambda >{\lambda }_c\left(h\right)$. The long-range magnetic order (present for $h<\mathrm{}{h}_c,\lambda <{\lambda }_c$) is destroyed in the current-carrying state where the correlations are characterized by power-law, oscillatory decay. The mechanism which generates the power-law correlations in the current-carrying state is discussed.

A Comment on the Letter by D. Gabrielli, G. Jona-Lasinin, and C. Landim, Phys. Rev. Lett. 77, 1202 (1996). The authors of the Letter offer a Reply.

A Reply to the Comment by J. L. Lebowitz, and H. Spohn.

We demonstrate the utility of a Rayleigh-Ritz scheme recently proposed to compute the nonequilibrium effective potential nonperturbatively in a strong noise regime far from equilibrium. A simple Kramers model of an ionic conductor is used to illustrate the efficiency of the method.

The vacuum stress between closely spaced conducting surfaces, due to the modification of the zero-point fluctuations of the electromagnetic field, has been conclusively demonstrated. The measurement employed an electromechanical system based on a torsion pendulum. Agreement with theory at the level of 5% is obtained.

We present analytical results for the macroscopic wave function of a Bose-Einstein condensate in a time dependent harmonic potential. The evolution of the spatial density is a dilatation, characterized by three scaling factors which allow a classical interpretation of the dynamics. This approach is an efficient tool for the analysis of recent experimental results on the expansion and collective excitation of a condensate.

We solve the time-dependent Gross-Pitaevskii equation by a variational ansatz to calculate the excitation spectrum of a Bose-Einstein condensate in a trap. The trial wave function is a Gaussian which allows an essentially analytical treatment of the problem. Our results reproduce numerical calculations over the whole range from small to large particle numbers, and agree exactly with the Stringari results in the strong interaction limit. Excellent agreement is obtained with the recent JILA experiment and predictions for the negative scattering length case are also made.