We investigate the motion of Brownian particles which have the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy. The resulting Langevin equation includes an additional acceleration term. The motion of the Brownian particles in a parabolic potential is discussed for two different cases: (i) continuous take-up of energy and (ii) take-up of energy at localized sources. If the take-up of energy is above a critical value, we found a limit-cycle motion of the particles, which, in case (ii), can be interrupted by stochastic influences. Including reflecting obstacles, we found for the deterministic case a chaotic motion of the particle.

In this paper we propose a new principle for stationary thermodynamic processes: The maximum of the local entropy production becomes minimal in stationary processes. In order to show the usefulness of the principle, we consider one-dimensional stationary heat transfer in monatomic gases. Here we solve extended moment schemes that follow from the Boltzmann equation. Such schemes require boundary conditions for all moments under consideration, and these are constructed by means of the new principle. Moreover, we show that the minimum principle for the global entropy production does not lead to good results in this case.

An investigation of the noise activated escape from a metastable state and between attractors in a bistable system has been undertaken. It is demonstrated, both theoretically and by means of digital simulations, that the application of an external time-periodic field can lead to a significant increase in the lifetime (averaged over one period of the field) of a metastable state and in the residence time of a bistable system. In particular, it is shown that these characteristic times can be increased beyond the inverse Kramers rate calculated in the absence of the field. This effect is observed when the frequency of the external field is smaller than the unperturbed Kramers rate.

For a simple example of on-off intermittency, an overdamped Kramers oscillator with multiplicative noise, we demonstrate a phenomenon of hypersensitivity to ultrasmall time-dependent signals.

In classical theory, a physical state is an equivalence class under gauge transformations. Is the same true in quantum theory? The physical quantum states are the solutions of Dirac's quantum constraint equation. They cannot be constructed as equivalence classes under the “simple” gauge transformations generated by the Dirac constraints. However, we show here that they can be constructed as equivalence classes under suitably defined “complete” gauge transformations. The complete gauge transformations are generated by the action of the quantum constraints on arbitrary individual components of the state.

Some general features of a new class of thermodynamic device combining a thermodynamic cycle with the externally applied steady flow of an open thermodynamic process are discussed and experimentally demonstrated in the context of a thermoacoustic refrigerator.

We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of corresponding observables. Solutions of master equations demonstrate that decoherence destroys quantum interference in Wigner distributions and washes out fine structure in classical distributions, bringing the two closer together. Correspondence between quantum and classical expectation values is also reestablished.

The nontrivial transformation of the phase space path integral measure under certain discretized analogs of canonical transformations is computed. This Jacobian is used to derive a quantum analog of the Hamilton-Jacobi equation for the generating function of a canonical transformation that maps any quantum system to a system with a vanishing Hamiltonian. A perturbative solution of the quantum Hamilton-Jacobi equation is given. This solution gives a new way to compute quantum corrections for any soliton equation for which action-angle variables are known.

Recent developments have made possible the computation of equilibrium dynamical correlators in quantum impurity problems. In many situations, however, one is interested in correlators subject to a nonequilibrium initial preparation. This is the case, for instance, for the occupation probability $P\left(t\right)$ in the double well problem of dissipative quantum mechanics. We show here how to handle this situation in the framework of integrable quantum field theories. This allows us to obtain new exact results for $P\left(t\right)$: for instance, we find that at large times (or small $g$), the leading behavior for $g<\mathrm{}\frac{1}{2}$ is $P\left(t\right)\propto e^{-\Gamma t}\cos \Omega t$, with the universal ratio $\frac{\Omega }{\Gamma }=\cot \frac{\pi g}{2(1-g)}$.

Considered is the relationship between the level dynamics and the integrable differential-difference equation. By applying the inverse scattering method to the Bogoyavlensky lattice, which is an extension of the Volterra model, the role of the exclusion statistics is clarified. Each dynamical variable is identified with an energy level. Briefly discussed is a generalization of the Yangian symmetric system, and the “Gentile” statistics is revealed.

We report on the experimental observation of environment induced decoherence in the quantum delta-kicked rotor. Ultracold cesium atoms are subjected to a pulsed standing wave of near resonant light. Spontaneous scattering of photons destroys dynamical localization thereby giving rise to a quantum diffusion, which approaches the classical diffusion with an increasing degree of decoherence. This tendency is enhanced by a stronger stochasticity in the underlying classical system. A comparison with theoretical predictions is presented.

A Comment on the Letter by G. Garcia-Calderon, J. L. Mateos, and M. Moshinsky, Phys. Rev. Lett. 74, 337 (1995). The authors of the Letter offer a Reply.

A Reply to the Comment by R. M. Cavalcanti.

We experimentally entangle freely propagating particles that never physically interacted with one another or which have never been dynamically coupled by any other means. This demonstrates that quantum entanglement requires the entangled particles neither to come from a common source nor to have interacted in the past. In our experiment we take two pairs of polarization entangled photons and subject one photon from each pair to a Bell-state measurement. This results in projecting the other two outgoing photons into an entangled state.

We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures $(0.6<\mathrm{}{T/T}_c<1.2\mathrm{})$ and for systems with ${10}^4$ to ${10}^8$ particles. The second sound modes (which exist only below $T_c$) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near $T_c$ recently observed at JILA in systems with ${10}^3$ particles match surprisingly well with those of the first and second sound modes of much larger systems.

We numerically study wave packet dynamics of a Bose-Einstein condensate in a periodically shaken trap. Dynamic splitting of the condensate, and dynamic stabilization against escape from the trap are analyzed in analogy with similar behavior of atoms in strong laser fields.

We solve the time-dependent Gross-Pitaevskii in 2D to simulate the flow of an object through a dilute Bose-Einstein condensate trapped in a harmonic well. We demonstrate vortex formation and study the process in terms of the accumulation of phase slip and the evolution of the fluid velocity.

The traditional basis of description of the many-particle systems in terms of the Green functions is here generalized when the system is nonextensive by incorporating the Tsallis form of the density matrix, indexed by a nonextensive parameter, $q$. This extension enables us to predict possible experimental tests for the validity of this framework by expressing some observable quantities in terms of the $q$ averages.

A Comment on the Letter by Mark E. Tuckerman, Christopher J. Mundy, and Michael L. Klein, Phys. Rev. Lett. 78, 2042 (1997). The authors of the Letter offer a Reply.

A Comment on the Letter by Mark E. Tuckerman, Christopher J. Mundy, and Michael L. Klein, Phys. Rev. Lett. 78, 2042 (1997). The authors of the Letter offer a Reply.