We investigate dissipative quantum motion of a particle in a discrete periodic asymmetric lattice coupled to an Ohmic bath and subjected to a nonbiased oscillatory field. In the adiabatic forcing regime we find analytically external forcing rectification resulting in a motor mechanism through persistent current creation. The direction and intensity of the motor operation is controlled by the competing mechanisms of discreteness induced Stark localization and phonon assisted ratchet delocalization. Maximal current of either sign is predicted at a parameter dependent characteristic temperature.

We have analyzed the effects of the addition of external noise to nondynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a wide class of nondynamical systems, covering situations of different nature. Some particular examples are discussed in detail.

The problem of state selection when multiple metastable states compete for occupation is considered for systems obeying a one-dimensional stochastic time-dependent Ginzburg-Landau equation in which a control parameter is ramped in time. The dynamics of the supercurrent in a narrow superconducting ring under the influence of an external electric field is used for illustration.

We simulated site dilute Ising models in $d=3\mathrm{}$ dimensions for several lattice sizes $L$. For each $L$ singular thermodynamic quantities $X$ were measured at criticality and their distributions $P\left(X\right)$ were determined for ensembles of several thousand random samples. For $L\to \infty$ the relative width of $P\left(X\right)$ tends to a universal constant: there is no self-averaging. The width of the distribution of the sample $\left(i\right)$ dependent pseudocritical temperatures $T_c(i,L)$ scales as $\delta T_c\left(L\right)\sim L^{-1\mathrm{}/\nu }$ and not as $\mathrm{\sim }{L}^{-d/2}$. The sample dependence of $X_i(T,L)$ enters dominantly, but not exclusively, via $T_c(i,L)$.

The entropy maximum approach to constructing equilibria in lattice kinetic equations is revisited. For a suitable entropy function, we derive explicitly the hydrodynamic local equilibrium, prove the $H$ theorem for lattice Bhatnagar-Gross-Krook models, and develop a systematic method to account for additional constraints.

The density matrix of a nonrelativistic wave packet in an arbitrary, one-dimensional, and time-dependent potential can be reconstructed by measuring hydrodynamical moments of the Wigner distribution. An $n$th order Taylor polynomial in the off-diagonal variable is obtained by measuring the probability distribution at $n+1\mathrm{}$ discrete time values.

We show how recent state-reconstruction techniques can be used to determine the Hamiltonian of an optical device that evolves the quantum state of radiation. A simple experimental setup is proposed for measuring the Liouvillian of phase-insensitive devices. The feasibility of the method with current technology is demonstrated on the basis of Monte Carlo simulated experiments.

The multiple scattering interferences due to the addition of several contiguous potential units are used to construct composite complex potentials that absorb at an arbitrary set of incident momenta or for a broad momentum interval.

A novel interferometer has been developed with which the complex index of refraction of thin self-supporting foils can be measured in the vacuum ultraviolet and soft x-ray region. It consists of two collinear undulators and a grating spectrometer. Taking advantage of the low emittance 855 MeV electron beam from the Mainz Microtron, distinct intensity oscillations have been observed as a function of the distance between the undulators. A foil placed between the undulators causes a phase shift and an attenuation of the oscillation amplitude. The complex index of refraction has been measured at the $K$-absorption edge of carbon.

We investigate the dynamics of second-order phase transitions in two dimensions, breaking a gauged U(1) symmetry. Using numerical simulations, we show that the density of the topological defects formed scales with the quench time scale ${\tau }_Q$ as $n\sim {\tau }_Q^{-1\mathrm{}/2}$ when the dynamics is overdamped at the instant when the freeze-out of thermal fluctuations takes place, and $n\sim {\tau }_Q^{-2\mathrm{}/3}$ in the underdamped case. This is predicted by the scenario proposed by one of us (W. H. Z.).

Comment on the Letter by Shiwu Gao, Phys. Rev. Lett. 79, 3101 (1997).

A Reply to the Comment by H. M. Wiseman and W. J. Munro.

It is shown that if a mixed state can be distilled to the singlet form it must violate partial transposition criterion [A. Peres, Phys. Rev. Lett. 76, 1413 (1996)]. It implies that there are two qualitatively different types of entanglement: “free” entanglement which is distillable, and “bound” entanglement which cannot be brought to the singlet form useful for quantum communication purposes. A possible physical meaning of the result is discussed.

The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These $\mathrm{PT}$ symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories.

It is shown that photons can be localized in space with an exponential falloff of the energy density and photodetection rates. The limits of localization are determined by the fundamental Paley-Wiener theorem. A direct mathematical connection between the spatial localization of photons and the decay in time of quantum mechanical systems is established.

We formulate energetics of the forced thermal ratchet [M. O. Magnasco, Phys. Rev. Lett. 71, 1477 (1993)] and evaluate its efficiency of energy transformation. We show that the presence of thermal fluctuation cannot increase the efficiency of the energy transformation in the original system of Magnasco, which is contrary to his claim that “There is a region of the operating regime where the efficiency is optimized at finite temperatures.” We also discuss the maximum efficiency of the forced thermal ratchet.

Extending the Painlevé approach to a more general form, one can get infinitely many new integrable models under the meanings that they possess conformal invariance and the Painlevé property in any space dimensions from a given lower dimensional integrable model. Using the Kadomtsev-Petviashvili, nonlinear Schrödinger, and Schwarz Korteweg–de Vries equations as simple examples, some explicit $(3+1)$-dimensional integrable models are given.

We develop an analytical approach for describing a birth of internal modes of solitary waves in nonintegrable nonlinear models. We show that a small perturbation of a proper sign to an integrable model can create a soliton internal mode bifurcating from the continuous wave spectrum. The theory is applied to the double sine-Gordon and discrete nonlinear Schrödinger equations, and an excellent agreement with numerical data is demonstrated.

We analyze several models of atomic detectors in the context of the measurement of coherence properties of matter waves. In particular, we show that an ionization scheme measures normally ordered correlation functions of the Schrödinger field, in analogy with the optical situation. However, it exhibits a sensitivity to exchange processes that is normally absent in optics.

We find that the fluctuations of the condensate in a weakly interacting Bose gas confined in a box of volume $V$ follow the law $〈\delta N_0^2〉\sim V^{4/3}$. This anomalous behavior arises from the occurrence of infrared divergencies due to phonon excitations and holds also for strongly correlated Bose superfluids. The analysis is extended to an interacting Bose gas confined in a harmonic trap where the fluctuations are found to exhibit a similar anomaly.