We use noise to extend signal propagation in one- and two-dimensional arrays of two-way coupled bistable oscillators. In a numerical model, we sinusoidally force one end of a chain of noisy oscillators. We record a signal-to-noise ratio at each oscillator. We demonstrate that moderate noise significantly extends the propagation of the sinusoidal input. Oscillators far from the input, where noise extends the signal, exhibit a classical stochastic resonance. We obtain similar results with two-dimensional arrays. The simplicity of the model suggests the generality of the phenomenon.

The Liouville-Bloch equation for a general spin $j$ in time-dependent external fields is solved as a unitary product of exponential operators. Operator noncommutativity is explicitly handled so as to leave behind a set of first-order differential equations for classical functions of time. Of these, only one is nontrivial and, once solved, the remaining yield to simple quadrature. Exact solutions or perturbative expansions of the classical equations can be used for analytical or numerical integration of the quantal equations.

An accurate test of the symmetrization postulate of quantum mechanics has been performed on the spin-0 ${}^{16}\mathrm{O}$ nuclei, by looking for transitions in the ${\mathrm{CO}}_2$ spectra involving states which are antisymmetric in the exchange of the nuclei. Using high-sensitivity laser spectroscopy, a bound of $2.1\times {10}^{-9\mathrm{}}$ has been set to a possible violation of such postulate, with an improvement of more than 2 orders of magnitude with respect to the previous limit.

A general algorithm toward the solution of the fermion sign problem in finite-temperature quantum Monte Carlo simulations has been formulated for discretized fermion path integrals with nearest-neighbor interactions in the Trotter direction. This multilevel approach systematically implements a simple blocking strategy in a recursive manner to synthesize the sign cancellations among different fermionic paths throughout the whole configuration space. The practical usefulness of the method is demonstrated for interacting electrons in a quantum dot.

We consider a system having decaying states with complex energies $E_j-i{\Gamma }_j/2$, and we define the “width-weighted spectrum” as $D\Gamma \left(E\right)=\Sigma j^{}{\Gamma }_j\delta \left({E-E}_j\right)$. We derive a semiclassical formula for this width-weighted spectrum, a formula which is analogous to the periodic-orbit representation of the density of states. The formula applies if classical motion is regular and if decay occurs by tunneling through a barrier. The semiclassical formula involves not periodic orbits or closed orbits, but action integrals associated with irreducible loops on the “extremal torus,” on which the particle climbs up the barrier and hangs at the top. Calculations confirm the validity of the formula.

Using the hydrodynamic theory of superfluids and the Lee-Huang-Yang equation of state for interacting Bose gases, we derive the first correction to the collective frequencies of a trapped gas, due to effects beyond the mean field approximation. The corresponding frequency shift, which is calculated at zero temperature and for large $N$, is compared with other corrections due to finite size, nonlinearity, and temperature. We show that for reasonable choices of the relevant parameters of the system, the non-mean-field correction is the leading contribution and amounts to about $1\%$. The role of the deformation of the trap is also discussed.

We have performed magnetic compression experiments with the two-dimensional gas of hydrogen atoms on liquid ${}^4\mathrm{He}$ at $T=120\mathrm{}–200\mathrm{mK}$. For 2D phase-space densities higher than 3, the probability of three-body dipole recombination is observed to decrease gradually by an order of magnitude in comparison to its low-density value $K_{\mathrm{bbb}}=8.4\mathrm{}\left(3.5\right)\times {10}^{-25\mathrm{}}{\mathrm{cm}}^4{\mathrm{s}}^{-1\mathrm{}}$. This is attributed to local coherence developing in a 2D quasicondensate. We have also determined the value $U/k=5.1\mathrm{}\left(5\right)\times {10}^{-15\mathrm{}}\mathrm{K}{\mathrm{cm}}^2$ for the mean-field energy of the gas.

We have used an atomic force microscope to make precision measurements of the Casimir force between a metallized sphere of diameter 196 μm and flat plate. The force was measured for plate-sphere surface separations from 0.1 to 0.9 μm. The experimental results are consistent with present theoretical calculations including the finite conductivity, roughness, and temperature corrections. The root mean square average deviation of 1.6 pN between theory and experiment corresponds to a $1\%$ deviation at the smallest separation.

A Comment on the Letter by H. Batelaan, T. J. Gay, and J. J. Schwendiman, Phys. Rev. Lett. 79, 4517 (1997). The authors of the Letter offer a Reply.

A Reply to the Comment by George H. Rutherford and Rainer Grobe.

Number partitioning is an $\mathrm{NP}$-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy- from the hard-to-solve instances and that reflects the pseudopolynomiality of number partitioning. The phase diagram and the value of the typical ground-state energy are calculated.

We present a potential realization of the Greenberger-Horne-Zeilinger “all or nothing” contradiction of quantum mechanics with local realism using phase measurement techniques in a simple photon number triplet. Such a triplet could be generated using nondegenerate parametric oscillation.

We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter at the critical point ( ${T=T}_c$) we show that instantonlike configurations, corresponding to the minima of the effective action functional, build up clusters with fractal geometry characterizing locally the critical fluctuations. The connection between the corresponding (local) fractal dimension and the critical exponents is derived. Possible extension of the local geometry of the system to a global picture is also discussed.

Quantum phase difference is used to analyze which-path detectors in which the loss of interference predicted by complementarity cannot be attributed to classical momentum transfer between the interfering particle and the measuring apparatus. It is shown that the dynamics of the measurement disturbs the interference via random classical phase shifts.

We present a unified account of damping of low-lying collective modes and of relaxation of temperature anisotropies in a trapped Bose gas in the collisionless regime. By means of variational techniques, we show that the relaxation times for the two situations are closely related to the simplest variational estimate of the viscous relaxation time. We derive rather precise theoretical expressions for the characteristic relaxation times and compare our results with experiment.

We investigate analytically the motion of underdamped particles subject to a deterministic periodic potential and a periodic temperature. Despite the fact that an underdamped particle experiences the temperature modulation many times in its escape out of a well and in its motion along the potential, a net directed current linear in the friction constant is found. If both the potential and the temperature modulation are sinusoidal with a phase lag $\delta$, this current is proportional to $\sin \delta$.

We measure the momentum of cold cesium atoms in a periodically pulsed standing wave of light. This system is an experimental realization of the quantum kicked rotor. The momentum diffusion in the (chaotic) classical analog of this system is typically suppressed by quantum localization. We find, however, that for certain pulse amplitudes where the classical system exhibits anomalous diffusion, our momentum distributions are not exponentially localized. We observe a predicted correspondence between the classical and quantum energy growth as a function of pulse amplitude and period.