We consider a noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable exit path as the parameters of the system are changed, and a corresponding nonanalyticity of the generalized activation energy. We also investigate the extent to which the bifurcation is related to the local breaking of time-reversal invariance.

We analyze the probabilities of large infrequent fluctuations in nonadiabatically driven systems. In a broad range of the driving field magnitudes, the logarithm of the fluctuation probability is linear in the field, and the response can be characterized by a logarithmic susceptibility (LS). We evaluate the activation energies for nucleation, with account taken of the field-induced lifting of time and spatial degeneracy of instantonlike nucleation trajectories. LS for nucleation in systems with nonconserved order parameter is shown to be a nonmonotonic function of $\omega$ and $\mathbf{k}$.

Brownian particles can be induced to undergo biased movement by a fluctuating periodic potential, if the potential within each period is asymmetric. In this Letter, we show that similar phenomenon can be obtained even when the periodic potential is symmetric, if (i) there are at least three states for the potential to fluctuate, (ii) the extrema of the nonflat potentials are properly shifted, and (iii) the potential is fluctuating among the states in a cyclic way. We found that biased movement occurs only when net cycling is present and the direction of the movement is closely related to that of the net cycling, similar to the movement of a chemically driven enzyme particle in a static periodic potential. The formalism and the model can be used in studying the movement of a bead on a microtubule filament powered by a single one-headed kinesin.

A theory for the Lamb shift of the absorption spectrum in a Bose-Einstein condensate is proposed. Because of stimulated process the shift has an extra term proportional to the number of atoms in the condensate, in addition to the well known shift value This correction is maximized when the excited atom wave function overlaps with the ground state atom wave function. By a zero-momentum transfer method the correction can be in the 100 MHz range and much greater than the stimulated emission line broadening.

We show how a previous demonstration of nonlocality without inequalities for two spin-half particles can be improved so that a greater proportion of the pairs are shown to be subject to a contradiction with local realism. This is achieved by considering more settings of the apparatus at each end. Also, we report on an experimental realization employing a tunable source of polarization entangled photons. The experimental results violate locality (modulo, the efficiency loophole).

A multibaker map is generalized in order to mimic the thermostating algorithm of transport models. Elementary calculations yield the irreversible entropy production caused by coarse graining of the phase-space density. For different systems, either in steady states (periodic or flux boundaries) or subjected to absorbing boundaries, the specific irreversible entropy production is shown to be $u^2/D$, where $u$ denotes the local streaming velocity (current per density) and $D$ is the diffusion coefficient.

Stationary matter wave optics and stationary light optics are equivalent when we consider one-particle systems in vacuum. We show that, in contrast, stationary optics of energy-entangled particles is completely different for matter waves and for light. This difference is illustrated comparing the two-particle interference patterns exhibited by matter waves and by light, respectively. The time-independent probability for simultaneous detection of the two massive particles or of the two photons is strikingly nonequivalent.

We develop the idea of selectively manipulating the condensate in a trapped Bose-condensed gas, without perturbing the thermal cloud. The idea is based on the possibility to modify the mean field interaction between atoms (scattering length) by nearly resonant incident light or by spatially uniform change of the trapping magnetic field. For the gas in the Thomas-Fermi regime we find analytical scaling solutions for the condensate wave function evolving under arbitrary variations of the scattering length $a$. The change of $a$ from positive to negative induces a global collapse of the condensate, and the final stages of the collapse will be governed by intrinsic decay processes.

We propose a new method for investigating the exclusion statistics of quasiparticles in conformal field theory (CFT) spectra. The method leads to one-particle distribution functions, which generalize the Fermi-Dirac distribution. For the simplest $\mathrm{SU}\left(n\right)$ invariant CFTs we find a generalization of Gentile parafermions, and we obtain new distributions for the simplest $Z_N$-invariant CFTs. In special examples, our approach reproduces distributions based on “fractional exclusion statistics” in the sense of Haldane. We comment on applications to fractional quantum Hall effect edge theories.

The Widom-Rowlinson model of a fluid mixture is studied using a new cluster algorithm that is an adaptation of the invaded cluster method previously applied to Potts models. The algorithm overcomes the difficulties of treating continuum hard-core systems and has almost no critical slowing down. Our estimates of $\beta /\nu$ and $\gamma /\nu$ for the two-component fluid are consistent with the Ising universality class in two and three dimensions. We also present preliminary results for the three-component fluid.

The model introduced by Van den Broeck, Parrondo, and Toral [Phys. Rev. Lett. 73, 3395 (1994)]—leading to a second-order-like noise-induced nonequilibrium phase transition which shows reentrance as a function of the (multiplicative) noise intensity $\sigma$—is investigated beyond the white-noise assumption. Through a Markovian approximation and within a mean-field treatment it is found that, in striking contrast with the usual behavior for equilibrium phase transitions, for noise self-correlation time $\tau >0\mathrm{}$, the stable phase for (diffusive) spatial coupling $D\to \infty$ is always the disordered one. Another surprising result is that a large noise “memory” also tends to destroy order. These results are supported by numerical simulations.

It is proposed that an unconstrained quantum system is completely specified by its configuration space $C$ and its group of symmetries $G$. It is then shown that the theory of projective unitary representations of $G$ on a certain Hilbert space determined by $C$ and $G$ leads to a definitive resolution of supposed ambiguities relating to superselection rules, choice of wave functions, topological properties of $G$ and $C$, anomalies, etc.

We consider the stability of vortices in trapped dilute Bose gases. For weak coupling the vortex is unstable to single-particle excitations: the Bose condensate cannot support persistent currents, and the gas is not superfluid. For stronger coupling the azimuthal symmetry of the rotating condensate is spontaneously broken, resulting in an off-center vortex that eventually spirals out of the trap.

We show that for stochastic dynamical systems out of equilibrium the violation of the fluctuation-dissipation equality is bounded by a function of the entropy production. The result applies to a much wider situation than “near equilibrium,” comprising diffusion as well as glasses and other macroscopic systems far from equilibrium. For aging systems this bounds the age-frequency regimes in which the susceptibilities satisfy the fluctuation-dissipation theorem in terms of the rate of decay of the $H$ function, a question intimately related to the reading of a thermometer placed in contact with the system.

The ordering kinetics in the Coulomb gas (CG) of half-integer charges is investigated via Monte Carlo simulations. Because of the long range Coulomb interaction, the phase ordering of this system is governed by an activation energy barrier with a logarithmic dependence on the domain size. This results in a genuine temperature-dependent growth and a roughening transition of the domain-wall morphology above $T_R\simeq 0.09\pm 0.01$. An analytical argument with numerical verification indicates that the classical CG of half-integer charges belongs to a new universality class from the viewpoint of Lai et al.'s classification of ordering kinetics [Phys. Rev. B 37, 9481 (1988)].

The multifractal dimensions $D_2^{\mu }$ and $D_2^{\psi }$ of the energy spectrum and eigenfunctions, respectively, are shown to determine the asymptotic scaling of the width of a spreading wave packet. For systems where the shape of the wave packet is preserved, the $k$th moment increases as $t^{k\beta }$ with $\beta {=D}_2^{\mu }/D_2^{\psi }$, while, in general, $t^{k\beta }$ is an optimal lower bound. Furthermore, we show that in $d$ dimensions asymptotically in time the center of any wave packet decreases spatially as a power law with exponent $D_2^{\psi }-d$, and present numerical support for these results.

We describe the blueprint of an experiment in which the decoherence of a mesoscopic superposition of radiation states (“Schrödinger cat”) becomes a reversible process. When the high $Q$ cavity containing the Schrödinger cat is coupled to another resonator, the mesoscopic quantum coherence first decays rapidly, then exhibits sharp revivals with the period of the energy exchange between the two cavities. The interpretation of this experiment emphasizes the link between decoherence and complementarity and leads to an illuminating quantitative interpretation of the usual irreversible decoherence phenomenon.

Stability of matter with Coulomb forces has been proved for nonrelativistic dynamics, including arbitrarily large magnetic fields, and for relativistic dynamics without magnetic fields. In both cases stability requires that the fine structure constant $\alpha$ be not too large. It was unclear what would happen for both relativistic dynamics and magnetic fields, or even how to formulate the problem clearly. We show that the use of the Dirac operator allows both effects, provided the filled negative energy “sea” is defined properly. The use of the free Dirac operator to define the negative levels leads to catastrophe for any $\alpha$, but the use of the Dirac operator with magnetic field leads to stability.

We study the Bose-Einstein condensate (BEC) with a fixed number of particles. On the basis of conventional statistical mechanics we introduce the, so called, Maxwell's demon ensemble, where only particle transfer (without energy exchange) is allowed. We show that this new ensemble can be used for the microcanonical description of the system. We apply our formalism to the case of BEC in a harmonic trap and give the analytic expressions for the ground state fluctuations. We compare these expressions with the exact numerical results obtained for relatively small condensates.

The formation process of a Bose-Einstein condensate in a trap is described using a master equation based on quantum kinetic theory, which can be well approximated by a description using only the condensate mode in interaction with a thermalized bath of noncondensate atoms. A rate equation of the form $\dot{n}{=2W}^{+}\left(n\right)[\left({1-e}^{\{{\mu }_n-\mu \}/\mathrm{kT}}\right)n+1\mathrm{}]$ is derived, in which the difference between the condensate chemical potential ${\mu }_n$ and the bath chemical potential $\mu$ gives the essential behavior. Solutions of this equation give a characteristic latency period for condensate formation and appear to be consistent with the observed behavior of both rubidium and sodium condensate formation.