We show a new mechanism to extract energy from nonequilibrium fluctuations typical of periodically driven non-Hermitian systems. The transduction of energy between the driving force and the system is revealed by an anomalous behavior of the susceptibility, leading to a diminution of the dissipated power and consequently to an improvement of the transport properties. The general framework is illustrated by the analysis of some relevant cases.

We discuss the regimes of quantum degeneracy in a trapped 1D gas and obtain the diagram of states. Three regimes have been identified: the Bose-Einstein condensation (BEC) regimes of a true condensate and quasicondensate, and the regime of a trapped Tonks gas (gas of impenetrable bosons). The presence of a sharp crossover to the BEC regime requires extremely small interaction between particles. We discuss how to distinguish between true and quasicondensates in phase coherence experiments.

We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic density decay. By universal we mean that all models in the class are described by a single phase diagram spanned by two reduced parameters. The phase diagram reveals four regimes, two of which contain the previously studied cases of ballistic annihilation. The two new phases are a direct consequence of the stochasticity. The solution is obtained through a matrix product approach and builds on properties of a $q$-deformed harmonic oscillator algebra.

Over two decades ago it was predicted that nonlinear interactions between thermally driven fluctuations in dissipative nonlinear nonequilibrium systems lead to deviations from mean-field theory. Here we report experimental observations of such deviations as a supercritical primary bifurcation is approached. We measured the mean-square director-angle fluctuations $〈{\theta }^2〉$ below the bifurcation to electroconvection of two different nematic liquid crystals. For ${\epsilon }_{\mathrm{mf}}\equiv V^2/V_{\mathrm{c},\mathrm{m}\mathrm{f}}^2-1\mathrm{}\lesssim -0.1\mathrm{}$ ( $V$ is the applied voltage) we find $〈{\theta }^2〉\propto |{\epsilon }_{\mathrm{mf}}{|}^{-\gamma }$ with $\gamma$ given by linear theory (LT). Closer to the bifurcation there are deviations from LT with a smaller $\gamma$ and with $V_c^2>V_{\mathrm{c},\mathrm{m}\mathrm{f}}^2$.

We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs, different functions “guide” walkers of different signs, the Gaussians used for members of a pair are correlated, and walkers can cancel so as to conserve their expected future contributions. We report results for free-fermion systems and a fermion fluid with 14 ${}^3\mathrm{He}$ atoms, where it proves stable and correct. Its computational complexity grows with particle number, but slowly enough to make interesting physics within the reach of contemporary computers.

Classical properties of an open quantum system emerge through its interaction with other degrees of freedom (decoherence). We treat the case where this interaction produces a Markovian master equation for the system. We derive the corresponding distinguished local basis (pointer basis) by three methods. The first demands that the pointer states mimic as closely as possible the local nonunitary evolution. The second demands that the local entropy production be minimal. The third imposes robustness on the inherent quantum and emerging classical uncertainties. All three methods lead to localized Gaussian pointer states, their formation and diffusion being governed by well-defined quantum Langevin equations.

We argue that while fluctuating fronts propagating into an unstable state should be in the standard Kardar-Parisi-Zhang (KPZ) universality class when they are pushed, they should not when they are pulled: The $1/t$ velocity relaxation of deterministic pulled fronts makes it unlikely that the KPZ equation is their proper effective long-wavelength low-frequency theory. Simulations in 2D confirm the proposed scenario, and yield exponents $\beta \approx 0.29\pm 0.01$, $\zeta \approx 0.40\pm 0.02$ for fluctuating pulled fronts, instead of the $(1+1)\mathrm{D}$ KPZ values $\beta =1\mathrm{}/3$, $\zeta =1\mathrm{}/2$. Our value of $\beta$ is consistent with an earlier result of Riordan et al., and with a recent conjecture that the exponents are the $(2+1)\mathrm{D}$ KPZ values.

We report a study of the thermodynamic properties of indium clusters on a $\mathrm{SiN}{}_x$ surface during the early stages of thin film growth using a sensitive nanocalorimetry technique. The measurements reveal the presence of abnormal discontinuities in the heat of melting below $100°\mathrm{C}$. These discontinuities, for which temperature separation corresponds to a spatial periodicity equal to the thickness of an indium monolayer, are found to be related to the atomic “magic numbers,” i.e., the number of atoms necessary to form a complete shell of atoms at particle surface.

We investigate the adiabatic evolution of a set of nondegenerate eigenstates of a parametrized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to the evolution of more than one state. We present several physical systems where these concepts can be applied, including an experiment on microwave cavities for which off-diagonal phases can be determined from published data.

The standard text book Green's function possesses a self-energy that is known to be an optical potential for elastic scattering. The introduction of an optical potential reduces the complex many-body scattering problem into a tractable one-body problem. In this paper inelastic Green's functions are introduced and discussed which possess self-energies that are optical potentials for inelastic scattering. If the projectile is indistinguishable from particles comprising the target, intriguing aspects arise even for noninteracting particles.

We study the generation of excitations due to an “impurity” (static perturbation) placed into an oscillating Bose-Einstein condensed gas in the time-dependent trapping field. It is shown that there are two regions for the position of the local perturbation. In the first region the condensate flows around the impurity without generation of excitations demonstrating superfluid properties. In the second region the creation of excitations occurs, at least within a limited time interval, revealing destruction of superfluidity. The phenomenon can be studied by measuring the damping of condensate oscillations at different positions of the impurity.

We argue that in a fluid, or magnet, confined by adsorbing walls which favor liquid, or the $(+)$ phase, the solvation (Casimir) force in the vicinity of the critical point is strongly influenced by capillary condensation which occurs below the bulk critical temperature $T_c$. At $T$ slightly below and above $T_c$, a small bulk field $h<\mathrm{}0\mathrm{}$, which favors gas, or the $(-)$ phase, leads to residual condensation and a solvation force which is much more attractive (at the same large wall separation) than that found exactly at the critical point. Our predictions are supported by results obtained from density-matrix renormalization-group calculations in a two-dimensional Ising strip subject to identical surface fields.

We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncyclic and unitary quantum evolution.

We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of noninteracting fermions, and apply it to harmonically confined systems of up to $N=1000\mathrm{}$ fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi approximation, the exact profiles show negative local pressure in the tails and a prominent shell structure which may become accessible to observation in magnetically trapped gases of fermionic alkali atoms.

We examine the problem of a repulsive, weakly interacting and harmonically trapped Bose-Einstein condensate under rotation. We derive a simple analytic expression for the energy incorporating the interactions when the angular momentum per particle is between zero and one and find that the interaction energy decreases linearly as a function of the angular momentum in agreement with previous numerical and limiting analytical studies.

We have observed and characterized the dynamics of singly quantized vortices in dilute-gas Bose-Einstein condensates. Our condensates are produced in a superposition of two internal states of ${}^{87}\mathrm{Rb}$, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value of the healing length. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the precession frequency of the vortex core about the condensate axis changes by only a factor of 2.

Recent calculations by Vorobev and Malyshenko [JETP Lett. 71, 39 (2000)] show that molecular hydrogen may stay liquid and superfluid in strong electric fields of the order of $4\times {10}^7\mathrm{V}/\mathrm{cm}$. I demonstrate that strong local electric fields of similar magnitude exist beneath a two-dimensional layer of electrons localized in the image potential above the surface of solid hydrogen. Even stronger local fields exist around charged particles (ions or electrons) if the surface or bulk of a solid hydrogen crystal is statically charged. Measurements of the frequency shift of the $1\to 2$ photoresonance transition in the spectrum of a two-dimensional layer of electrons above a positively or negatively charged solid hydrogen surface performed in the temperature range 7–13.8 K support the prediction of electric field induced surface melting. The range of surface charge density necessary to stabilize the liquid phase of molecular hydrogen at the temperature of superfluid transition is estimated.

Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring at the collapse of the system. The model is analyzed using a probabilistic approach suited to smooth fluctuations. The branching ratio shows a behavior analogous to the magnetization in known magnetic systems with second-order phase transitions. We obtain a universal critical exponent $\beta \approx 0.5$ independent of the probability distribution used to assign the strengths of individual fibers.

We introduce the definition of generic bound entanglement for the case of continuous variables. We provide some examples of bound entangled states for that case, and discuss their physical sense in the context of quantum optics. We raise the question of whether the entanglement of these states is generic. As a by-product we obtain a new many parameter family of bound entangled states with positive partial transpose. We also point out that the “entanglement witnesses” and positive maps revealing the corresponding bound entanglement can easily be constructed.

Central potentials, independent of both the energy and the angular momentum $l$, are constructed from elastic phase shifts. The ambiguities of a fixed- $l$ inversion are exploited to fit the phase shifts of other partial waves. The fitted quantities are the energy and normalization constant of forbidden bound states, and the small-distance behavior of the potential. The method is based on supersymmetric transformations of the radial Schrödinger equation. It is applied to the $\alpha +\alpha$ collision in nuclear physics, and to the $e^{-}+\mathrm{Ne}$ collision in atomic physics.