Emergence and destruction of macroscopic wave functions

The concept of the macroscopic wave function is a key for understanding macroscopic quantum phenomena. The existence of this object reflects a certain order, as is present in a Bose-Einstein condensate when a single-particle orbital is occupied by a macroscopic number of bosons. We extend these ideas to situations in which a condensate is acted on by an explicitly time-dependent force. While one might assume that such a force would necessarily degrade any pre-existing order, we demonstrate that macroscopic wave functions can persist even under strong forcing. Our definition of the time-dependent order parameter is based on a comparison of the evolution of $N$-particle states on the one hand, and of states with $N - 1$ particles on the other. Our simulations predict the possibility of an almost instantaneous dynamical destruction of a macroscopic wave function under currently accessible experimental conditions.Comment: 6 pages, 5 figure

Does A Loss of Social Credibility Impact Robot Safety?

This position paper discusses the safety-related functions performed by assistive robots and explores the relationship between trust and effective safety risk mitigation. We identify a measure of the robot’s social effectiveness, termed social credibility, and present a discussion of how social credibility may be gained and lost. This paper’s contribution is the identification of a link between social credibility and safety-related performance. Accordingly, we draw on analyses of existing systems to demonstrate how an assistive robot’s safety-critical functionality can be impaired by a loss of social credibility. In addition, we present a discussion of some of the consequences of prioritising either safety-related functionality or social engagement. We propose the identification of a mixed-criticality scheduling algorithm in order to maximise both safety-related performance and social engagement

Maxwell's Demon at work: Two types of Bose condensate fluctuations in power-law traps

After discussing the key idea underlying the Maxwell's Demon ensemble, we employ this idea for calculating fluctuations of ideal Bose gas condensates in traps with power-law single-particle energy spectra. Two essentially different cases have to be distinguished. If the heat capacity remains continuous at the condensation point in the large-N-limit, the fluctuations of the number of condensate particles vanish linearly with temperature, independent of the trap characteristics. If the heat capacity becomes discontinuous, the fluctuations vanish algebraically with temperature, with an exponent determined by the trap. Our results are based on an integral representation that yields the solution to both the canonical and the microcanonical fluctuation problem in a singularly transparent manner.Comment: 10 pages LaTeX and 3 eps-figures, published versio

Classical and Quantum Dynamics of a Periodically Driven Particle in a Triangular Well

We investigate the correspondence between classical and quantum mechanics for periodically time dependent Hamiltonian systems, using the example of a periodically forced particle in a one-dimensional triangular well potential. In particular, we consider quantum mechanical Floquet states associated with resonances in the classical phase space. When the classical motion exhibits {\it sub}harmonic resonances, the corresponding Floquet states maintain the driving field's periodicity through dynamical tunneling. This principle applies both to Floquet states associated with classical invariant vortex tubes surrounding stable, elliptic periodic orbits and to Floquet states that are associated with unstable, hyperbolic periodic orbits. The triangular well model also poses a yet unsolved mathematical problem, related to perturbation theory for systems with a dense pure point spectrum. The present approximate analytical and numerical results indicate that quantum tunneling between different resonance zones is of crucial importance for the question whether the driven triangular well has a dense point or an absolutely continuous quasienergy spectrum, or whether there is a transition from the one to the other.Comment: revtex, 36 pages, 18 figures (available upon request), to appear in Annals of Physic