Statistical Mechanics of finite arrays of coupled bistable elements

We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter space. The results obtained in prior works in the asymptotic infinite size limit are significantly different from the finite size results. A procedure to construct approximate 1-dimensional Langevin equation is adopted. This equation provides a useful tool to understand the collective behavior even in the presence of an external driving force

Vacuum fluctuations and the conditional homodyne detection of squeezed light

Conditional homodyne detection of quadrature squeezing is compared with standard nonconditional detection. Whereas the latter identifies nonclassicality in a quantitative way, as a reduction of the noise power below the shot noise level, conditional detection makes a qualitative distinction between vacuum state squeezing and squeezed classical noise. Implications of this comparison for the realistic interpretation of vacuum fluctuations (stochastic electrodynamics) are discussed.Comment: 14 pages, 7 figures, to appear in J. Opt. B: Quantum Semiclass. Op

Checking the validity of truncating the cumulant hierarchy description of a small system

We analyze the behavior of the first few cumulant in an array with a small number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf 19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global coupling and derived an infinite hierarchy of differential equations for the cumulant moments. They focused on the behavior of infinite size systems using a strategy based on truncating the hierarchy. In this work we explore the reliability of such an approach to describe systems with a small number of elements. We carry out an extensive numerical analysis of the truncated hierarchy as well as numerical simulations of the full set of Langevin equations governing the dynamics. We find that the results provided by the truncated hierarchy for finite systems are at variance with those of the Langevin simulations for large regions of parameter space. The truncation of the hierarchy leads to a dependence on initial conditions and to the coexistence of states which are not consistent with the theoretical expectations based on the multidimensional linear Fokker-Planck equation for finite arrays

Dynamics of an inhomogeneous quantum phase transition

We argue that in a second order quantum phase transition driven by an inhomogeneous quench density of quasiparticle excitations is suppressed when velocity at which a critical point propagates across a system falls below a threshold velocity equal to the Kibble-Zurek correlation length times the energy gap at freeze-out divided by $\hbar$. This general prediction is supported by an analytic solution in the quantum Ising chain. Our results suggest, in particular, that adiabatic quantum computers can be made more adiabatic when operated in an "inhomogeneous" way.Comment: 7 pages; version to appear in a special issue of New J. Phy

Quantum Zeno and anti-Zeno effects in surface diffusion of interacting adsorbates

Surface diffusion of interacting adsorbates is here analyzed within the context of two fundamental phenomena of quantum dynamics, namely the quantum Zeno effect and the anti-Zeno effect. The physical implications of these effects are introduced here in a rather simple and general manner within the framework of non-selective measurements and for two (surface) temperature regimes: high and very low (including zero temperature). The quantum intermediate scattering function describing the adsorbate diffusion process is then evaluated for flat surfaces, since it is fully analytical in this case. Finally, a generalization to corrugated surfaces is also discussed. In this regard, it is found that, considering a Markovian framework and high surface temperatures, the anti-Zeno effect has already been observed, though not recognized as such.Comment: 17 pages, 1 figur

The nature of dark matter and the density profile and central behavior of relaxed halos

We show that the two basic assumptions of the model recently proposed by Manrique and coworkers for the universal density profile of cold dark matter (CDM) halos, namely that these objects grow inside out in periods of smooth accretion and that their mass profile and its radial derivatives are all continuous functions, are both well understood in terms of the very nature of CDM. Those two assumptions allow one to derive the typical density profile of halos of a given mass from the accretion rate characteristic of the particular cosmology. This profile was shown by Manrique and coworkers to recover the results of numerical simulations. In the present paper, we investigate its behavior beyond the ranges covered by present-day N-body simulations. We find that the central asymptotic logarithmic slope depends crucially on the shape of the power spectrum of density perturbations: it is equal to a constant negative value for power-law spectra and has central cores for the standard CDM power spectrum. The predicted density profile in the CDM case is well fitted by the 3D S\'ersic profile over at least 10 decades in halo mass. The values of the S\'ersic parameters depend on the mass of the structure considered. A practical procedure is provided that allows one to infer the typical values of the best NFW or S\'ersic fitting law parameters for halos of any mass and redshift in any given standard CDM cosmology.Comment: 9 pages, 6 figures, to appear in the ApJ vol. 647, september 20, 2007. Minor changes to match the published versio

Line Shape Broadening in Surface Diffusion of Interacting Adsorbates with Quasielastic He Atom Scattering

The experimental line shape broadening observed in adsorbate diffusion on metal surfaces with increasing coverage is usually related to the nature of the adsorbate-adsorbate interaction. Here we show that this broadening can also be understood in terms of a fully stochastic model just considering two noise sources: (i) a Gaussian white noise accounting for the surface friction, and (ii) a shot noise replacing the physical adsorbate-adsorbate interaction potential. Furthermore, contrary to what could be expected, for relatively weak adsorbate-substrate interactions the opposite effect is predicted: line shapes get narrower with increasing coverage.Comment: 4 pages, 2 figures (slightly revised version