Quantum Fluctuations of Coulomb Potential as a Source of Flicker Noise. The Influence of External Electric Field

Fluctuations of the electromagnetic field produced by quantized matter in external electric field are investigated. A general expression for the power spectrum of fluctuations is derived within the long-range expansion. It is found that in the whole measured frequency band, the power spectrum of fluctuations exhibits an inverse frequency dependence. A general argument is given showing that for all practically relevant values of the electric field, the power spectrum of induced fluctuations is proportional to the field strength squared. As an illustration, the power spectrum is calculated explicitly using the kinetic model with the relaxation-type collision term. Finally, it is shown that the magnitude of fluctuations produced by a sample generally has a Gaussian distribution around its mean value, and its dependence on the sample geometry is determined. In particular, it is demonstrated that for geometrically similar samples, the power spectrum is inversely proportional to the sample volume. Application of the obtained results to the problem of flicker noise is discussed.Comment: 14 pages, 3 figure

On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Periodic orbits of period 3 in the disc

Let f be an orientation preserving homeomorphism of the disc D2 which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2 pi /3 or 4 pi /3, or f has a periodic point of least period n for each n in N*.Comment: 7 page

A discrete invitation to quantum filtering and feedback control

The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a novel field of application for stochastic estimation and control theory. In this expository paper we demonstrate estimation and feedback control of quantum mechanical systems in what is essentially a noncommutative version of the binomial model that is popular in mathematical finance. The model is extremely rich and allows a full development of the theory, while remaining completely within the setting of finite-dimensional Hilbert spaces (thus avoiding the technical complications of the continuous theory). We introduce discretized models of an atom in interaction with the electromagnetic field, obtain filtering equations for photon counting and homodyne detection, and solve a stochastic control problem using dynamic programming and Lyapunov function methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be found at http://minty.caltech.edu/papers.ph

In vitro fermentation of different ratios of alfalfa and starch or inulin incubated with an equine faecal inoculum

The aim of this work was to assess the impact of substituting starch (S) or inulin (I) with high-temperature dried alfalfa (HTDA) as substrates for in vitro fermentation with an equine faecal inoculum. A series of experiments were conducted to assess the fermentation kinetics of HTDA (chopped [CA] or ground [GA]) and either S or I mixed in the following ratios; 100:0, 80:20, 60:40, 40:60 and 20:80S/I: CA/GA, respectively. For each experiment, a further set of bottles containing identical ratios of S/I: CA/GA were also prepared, with the exception that the alfalfa received a simulated foregut digestion treatment (SFD) as prior to incubation. Total gas production increased (P<0.05) as the ratio of S/I to alfalfa increased. Total gas production was lower in bottles containing SFD-treated alfalfa (P<0.001). Dry matter loss decreased proportionately with increasing level of alfalfa substitution of S/I (P<0.001). Values for pH were lower in bottles containing S or I, with pH values in bottles containing S alone falling to almost 6 and those with I dropping to pH 5 and under. However, the substitution of S or I with 40% alfalfa produced pH values above 6.7, which is within physiological levels encountered in the large intestine of the horse. Consequently, there appears to be considerable potential to buffer the deleterious effects of high-starch/fructan diets with the substitution of these substrates with high-temperature dried alfalfa

Acidification increases microbial polysaccharide degradation in the ocean

© The Authors, 2010. This article is distributed under the terms of the Creative Commons Attribution 3.0 License. The definitive version was published in Biogeosciences 7 (2010): 1615–1624, doi:10.5194/bg-7-1615-2010.With the accumulation of anthropogenic carbon dioxide (CO2), a proceeding decline in seawater pH has been induced that is referred to as ocean acidification. The ocean's capacity for CO2 storage is strongly affected by biological processes, whose feedback potential is difficult to evaluate. The main source of CO2 in the ocean is the decomposition and subsequent respiration of organic molecules by heterotrophic bacteria. However, very little is known about potential effects of ocean acidification on bacterial degradation activity. This study reveals that the degradation of polysaccharides, a major component of marine organic matter, by bacterial extracellular enzymes was significantly accelerated during experimental simulation of ocean acidification. Results were obtained from pH perturbation experiments, where rates of extracellular α- and β-glucosidase were measured and the loss of neutral and acidic sugars from phytoplankton-derived polysaccharides was determined. Our study suggests that a faster bacterial turnover of polysaccharides at lowered ocean pH has the potential to reduce carbon export and to enhance the respiratory CO2 production in the future ocean.This study was supported by the Helmholtz Association (HZ-NG-102) and the Belgian Science Policy (SD/CS/03)

The politics of time: Political entropy, settler colonialism and urban ruination in Hebron / Al-Khalil, Palestine

This paper explores the relationships between settler colonialism and temporal regimes of urban ruination in the Palestinian city of Hebron/Al-Khalil. The city is divided into two sectors: H1, controlled by the Palestinian National Authority, and H2, roughly 20% of the city, including 33,000 Palestinians and 700 Jewish settlers, living under direct Israeli military occupation. Drawing on fieldwork in H2, we identify several temporal formations shaping H2: the settler-messianic time that spatializes the past as a platform to facilitate colonial expansion; contemporary military control that seeks to destabilize Palestinian homes, their everyday lives and ontological security in the present; and the Palestinian effort to recalibrate the rhythm of elimination and recover the future. The paper develops the concept of political entropy: a temporal technology of control that builds on the process of natural decay. Israel uses the power of time and entropy to let Palestinian assets decay slowly while prohibiting proper renovation and maintenance. The mundane violence of political entropy tends to remain unseen, as the harm is done slowly, allegedly naturally. Facing the settler colonial temporalities that maintain a state of undecidedness, where deferral itself becomes a weapon which lets entropy operate without interruption, Hebron\u27s Palestinian inhabitants aim at slowing down the effects of time by applying friction to the process of ruination, as well as by their insistence on futurability. By identifying the temporalities trapping the city\u27s Palestinian population, our paper thus frames Hebron\u27s H2 as space that is simultaneously ruined and reclaimed

A Classification of Minimal Sets of Torus Homeomorphisms

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.Comment: Published in Mathematische Zeitschrift, June 2013, Volume 274, Issue 1-2, pp 405-42

Automorphisms of graphs of cyclic splittings of free groups

We prove that any isometry of the graph of cyclic splittings of a finitely generated free group $F_N$ of rank $N\ge 3$ is induced by an outer automorphism of $F_N$. The same statement also applies to the graphs of maximally-cyclic splittings, and of very small splittings.Comment: 22 pages, 5 figures. Small modifications. To appear in Geometriae Dedicat

Sliding mode control of quantum systems

This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e., eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum sliding mode control systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of main features of the proposed method is that the designed control laws can guarantee desired control performance in the presence of uncertainties in the system Hamiltonian. This sliding mode control approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.Comment: 18 pages, 4 figure