Exact Markovian kinetic equation for a quantum Brownian oscillator

We derive an exact Markovian kinetic equation for an oscillator linearly coupled to a heat bath, describing quantum Brownian motion. Our work is based on the subdynamics formulation developed by Prigogine and collaborators. The space of distribution functions is decomposed into independent subspaces that remain invariant under Liouville dynamics. For integrable systems in Poincar\'e's sense the invariant subspaces follow the dynamics of uncoupled, renormalized particles. In contrast for non-integrable systems, the invariant subspaces follow a dynamics with broken-time symmetry, involving generalized functions. This result indicates that irreversibility and stochasticity are exact properties of dynamics in generalized function spaces. We comment on the relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.Comment: A few typos in the published version are correcte

Spin-mediated dissipation and frequency shifts of a cantilever at milliKelvin temperatures

We measure the dissipation and frequency shift of a magnetically coupled cantilever in the vicinity of a silicon chip, down to $25$ mK. The dissipation and frequency shift originates from the interaction with the unpaired electrons, associated with the dangling bonds in the native oxide layer of the silicon, which form a two dimensional system of electron spins. We approach the sample with a $3.43$ $\mu$m-diameter magnetic particle attached to an ultrasoft cantilever, and measure the frequency shift and quality factor as a function of temperature and the distance. Using a recent theoretical analysis [J. M. de Voogd et al., arXiv:1508.07972 (2015)] of the dynamics of a system consisting of a spin and a magnetic resonator, we are able to fit the data and extract the relaxation time $T_1=0.39\pm0.08$ ms and spin density $\sigma=0.14\pm0.01$ spins per nm$^2$. Our analysis shows that at temperatures $\leq500$ mK magnetic dissipation is an important source of non-contact friction.Comment: 5 pages, 3 figure

Explaining two circumnuclear star forming rings in NGC5248

The distribution of gas in the central kiloparsec of a galaxy has a dynamically rapid evolution. Nonaxisymmetries in the gravitational potential of the galactic disk, such as a large scale stellar bar or spiral, can lead to significant radial motion of gaseous material from larger radii to the central region. The large influx of gas and the subsequent star formation keep the central region constantly changing. However, the ability of gas to reach the nucleus proper to fuel an AGN phase is not guaranteed. Gas inflow can be halted at a circumnuclear star forming ring several hundred parsec away. The nearby galaxy NGC5248 is especially interesting in this sense since it is said to host 2 circumnuclear star forming rings at 100pc and 370pc from its quiescent nucleus. Here we present new subarcsecond PdBI+30m CO(2-1) emission line observations of the central region. For the first time the molecular gas distribution at the smallest stellar ring is resolved into a gas ring, consistent with the presence of a quiescent nucleus. However, the molecular gas shows no ring structure at the larger ring. We combine analyses of the gaseous and stellar content in the central kiloparsec of this galaxy to understand the gas distribution and dynamics of this star forming central region. We discuss the probability of two scenarios leading to the current observations, given our full understanding of this system, and discuss whether there are really two circumnuclear star forming rings in this galaxy.Comment: Accepted for publication in A&A, 14pages + long tabl

Extreme value distributions and Renormalization Group

In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show, however, that more general rescalings are natural and lead to new limit distributions, apart from the Gumbel, Weibull, and Fr\'echet families. The problem is approached using the language of Renormalization Group transformations in the space of probability densities. The limit distributions are fixed points of the transformation and the study of the differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections.Comment: 16 pages, 5 figures. Final versio

Extreme fluctuations in noisy task-completion landscapes on scale-free networks

We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short-tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.Comment: 16 pages, 6 figures, revte

Complete determination of the reflection coefficient in neutron specular reflection by absorptive non-magnetic media

An experimental method is proposed which allows the complete determination of the complex reflection coefficient for absorptive media for positive and negative values of the momenta. It makes use of magnetic reference layers and is a modification of a recently proposed technique for phase determination based on polarization measurements. The complex reflection coefficient resulting from a simulated application of the method is used for a reconstruction of the scattering density profiles of absorptive non-magnetic media by inversion.Comment: 14 pages, 4 figures, reformulation of abstract, ref.12 added, typographical correction

Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Given a sequence $(M_{n},Q_{n})_{n\ge 1}$ of i.i.d.\ random variables with generic copy $(M,Q) \in GL(d, \R) \times \R^d$, we consider the random difference equation (RDE) $$R_{n}=M_{n}R_{n-1}+Q_{n},$$ $n\ge 1$, and assume the existence of $\kappa >0$ such that \lim_{n \to \infty}(\E{\norm{M_1 ... M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that the sequence $S_n = R_1 + ... + R_n$, appropriately normalized, converges in law to a multidimensional stable distribution with index $\kappa$. As a by-product, we show that the unique stationary solution $R$ of the RDE is regularly varying with index $\kappa$, and give a precise description of its tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page

Radiotherapy for patients with ledderhose disease:long-term effects, side effects and patient-rated outcome

BACKGROUND: The purpose of this study was to investigate the long-term effects of radiotherapy for patients with Ledderhose disease. METHODS: Questionnaires were sent to all patients with Ledderhose disease who had been treated with radiotherapy at our centre between 2008 and 2017 and who consented to participate. Radiotherapy was performed with orthovolt or electrons in two separate courses of five daily fractions of 3 Gy. The questionnaires addressed items such as pain from Ledderhose disease (Brief Pain Inventory), quality of life (EURO-QOL-5D-5L), long-term side effects, and patients' levels of satisfaction with the effect of treatment. Descriptive statistics and non-parametric tests were used to analyse the results. RESULTS: A total of 102 feet were irradiated in 67 patients (28 men, 39 women). Radiotherapy resulted in significant pain reduction: the mean pain score prior to radiotherapy, collected retrospectively, was 5.7 and 1.7 at time of assessment (p-value<0.001). The following pain response scores were reported: progressive pain (0%), no change (22%; 22 feet), partial pain response (37%; 38 feet) and complete pain response (absence of pain) (41%; 42 feet). Seventy-eight percent of patients were satisfied with the treatment effect and 57% did not consider radiotherapy burdensome. The scores for societal perspective (0.856) and patients' perspective on quality of life (82.3) were each comparable to the reference values from the Dutch population in the same age category (0.857 and 80.6, respectively). The most commonly reported residual long-term side effect was dryness of the skin (n=10; 15%). CONCLUSION: Radiotherapy for Ledderhose disease results in long-term pain reduction in the majority of patients and has limited side effects. The treatment is well tolerated, patients feel satisfied, and quality of life is comparable to the reference population