Coagulation kinetics beyond mean field theory using an optimised Poisson representation

Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics can be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants. This can be a poor approximation when the mean populations are small. However, using the Poisson representation it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work we encounter instabilities that can be eliminated using a suitable 'gauge' transformation of the problem [P. D. Drummond, Eur. Phys. J. B38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation

New Renormalization Group Equations and the Naturalness Problem

Looking for an observable manifestation of the so-called unnaturalness of scalar fields we introduce a seemingly new set of differential equations for connected Green functions. These equations describe the momentum dependence of the Green functions and are close relatives to the previously known renormalization group equations. Applying the new equations to the theory of scalar field with $\phi^4$ interaction we identify a relation between the four-point Green function and the propagator which expresses the unnaturalness of the scalar field. Possible manifestations of the unnaturalness at low momenta are briefly discussed.Comment: 12 revtex pages; a coefficient has been corrected in eq. (34), four new references added; final version to appear in Phys. Rev.

Generating Functional for Strong and Nonleptonic Weak Interactions

The generating functional for Green functions of quark currents is given in closed form to next-to-leading order in the low-energy expansion for chiral SU(3), including one-loop amplitudes with up to three meson propagators. Matrix elements and form factors for strong and nonleptonic weak processes with at most six external states can be extracted from this functional by performing three-dimensional flavour traces. To implement this procedure, a Mathematica program is provided that evaluates amplitudes with at most six external mesons, photons (real or virtual) and virtual W (semileptonic form factors). The program is illustrated with several examples that can be compared with existing calculations.Comment: 26 pages; references added, comparison with other programs added, small changes in the text, version to appear in JHE

The exact equivalence of the two-flavour strong coupling lattice Schwinger model with Wilson fermions to a vertex model

In this paper a method previously employed by Salmhofer to establish an exact equivalence of the one-flavour strong coupling lattice Schwinger model with Wilson fermions to some 8-vertex model is applied to the case with two flavours. As this method is fairly general and can be applied to strong coupling QED and purely fermionic models with any (sufficiently small) number of Wilson fermions in any dimension the purpose of the present study is mainly a methodical one in order to gain some further experience with it. In the paper the vertex model equivalent to the two-flavour strong coupling lattice Schwinger model with Wilson fermions is found. It turns out to be some modified 3-state 20-vertex model on the square lattice, which can also be understood as a regular 6-state vertex model. In analogy with the one- flavour case, this model can be viewed as some loop model.Comment: 22 pages LaTe

Heisenberg XXZ Model and Quantum Galilei Group

The 1D Heisenberg spin chain with anisotropy of the XXZ type is analyzed in terms of the symmetry given by the quantum Galilei group Gamma_q(1). We show that the magnon excitations and the s=1/2, n-magnon bound states are determined by the algebra. Thus the Gamma_q(1) symmetry provides a description that naturally induces the Bethe Ansatz. The recurrence relations determined by Gamma_q(1) permit to express the energy of the n-magnon bound states in a closed form in terms of Tchebischeff polynomials.Comment: (pag. 10

Quantum repeaters and quantum key distribution: analysis of secret key rates

We analyze various prominent quantum repeater protocols in the context of long-distance quantum key distribution. These protocols are the original quantum repeater proposal by Briegel, D\"ur, Cirac and Zoller, the so-called hybrid quantum repeater using optical coherent states dispersively interacting with atomic spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using atomic ensembles together with linear optics and, in its most recent extension, heralded qubit amplifiers. For our analysis, we investigate the most important experimental parameters of every repeater component and find their minimally required values for obtaining a nonzero secret key. Additionally, we examine in detail the impact of device imperfections on the final secret key rate and on the optimal number of rounds of distillation when the entangled states are purified right after their initial distribution.Comment: Published versio

Deformed Quantum Cohomology and (0,2) Mirror Symmetry

We compute instanton corrections to correlators in the genus-zero topological subsector of a (0,2) supersymmetric gauged linear sigma model with target space P1xP1, whose left-moving fermions couple to a deformation of the tangent bundle. We then deduce the theory's chiral ring from these correlators, which reduces in the limit of zero deformation to the (2,2) ring. Finally, we compare our results with the computations carried out by Adams et al.[ABS04] and Katz and Sharpe[KS06]. We find immediate agreement with the latter and an interesting puzzle in completely matching the chiral ring of the former.Comment: AMSLatex, 30 pages, one eps figure. V4: typos corrected, final version appearing in JHE

Selective cognitive and psychiatric manifestations in Wolfram Syndrome

BACKGROUND: Wolfram Syndrome (WFS) is known to involve diabetes mellitus, diabetes insipidus, optic nerve atrophy, vision loss, hearing impairment, motor abnormalities, and neurodegeneration, but has been less clearly linked to cognitive, sleep, and psychiatric abnormalities. We sought to determine whether these abnormalities are present in children, adolescents, and young adults with WFS compared to age- and gender-matched individuals with and without type 1 diabetes using standardized measures. METHODS: Individuals with genetically-confirmed WFS (n = 19, ages 7–27) were compared to age- and gender- equivalent groups of individuals with type 1 diabetes (T1DM; n = 25), and non-diabetic healthy controls (HC: n = 25). Cognitive performance across multiple domains (verbal intelligence, spatial reasoning, memory, attention, smell identification) was assessed using standardized tests. Standardized self- and parent-report questionnaires on psychiatric symptoms and sleep disturbances were acquired from all groups and an unstructured psychiatric interview was performed within only the WFS group. RESULTS: The three groups were similar demographically (age, gender, ethnicity, parental IQ). WFS and T1DM had similar duration of diabetes but T1DM had higher Hb(A1C) levels than WFS and as expected both groups had higher levels than HC. The WFS group was impaired on smell identification and reported sleep quality, but was not impaired in any other cognitive or self-reported psychiatric domain. In fact, the WFS group performed better than the other two groups on selected memory and attention tasks. However, based upon a clinical evaluation of only WFS patients, we found that psychiatric and behavioral problems were present and consisted primarily of anxiety and hypersomnolence. CONCLUSIONS: This study found that cognitive performance and psychological health were relatively preserved WFS patients, while smell and sleep abnormalities manifested in many of the WFS patients. These findings contradict past case and retrospective reports indicating significant cognitive and psychiatric impairment in WFS. While many of these patients were diagnosed with anxiety and hypersomnolence, self-reported measures of psychiatric symptoms indicated that the symptoms were not of grave concern to the patients. It may be that cognitive and psychiatric issues become more prominent later in life and/or in later stages of the disease, but this requires standardized assessment and larger samples to determine. In the relatively early stages of WFS, smell and sleep-related symptoms may be useful biomarkers of disease and should be monitored longitudinally to determine if they are good markers of progression as well. TRIAL REGISTRATION: Current Clinicaltrials.gov Trial NCT02455414

Speed and entropy of an interacting continuous time quantum walk

We present some dynamic and entropic considerations about the evolution of a continuous time quantum walk implementing the clock of an autonomous machine. On a simple model, we study in quite explicit terms the Lindblad evolution of the clocked subsystem, relating the evolution of its entropy to the spreading of the wave packet of the clock. We explore possible ways of reducing the generation of entropy in the clocked subsystem, as it amounts to a deficit in the probability of finding the target state of the computation. We are thus lead to examine the benefits of abandoning some classical prejudice about how a clocking mechanism should operate.Comment: 25 pages, 14 figure

A large sample study of spin relaxation and magnetometric sensitivity of paraffin-coated Cs vapor cells

We have manufactured more than 250 nominally identical paraffin-coated Cs vapor cells (30 mm diameter bulbs) for multi-channel atomic magnetometer applications. We describe our dedicated cell characterization apparatus. For each cell we have determined the intrinsic longitudinal, \sGamma{01}, and transverse, \sGamma{02}, relaxation rates. Our best cell shows \sGamma{01}/2\pi\approx 0.5 Hz, and \sGamma{02}/2\pi\approx 2 Hz. We find a strong correlation of both relaxation rates which we explain in terms of reservoir and spin exchange relaxation. For each cell we have determined the optimal combination of rf and laser powers which yield the highest sensitivity to magnetic field changes. Out of all produced cells, 90% are found to have magnetometric sensitivities in the range of 9 to 30 fTHz. Noise analysis shows that the magnetometers operated with such cells have a sensitivity close to the fundamental photon shot noise limit