Optimization of photomixers and antennas for continuous-wave terahertz emission

We have studied terahertz emission from interdigitated finger photomixers coupled to planar antenna structures. Using both pulsed and continuous-wave excitation, polarization measurements reveal that the antenna design dominates the properties of the radiated output at frequencies below 0.6 THz, while the efficiency at higher frequencies is additionally dependent on the design of the photomixer fingers. We have produced terahertz maps of the device, characterizing the photomixer by measuring the generated power as a function of the excitation position. Together, these measurements have allowed us to understand better the distinct roles of the photomixer and antenna in emission at different fre

A simple proof of Hardy-Lieb-Thirring inequalities

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).Comment: 12 page

Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics

We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator is semi-bounded below and that its spectral subspaces corresponding to energies below the ionization threshold are exponentially localized. Both results hold true, for arbitrary values of the fine-structure constant, $e^2$, and the ultra-violet cut-off, $\Lambda$, and for all nuclear charges less than the critical charge without radiation field, $Z_c=e^{-2}2/(2/\pi+\pi/2)$. We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of $e^2$ and $\Lambda$ and for nuclear charges less than $e^{-2}2/\pi$.Comment: 37 page

Comments about quantum symmetries of SU(3) graphs

For the SU(3) system of graphs generalizing the ADE Dynkin digrams in the classification of modular invariant partition functions in CFT, we present a general collection of algebraic objects and relations that describe fusion properties and quantum symmetries associated with the corresponding Ocneanu quantum groupo\"{i}ds. We also summarize the properties of the individual members of this system.Comment: 36 page

Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics

Number--conserving model for boson pairing

An independent pair ansatz is developed for the many body wavefunction of dilute Bose systems. The pair correlation is optimized by minimizing the expectation value of the full hamiltonian (rather than the truncated Bogoliubov one) providing a rigorous energy upper bound. In contrast with the Jastrow model, hypernetted chain theory provides closed-form exactly solvable equations for the optimized pair correlation. The model involves both condensate and coherent pairing with number conservation and kinetic energy sum rules satisfied exactly and the compressibility sum rule obeyed at low density. We compute, for bulk boson matter at a given density and zero temperature, (i) the two--body distribution function, (ii) the energy per particle, (iii) the sound velocity, (iv) the chemical potential, (v) the momentum distribution and its condensate fraction and (vi) the pairing function, which quantifies the ODLRO resulting from the structural properties of the two--particle density matrix. The connections with the low--density expansion and Bogoliubov theory are analyzed at different density values, including the density and scattering length regime of interest of trapped-atoms Bose--Einstein condensates. Comparison with the available Diffusion Monte Carlo results is also made.Comment: 21 pages, 12 figure

Flavour Universal Dynamical Electroweak Symmetry Breaking

The top condensate see-saw mechanism of Dobrescu and Hill allows electroweak symmetry to be broken while deferring the problem of flavour to an electroweak singlet, massive sector. We provide an extended version of the singlet sector that naturally accommodates realistic masses for all the standard model fermions, which play an equal role in breaking electroweak symmetry. The models result in a relatively light composite Higgs sector with masses typically in the range of (400-700)~GeV. In more complete models the dynamics will presumably be driven by a broken gauged family or flavour symmetry group. As an example of the higher scale dynamics a fully dynamical model of the quark sector with a GIM mechanism is presented, based on an earlier top condensation model of King using broken family gauge symmetry interactions (that model was itself based on a technicolour model of Georgi). The crucial extra ingredient is a reinterpretation of the condensates that form when several gauge groups become strong close to the same scale. A related technicolour model of Randall which naturally includes the leptons too may also be adapted to this scenario. We discuss the low energy constraints on the massive gauge bosons and scalars of these models as well as their phenomenology at the TeV scale.Comment: 22 pages, 3 fig

Riparian buffer strips influence nitrogen losses as nitrous oxide and leached N from upslope permanent pasture

Riparian buffer strips can have a significant role in reducing nitrogen (N) transfers from agricultural land to freshwater primarily via denitrification and plant uptake processes, but an unintended trade-off can be elevated nitrous oxide (N2O) production rates. Against this context, our replicated bounded plot scale study investigated N2O emissions from un-grazed ryegrass pasture served by three types of riparian buffer strips with different vegetation, comprising: (i) grass riparian buffer with novel deep-rooting species, (ii) willow (young trees at establishment phase) riparian buffer, and (iii) deciduous woodland (also young trees at establishment phase) riparian buffer. The experimental control was ryegrass pasture with no buffer strip. N2O emissions were measured at the same time as total oxidized N in run-off, and soil and environmental characteristics in the ri parian buffer strips and upslope pasture between 2018 and 2019. During most of the sampling days, the no-buffer control treatment showed significantly (P < 0.05) greater N2O fluxes and cumulative N2O emissions compared to the remainder of the treatments. Our results also showed that the grass riparian buffer strip is a sink of N2O equivalent to − 2310.2 g N2O-N ha− 1 day− 1 (95% confidence interval:− 535.5 to 492). Event-based water quality results obtained during storms (12 November 2018 and 11 February 2019) showed that the willow riparian buffer treatment had the highest flow-weighted mean N concentrations (N-FWMC) of 0.041 ± 0.022 and 0.031 ± 0.015 mg N L− 1, when compared to the other treatments. Our 9-month experiment therefore, shows that ri parian buffer strips with novel deep-rooting grass can therefore potentially address emissions to both water and air. The results imply that over a shorter timeline similar to the current study, the grass riparian buffer strip can potentially address N emission to both air and water, particularly when serving a permanent pasture in similar settings as the current experiment.Fil: Dlamini, J.C. Crop and Climate Sciences. Departament of Soil; Sudáfrica. Rothamsted Research. Sustainable Agriculture Sciences; Reino Unido. University of Pretoria. Department of Plant and Soil Sciences; SudáfricaFil: Cardenas, L.M. Rothamsted Research. Sustainable Agriculture Sciences; Reino Unido.Fil: Tesfamarian, E.H. University of Pretoria. Department of Plant and Soil Sciences; SudáfricaFil: Dunn, R.M. Rothamsted Research. Sustainable Agriculture Sciences; Reino Unido.Fil: Loick, N. Rothamsted Research. Sustainable Agriculture Sciences; Reino Unido.Fil: Charteris, A.F. Rothamsted Research. Sustainable Agriculture Sciences; Reino Unido.Fil: Cocciaglia, L. Università degli Studi di Perugia. Dipartimento di Scienze Agrarie, Alimentari e Ambientali; ItaliaFil: Vangeli, Sebastián. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Clima y Agua; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Ingeniería Agrícola y Uso de la Tierra. Cátedra de Manejo y Conservación de Suelo; ArgentinaFil: Blackwell, M.S.A. Rothamsted Research. Sustainable Agriculture Sciences; Reino Unido.Fil: Upadhayay, H.R. Rothamsted Research. Sustainable Agriculture Sciences; Reino Unido.Fil: Hawkins, J.M.B. Rothamsted Research. Sustainable Agriculture Sciences; Reino Unido.Fil: Evans, J. Rothamsted Research. Computational and Analytical Sciences; Reino UnidoFil: Collins, A.L. Rothamsted Research. Sustainable Agriculture Sciences; Reino Unido

Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations

We prove existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler-Poisson (EP) equations in 3 spatial dimensions, with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty-Beals paper. We prove the nonlinear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove local in time stability of W^{1, \infty}(\RR^3) solutions where the perturbations are entropy-weak solutions of the EP equations. Finally, we give a uniform (in time) a-priori estimate for entropy-weak solutions of the EP equations

Heat release by controlled continuous-time Markov jump processes

We derive the equations governing the protocols minimizing the heat released by a continuous-time Markov jump process on a one-dimensional countable state space during a transition between assigned initial and final probability distributions in a finite time horizon. In particular, we identify the hypotheses on the transition rates under which the optimal control strategy and the probability distribution of the Markov jump problem obey a system of differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh tends to zero, these equations converge to those satisfied by the diffusion process minimizing the heat released in the Langevin formulation of the same problem. We also show that in full analogy with the continuum case, heat minimization is equivalent to entropy production minimization. Thus, our results may be interpreted as a refined version of the second law of thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure