Feynman-Jackson integrals

We introduce perturbative Feynman integrals in the context of q-calculus generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide analytic as well as combinatorial interpretations for the Feynman-Jackson integrals.Comment: Final versio

Tunable coupling to a mechanical oscillator circuit using a coherent feedback network

We demonstrate a fully cryogenic microwave feedback network composed of modular superconducting devices connected by transmission lines and designed to control a mechanical oscillator coupled to one of the devices. The network features an electromechanical device and a tunable controller that coherently receives, processes and feeds back continuous microwave signals that modify the dynamics and readout of the mechanical state. While previous electromechanical systems represent some compromise between efficient control and efficient readout of the mechanical state, as set by the electromagnetic decay rate, the tunable controller produces a closed-loop network that can be dynamically and continuously tuned between both extremes much faster than the mechanical response time. We demonstrate that the microwave decay rate may be modulated by at least a factor of 10 at a rate greater than $10^4$ times the mechanical response rate. The system is easy to build and suggests that some useful functions may arise most naturally at the network-level of modular, quantum electromagnetic devices.Comment: 11 pages, 6 figures, final published versio

Interparticle interactions:Energy potentials, energy transfer, and nanoscale mechanical motion in response to optical radiation

In the interactions between particles of material with slightly different electronic levels, unusually large shifts in the pair potential can result from photoexcitation, and on subsequent electronic excitation transfer. To elicit these phenomena, it is necessary to understand the fundamental differences between a variety of optical properties deriving from dispersion interactions, and processes such as resonance energy transfer that occur under laser irradiance. This helps dispel some confusion in the recent literature. By developing and interpreting the theory at a deeper level, one can anticipate that in suitable systems, light absorption and energy transfer will be accompanied by significant displacements in interparticle separation, leading to nanoscale mechanical motion

Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

SM(2,4k) fermionic characters and restricted jagged partitions

A derivation of the basis of states for the $SM(2,4k)$ superconformal minimal models is presented. It relies on a general hypothesis concerning the role of the null field of dimension $2k-1/2$. The basis is expressed solely in terms of $G_r$ modes and it takes the form of simple exclusion conditions (being thus a quasi-particle-type basis). Its elements are in correspondence with $(2k-1)$-restricted jagged partitions. The generating functions of the latter provide novel fermionic forms for the characters of the irreducible representations in both Ramond and Neveu-Schwarz sectors.Comment: 12 page

An ALMA 3mm continuum census of Westerlund 1

Context. Massive stars play an important role in both cluster and galactic evolution and the rate at which they lose mass is a key driver of both their own evolution and their interaction with the environment up to and including their terminal SNe explosions. Young massive clusters provide an ideal opportunity to study a co-eval population of massive stars, where both their individual properties and the interaction with their environment can be studied in detail. Aims. We aim to study the constituent stars of the Galactic cluster Westerlund 1 in order to determine mass-loss rates for the diverse post-main sequence population of massive stars. Methods. To accomplish this we made 3mm continuum observations with the Atacama Large Millimetre/submillimetre Array. Results. We detected emission from 50 stars in Westerlund 1, comprising all 21 Wolf-Rayets within the field of view, plus eight cool and 21 OB super-/hypergiants. Emission nebulae were associated with a number of the cool hypergiants while, unexpectedly, a number of hot stars also appear spatially resolved. Conclusions. We were able to measure the mass-loss rates for a unique population of massive post-main sequence stars at every stage of evolution, confirming a significant increase as stars transitioned from OB supergiant to WR states via LBV and/or cool hypergiant phases. Fortuitously, the range of spectral types exhibited by the OB supergiants provides a critical test of radiatively-driven wind theory and in particular the reality of the bi-stability jump. The extreme mass-loss rate inferred for the interacting binary Wd1-9 in comparison to other cluster members confirmed the key role binarity plays in massive stellar evolution. The presence of compact nebulae around a number of OB and WR stars is unexpected; by analogy to the cool super-/hypergiants we attribute this to confinement and sculpting of the stellar wind via interaction with the intra-cluster medium/wind. Given the morphology of core collapse SNe depend on the nature of the pre-explosion circumstellar environment, if this hypothesis is correct then the properties of the explosion depend not just on the progenitor, but also the environment in which it is located

First order phase transition in the quark matter

We investigate chiral phase transition of the first order in the quark matter. Using the Nambu-Jona-Lasinio model, an equation of state of the quark matter which is similar to the van der Waals' one is obtained. Moreover the specific heat and the compressibility are calculated. It is shown that they are enhanced in the symmetry broken phase, in particular diverge near the tricritical point.Comment: 6 pages, 7 figure

Level Density of a Bose Gas and Extreme Value Statistics

We establish a connection between the level density of a gas of non-interacting bosons and the theory of extreme value statistics. Depending on the exponent that characterizes the growth of the underlying single-particle spectrum, we show that at a given excitation energy the limiting distribution function for the number of excited particles follows the three universal distribution laws of extreme value statistics, namely Gumbel, Weibull and Fr\'echet. Implications of this result, as well as general properties of the level density at different energies, are discussed.Comment: 4 pages, no figure

Enhancing Optical Up-Conversion Through Electrodynamic Coupling with Ancillary Chromophores

In lanthanide-based optical materials, control over the relevant operating characteristics–for example transmission wavelength, phase and quantum efficiency–is generally achieved through the modification of parameters such as dopant/host combination, chromophore concentration and lattice structure. An alternative avenue for the control of optical response is through the introduction of secondary, codoped chromophores. Here, such secondary centers act as mediators, commonly bridging the transfer of energy between primary absorbers of externally sourced optical input and other sites of frequency-converted emission. Utilizing theoretical models based on experimentally feasible, three-dimensional crystal lattice structures; a fully quantized theoretical framework provides insights into the locally modified mechanisms that can be implemented within such systems. This leads to a discussion of how such effects might be deployed to either enhance, or potentially diminish, the efficiency of frequency up-conversion