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We present a method characterizing thermal noise in an optical cavity independent from quantum noise despite the thermal noise falling below the quantum noise limit. Using this method, we measured the thermal noise contribution from a GaAs AlGaAs micro-mirror suspended on a GaAs cantilever microresonator when brought to a cryogenic temperature (approximately 25 K) and incorporated into a Fabry Perot cavity. An optical spring is formed in this optical cavity. Previously, this setup exploited an optical spring to produce a displacement sensitivity falling 2.8 dB below the free-mass standard quantum limit (SQL), as reported by Cullen et. al. Here we use a similar setup to measure thermal noise which fell a maximum of 5 dB below the SQL. This measurement, in turn, allowed for an investigation of quantum noise suppression resulting from the optical spring effect, falling a maximum of 10 dB below the SQL.
Answering a question of Dobrinen and Todorcevic, we prove that below any stable ordered-union ultrafilter $\mathcal{U}$, there are exactly four nonprincipal Tukey classes: $[\mathcal{U}], [\mathcal{U}_{\operatorname{min}}], [\mathcal{U}_{\operatorname{max}}]$, and $[\mathcal{U}_{\operatorname{minmax}}]$. This parallels the classification of ultrafilters Rudin-Keisler below $\mathcal{U}$ by Blass. A key step in the proof involves modifying the proof of a canonization theorem of Klein and Spinas for Borel functions on $\mathrm{FIN}^{[\infty]}$ to obtain a simplified canonization theorem for fronts on $\mathrm{FIN}^{[\infty]}$, recovering Lefmann's canonization for fronts of finite uniformity rank as a special case. We use this to classify the Rudin-Keisler classes of all ultrafilters Tukey below $\mathcal{U}$, which is then applied to achieve the main result.
The elements of a finite field of prime order canonically correspond to the integers in an interval. This induces an ordering on the elements of the field. Using this ordering, Kiss and Somlai recently proved interesting properties of the set of points below the diagonal line. In this paper, we investigate the set of points lying below a parabola. We prove that in some sense, this set of points looks the same from all but two directions, despite having only one non-trivial automorphism. In addition, we study the sizes of these sets, and their intersection numbers with respect to lines.
In this paper, we establish nonlinear Landau damping below survival threshold for collisionless charged particles following the meanfield Vlasov theory near general radial equilibria. In absence of collisions, the long-range Coulomb pair interaction between particles self-consistently gives rise to oscillations, known in the physical literature as plasma oscillations or Langmuir's oscillatory waves, that disperse in space like a Klein-Gordon's dispersive wave. As a matter of fact, there is a non-trivial survival threshold of wave numbers that characterizes the large time dynamics of a plasma: {\em phase mixing} above the threshold driven by the free transport dynamics and {\em plasma oscillations} below the threshold driven by the collective meanfield interaction. The former mechanism provides exponential damping, while the latter is much slower and dictated by Klein-Gordon's dispersion which gives decay of the electric field precisely at rate of order $t^{-3/2}$. Up to date, all the works in the mathematical literature on nonlinear Landau damping fall into the phase mixing regime, in which plasma oscillations were absent. The present work resolves the problem in the plasma oscilla
In this Letter, the quantum correlation measurement technique as a method of power noise monitoring is investigated. Its principal idea of correlating two photodetector signals is introduced and contrasted to the conventional approach, which uses only a single photodetector. We discuss how this scheme can be used to obtain power noise information below the shot noise of the detected beam and also below the electronic dark noise of the individual photodetectors, both of which is not possible with the conventional approach. Furthermore, experimental results are presented, that demonstrate a detection of technical laser power noise one order of magnitude below the shot noise of the detected beam.
We construct examples of bounded below, noncontractible, acyclic complexes of finitely generated projective modules over some rings $S$, as well as bounded above, noncontractible, acyclic complexes of injective modules. The rings $S$ are certain rings of infinite matrices with entries in the rings of commutative polynomials or formal power series in infinitely many variables. In the world of comodules or contramodules over coalgebras over fields, similar examples exist over the cocommutative symmetric coalgebra of an infinite-dimensional vector space. A simpler, universal example of a bounded below, noncontractible, acyclic complex of free modules with one generator, communicated to the author by Canonaco, is included at the end of the paper.
Gaia19bxc is a transient detected on 2019 May 9 by the Gaia Photometric Science Alerts Team. I analyzed the past public Zwicky Transient Facility (ZTF) data and found that Gaia19bxc has a period of 0.04473647(3) d and two different maxima in one cycle. This object also showed high and low states in the ZTF data. Based on the high amplitude (2.0 mag) of the short-term variations, short period, almost zero color indices between the different ZTF bands and the absence of a longer period, I classified it to be a likely polar. There has been no established polar below the period minimum of cataclysmic variables (CVs) and Gaia19bxc could be the first such an object. CVs below the period minimum usually have a secondary star with a stripped evolved core and Gaia19bxc is expected to have a similar secondary. If this is indeed the case, Gaia19bxc could become a highly magnetized exotic ultracompact binary during its secular evolution.
The presence of subphases in spin-density wave (SDW) phase of (TMTSF)2PF6 below T* ~ 4K has been suggested by several experiments but the nature of the new phase is still controversial. We have investigated the temperature dependence of the angular dependence of the magnetoresistance in the SDW phase which shows different features for temperatures above and below T*. For T > 4K the magnetoresistance can be understood in terms of the Landau quantization of the quasiparticle spectrum in a magnetic field, where the imperfect nesting plays the crucial role. We propose that below T* ~ 4K the new unconventional SDW (USDW) appears modifying dramatically the quasiparticle spectrum. Unlike conventional SDW the order parameter of USDW depends on the quasiparticle momentum. The present model describes many features of the angular dependence of magnetoresistance reasonably well. Therefore, we may conclude that the subphase in (TMTSF)2PF6 below T* ~ 4K is described as SDW plus USDW.
Negative mass phenomena occurring below a cut-off frequency is examined by both theoretical and experimental methods. The paper begins with the investigation on a mass-spring structure, the effective mass of which is shown to be negative below a specific frequency. Due to the decaying nature of lattice waves in the negative-mass system, the transmission drop induced by negative effective mass is demonstrated experimentally. Further investigation is conducted for a rectangular solid waveguide with clamped boundary conditions. It is shown that the lowest bandgap mode of the clamped waveguide can be attributed to negative effective mass below a cut-off frequency. Based on this observation, elastic metamaterials made of the steel grid filled by styrene butadiene rubber are designed and fabricated. Both simulation and experimental analyses demonstrate that the designed metamaterial have negative effective mass below a cut-off frequency.
WIYN/HYDRA spectra in the Li 6708 Angstrom region have been obtained for 332 probable members of the old open cluster, NGC 6819. Preliminary analysis shows a pattern of Li depletion from the top of the turnoff to the base of the giant branch. Starting one magnitude below the level of the clump, all brighter giants have A(Li) below 1.0, with most having upper limits below 0.5. Star W007017, located BELOW the first-ascent red giant bump is Li-rich with A(Li) = 2.3. As a highly probable single-star astrometric and radial-velocity cluster member, its discrepant asteroseismic membership could be a by-product of the processes that triggered Li-enhancement. Its color-magnitude diagram location is consistent with only one proposed enhanced mixing process among first-ascent red giants.
Analysis of the a-b plane optical conductivity $σ_{ab}$ for both twinned and untwinned YBa$_{2}$Cu$_{3}$O$_{7-δ}$ as a function of temperature and doping shows that below a well defined temperature T*, a dip in the spectrum systematically appears separating the infrared charge excitation spectrum into two components with distinct energy scales. The change from monotonic behaviour in $σ_{ab}$ is found to be concurrent with the onset of phonon anomalies in Raman and infrared spectra below T*. The optical data are suggested to be evidence for the appearance of an inhomogeneous distribution of carriers rather than the opening of a simple gap for charge excitations below T*, an interpretation wich is consistent with recent angle-resoved photoemission and electronic Raman spectra. We find that the behaviour below T* and the absence of any anomalies at Tc can be interpreted assuming a Bose-Einstein condensation of preformed pairs.
An analytic relation between the statistics of photons in pixels and the number counts of multi-photon point sources is used to constrain the distribution of gamma-ray point sources below the Fermi detection limit at energies above 1 GeV and at latitudes below and above 30 degrees. The derived source-count distribution is consistent with the distribution found by the Fermi collaboration based on the first Fermi point source catalogue. In particular, we find that the contribution of resolved and unresolved active galactic nuclei (AGN) to the total gamma-ray flux is below 20% - 25%. In the best fit model, the AGN-like point source fraction is 17% +- 2%. Using the fact that the Galactic emission varies across the sky while the extra-galactic diffuse emission is isotropic, we put a lower limit of 51% on Galactic diffuse emission and an upper limit of 32% on the contribution from extra-galactic weak sources, such as star-forming galaxies. Possible systematic uncertainties are discussed.
The charge response in the barium vanadium sulfide (BaVS3) single crystals is characterized by dc resistivity and low frequency dielectric spectroscopy. A broad relaxation mode in MHz range with huge dielectric constant ~= 10^6 emerges at the metal-to-insulator phase transition TMI ~= 67 K, weakens with lowering temperature and eventually levels off below the magnetic transition Tchi ~= 30 K. The mean relaxation time is thermally activated in a manner similar to the dc resistivity. These features are interpreted as signatures of the collective charge excitations characteristic for the orbital ordering that gradually develops below TMI and stabilizes at long-range scale below Tchi.
Recent precise measurements of primary and secondary cosmic rays (CRs) in the TV rigidity domain have unveiled a bump in their spectra, located between 0.5-50 TV. We argue that a local shock may generate such a bump by increasing the rigidity of the preexisting CRs below 50 TV by a mere factor of ~1.5. Reaccelerated particles below ~0.5 TV are convected with the interstellar medium (ISM) flow and do not reach the Sun, thus creating the bump. This single universal process is responsible for the observed spectra of all CR species in the rigidity range below 100 TV. We propose that one viable shock candidate is the Epsilon Eridani star at 3.2 pc from the Sun, which is well-aligned with the direction of the local magnetic field. Other shocks, such as old supernova shells, may produce a similar effect. We provide a simple formula, Eq. (9), that reproduces the spectra of all CR species with only two nonadjustable shock parameters, uniquely derived from the proton data. We show how our formalism predicts helium and carbon spectra and the B/C ratio.
$Context$. The thermal structure of the penumbra below its visible surface (i.e., $τ_5 \ge 1$) has important implications for our present understanding of sunspots and their penumbrae: their brightness and energy transport, mode conversion of magneto-acoustic waves, sunspot seismology, and so forth. $Aims$. We aim at determining the thermal stratification in the layers immediately beneath the visible surface of the penumbra: $τ_5 \in [1,3]$ ($\approx 70-80$ km below the visible continuum-forming layer). $Methods$. We analyzed spectropolarimetric data (i.e., Stokes profiles) in three Fe \textsc{i} lines located at 1565 nm observed with the GRIS instrument attached to the 1.5-meter solar telescope GREGOR. The data are corrected for the smearing effects of wide-angle scattered light and then subjected to an inversion code for the radiative transfer equation in order to retrieve, among others, the temperature as a function of optical depth $T(τ_5)$. $Results$. We find that the temperature gradient below the visible surface of the penumbra is smaller than in the quiet Sun. This implies that in the region $τ_5 \ge 1$ the penumbral temperature diverges from that of the quiet Sun. The same
The dynamics of soft colloids in solutions is characterized by internal collective motion as well as center-of-mass diffusion. Using neutron scattering we demonstrate that the competition between the relaxation processes associated with these two degrees of freedom results in strong dependence of dynamics and structure on colloid concentration, c, even well below the overlap concentration c*. We show that concurrent with increasing inter-particle collisions, substantial structural dehydration and slowing-down of internal dynamics occur before geometrically defined colloidal overlap develops. While previous experiments have shown that the average size of soft colloids changes very little below c*, we find a marked change in both the internal structure and internal dynamics with concentration. The competition between these two relaxation processes gives rise to a new dynamically-defined dilute threshold concentration well below c*.
Using the activation-relaxation technique (ART), we study the nature of relaxation events in a binary Lennard-Jones system above and below the glass transition temperature (T_g). ART generates trajectories with almost identical efficiency at all temperature, thus avoiding the exponential slowing down below T_g and providing extensive sampling everywhere. Comparing these runs, we find that the number of atoms involved in an event decreases strongly with temperature. In particular, while in the supercooled liquid activated events are collective, involving on average thirty atoms or more, events below T_g involve mostly single atoms and produce minimal disturbance of the local environment. These results confirm the interpretation and the generality of recent NMR results by Tang et al (Nature 402, 160 (1999)).
We briefly review the status of various conventional quark-antiquark mesons below 2 GeV and outline some open questions: the status of the strange-antistrange orbitally excited vector meson, the status of the nonet of axial-tensor mesons (chiral partners of the well known tensor mesons), and the isoscalar mixing angle in the pseudotensor sector, which can eventually represent a novel manifestation of the chiral anomaly.
We examine a commonly used relative poverty measure called the headcount ratio ($H_p$), defined to be the proportion of incomes falling below the relative poverty line, which is defined to be a fraction $p$ of the median income. We do this by considering this concept for theoretical income populations, and its potential for determining actual changes following transfer of incomes from the wealthy to those whose incomes fall below the relative poverty line. In the process we derive and evaluate the performance of large sample confidence intervals for $H_p$. Finally, we illustrate the estimators on real income data sets.
We analyse some enumerative and asymptotic properties of lattice paths below a line of rational slope. We illustrate our approach with Dyck paths under a line of slope $2/5$. This answers Knuth's problem #4 from his "Flajolet lecture" during the conference "Analysis of Algorithms" (AofA'2014) in Paris in June 2014. Our approach extends the work of Banderier and Flajolet for asymptotics and enumeration of directed lattice paths to the case of generating functions involving several dominant singularities, and has applications to a full class of problems involving some "periodicities". A key ingredient in the proof is the generalization of an old trick by Knuth himself (for enumerating permutations sortable by a stack), promoted by Flajolet and others as the "kernel method". All the corresponding generating functions are algebraic, and they offer some new combinatorial identities, which can also be tackled in the A=B spirit of Wilf-Zeilberger-Petkovsek. We show how to obtain similar results for any rational slope. An interesting case is e.g. Dyck paths below the slope $2/3$ (this corresponds to the so-called Duchon's club model), for which we solve a conjecture related to the asymptot