ShantanuT01/DACTYL-Pretraining huggingface dataset:
The simultaneous ground-state cooling of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity-field mode has become an outstanding challenge in cavity optomechanics. This is because the dark modes formed by these mechanical modes decouple from the cavity mode and prevent extracting energy from the dark modes through the cooling channel of the cavity mode. Here we propose a universal and reliable dark-mode-breaking method to realize the simultaneous ground-state cooling of two degenerate or nondegenerate mechanical modes by introducing a phasedependent phonon-exchange interaction, which is used to form a loop-coupled configuration. We find an asymmetrical cooling performance for the two mechanical modes and expound this phenomenon based on the nonreciprocal energy transfer mechanism, which leads to the directional flow of phonons between the two mechanical modes. We also generalize this method to cool multiple mechanical modes. The physical mechanism in this cooling scheme has general validity and this method can be extended to break other dark-mode and dark-state effects in physics.
We prove a canonical identifications of the spaces of generalized theta functions on the moduli spaces of anti-invariant vector bundles in the ramified case and the conformal blocks associated to twisted Kac-Moody affine algebras.
We consider colliding wave packets consisting of hybrid mixtures of electromagnetic, gravitational and scalar waves. Irrespective of the scalar field, the electromagnetic wave still reflects from the gravitational wave. Some reflection processes are given for different choice of packets in which the Coulomb-like component $\Psi_2$ vanishes. Exact solution for multiple reflection of an electromagnetic wave from successive impulsive gravitational waves is obtained in a closed form. It is shown that a succesive sign flip in the Maxwell spinor arises as a result of encountering with an impulsive train (i.e. the Dirac's comb curvature) of gravitational waves. Such an observable effect may be helpful in the detection of gravitational wave bursts.
In this article we derive the explicit solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity $\mathbf{v}_\infty$ at infinity. It turned out it is the first application of the associated Weber-Orr transform to mathematical physics in comparison to classical Weber-Orr transform which is used in many researches. From no-slip condition for velocity field we will obtain Robin-type boundary condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber-Orr transform. Also the explicit formula of Biot-Savart Law in polar coordinates will be given.
A local resolution of the Problem of Time has recently been given, alongside reformulation as a local theory of Background Independence. The classical part of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in subsequent Topology and Differential Geometry developments and extended to the setting of contemporary Physics' state spaces. We now generalize this approach by mild recategorization to one based on Nijenhuis' generalization of Lie's Mathematics, as follows. 1) Relationalism is encoded using the Nijenhuis-Lie derivative. 2) Closure is assessed using the Schouten-Nijenhuis bracket, and a `Schouten-Nijenhuis Algorithm' analogue of the Dirac and Lie Algorithms. This produces a class of Gerstenhaber algebraic structures of generators or of constraints. 3) Observables are defined by a Schouten--Nijenhuis brackets relation, reformulating the constrained canonical case as explicit PDEs to be solved using the Flow Method, and forming their own Gerstenhaber algebras of observables. Lattices of Schouten-Nijenhuis-Gerstenhaber constraint or generator algebraic substructures furthermore induce dual lattices of Gerstenhaber observables subalgebras. 4) Deformation of Gerstenhaber algebraic structures of generators or constraints encountering Rigidity gives a means of Constructing more structure from less. 5) Reallocation of Intermediary-Object Invariance gives the general Schouten-Nijenhuis-Gerstenhaber algebraic structure's analogue of posing Refoliation Invariance for GR. We finally point to general Gerstenhaber bracket and Vinogradov bracket generalizations, with the former likely to play a significant role in Backgound-Independent Deformation Quantization and Quantum Operator Algebras.
Gluons may converge to a stable state at a critical momentum in hadrons. This gluon condensation is predicted by a nonlinear QCD evolution equation. We review the understanding of the gluon condensation and present a clear physical picture that produces the gluon condensation from the colour glass condensate. We summarize the applications of the GC effect in the $p-p(A)$ collisions and predict that the $p-Pb$ and $Pb-Pb$ collisions at the LHC are close to the energy region of the gluon condensation. We warn that for the next generation of hadron colliders with the increasing of the collision energy, the extremely strong gamma-rays will be emitted in a narrow space of the accelerator due to the gluon condensation effect. Such artificial mini gamma-ray bursts in the laboratory may damage the detectors.
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained finite systems from this formalism. Once this has been achieved we go on to calculate the wavevector as a function of time, in order to demonstrate the use of matrix methods with respect to several concrete examples. Interesting results are derived for elliptic curves and periodic orbits on higher dimensional non-commutative geometries.
The results for meson condensation in the literature vary markedly depending on whether one uses chiral perturbation theory or the current-algebra-plus-PCAC approach. To elucidate the origin of this discrepancy, we re-examine the role of the sigma-term in meson condensation. We find that the resolution of the existing discrepancy requires a knowledge of terms in the Lagrangian that are higher order in density than hitherto considered.
We apply the Lee-Suzuki iteration method to calculate the linked-folded diagram series for a new Nijmegen local NN potential. We obtain an exact starting-energy-independent effective two-body interaction for a multi-shell, no-core, harmonic-oscillator model space. It is found that the resulting effective-interaction matrix elements can be well approximated by the Brueckner G-matrix elements evaluated at starting energies selected in a simple way. These starting energies are closely related to the energies of the initial two-particle states in the ladder diagrams. The ``exact'' and approximate effective interactions are used to calculate the energy spectrum of 6Li in order to test the utility of the approximate form.
Context. The observed physical properties of outflows from low-mass sources put constraints on possible ejection mechanisms. Historically, these quantities have been derived from CO using ground-based observations. It is thus important to investigate whether parameters such as momentum rate (thrust) and mechanical luminosity (power) are the same when different molecular tracers are used. Aims. We aim at determining the outflow momentum, dynamical time-scale, thrust, energy and power using CO and H2O as tracers of outflow activity. Methods. Within the framework of the WISH key program, three molecular outflows from Class 0 sources have been mapped using the HIFI instrument aboard Herschel. We use these observations together with previously published H2 data to infer the physical properties of the outflows. We compare the physical properties derived here with previous estimates based on CO observations. Results. Inspection of the spatial distribution of H2O and H2 confirms that these molecules are co-spatial. The most prominent emission peaks in H2 coincide with strong H2O emission peaks and the estimated widths of the flows when using the two tracers are comparable. Conclusions. For the momentum rate and the mechanical luminosity, inferred values are independent of which tracer that is used, i.e., the values agree to within a factor of 4 and 3 respectively.
It is known that in loop quantum cosmology (LQC) the universe avoids the singularity by a bounce when the matter density approaches the critical density $\rho_c$ (the order of Planck density). After incorporating the inverse volume modifications both in the gravitational and matter part in the improved framework of LQC, we find that the inverse volume modification can decrease the bouncing energy scale, and the presence of nonsingular bounce is generic. For the backward evolution in the expanding branch, in terms of different initial states the evolution trajectories classify into two classes. One class with larger initial energy density leads to the occurrence of bounce in the region $a>a_{ch}$ where $a_{ch}$ marks the different inverse volume modification region. The other class with smaller initial energy density evolves back into the region $a<a_{ch}$. In this region, both the energy density for the scalar field and the bouncing energy scale decrease with the backward evolution. However, in the deep modification region, because of the inverse volume modification the scalar field is frozen, such that the bounce is present when the bouncing energy scale decreases to be equal to the energy density of the scalar field. Using numerical method, we show the evolution picture for the second class bounce.
We define a morphism based upon a Latin square that generalizes the Thue-Morse morphism. We prove that fixed points of this morphism are overlap-free sequences generalizing results of Allouche - Shallit and Frid.
We provide a necessary and sufficient condition for $n!$ to be a sum of three squares. The condition is based on the binary representation of $n$ and can be expressed by the operation of an automaton.
In these lecture notes we give an introduction to Bridgeland stability conditions on smooth complex projective varieties with a particular focus on the case of surfaces. This includes basic definitions of stability conditions on derived categories, basics on moduli spaces of stable objects and variation of stability. These notes originated from lecture series by the first author at the summer school "Recent advances in algebraic and arithmetic geometry", Siena, Italy, August 24-28, 2015 and at the school "Moduli of Curves", CIMAT, Guanajuato, Mexico, February 22 - March 4, 2016.
We construct a supersymmetric model of interacting Majorana fermions on the kagome lattice. In the infinite-coupling limit, the model exhibits an extensively degenerate ground state manifold separated in two topological sectors, in addition to two parity supersectors. An exact solution for thin-torus geometries allows us to analytically construct the entire zero-energy ground state manifold. Upon inclusion of hopping terms with energy scale $g$, the supersymmetry is spontaneously broken with the ground state energy density scaling as $g^4$. We also briefly discuss the non-interacting limit of the model, which exhibits a zero-energy flat band and Majorana Chern bands.
This brief review describes some of the observed properties of the populations of massive asymptotic giant branch (AGB) stars and red supergiants (RSGs) found in nearby galaxies, with a focus on their luminosity functions, mass-loss rates and dust production. I do this within the context of their role as potential supernova (SN) progenitors, and the evolution of SNe and their remnants. The paper ends with an outlook to the near future, in which new facilities such as the James Webb Space Telescope offer a step change in our understanding of the evolution and fate of the coolest massive stars in the Universe.
We summarize the consequences of the twin assumptions of (discrete) self-similarity and spherical symmetry for the global structure of a spacetime. All such spacetimes can be constructed from two building blocks, the "fan" and "splash". Each building block contains one radial null geodesic that is invariant under the self-similarity (self-similarity horizon).
The convex hull peeling of a point set is obtained by taking the convex hull of the set and repeating iteratively the operation on the interior points until no point remains. The boundary of each hull is called a layer. We study the number of k-dimensional faces and the outer defect intrinsic volumes of the first layers of the convex hull peeling of a homogeneous Poisson point process in the unit ball whose intensity goes to infinity. More precisely we provide asymptotic limits for their expectation and variance as well as a central limit theorem. In particular, the growth rates do not depend on the layer.
In this paper we consider two numerical scheme based on trapezoidal rule in time for the linearized KdV equation in one space dimension. The goal is to derive some suitable artificial boundary conditions for these two full discretization using Z-transformation. We give some numerical benchmark examples from the literature to illustrate our findings.
Classical chaos refers to the property of trajectories to diverge exponentially as time tends to infinity. It is characterized by a positive Lyapunov exponent.   There are many different descriptions of quantum chaos. The one related to the notion of generalized (quantum) Lyapunov exponent is based either on qualitative physical considerations or on the so-called symplectic tomography map.   The purpose of this note is to show how the definition of quantum Lyapunov exponent naturally arises in the framework of the Moyal phase space formulation of quantum mechanics and is based on the notions of quantum trajectories and the family of quantizers. The role of the Heisenberg uncertainty principle in the statement of the criteria for quantum chaos is made explicit.
We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production is also provided which properly describes quantum systems in a nonequilibrium stationary state. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance.
Shock waves are simulated passing through the Alfv\'en-acoustic equipartition layer in a stratified isothermal magneto-atmosphere. The recent ray-theoretic calculations of N\'u\~nez (2019) predicted smoothing of the shock through this layer, causing both the fast and slow components to emerge as continuous waves. However, it is found that the partial mode conversion expected from linear theory for oblique incidence of the shock on the magnetic field is accompanied by a smoothing of the slow-shock only, whilst the fast-shock persists. Explanations are presented based on MHD mode conversion and shock theory.
This book is a valuable introduction to astrophyscial plasmas and fluids for graduate students of astronomy preparing either for a research career in the field or just aspiring to achieve a decent degree of familiarity with 99% of the cosmos.   The contents provide a true representation of the phenomenal diversity of dominant roles that plasmas and fluids play in the near and far reaches of the universe. The breadth of coverage of basic physical processes is a particularly attractive feature of this text book. By first using the Liouville equation to derive the kinetic, the two-fluid and single-fluid, descriptions of a plasma and a fluid, and then demonstrating the use of these descriptions for specific situations in the rest of the book, the author has probably chosen the most efficient way of handling this large technical subject. The two major astrophysical issues, fluid or plasma configurations and their radiative signatures, figure prominently througout the book. The problems are designed to give the reader a feel for the quantititative properties of celestial objects.
Understanding the origin of the accelerated expansion of the Universe poses one of the greatest challenges in physics today. Lacking a compelling fundamental theory to test, observational efforts are targeted at a better characterization of the underlying cause. If a new form of mass-energy, dark energy, is driving the acceleration, the redshift evolution of the equation of state parameter w(z) will hold essential clues as to its origin. To best exploit data from observations it is necessary to develop a robust and accurate reconstruction approach, with controlled errors, for w(z). We introduce a new, nonparametric method for solving the associated statistical inverse problem based on Gaussian Process modeling and Markov chain Monte Carlo sampling. Applying this method to recent supernova measurements, we reconstruct the continuous history of w out to redshift z=1.5.
In this paper, we give several matrix representations for the Horadam quaternions. We derive several identities related to these quaternions by using the matrix method. Since quaternion multiplication is not commutative, some of our results are non-commutative analogues of the well known identities for the Fibonacci-like integer sequences. Lastly, we derive some binomial-sum identities for the Horadam quaternions as an application of the matrix method.
Perovskite solar cells have shown remarkable efficiencies beyond 22%, through organic and inorganic cation alloying. However, the role of alkali-metal cations is not well-understood. By using synchrotron-based nano-X-ray fluorescence and complementary measurements, we show that when adding RbI and/or CsI the halide distribution becomes homogenous. This homogenization translates into long-lived charge carrier decays, spatially homogenous carrier dynamics visualized by ultrafast microscopy, as well as improved photovoltaic device performance. We find that Rb and K phase-segregate in highly concentrated aggregates. Synchrotron-based X-ray-beam-induced current and electron-beam-induced current of solar cells show that Rb clusters do not contribute to the current and are recombination active. Our findings bring light to the beneficial effects of alkali metal halides in perovskites, and point at areas of weakness in the elemental composition of these complex perovskites, paving the way to improved performance in this rapidly growing family of materials for solar cell applications.
Deep HST broad-band images taken with ACS and WFPC2 of the giant ($\sim 1000$ AU diameter) dark silhouette proplyd 114-426 in the Orion Nebula show that this system is tilted, asymmetric, warped and photoevaporated. The exquisite angular resolution of ACS allows us to map the distribution of dust grains at the northern translucent edge of the disk, dominated by the photoevaporative flow. Using the Mie theory for standard circumstellar disk grains, we find evidence for a spatial gradient in grain size. The typical dust radius, $\simeq 0.2-0.7 \mu$m (less than what reported by previous studies) becomes smaller as the distance from the disk center increases, consistent with the expectations for the dynamic of dust entrained in a gaseous photoevaporative wind. Our analysis of the disk morphology and location within the nebula indicates that this system is photoevaporated by the diffuse radiation field of the Orion Nebula, while being shielded from the radiation coming directly from the central Trapezium stars. We estimate the mass-loss rate from the disk surface and the time-scale for total disk dissipation, which turns out to be of the order of $10^4$yr. Such a short time, of the order of 1/100 of the cluster age, indicates that this system is seen on the verge of destruction. This is compatible with the exceptional nature of the disk, namely its combination of huge size and low mass. Finally, we briefly discuss the viability of possible mechanisms that may lead to the peculiar morphology of this system: external UV flux, binary star and past close encounter.
The hydrogen Ly$\alpha$ forest is an important probe of the $z>2$ Universe that is otherwise challenging to observe with galaxy redshift surveys, but this technique has traditionally been limited to 1D studies in front of bright quasars. However, by pushing to faint magnitudes ($g>23$) with 8-10m large telescopes it becomes possible to exploit the high area density of high-redshift star-forming galaxies to create 3D tomographic maps of large-scale structure in the foreground. I describe the first pilot observations using this technique, as well discuss future surveys and the resulting science possibilities for galaxy evolution and cosmology.
We report on timing and spectral observations of the microquasar XTE J1550-564 during its 2000 outburst made by the Rossi X-ray Timing Experiment (RXTE). We study the spectral properties of the source during both the rise to the outburst and its decline. We observe transitions from a low hard state to an intermediate state, and vice versa, before the source returns to quiescence. We show that the first transition likely reflects a change in the relative importance of the emitting media, instead of a change in the total accretion rate, contrary to the second transition.   We investigate the temporal properties of the source, and follow the evolution of a low frequency Quasi Periodic Oscillations (QPO).
We have measured details of the quasi one-dimensional Fermi-surface sections in the organic superconductor kappa-(BEDT-TTF)_2 Cu(NCS)_2 and its deuterated analogue using angle-dependent millimetre-wave techniques. There are significant differences in the corrugations of the Fermi surfaces in the deuterated and undeuterated salts. We suggest that this is important in understanding the inverse isotope effect, where the superconducting transition temperature rises on deuteration. The data support models for superconductivity which invoke electron-electron interactions depending on the topological properties of the Fermi surface.
We study charge ordering driven by Coulomb interactions on triangular lattices relevant to the Wigner-Mott transition in two dimensions. Dynamical mean-field theory reveals the pinball liquid phase, a charge ordered metallic phase containing quasi-localized (pins) coexisting with itinerant (balls) electrons. Based on an effective periodic Anderson model for this phase, we find an antiferromagnetic Kondo coupling between pins and balls and strong quasiparticle renormalization. Non-Fermi liquid behavior can occur in such charge ordered systems due to spin-flip scattering of itinerant electrons off the pins in analogy with heavy fermion compounds.
It is shown in this work that all free physical fields should have a nonzero rest mass according to the field theory of gravitation.