ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the present review we make a comprehensive analysis of our understanding on electron transport in mesoscopic single-channel rings and multi-channel cylinders within a tight-binding framework. A spectacular mesoscopic phenomenon where a non-decaying current circulates in a small conducting loop is observed upon the application of an Aharonov-Bohm flux $\phi$. To understand its behavior one has to focus attention on the interplay of quantum phase coherence, electron-electron correlation and disorder. This is a highly challenging problem and here we address it for some simple loop geometries with their detailed energy band structures to get an entire picture at the microscopic level. The behavior of low-field magnetic response of persistent current and its temperature dependence are also discussed.
Recent studies have suggested that red quasars are a phase in quasar evolution when feedback from black hole accretion evacuates obscuring gas from the nucleus of the host galaxy. Here, we report a direct link between dust-reddening and molecular outflows in quasars at $z\sim2.5$. By examining the dynamics of warm molecular gas in the inner region of galaxies, we detect outflows with velocities 500--1000 km s$^{-1}$ and infer timescales of $\approx0.1$ Myr that are due to ongoing quasar energy output. We observe outflows only in systems where quasar radiation pressure on dust in the vicinity of the black hole is sufficiently large to expel their obscuring gas column densities. This result is in agreement with theoretical models that predict radiative feedback regulates gas in the nuclear regions of galaxies and is a major driving mechanism of galactic-scale outflows of cold gas. Our findings suggest that radiative quasar feedback ejects star-forming gas from within nascent stellar bulges at velocities comparable to those seen on larger scales, and that molecules survive in outflows even from the most luminous quasars.
Unless some unknown symmetry in Nature prevents or suppresses a non-minimal coupling in the dark sector, the dark energy field may interact with the pressureless component of dark matter. In this paper, we investigate some cosmological consequences of a general model of interacting dark matter-dark energy characterized by a dimensionless parameter $\epsilon$. We derive a coupled scalar field version for this general class of scenarios and carry out a joint statistical analysis involving SNe Ia data ({Legacy} and {Constitution} sets), measurements of baryon acoustic oscillation peak at $z = 0.20$ (2dFGRS) and $z = 0.35$ (SDSS), and measurements of the Hubble evolution $H(z)$. For the specific case of vacuum decay ($w = -1$), we find that, although physically forbidden, a transfer of energy from dark matter to dark energy is favored by the data.
We are studying the Diophantine exponent \mu_{n,l}$ defined for integers 1 \leq l < n and a vector \alpha \in \mathbb{R}^n by letting \mu_{n,l} = \sup{\mu \geq 0: 0 < ||x \cdot \alpha|| < H(x)^{-\mu} for infinitely many x \in C_{n,l} \cap \mathbb{Z}^n}, where \cdot is the scalar product and || . || denotes the distance to the nearest integer and C_{n,l} is the generalised cone consisting of all vectors with the height attained among the first l coordinates. We show that the exponent takes all values in the interval [l+1, \infty), with the value n attained for almost all \alpha. We calculate the Hausdorff dimension of the set of vectors \alpha with \mu_{n,l} (\alpha) = \mu for \mu \geq n. Finally, letting w_n denote the exponent obtained by removing the restrictions on x, we show that there are vectors \alpha for which the gaps in the increasing sequence \mu_{n,1} (\alpha) \leq ... \leq \mu_{n,n-1} (\alpha) \leq w_n (\alpha) can be chosen to be arbitrary.
After the justification of the maximum entropy principle for equilibrium mechanical system from the principle of virtual work, i.e., the virtual work of microscopic forces on the elements of a mechanical system vanishes in thermodynamic equilibrium, we present in this paper an application of the same principle to dynamical systems out of equilibrium. The aim of this work is to justify a least action principle and the concurrent maximum path entropy principle for nonequilibrium thermodynamic systems.
We consider the nonlocal formulation of continuum mechanics described by peridynamics. We provide a link between peridynamic evolution and brittle fracture evolution for a broad class of peridynamic potentials associated with unstable peridynamic constitutive laws. Distinguished limits of peridynamic evolutions are identified that correspond to vanishing peridynamic horizon. The limit evolution is associated with dynamic brittle fracture and satisfies a dynamic energy inequality expressed in terms of the kinetic energy of the motion together with a bulk elastic energy and a Griffith surface energy. It corresponds to the simultaneous evolution of elastic displacement and brittle fracture with displacement fields satisfying the wave equation inside the cracking domain. The wave equation provides the dynamic coupling between elastic waves and the evolving fracture path inside the media. The elastic moduli, wave speed and energy release rate for the evolution are explicitly determined by moments of the peridynamic influence function and the peridynamic potential energy.
We derive an analytic, albeit approximate, expression for the ground state energy of N Coulomb interacting anyons with fractional statistics nu, 0<= |nu| <= 1, confined in a two-dimensional well (with characteristic frequency omega_0 ) and subjected to an external magnetic field (with cyclotron frequency omega_c ). We apply a variational principle combined with a regularization procedure which consists of fitting a cut-off parameter to existing exact analytical results in the non-interacting case, and to numerical calculations for electrons in quantum dots in the interacting case. The resulting expression depends upon parameters of the system |nu|, N, omega_0, r_0, a_B and omega_c, where r_0 represents a characteristic unit length and a_B the Bohr radius. Validity of the result is critically assessed by comparison with exact, approximate, and numerical results from the literature.
We study magnon spectra at finite temperature in yttrium iron garnet from tight-binding model with nearest neighboring exchange interaction. The spin reduction due to thermal magnon excitation are taken into account via the mean field approximation to the local spin and found to be different at two sets of iron atoms. The resulting temperature dependence of the spin wave gap shows good agreement with experiment. We find only two magnon modes are relevant to ferromagnetic resonance.
The column density probability distribution function (N-PDF) of GMCs has been used as a diagnostic of star formation. Simulations and analytic predictions have suggested the N-PDF is composed of a low density lognormal component and a high density power-law component, tracing turbulence and gravitational collapse, respectively. In this paper, we study how various properties of the true 2D column density distribution create the shape, or "anatomy" of the PDF. We test our ideas and analytic approaches using both a real, observed, PDF based on Herschel observations of dust emission as well as a simulation that uses the ENZO code. Using a dendrogram analysis, we examine the three main components of the N-PDF: the lognormal component, the power-law component, and the transition point between these two components. We find that the power-law component of an N-PDF is the summation of N-PDFs of power-law substructures identified by the dendrogram algorithm. We also find that the analytic solution to the transition point between lognormal and power-law components proposed by Burkhart, Stalpes & Collins (2017) is applicable when tested on observations and simulations, within the uncertainties. We reconfirm and extend the results of Lombardi, Alves & Lada (2015), which stated that the lognormal component of the N-PDF is difficult to constrain due to the artificial choice of the map area. Based on the resulting anatomy of the N-PDF, we suggest avoiding analyzing the column density structures of a star forming region based solely on fits to the lognormal component of an N-PDF. We also suggest applying the N-PDF analysis in combination with the dendrogram algorithm, to obtain a more complete picture of the global and local environments and their effects on the density structures.
By using the arc-melting method, we successfully synthesized the compound Sc$_{0.5}$Zr$_{0.5}$Co with the space group of $Pm$-$3m$. Both the resistivity and magnetic susceptibility measurements reveal a phase transition at about 86 K. This transition might be attributed to the establishment of an antiferromagnetic order. The magnetization hysteresis loop measurements in wide temperature region show a weak ferromagnetic feature, which suggests a possible canted arrangement of the magnetic moments. Bounded by the phase transition temperature, the resistivity at ambient pressure shows a change from Fermi liquid behavior to a super-linear behavior as temperature increases. By applying pressures up to 32.1 GPa, the transition temperature does not show a clear change and no superconductivity is observed above 2 K. The density functional theory (DFT) calculations confirm the existence of the antiferromagnetic order and reveal a gap between the spin-up and spin-down $d$-orbital electrons. This kind of behavior may suggest that the antiferromagnetic order in this compound originates from the localized $d$-electrons which do not contribute to the conductance. Thus the itinerant and localized $d$-orbital electrons in the compound are decoupled.
The most X-ray luminous cluster known, RXJ1347-1145 (z=0.45), has been the object of extensive study across the electromagnetic spectrum. We have imaged the Sunyaev-Zel'dovich Effect (SZE) at 90 GHz (3.3 mm) in RXJ1347-1145 at 10" resolution with the 64-pixel MUSTANG bolometer array on the Green Bank Telescope (GBT), confirming a previously reported strong, localized enhancement of the SZE 20" to the South-East of the center of X-ray emission. This enhancement of the SZE has been interpreted as shock-heated (> 20 keV) gas caused by an ongoing major (low mass-ratio) merger event. Our data support this interpretation. We also detect a pronounced asymmetry in the projected cluster pressure profile, with the pressure just east of the cluster core ~1.6 times higher than just to the west. This is the highest resolution image of the SZE made to date.
Magnetohydrodynamic (MHD) waves are often reported in the solar atmosphere and usually classified as slow, fast, or Alfv\'en. The possibility that these waves have mixed properties is often ignored. The goal of this work is to study and determine the nature of MHD kink waves. This is done by calculating the frequency, the damping rate and the eigenfunctions of MHD kink waves for three widely different MHD waves cases: a compressible pressure-less plasma, an incompressible plasma and a compressible plasma with non-zero plasma pressure which allows for MHD radiation. In all three cases the frequency and the damping rate are for practical purposes the same as they differ at most by terms proportional to $(k_z R)^2$. In the magnetic flux tube the kink waves are in all three cases, to a high degree of accuracy incompressible waves with negligible pressure perturbations and with mainly horizontal motions. The main restoring force of kink waves in the magnetised flux tube is the magnetic tension force. The total pressure gradient force cannot be neglected except when the frequency of the kink wave is equal or slightly differs from the local Alfv\'{e}n frequency, i.e. in the resonant layer. Kink waves are very robust and do not care about the details of the MHD wave environment. The adjective fast is not the correct adjective to characterise kink waves. If an adjective is to be used it should be Alfv\'{e}nic. However, it is better to realize that kink waves have mixed properties and cannot be put in one single box.
The properties of molecular gas, the fuel that forms stars, inside the cavity of the circumnuclear disk (CND) are not well constrained. We present results of a velocity-resolved submillimeter scan (~480 to 1250 GHz}) and [CII]158um line observations carried out with Herschel/HIFI toward Sgr A*; these results are complemented by a ~2'x2' CO (J=3-2) map taken with the IRAM 30 m telescope at ~7'' resolution. We report the presence of high positive-velocity emission (up to about +300 km/s) detected in the wings of CO J=5-4 to 10-9 lines. This wing component is also seen in H2O (1_{1,0}-1_{0,1}) a tracer of hot molecular gas; in [CII]158um, an unambiguous tracer of UV radiation; but not in [CI]492,806 GHz. This first measurement of the high-velocity CO rotational ladder toward Sgr A* adds more evidence that hot molecular gas exists inside the cavity of the CND, relatively close to the supermassive black hole (< 1 pc). Observed by ALMA, this velocity range appears as a collection of CO (J=3-2) cloudlets lying in a very harsh environment that is pervaded by intense UV radiation fields, shocks, and affected by strong gravitational shears. We constrain the physical conditions of the high positive-velocity CO gas component by comparing with non-LTE excitation and radiative transfer models. We infer T_k~400 K to 2000 K for n_H~(0.2-1.0)x10^5 cm^-3. These results point toward the important role of stellar UV radiation, but we show that radiative heating alone cannot explain the excitation of this ~10-60 M_Sun component of hot molecular gas inside the central cavity. Instead, strongly irradiated shocks are promising candidates.
A spin interaction Hamiltonian for topological basis is constructed in this paper. When we select proper parameters, this Hamiltonian system can be simulated by a quantum double well potential system. If the parameter $\Delta=0$, the topological system is equivalent to two independent quantum wells. If the parameter $\Delta\neq 0$, the system is equivalent to a double well potential with finite potential barrier. The quantum tunneling effect and quantum Zeno effect for this topological system are investigated in detail.
In a recent paper, Andrews and Newman introduced certain families of partition functions using the minimal excludant or "mex" function. In this article, we study two of the families of functions Andrews and Newman introduced, namely $p_{t,t}(n)$ and $p_{2t,t}(n)$. We establish identities connecting the ordinary partition function $p(n)$ to $p_{t,t}(n)$ and $p_{2t,t}(n)$ for all $t\geq 1$. Using these identities, we prove that the Ramanujan's famous congruences for $p(n)$ are also satisfied by $p_{t,t}(n)$ and $p_{2t,t}(n)$ for infinitely many values of $t$. Very recently, da Silva and Sellers provide complete parity characterizations of $p_{1,1}(n)$ and $p_{3,3}(n)$. We prove that $p_{t,t}(n)\equiv \overline{C}_{4t,t}(n) \pmod{2}$ for all $n\geq 0$ and $t\geq 1$, where $\overline{C}_{4t,t}(n)$ is the Andrews' singular overpartition function. Using this congruence, the parity characterization of $p_{1,1}(n)$ given by da Silva and Sellers follows from that of $\overline{C}_{4,1}(n)$. We also give elementary proofs of certain congruences already proved by da Silva and Sellers.
Back in the nineties Pak and Stanley introduced a labeling of the regions of a k-Shi arrangement by k-parking functions and proved its bijectivity. Duval, Klivans, and Martin considered a modification of this construction associated with a graph G. They introduced the G-Shi arrangement and a labeling of its regions by G-parking functions. They conjectured that their labeling is surjective, i.e. that every G-parking function appears as a label of a region of the G-Shi arrangement. Later Hopkins and Perkinson proved this conjecture. In particular, this provided a new proof of the bijectivity of Pak-Stanley labeling in the k=1 case. We generalize Hopkins-Perkinson's construction to the case of arrangements associated with oriented multigraphs. In particular, our construction provides a simple straightforward proof of the bijectivity of the original Pak-Stanley labeling for arbitrary k.
By using higher K-theory, we reinterpret and generalize an idea on eliminating obstructions to deforming cycles, which is known to Mark Green, Phillip Griffiths and TingFai Ng(for the divisor case). As an application, we show how to eliminate obstructions to deforming curves on a 3-fold. This answers affirmatively an open question by TingFai Ng.
Ab initio nuclear many-body frameworks require extensive computational resources, especially when targeting heavier nuclei. Importance-truncation (IT) techniques allow to significantly reduce the dimensionality of the problem by neglecting unimportant contributions to the solution of the many-body problem. In this work, we apply IT methods to the nonperturbative in-medium similarity renormalization group (IMSRG) approach and investigate the induced errors for ground-state energies in different mass regimes based on different nuclear Hamiltonians. We study various importance measures, which define the IT selection, and identify two measures that perform best, resulting in only small errors to the full IMSRG(2) calculations even for sizable compression ratios. The neglected contributions are accounted for in a perturbative way and serve as an estimate of the IT-induced error. Overall we find that the IT-IMSRG(2) performs well across all systems considered, while the largest compression ratios for a given error can be achieved when using soft Hamiltonians and for large single-particle bases.
An explicit lifespan estimate is presented for the derivative Schr\"odinger equations with periodic boundary condition.
We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By $\Gamma$-convergence we derive a one-dimensional limit theory and show that isolated local minimizers of the limit model can be approached by local minimizers of the three-dimensional model. In the case of isotropic materials and for two-layers prestrained three-dimensional models the limit energy further simplifies to that of a Kirchhoff rod-model of an intrinsically curved beam. In this case we study the limit theory and investigate global and/or local stability of straight and helical configurations. Through some simple simulations we finally compare our results with real experiments.
In many hybrid quantum systems, a superconducting circuit is required that combines DC-control with a coplanar waveguide (CPW) microwave resonator. The strategy thus far for applying a DC voltage or current bias to microwave resonators has been to apply the bias through a symmetry point in such a way that it appears as an open circuit for certain frequencies. Here, we introduce a microwave coupler for superconducting CPW cavities in the form of a large shunt capacitance to ground. Such a coupler acts as a broadband mirror for microwaves while providing galvanic connection to the center conductor of the resonator. We demonstrate this approach with a two-port $\lambda/4$-transmission resonator with linewidths in the MHz regime ($Q\sim10^3$) that shows no spurious resonances and apply a voltage bias up to $80$ V without affecting the quality factor of the resonator. This resonator coupling architecture, which is simple to engineer, fabricate and analyse, could have many potential applications in experiments involving superconducting hybrid circuits.
We explain an effective Kawamata boundedness result for Mori-Fano 3-folds. In particular, we describe a list of 39,550 possible Hilbert series of semistable Mori-Fano 3-folds, with examples to explain its meaning, its relationship to known classifications and the wealth of more general Fano 3-folds it contains, as well as its application to the on-going classification of Fano 3-folds.
The H dibaryon, a single, triply magic bag containing two up, two down and two strange quarks, has long been sought after in a variety of experiments. Its creation has been attempted in $K^-$, proton and most recently in relativistic heavy ion induced reactions. We concentrate on the latter, but our conclusions are more generally applicable. The two baryons coalescing to form the single dibaryon, likely $\Lambda \Lambda$ in the case of heavy ions, must penetrate the short range repulsive barrier which is expected to exist between them. We find that this barrier can profoundly affect the probability of producing the H state, should it actually exist.
Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.
We present an analysis of the results of long-term multi-band photometric monitoring of the enigmatic star, KIC 8462852. Observations in the $B$, $g'$, $V$, $r'$ and $I_C$ passbands have been acquired at University College London Observatory (UCLO) between May 2017 and September 2018. We interrogate the wavelength dependence of the $\sim$month-long dimming and brightening exhibited by the target star over an 85-day interval, immediately following a days-long $\sim5$ per cent drop in brightness on Julian Date (JD) 2458203. Between JD 2458215--300 we measure brightness variations which correspond to relative extinctions of $A_B/A_V = 1.39\pm0.27$, $A_{g'}/A_V = 1.16\pm0.11$, $A_{r'}/A_V = 0.80\pm0.25$ and $A_{Ic}/A_V = 0.49\pm0.19$, from which we infer an Angstr\"om absorption coefficient of $1.33\pm0.43$ ($R_V \simeq 3.2^{+2.6}_{-1.0}$). As with the days-long `dips', the wavelength dependence of the longer-term brightness variations must also be associated with extinction arising from a dust distribution containing a substantial fraction of sub-micron-sized grains. This implies some common mechanism is responsible for the star's variability over both these short and longer timescales.
Let $\Gamma$ be a finitely presented group and $G$ a linear algebraic group over $\mathbb{R}$. A representation $\rho:\Gamma\rightarrow G(\mathbb{R})$ can be seen as an $\mathbb{R}$-point of the representation variety $\mathfrak{R}(\Gamma, G)$. It is known from the work of Goldman and Millson that if $\Gamma$ is the fundamental group of a compact K{\"a}hler manifold and $\rho$ has image contained in a compact subgroup then $\rho$ is analytically defined by homogeneous quadratic equations in $\mathfrak{R}(\Gamma, G)$. When $X$ is a smooth complex algebraic variety, we study a certain criterion under which this same conclusion holds.
We determine the minimum energy required to control the evolution of any mesoscopic quantum system in the presence of arbitrary Markovian noise processes. This result provides the mesoscopic equivalent of the fundamental cost of refrigeration, sets the minimum power consumption of mesoscopic devices that operate out of equilibrium, and allows one to calculate the efficiency of any control protocol, whether it be open-loop or feedback control. As examples we calculate the energy cost of maintaining a qubit in the ground state, the efficiency of resolved-sideband cooling of nano-mechanical resonators, and discuss the energy cost of quantum information processing.
We present a theoretical study of the shift current in a noncentrosymmetric polytype of graphitic BC$_2$N. We find that the photoconductivity near the fundamental gap is strongly anisotropic due to the vanishing of particular tensor components not foretold by point-group symmetry arguments; this is a consequence of dipole selection rules imposed by mirror symmetry, which imply that the relative parities between valence and conduction bands are key for determining the directionality of the band-edge response. In addition, the band-edge photoconductivity turns out to be rather large, with the peak value occurring in an energy range suitable for optical manipulation