ShantanuT01/DACTYL-Pretraining huggingface dataset:
Many-polaron systems with finite charge-carrier density are often encountered experimentally. However, until recently, no satisfactory theoretical description of these systems was available even in the framework of simple models such as the one-dimensional spinless Holstein model considered here. In this work, previous results obtained using numerical as well as analytical approaches are reviewed from a unified perspective, focussing on spectral properties which reveal the nature of the quasiparticles in the system. In the adiabatic regime and for intermediate electron-phonon coupling, a carrier-density driven crossover from a polaronic to a rather metallic system takes place. Further insight into the effects due to changes in density is gained by calculating the phonon spectral function, and the fermion-fermion and fermion-lattice correlation functions. Finally, we provide strong evidence against the possibility of phase separation.
According to a recent ray-based asymptotic theory, the high-frequency p-mode spectrum of rapidly rotating stars is a superposition of frequency subsets associated with dynamically independent regions of the ray-dynamics phase space. At high rotation rates corresponding to typical $\delta$ Scuti stars, two frequency subsets are expected to be visible : a regular frequency subset described by a Tassoul like formula and an irregular frequency subset with specific statistical properties. In this paper, we investigate whether the regular patterns can be detected in the resulting spectrum. We compute the autocorrelation function of synthetic spectra where the frequencies follow the asymptotic theory, the relative amplitudes are simply given by the modes' disk-averaging factors, and the frequency resolution is that of a CoRoT long run. Our first results are that (i) the detection of regular patterns strongly depends on the ratio of regular over irregular modes, (ii) low inclination angle configurations are more favorable than near equator-on configurations, (iii) in the absence of differential rotation, the $2 \Omega$ rotational splitting between $m=1$ and $m=-1$ modes is an easy feature to detect.
Let $L$ be a nonnegative, self-adjoint operator on $L^2(\mathbb{R}^n)$ with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space $\mathcal{L}^{2,\lambda}_{-\Delta}(\mathbb R^n)$, in \cite{DXY} the quadratic Campanato space $\mathcal{L}_L^{2,\lambda}(\mathbb{R}^n)$ is defined by a variant of the maximal function associated with the semigroup $\{e^{-tL}\}_{t\geq 0}$. On the basis of \cite{DX} and \cite{YY} this paper addresses the preduality of $\mathcal{L}_L^{2,\lambda}(\mathbb{R}^n)$ through an induced atom (or molecular) decomposition. Even in the case $L=-\Delta$ the discovered predual result is new and natural.
As a continuation of the study of the herding model proposed in (Bae et al. in arXiv:1712.01085, 2017), we consider in this paper the derivation of the kinetic version of the herding model, the existence of the measure-valued solution and the corresponding herding behavior at the kinetic level. We first consider the mean-field limit of the particle herding model and derive the existence of the measure-valued solutions for the kinetic herding model. We then study the herding phenomena of the solutions in two different ways by introducing two different types of herding energy functionals. First, we derive a herding phenomena of the measure-valued solutions under virtually no restrictions on the parameter sets using the Barbalat's lemma. We, however, don't get any herding rate in this case. On the other hand, we also establish a Gr\"onwall type estimate for another herding functional, leading to the exponential herding rate, under comparatively strict conditions. These results are then extended to smooth solutions.
We show that if all gamma-ray bursts emit X-rays in a way similar to those observed by BeppoSax, much of the extinction along the line of sight in the host galaxy of the burst can be destroyed. Two mechanisms are principally responsible for dust destruction: grain heating and grain charging. The latter, which can lead to electrostatic stresses greater than the tensile strength of the grains, is often the more important. Grains may regularly be destroyed at distances as large as 100 parsecs. This dust destruction can permit us to see the UV/optical afterglow even when the burst is embedded deep within a highly-obscured region. Because the destruction rate depends on grain composition and size, it may be possible to observe the amount and wavelength-dependence of extinction change during the course of the burst and first few minutes of the afterglow. It may also be possible to detect interstellar absorption lines in the afterglow spectrum that would not exist but for the return of heavy elements to the gas phase.
Aims: We present a study of the Galactic supernova remnant SNR G15.9+0.2 with archival XMM-Newton observations. Methods: EPIC data are used to investigate the morphological and spectral properties of the remnant, searching in particular for supernova ejecta and Fe K line emission. By comparing the SNR's X-ray absorption column density with the atomic and molecular gas distribution along the line of sight, we attempt to constrain the distance to the SNR. Results: Prominent line features reveal the presence of ejecta. Abundance ratios of Mg, Si, S, Ar, and Ca strongly suggest that the progenitor of SNR G15.9+0.2 was a massive star with a main sequence mass likely in the range 20-25 $M_{\odot}$, strengthening the physical association with a candidate central compact object detected with Chandra. Using EPIC's collective power, Fe K line emission from SNR G15.9+0.2 is detected for the first time. We measure the line properties and find evidence for spatial variations. We discuss how the source fits within the sample of SNRs with detected Fe K emission and find that it is the core-collapse SNR with the lowest Fe K centroid energy. We also present some caveats regarding the use of Fe K line centroid energy as a typing tool for SNRs. Only a lower limit of 5 kpc is placed on the distance to SNR G15.9+0.2, constraining its age to $t_{SNR} \gtrsim 2$ kyr.
The supernova remnant (SNR) G51.26+0.11 was recently discovered and little is known about its properties and environment. Using data from the \emph{Fermi} Large Area Telescope we study the GeV emission seen in the direction of G51.26+0.11 to constrain the origin of the gamma rays and their possible relation to this SNR or to a star-forming region. We also search for emission from molecular gas in the region that could provide dense material for the production of gamma rays. By modeling the multi-wavelength spectrum of G51.26+0.11 from radio to gamma rays we derive the properties of the particle populations that could produce the emission in several possible scenarios. We rule out the star-forming regions (such as G051.010+00.060) seen nearby as the origin of the GeV emission. The correspondence seen between the gamma-ray and radio morphologies support a scenario where G51.26+0.11 is the cause of the gamma rays. The flat spectral energy distribution observed at GeV energies is best fit by hadronic or inverse Compton emission, while a bremsstrahlung model cannot properly account for the radio fluxes under a simple one-zone scenario. A pulsar wind nebula origin of the high-energy photons cannot be ruled out or confirmed.
This study explores the reconstruction of a signal using spectral quantities associated with some self-adjoint realization of an h-dependent Schr\"odinger operator when the parameter h tends to 0. Theoretical results in semi-classical analysis are proved. Some numerical results are also presented. We first consider as a toy model the sech^2 function. Then we study a real signal given by arterial blood pressure measurements. This approach seems to be very promising in signal analysis. Indeed it provides new spectral quantities that can give relevant information on some signals as it is the case for arterial blood pressure signal.
We analyse the momentum dependence of static non-uniform susceptibilities of layered local-moment systems below Curie (Neel) temperature within the 1/S-expansion, the renormalization-group approach, and first order of 1/N-expansion. We argue that the previously known results of the spin-wave theory and renormalization-group approach for the transverse spin susceptibility acquire strong corrections already at sufficiently low temperatures, which appear due to the interaction of the incomping magnon having momentum q with magnons with momenta k<q. Such corrections can not be treated in the standard renormalization-group approach, but can be described by both, 1/S and 1/N expansions. The results of these expansions can be successfully extrapolated to the magnetic transition temperature T=T_M yielding the correct weight of static spin fluctuations, determined by the O(3) symmetry. For the longitudinal susceptibility, the summation of leading terms of 1/S expansion within the parquet approach allows to fulfill the sumrule for the weights of transverse and longitudinal fluctuations in a broad temperature region below T_M outside the critical regime. We also discuss the effect of longitudinal spin fluctuations on the (sublattice) magnetization of layered systems.
A unified model of dark energy and matter is presented using the modified variable Chaplygin gas for interacting dark energy in a non-flat universe. The two entities interact with each other non-gravitationally which involves a coupling constant. Due to dynamic interaction, the variation in this constant arises that henceforth changes the equations of state of these quantities. We have derived the effective equations of state corresponding to matter and dark energy in this interacting model. Moreover, the case of phantom energy is deduced by putting constraints on the parameters involved.
Two-component, ideal, self-gravitating fluids are conceived as macrogases, and the related equation of state is expressed using the virial theorem for subsystems, under the restriction of homeoidally striated density profiles. Shallower density profiles are found to yield an equation of state, \phi=\phi(y,m), characterized (for assigned values of the fractional mass, m=M_j/ M_i) by the occurrence of two extremum points, a minimum and a maximum. Steeper density profiles produce a similar equation of state, which implies that a special value of m is related to a critical curve where the above mentioned extremum points reduce to a single horizontal inflexion point, and curves below the critical one show no extremum points. The similarity of the isofractional mass curves to van der Waals' isothermal curves, suggests the possibility of a phase transition in a bell-shaped region of the (O y \phi) plane, where the fractional truncation radius along a selected direction is y=R_j/R_i, and the fractional virial potential energy is \phi=(E_{ji})_{vir}/(E_{ij})_{vir}. Further investigation is devoted to mass distributions described by Hernquist (1990) density profiles, for which an additional relation can be used to represent a sample of N=16 elliptical galaxies (EGs) on the (O y \phi) plane, under the assumption that the fractional mass related to EGs and their hosting dark matter (DM) haloes, has a universal value. In the light of the model, the evolution of isolated EGs appears to be other than strictly homologous, due to different values of fractional truncation radii, y, or fractional scaling radii, y^\dagger, deduced from sample objects.
The cosmological (upper) limit on the Peccei-Quinn constant, related to the primordial oscillations of the axion field, can be relaxed for a mirror axion model. The simple reason is that the mirror world is colder and so the behavior of the axion temperature-dependent mass is dominated by the contribution from the mirror sector. So the coherent oscillations start earlier and correspondingly the axion mass density \Omega_a h^2 is reduced.
We present a scenario for the production of dynamically cold rings around the Milky Way via a high-eccentricity, flyby encounter. These initial conditions are more cosmologically motivated than those considered in previous works. We find that the encounters we examine generically produce a series of nearly dynamically cold ring-like features on low-eccentricity orbits that persist over timescales of ~2-4 Gyr via the tidal response of the primary galaxy to the close passage of the satellite. Moreover, they are both qualitatively and quantitatively similar to the distribution, kinematics, and stellar population of the Monoceros ring. Therefore, we find that a high eccentricity flyby by a satellite galaxy represents a cosmologically appealing scenario for forming kinematically distinct ring-like features around the Milky Way.
In this study, we consider one-dimension (1D) quantum spin systems with the translation and discrete symmetries (spin reversal, space inversion and time reversal symmetries). By combining the continuous U(1) symmetry with the discrete symmetries and using the extended Lieb-Schultz-Mattis theorem \cite{Lieb-Schultz-Mattis-1961}\cite{Nomura-Morishige-Isoyama-2015}, we investigate the relation between the ground states, energy spectra and symmetries. For half-integer spin cases, we generalize the dimer and N\'eel concepts using the discrete symmetries, and we can reconcile the LSM theorem with the dimer or N\'eel states, since there was a subtle dilemma. Furthermore, a part of discrete symmetries is enough to classify possible phases. Thus we can deepen our understanding of the relation between the LSM theorem and the discrete symmetries.
There is a completely natural and intimate relationship between the diffeomorphism group of the circle and the Teichm\"uller spaces of Riemann surfaces discovered by us in 1988. Such a relationship had been sought-after by physicists from conjectures connecting the loop-space approach to string theory with the path-integral approach. Precisely, the remarkable homogeneous space Diff$(S^1)$/$SL(2,R)$ (which is one of the two possible quantizable coadjoint orbits of Diff$(S^1)$), embeds as a complex analytic and K\"ahler submanifold of the universal Teichm\"uller space. Furthermore, this very homogeneous space, Diff$(S^1)$/$SL(2,R)$, considered by the previous work as a K\"ahler submanifold of the universal Teichm\"uller space, allows on it a natural holomorphic period mapping, $\Pi$, that generalises the classical map associating to a genus $g$ Riemann surface its period matrix. Utilising the fact that the group of quasiconformal homeomorphisms of $S^1$ acts symplectically on the Sobolev space of order $1/2$ on the circle, we (with Dennis Sullivan) have recently extended $\Pi$ to the entire universal Teichm\"uller space. All this is related to non-perturbative string theory.
We present numerical experiments aimed to study the correlation between the magnetic field strength, $B$, and the density, $n$, in the cold atomic interstellar medium (CNM). We analyze 24 magneto-hydrodynamic models with different initial magnetic field intensities ($B_0=$0.4, 2.1, 4.2, and 8.3 $\mu$G) and/or mean densities (2, 3, and 4 cm$^{-3}$), in the presence of driven and decaying turbulence, with and without self-gravity, in a cubic computational domain with 100 pc by side. Our main findings are: i) For forced simulations, which reproduce the main observed physical conditions of the CNM in the Solar neighborhood, a positive correlation between $B$ and $n$ develops for all the $B_0$ values. ii) The density at which this correlation becomes significant ($\lesssim 30$ cm$^{-3}$) depends on $B_0$ but is not sensitive to the presence of self-gravity. iii) The effect of self-gravity, when noticeable, consists of producing a shallower correlation at high densities, suggesting that, in the studied regime, self-gravity induces motions along the field lines. iv) Self-gravitating decaying models where the CNM is subsonic and sub-Alfv\'enic with $\beta\lesssim 1$ develop a high density positive correlation whose slopes are consistent with a constant $\beta(n)$. v) Decaying models where the low density CNM is subsonic and sub-Alfv\'enic with $\beta>1$ show a negative correlation at intermediate densities, followed by a high density positive correlation.
The third flight of the High-Resolution Coronal Imager (Hi-C 2.1) occurred on May 29, 2018, the Sounding Rocket was launched from White Sands Missile Range in New Mexico. The instrument has been modified from its original configuration (Hi-C 1) to observe the solar corona in a passband that peaks near 172 Angstrom and uses a new, custom-built low-noise camera. The instrument targeted Active Region 12712, and captured 78 images at a cadence of 4.4 sec (18:56:22 - 19:01:57 UT; 5 min and 35 sec observing time). The image spatial resolution varies due to quasi-periodic motion blur from the rocket; sharp images contain resolved features of at least 0.47 arcsec. There are coordinated observations from multiple ground- and space-based telescopes providing an unprecedented opportunity to observe the mass and energy coupling between the chromosphere and the corona. Details of the instrument and the data set are presented in this paper.
In this paper we compare the performances of the chi-square and median likelihood analysis in the determination of cosmological constraints using type Ia supernovae data. We perform a statistical analysis using the 307 supernovae of the Union 2 compilation of the Supernova Cosmology Project and find that the chi-square statistical analysis yields tighter cosmological constraints than the median statistic if only supernovae data is taken into account. We also show that when additional measurements from the Cosmic Microwave Background and Baryonic Acoustic Oscillations are considered, the combined cosmological constraints are not strongly dependent on whether one applies the chi-square statistic or the median statistic to the supernovae data. This indicates that, when complementary information from other cosmological probes is taken into account, the performances of the chi-square and median statistics are very similar, demonstrating the robustness of the statistical analysis.
The correlation of weak lensing and Cosmic Microwave Anisotropy (CMB) data traces the pressure distribution of the hot, ionized gas and the underlying matter density field. The measured correlation is dominated by baryons residing in halos. Detecting the contribution from unbound gas by measuring the residual cross-correlation after masking all known halos requires a theoretical understanding of this correlation and its dependence with model parameters. Our model assumes that the gas in filaments is well described by a log-normal probability distribution function, with temperatures $10^{5-7}$K and overdensities $\xi\le 100$. The lensing-comptonization cross-correlation is dominated by gas with overdensities in the range $\xi\approx[3-33]$; the signal is generated at redshifts $z\le 1$. If only 10\% of the measured cross-correlation is due to unbound gas, then the most recent measurements set an upper limit of $\bar{T}_e\lesssim 10^6$K on the mean temperature of Inter Galactic Medium. The amplitude is proportional to the baryon fraction stored in filaments. The lensing-comptonization power spectrum peaks at a different scale than the gas in halos making it possible to distinguish both contributions. To trace the distribution of the low density and low temperature plasma on cosmological scales, the effect of halos will have to be subtracted from the data, requiring observations with larger signal-to-noise ratio than currently available.
We introduce M\"obius functions of higher rank, a new class of arithmetic functions so that the classical M\"obius function is of rank 2. With this idea, we evaluate Dirichlet series on the sum of the reciprocal square of all $r$-free numbers. For the proof, the Riemann zeta function and cyclotomic polynomials play a key role.
We have theoretically analyzed coherent nuclear-spin dynamics induced by electron transport through a quantum-dot spin valve. The hyperfine interaction between electron and nuclear spins in a quantum dot allows for the transfer of angular momentum from spin-polarized electrons injected from ferromagnetic or half-metal leads to the nuclear spin system under a finite voltage bias. Accounting for a local nuclear-spin dephasing process prevents the system from becoming stuck in collective dark states, allowing a large nuclear polarization to be built up in the long-time limit. After reaching a steady state, reversing the voltage bias induces a transient current response as the nuclear polarization is reversed. Long-range nuclear-spin coherence leads to a strong enhancement of spin-flip transition rates (by an amount proportional to the number of nuclear spins) and is revealed by an intense current burst, analogous to superradiant light emission. The crossover to a regime with incoherent spin flips occurs on a relatively long time scale, on the order of the single-nuclear-spin dephasing time, which can be much longer than the time scale for the superradiant current burst. This conclusion is confirmed through a general master equation. For the two limiting regimes (coherent/incoherent spin flips) the general master equation recovers our simpler treatment based on rate equations, but is also applicable at intermediate dephasing. Throughout this work we assume uniform hyperfine couplings, which yield the strongest coherent enhancement. We propose realistic strategies, based on isotopic modulation and wavefunction engineering in core-shell nanowires, to realize this analytically solvable "box-model" of hyperfine couplings.
We report electron-hole conduction asymmetry in monolayer graphene. Previously, it has been claimed that electron-hole conduction asymmetry is due to imbalanced carrier injection from metallic electrodes. Here, we show that metallic contacts have negligible impact on asymmetric conduction and may be either sample or device-dependent phenomena. Electrical measurements show that monolayer graphene based devices exhibit suppressed electron conduction compared to hole conduction due to the presence of donor impurities which scatter electrons more efficiently. This can be explained by the relativistic nature of charge carriers in a graphene monolayer and can be reconciled with the fact that in a relativistic quantum system transport cross section does depend on the sign of scattering potential in contrast to a nonrelativistic quantum system.
In this paper, we prove the Girsanov formula for $G$-Brownian motion without the non-degenerate condition. The proof is based on the perturbation method in the nonlinear setting by constructing a product space of the $G$-expectation space and a linear space that contains a standard Brownian motion. The estimates for exponential martingale of $G$-Brownian motion are important for our arguments.
We study the stochastic quantization of two-dimensional nonlinear sigma model in the large $N$ limit. Our main tool is the {\it effective} Langevin equation with which we investigate nonperturbative phenomena and derive the results which are same as the path integral approach gives.
After deriving inequalities on coefficients arising in the expansion of a Schur $P$-function in terms of Schur functions we give criteria for when such expansions are multiplicity free. From here we study the multiplicity of an irreducible spin character of the twisted symmetric group in the product of a basic spin character with an irreducible character of the symmetric group, and determine when it is multiplicity free.