ShantanuT01/DACTYL-Pretraining huggingface dataset:
For hyperbolic systems of conservation laws, uniqueness of solutions is still largely open. We aim to expand the theory of uniqueness for systems of conservation laws. One difficulty is that many systems have only one entropy. This contrasts with scalar conservation laws, where many entropies exist. It took until 1994 to show that one entropy is enough to ensure uniqueness of solutions for the scalar conservation laws (see Panov [Mat. Zametki, 55(5):116--129, 159, 1994]). This single entropy result was proven again by De Lellis, Otto and Westdickenberg about 10 years later [Quart. Appl. Math., 62(4):687--700, 2004]. These two proofs both rely on the special connection between Hamilton--Jacobi equations and scalar conservation laws in one space dimension. However, this special connection does not extend to systems. In this paper, we prove the single entropy result for scalar conservation laws without using Hamilton--Jacobi. Our proof lays out new techniques that are promising for showing uniqueness of solutions in the systems case.
A general system of equations is derived, using the 1+3 orthonormal tetrad formalism, describing the influence of a plane-fronted-parallel gravitational wave on a warm relativistic two-component plasma. We focus our attention on phenomena that are induced by terms that are higher order in the gravitational wave amplitude. In particular, it is shown that parametric excitations of ion-acoustic waves takes place, due to these higher order gravitational non-linearities. The implications of the results are discussed.
We consider a Navier-Stokes model for compressible fluids in one space dimension. We show that it can be approximated by a time-discrete scheme combining the discretization of a trivial stochastic differential equation and the application of a suitable monotonic rearrangement operator In addition, our result can be easily extended to a related Navier-Stokes-Poisson system.
We present a chemical composition analysis of three dozen giant stars in the nearby ``CN-bimodal'' mildly metal-poor (<[Fe/H]> = -1.18) globular cluster M4. The analysis combined traditional spectroscopic abundance methods with modifications to the line-depth ratio technique pioneered by Gray (1994). Silicon and aluminum are found to be primordially overabundant by factors exceeding the mild overabundances usually seen in alpha- and light odd elements among halo field and globular cluster giants of comparable metallicity. In addition, barium is found to be overabundant by a factor of about four. Superimposed on the primordial abundance distribution in M4, there is evidence for the existence of proton-capture synthesis of C, O, Ne, and Mg.
This is a Reply to a Comment by Tanaka and Machida. We provide some details of the derivation of the effective field theory for integer quantum Hall transitions using the non-Abelian chiral anomaly.
We demonstrate the strong impact of the oscillator agility on the line broadening by studying spin transfer induced microwave emission in MgO-based tunnel junctions with current. The linewidth is almost not affected by decreasing the temperature. At very low currents, a strong enhancement of the linewidth at low temperature is attributed to an increase of the non linearity, probably due to the field-like torque. Finally we evidence that the noise is not dominated by thermal fluctuations but rather by the chaotization of the magnetization system induced by the spin transfer torque.
In view of the recent Fermi observations of GRB prompt emission spectra, we develop a theory of photosphere emission of a hybrid relativistic outflow with a hot fireball component (defined by dimensionless entropy $\eta$) and a cold Poynting-flux component (defined by magnetization $\sigma_0$ at the central engine). We consider the scenarios both without and with sub-photospheric magnetic dissipations. Based on a simplified toy model of jet dynamics, we develop two approaches: a "bottom-up" approach to predict the temperature (for a non-dissipative photosphere) and luminosity of the photosphere emission and its relative brightness for a given pair of $(\eta,\sigma_0)$; and a "top-down" approach to diagnose central engine parameters ($\eta$ and $\sigma_0$) based on the observed quasi-thermal photosphere emission properties. We show that a variety of observed GRB prompt emission spectra with different degrees of photosphere thermal emission can be reproduced by varying $\eta$ and $\sigma_0$ within the non-dissipative photosphere scenario. In order to reproduce the observed spectra, the outflows of most GRBs need to have a significant $\sigma$, both at the central engine, and at the photosphere. The $\sigma$ value at $10^{15}$ cm from the central engine (a possible non-thermal emission site) is usually also greater than unity, so that internal-collision-induced magnetic reconnection and turbulence (ICMART) may be the mechanism to power the non-thermal emission. We apply our top-down approach to GRB 110721A, and find that the temporal evolution behavior of its blackbody component can be well interpreted with a time-varying $(\eta,\sigma_0)$ at the central engine, instead of invoking a varying engine base size $r_0$ as proposed by previous authors.
Aimed at identifying the role of microscopic Hamiltonian parameters on spin wave excitations, orbital order, and magnetic moments in the $(\pi,0)$ SDW state, two different three band models for iron pnictides are compared --- one at two-third filling ($n=4$) and another at half filling $(n=3)$ --- both of which yield qualitatively correct Fermi surface structure in the paramagnetic state. Spin wave analysis of the model at $n=4$ shows instability of the SDW state, which is attributed to weakly developed magnetic moments and weak magnetic couplings due to overfilling, as inferred from the observed stabilization of the SDW state and enhancement of magnetic excitation energies upon hole doping. In contrast, the model at $n=3$ (half filling) yields a gapped SDW state with well developed magnetic moments and the calculated spin wave excitations are in excellent agreement with INS experiments. The sign of the orbital order ($n_{xz} - n_{yz} \approx +0.2$) is also in agreement with experiments. Both the zone boundary spin wave energies in the F and AF directions as well as the orbital order are shown to peak near half filling, highlighting the correlation between orbital order and SDW state stabilization.
We investigate the magnetic field dependent thermopower, thermal conductivity, resistivity and Hall effect in the heavy fermion metal YbRh2Si2. In contrast to reports on thermodynamic measurements, we find in total three transitions at high fields, rather than a single one at 10 T. Using the Mott formula together with renormalized band calculations, we identify Lifshitz transitions as their origin. The predictions of the calculations show that all experimental results rely on an interplay of a smooth suppression of the Kondo effect and the spin splitting of the flat hybridized bands.
Running quantum algorithms on real hardware is essential for understanding their strengths and limitations, especially in the noisy intermediate scale quantum (NISQ) era. Herein we focus on the practical aspect of quantum computational calculations of solid-state crystalline materials based on theory developed in our group by using real quantum hardware with a novel noise mitigation technique referred to as partition-measurement symmetry verification, which performs post-selection of shot counts based on $Z_{2}$ and $U_{1}$ symmetry verification. We select two periodic systems with different level of complexity for these calculations. One of them is the distorted hydrogen chain as an example of very simple systems, and the other one is iron crystal in the BCC and FCC phases as it is considered to be inaccessible by using classical computational wavefunction methods. The ground state energies are evaluated based on the translational quantum subspace expansion (TransQSE) method for the hydrogen chain, and periodic boundary condition adapted VQE for our iron models. By applying these techniques for the simplest 2 qubit iron model systems, the correlation energies obtained by the hardware calculations agree with those of the state-vector simulations within $\sim$5 kJ/mol. Although the quantum computational resources used for those experiments are still limited, the techniques applied to obtain our simplified models will be applicable in essentially the same manner to more complicated cases as quantum hardware matures.
Using the theory of equitable decompositions it is possible to decompose a matrix $M$ appropriately associated with a given graph. The result is a collection of smaller matrices whose collective eigenvalues are the same as the eigenvalues of the original matrix $M$. This is done by decomposing the matrix over a graph symmetry. Previously it was shown that a matrix can be equitably decomposed over any uniform, basic, or separable automorphism. Here we extend this theory to show that it is possible to equitably decompose a matrix over any automorphism of a graph, without restriction. Moreover, we give a step-by-step procedure which can be used to generate such a decomposition. We also prove under mild conditions that if a matrix $M$ is equitably decomposed the resulting divisor matrix, which is the divisor matrix of the associated equitable partition, will have the same spectral radius as the original matrix $M$.
The coupling of the charge carriers passing through a molecule bridging two bulky conductors with local vibrational modes of the molecule, gives rise to distinct features in the electronic transport properties on one hand, and to nonequilibrium features in the vibrations' properties, e.g., their population, on the other. Here we explore theoretically a generic model for a molecular junction biased by an arbitrary dc voltage in the weak-coupling regime. We analyze the signature of the electron-vibration interaction on the full-counting statistics of the current fluctuations (i.e., the cumulant generating-function of the current correlations), we give a detailed account of the response to an ac field exerted on the junction (on top of the dc bias voltage), we study the nonequilibrium distribution of the vibrational modes and the fluctuations they cause in the displacement of the molecule center of mass. The calculations use the technique of nonequilibrium Green's functions, and treat the electron-vibration coupling in perturbation theory, within the random-phase approximation when required.
We show that spin systems with infinite-range interactions can violate at thermal equilibrium a multipartite Bell inequality, up to a finite critical temperature $T_c$. Our framework can be applied to a wide class of spin systems and Bell inequalities, to study whether nonlocality occurs naturally in quantum many-body systems close to the ground state. Moreover, we also show that the low-energy spectrum of the Bell operator associated to such systems can be well approximated by the one of a quantum harmonic oscillator, and that spin-squeezed states are optimal in displaying Bell correlations for such Bell inequalities.
We consider a source of gravitational waves of frequency $\omega$, located near the center of a massive galaxy of mass $M$ and radius $R$, with $\omega\gg R^{-1}$. In the case of a perfect fluid galaxy, and of odd-parity waves, there is no direct matter-wave interaction and the propagation of the waves is affected by the galaxy only through the curvature of the spacetime background through which the waves propagate. We find that, in addition to the expected redshift of the radiation emerging from the galaxy, there is a small amount of backscatter, of order $M/\omega^2R^3$. We show that there is no suppression of radiative power by the factor $1+\omega^2M^2/4$ as has been recently predicted by Kundu. The origin of Kundu's suppression lies in the interpretation of a term in the expansion of the exterior field of the galaxy in inverse powers of radius. It is shown why that term is not related to the source strength or to the strength of the emerging radiation.
The melting curve of aluminium has been determined from 0 to ~150 GPa using first principles calculations of the free energies of both the solid and liquid. The calculations are based on density functional theory within the generalised gradient approximation using ultrasoft Vanderbilt pseudopotentials. The free energy of the harmonic solid has been calculated within the quasiharmonic approximation using the small-displacement method; the free energy of the liquid and the anharmonic correction to the free energy of the solid have been calculated via thermodynamic integration from suitable reference systems, with thermal averages calculated using ab-initio molecular dynamics. The resulting melting curve is in good agreement with both static compression measurements and shock data.
A model for the nucleon-antinucleon interaction is presented which is based on meson-baryon dynamics. The elastic part is the $G$-parity transform of the Bonn $NN$ potential. Annihilation into two mesons is described in terms of microscopic baryon-exchange processes including all possible combinations of $\pi,\eta,\rho,\omega,a_0,f_0,a_1,f_1,a_2,f_2,K,K^*$. The remaining annihilation part is taken into account by a phenomenological energy- and state independent optical potential of Gaussian form. The model enables a simultaneous description of nucleon-antinucleon scattering and annihilation phenomena with fair quality.
At intermediate energies it appears advantageous to work without partial wave decomposition and use directly the momentum vectors. We derived a finite set of coupled Lippmann-Schwinger equations using helicities. They can be used for any type of realistic NN forces, which are given in operator form. As an example we have chosen the Bonn OBEPR NN potential.
Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large denominators. However, such representations normally use a very sparse subset of the positive integers up to the largest demoninator. We show that for every positive rational there exist Egyptian fractions whose largest denominator is at most N and whose denominators form a positive proportion of the integers up to N, for sufficiently large N; furthermore, the proportion is within a small factor of best possible.
Let $G$ be a finite abelian group. The Erd{\H o}s--Ginzburg--Ziv constant $\mathsf s (G)$ of $G$ is defined as the smallest integer $l \in \mathbb N$ such that every sequence \ $S$ \ over $G$ of length $|S| \ge l$ \ has a zero-sum subsequence $T$ of length $|T| = \exp (G)$. If $G$ has rank at most two, then the precise value of $\mathsf s (G)$ is known (for cyclic groups this is the Theorem of Erd{\H o}s-Ginzburg-Ziv). Only very little is known for groups of higher rank. In the present paper, we focus on groups of the form $G = C_n^r$, with $n, r \in \N$ and $n \ge 2$, and we tackle the study of $\mathsf s (G)$ with a new approach, combining the direct problem with the associated inverse problem.
We present three interesting projective models of the supersingular K3 surface X in characteristic 5 with Artin invariant 1. For each projective model, we determine smooth rational curves on X with the minimal degree and the projective automorphism group. Moreover, by using the superspecial abelian surface, we construct six sets of 16 disjoint smooth rational curves on X, and show that they form a beautiful configuration.
We establish a conjectured result of Dummit, Granville and Kisilevsky for the maximum bias in P2 races, which compare the number of P2's $\leq x$ whose prime factors, evaluated at a given quadratic character, take specifc values.
I review our current understanding of massive black hole (MBH) formation and evolution along the cosmic history. After a brief introductory overview of the relevance of MBHs in the hierarchical structure formation paradigm, I discuss the main viable channels for seed BH formation at high redshift and for their subsequent mass growth and spin evolution. The emerging hierarchical picture, where MBHs grow through merger triggered accretion episodes, acquiring their mass while shining as quasars, is overall robust, but too simplistic to explain the diversity observed in MBH phenomenology. I briefly discuss which future observations will help to shed light on the MBH cosmic history in the near future, paying particular attention to the upcoming gravitational wave window.
Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.
X(5) is a paradigm for the structure at the critical point of a particular first-order phase transition for which the intrinsic energy surface has two degenerate minima separated by a low barrier. For a finite system, we show that the dynamics at such a critical point can be described by an effective deformation determined by minimizing the energy surface after projection onto angular momentum zero, and combined with two-level mixing. Wave functions of a particular analytic form are used to derive estimates for energies and quadrupole rates at the critical point.
Two magnetic atoms, one attached to the tip of a Scanning Tunneling Microscope (STM) and one adsorbed on a metal surface, each constituting a Kondo system, have been proposed as one of the simplest conceivable systems potentially exhibiting quantum critical behaviour. We have succeeded in implementing this concept experimentally for cobalt dimers clamped between an STM tip and a gold surface. Control of the tip-sample distance with sub-picometer resolution allows us to tune the interaction between the two cobalt atoms with unprecedented precision. Electronic transport measurements on this two-impurity Kondo system reveal a rich physical scenario which is governed by a crossover from local Kondo screening to non-local singlet formation due to antiferromagnetic coupling as a function of separation of the cobalt atoms.
We consider a brane world residing in the interior region inside the horizon of the D3-brane. The horizon size then can be interpreted as the compactification size. The macroscopically large size of extra dimensions can be derived from the underlying string theory that has only one physical scale, {\it i.e.,} the string scale. Then, the hierarchy between the string scale and the Planck scale is provided by Ramon-Ramon charge of the D3-brane. This picture also offers a new perspective on various issues associated with the brane world scenarios including the cosmological constant.
Evans defines a notion of what it means for a set B to be polar for a process indexed by a tree. The main result herein is that a tree picked from a Galton-Watson measure whose offspring distribution has mean m and finite variance will almost surely have precisely the same polar sets as a deterministic tree of the same growth rate. This implies that deterministic and nondeterministic trees behave identically in a variety of probability models. Mapping subsets of Euclidean space to trees and polar sets to capacity criteria, it follows that certain random Cantor sets are capacity-equivalent to each other and to deterministic Cantor sets. An extension to branching processes in varying environment is also obtained.
We introduce gauge theories based on a class of disconnected gauge groups, called principal extensions. Although in this work we focus on 4d theories with N=2 SUSY, such construction is independent of spacetime dimensions and supersymmetry. These groups implement in a consistent way the discrete gauging of charge conjugation, for arbitrary rank. Focusing on the principal extension of SU(N), we explain how many of the exact methods for theories with 8 supercharges can be put into practice in that context. We then explore the physical consequences of having a disconnected gauge group: we find that the Coulomb branch is generically non-freely generated, and the global symmetry of the Higgs branch is modified in a non-trivial way.
We have studied the low energy spin dynamics between 4.6K and 0.07K in a Tb2Ti2O7 single crystal sample, by means of inelastic neutron scattering experiments. The spectra consist in a dual response, with a static and an inelastic contribution, showing striking Q-dependences. We propose an interpretation involving an anisotropic exchange interaction in combination with a breaking of the threefold symmetry at the rare earth site. Simulations of the Q-dependent scattering in the Random Phase Approximation account well for the inelastic response.
We find that in an opaque quark-gluon plasma, significant particle production at high transverse momenta can occur via acceleration of (initially) lower-momentum partons. This new mechanism, which is the opposite of parton energy loss (jet quenching), has important implications for observables, such as elliptic flow, in heavy-ion collisions at RHIC energies and above.
We present deep (9 hours) Gemini-N/GNIRS near-infrared spectroscopic observations of ULAS J1342+0928, a luminous quasar at z=7.54. Various broad emission lines were detected, as well as the underlying continuum and iron forests over the rest-frame wavelength 970-2930A. There is a clear trend that higher-ionization emission lines show larger blueshifts with CIV1549 exhibiting 5510^{+240}_{-110} km s-1 blueshift with respect to the systematic redshift from the far-infrared [CII] 158um emission line. Those high ionization lines have wide profiles with FWHM more than 10000 km s-1. A modest blueshift of 340^{+110}_{-80} km s-1 is also seen in MgII, the lowest ionization line identified in the spectrum. The updated MgII-based black hole mass of M_BH=9.1_{-1.3}^{+1.4} x 10^8 M_sun and the Eddington ratio of L_bol/L_Edd=1.1_{-0.2}^{+0.2} confirm that ULAS J1342+0928 is powered by a massive and actively accreting black hole. There is no significant difference in the emission line ratios such as SiIV/CIV and AlIII/CIV when compared to lower-redshift quasars in a similar luminosity range, which suggests early metal pollution of the broad-line-region clouds. This trend also holds for the FeII/MgII line ratio, known as a cosmic clock that traces the iron enrichment in the early universe. Different iron templates and continuum fitting ranges were used to explore how the FeII/MgII measurement changes as a function of spectral modeling. Quasars at even higher redshift or at fainter luminosity range (L_bol<10^46 erg s-1) are needed to probe the sites of early metal enrichment and a corresponding change in the FeII/MgII ratio.
We propose the multiband extension of the spin-fermion model to address the superconducting d-wave pairing due to magnetic interaction near critical point. We solve the unrestricted gap equation with a general d-wave symmetry gap and find that divergent magnetic correlation length $\xi$ leads to the very unharmonic shape of the gap function with shallow gap regions near nodes. These regions are extremely sensitive to disorder. Small impurity concentration induces substantial residual density of states. We argue that we can understand the large $N_{res}(0) = \lim_{T\to 0} C_p(T)/T$ value and its pressure dependence of the recently discovered $CeRhIn_5$ superconductor under pressure within this approach.