ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider a disentanglement process in which local properties of an entangled state are preserved, while the entanglement between the subsystems is erased. Sufficient conditions for a perfect disentanglement (into product states and into separable states) are derived, and connections to the conditions for perfect cloning and for perfect broadcasting are observed.
Einstein's theory of Brownian motion is revisited in order to formulate generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement distribution are relaxed, the fractional derivative naturally appears in the diffusion equation. This is the first demonstration of the physical origin of the fractional derivative, in marked contrast to the usual phenomenological introduction of it. Furthermore, Einstein's approach is generalized to nonlinear kinetic theory to derive the porous-medium-type equation by the appropriate use of the escort distribution.
We study stability of solutions of the Cauchy problem for the Hunter-Saxton equation $u_t+uu_x=\frac14(\int_{-\infty}^xu_x^2 dx-\int_{x}^\infty u_x^2 dx)$ with initial data $u_0$. In particular, we derive a new Lipschitz metric $d_\D$ with the property that for two solutions $u$ and $v$ of the equation we have $d_\D(u(t),v(t))\le e^{Ct} d_\D(u_0,v_0)$.
We report on structural, magnetic and Electron Spin Resonance (ESR) investigations in the manganite system LaMn_{1-x}Cr_{x}O_{3} (x<=0.5). Upon Cr-doping we observe a reduction of the Jahn-Teller distortion yielding less distorted orthorhombic structures. A transition from the Jahn-Teller distorted O' to the pseudocubic O phase occurs between 0.3<x<0.4. A clear connection between this transition and the doping dependence of the magnetic and ESR properties has been observed. The effective moments determined by ESR seem reduced with respect to the spin-only value of both Mn^{3+} and Cr^{3+} ions.
Considering corrections produced by modified dispersion relations on the equation of state parameter of radiation, we study the induced black hole metric inspired by Kiselev's ansatz, thus defining a deformed Reissner-Nordstr\"{o}m metric. In particular, we consider thermodynamic properties of such a black hole from the combined viewpoints of the modified equation of state parameter and the phenomenological approach to the quantum gravity problem called rainbow gravity.
A class of non static solutions around a global monopole resulting from the breaking of a global S0(3) symmetry based on Lyra geometry are obtained. The solutions are obtained using the functional separability of the metric coefficients. We have shown that the monopole exerts attractive gravitational effects on test particles.
It was recently shown that vapor-liquid coexistence densities derived from Mie and Yukawa models collapse to define a single master curve when represented against the difference between the reduced second virial coefficient at the corresponding temperature and that at the critical point. In this work we further test this proposal for another generalization of the Lennard-Jones pair potential. This is carried out for vapor-liquid coexistence densities, surface tension, and vapor pressure, along a temperature window set below the critical point. For this purpose we perform molecular dynamics simulations by varying the potential softness parameter to produce from very short to intermediate attractive ranges. We observed all properties to collapse and yield master curves. Moreover, the vapor-liquid curve is found to share the exact shape of the Mie and attractive Yukawa. Furthermore, the surface tension and the logarithm of the vapor pressure are linear functions of this difference of reduced second virial coefficients.
We prove Berry-Esseen type rates of convergence for central limit theorems (CLTs) of regenerative processes which generalize previous results of Bolthausen under weaker moment assumptions. We then show how this general result can be applied to obtain rates of convergence for (1) CLTs for additive functionals of positive recurrent Markov chains under certain conditions on the strong mixing coefficients, and (2) annealed CLTs for certain ballistic random walks in random environments.
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties. We provide a construction of the central seminormalization by a decomposition theorem in elementary central gluings. The existence of a central seminormalization is established in the affine case and for real schemes.
The LHC energies are those at which the asymptotic regime in hadron-hadron diffractive collisions ($pp,\pi p,\pi\pi$) might be switched on. Based on results of the Dakhno-Nikonov eikonal model which is a generalization of the Good-Walker eikonal approach for a continuous set of channels, we present a picture for transformation of the constituent quark mode to the black disk one. In the black disk mode ($\sqrt s \geq 10$ TeV) we have a growth of the logarithm squared type for total and elastic cross sections, $\sigma_{tot}\sim\ln^2s$ and $\sigma_{el}\sim\ln^2s$, and $(\tau={\bf q}_\perp^2\sigma_{tot})$-scaling for diffractive scattering and diffractive dissociation of hadrons. The diffractive dissociation cross section grows as $\sigma_{D}\sim\ln{s}$, $\sigma_{DD}\sim\ln{s}$, and their relative contribution tends to zero: $\sigma_{D}/\sigma_{tot}\to 0$, $\sigma_{DD}/\sigma_{tot}\to 0$. Asymptotic characteristics of diffractive and total cross sections are universal, and this results in the asymptotical equality of cross sections for all types of hadrons (the Gribov's universality). The energy scale for switching on the asymptotic mode is estimated for different processes.
For a fixed integer $\ell$ a path is long if its length is at least $\ell$. We prove that for all integers $k$ and $\ell$ there is a number $f(k,\ell)$ such that for every graph $G$ and vertex sets $A,B$ the graph $G$ either contains $k$ edge-disjoint long $A$-$B$-paths or it contains an edge set $F$ of size $|F|\leq f(k,\ell)$ that meets every long $A$-$B$-path. This is the edge analogue of a theorem of Montejano and Neumann-Lara (1984). We also prove a similar result for long $A$-paths and long $\mathcal{S}$-paths.
We describe radio observations at 244 and 610 MHz of a sample of 20 luminous and ultra-luminous IRAS galaxies. These are a sub-set of a sample of 31 objects that have well-measured radio spectra up to at least 23 GHz. The radio spectra of these objects below 1.4 GHz show a great variety of forms and are rarely a simple power-law extrapolation of the synchrotron spectra at higher frequencies. Most objects of this class have spectral turn-overs or bends in their radio spectra. We interpret these spectra in terms of free-free absorption in the starburst environment.   Several objects show radio spectra with two components having free-free turn-overs at different frequencies (including Arp 220 and Arp 299), indicating that synchrotron emission originates from regions with very different emission measures. In these sources, using a simple model for the supernova rate, we estimate the time for which synchrotron emission is subject to strong free-free absorption by ionized gas, and compare this to expected HII region lifetimes. We find that the ionized gas lifetimes are an order of magnitude larger than plausible lifetimes for individual HII regions. We discuss the implications of this result and argue that those sources which have a significant radio component with strong free-free absorption are those in which the star formation rate is still increasing with time.   We note that if ionization losses modify the intrinsic synchrotron spectrum so that it steepens toward higher frequencies, the often observed deficit in fluxes higher than ~10 GHz would be much reduced.
The ground state phase diagram of a spin $S=1/2$ $XXZ$ Heisenberg chain with spatially modulated Dzyaloshinskii-Moriya (DM) interaction $ {\cal H}= \sum_n J\left[\left(S^x_n S^x_{n+1} +S^y_n S^y_{n+1}+\Delta S^z_n S^z_{n+1}\right)+(D_0+(-1)^n D_1)\left(S^x_n S^y_{n+1} -S^y_n S^{x}_{n+1} \right) \right] $ is studied using the continuum-limit bosonization approach and extensive density matrix renormalization group computations. It is shown that the effective continuum-limit bosonized theory of the model is given by the double frequency sine-Gordon model (DSG) where the frequences i.e. the scaling dimensions of the two competing cosine perturbation terms depend on the effective anisotropy parameter $\gamma^*=J\Delta /\sqrt{J^2+D_0^2+D_1^2}$. Exploring the ground state properties of the DSG model we have shown that the zero-temperature phase diagram contains the following four phases: (i) the ferromagnetic phase at $\gamma^*<-1$; (ii) the gapless Luttinger-liquid (LL) phase at $-1<\gamma^*< \gamma^*_{c1}=-1/\sqrt{2}$; (iii) the gapped composite (C1) phase characterized by coexistence of the long-range-ordered (LRO) dimerization pattern $\epsilon \sim (-1)^n (S_n S_{n+1})$ with the LRO alternating spin chirality pattern $\kappa \sim (-1)^{n}\left(S^{x}_{n}S^{y}_{n+1} -S^{y}_{n}S^{x}_{n+1} \right)$ at $\gamma^{\ast}_{c1}<\gamma^{\ast} <\gamma^{\ast}_{c2}$; and (iv) at $\gamma^{\ast} >\gamma^{\ast}_{c2}>1$ the gapped composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. The transition from the LL to the C1 phase at $\gamma^*_{c1}$ belongs to the Berezinskii-Kosterlitz-Thouless universality class, while the transition at $\gamma^*_{c2}$ from C1 to C2 phase is of the Ising type.
The presence of dark matter in the Universe is nowadays widely supported by a large body of astronomical and cosmological observations. The central region of the Milky Way is expected to harbor a large amount of dark matter. Very-high-energy (>100 GeV) gamma-ray observations with the H.E.S.S. array of Imaging Atmospheric Cherenkov Telescopes are powerful probes to look for self-annihilations of dark matter particles toward the Galactic Centre. A new search for a dark matter signal has been carried out on the full H.E.S.S.-I dataset of 2004-2014 observations with a 2D-binned likelihood method using spectral and spatial properties of signal and background. Updated constraints are derived on the velocity-weighted annihilation cross section. Higher statistics from the 10-year Galactic Center dataset of H.E.S.S. I together with a novel analysis technique allow to significantly improve the sensitivity. New results are presented.
In 2003, Kedlaya gave an algorithm to compute the zeta function associated to a hyperelliptic curve over a finite field, by computing the rigid cohomology of the curve. Edixhoven remarked that it is actually possible to compute the crystalline cohomology of the curve, which is a lattice in the rigid cohomology. Following a method of Wach, we first explain how to use this lattice to compute the $(\varphi,\Gamma)$-module associated to an hyperelliptic curve. We also explain an alternative way to get the $(\varphi,\Gamma)$-module mod $p$ that relies on the Deligne-Illusie morphism.
An unresolved problem in J/psi phenomenology is a systematic understanding of the differential photoproduction cross section, dsigma/dz [gamma + p -> J/psi + X], where z= E_psi/E_gamma in the proton rest frame. In the non-relativistic QCD (NRQCD) factorization formalism, fixed-order perturbative calculations of color-octet mechanisms suffer from large perturbative and nonperturbative corrections that grow rapidly in the endpoint region, z -> 1. In this paper, NRQCD and soft collinear effective theory are combined to resum these large corrections to the color-octet photoproduction cross section. We derive a factorization theorem for the endpoint differential cross section involving the parton distribution function and the color-octet J/psi shape functions. A one loop matching calculation explicitly confirms our factorization theorem at next-to-leading order. Large perturbative corrections are resummed using the renormalization group. The calculation of the color-octet contribution to dsigma/dz is in qualitative agreement with data. Quantitative tests of the universality of color-octet matrix elements require improved knowledge of shape functions entering these calculations as well as resummation of the color-singlet contribution which accounts for much of the total cross section and also peaks near the endpoint.
Magnetars, the likely sources of Fast Radio Bursts (FRBs), produce both steady highly relativistic magnetized winds, and occasional ejection events. We demonstrate that the requirement of conservation of the magnetic flux dominates the overall dynamics of magnetic explosions. This is missed in conventional hydrodynamic models of the ejections as expanding shell with parametrically added magnetic field, as well as one-dimensional models of magnetic disturbances. Most of the initial free energy of an explosion is actually spent on stretching its own internal magnetic field, while doing minimal $pdV$ work against the surrounding. Magnetic explosions from magnetars come into force balance with the pre-flares wind close to the light cylinder. They are then advected quietly with the wind, or propagate as electromagnetic disturbances. No powerful shock waves are generated in the wind.
We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of 'topological' edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.
We review results about protoplanetary disk models, protoplanet migration and formation of giant planets with migrating cores. We first model the protoplanetary nebula as an \alpha-accretion disk and present steady state calculations for different values of \alpha and gas accretion rate through the disk. We then review the current theories of protoplanet migration in the context of these models, focusing on the gaseous disk-protoplanet tidal interaction. According to these theories, the migration timescale may be shorter than the planetary formation timescale. Therefore we investigate planet formation in the context of a migrating core, considering both the growth of the core and the build-up of the envelope in the course of the migration.
We present an algorithm for generating merger histories of dark matter haloes. The algorithm is based on the excursion set approach with moving barriers whose shape is motivated by the ellipsoidal collapse model of halo formation. In contrast to most other merger-tree algorithms, ours takes discrete steps in mass rather than time. This allows us to quantify effects which arise from the fact that outputs from numerical simulations are usually in discrete time bins. In addition, it suggests a natural set of scaling variables for describing the abundance of halo progenitors; this scaling is not as general as that associated with a spherical collapse. We test our algorithm by comparing its predictions with measurements in numerical simulations. The progenitor mass fractions and mass functions are in good agreement, as is the predicted scaling law. We also test the formation-redshift distribution, the mass distribution at formation, and the redshift distribution of the most recent major merger; all are in reasonable agreement with N-body simulation data, over a broad range of masses and redshifts. Finally, we study the effects of sampling in discrete time snapshots. In all cases, the improvement over algorithms based on the spherical collapse assumption is significant.
Ultrafast magnetization dynamics in metallic heterostructures consists of a combination of local demagnetization in the ferromagnetic constituent and spin-dependent transport contributions within and in between the constituents. Separation of these local and non-local contributions is essential to obtain microscopic understanding and for potential applications of the underlying microscopic processes. By comparing the ultrafast changes of the polarization rotation and ellipticity in the magneto-optical Kerr effect (MOKE) we observe a time-dependent magnetization profile M(z,t) in Co/Cu(001) films by exploiting the effective depth sensitivity of the method. By analyzing the spatio-temporal correlation of these profiles we find that on time scales before hot electron thermalization (<100 fs) the transient magnetization of Co films is governed by spin-dependent transport effects, while after hot electron thermalization (>200 fs) local spin-flip processes dominate.
The spectrum of a quasar contains important information about its properties. Thus, it can be expected that two quasars with similar spectra will have similar properties, but just how similar has not before been quantified. Here we compare the ultraviolet spectra of a sample of 5553 quasars from Data Release 7 of the Sloan Digital Sky Survey, focusing on the $1350$ \AA \ $\leq \lambda \leq 2900$ \AA \ rest-frame region which contains prominent emission lines from \SiIV, O IV], \CIV, \CIII, and \MgII\ species. We use principal component analysis to determine the dominant components of spectral variation, as well as to quantitatively measure spectral similarity. As suggested by both the Baldwin effect and modified Baldwin effect, quasars with similar spectra have similar properties: bolometric luminosity, Eddington fraction, and black hole mass. The latter two quantities are calculated from the luminosity in conjunction with spectral features, and the variation between quasars with virtually identical spectra (which we call doppelg\"angers) is driven by the variance in the luminosity plus measurement uncertainties. In the doppelgangers the luminosity differences show 1$\sigma$ uncertainties of 57\% (or 0.63 magnitudes) and $\sim$70\% 1$\sigma$ uncertainties for mass and Eddington fraction. Much of the difference in luminosities may be attributable to time lags between the spectral lines and the continuum. Furthermore, we find that suggestions that the mostly highly accreting quasars should be better standard candles than other quasars are not bourne out for doppelgangers. Finally, we discuss the implications for using quasars as cosmological probes and the nature of the first two spectral principal components.
The purpose of this paper is to give the explicit formulae of p-adic l-functions and sums of powers which are related to Euler numbers.
Possible consequences of ferromagnetic transition in dense matter suggested recently by Kutschera and W{\'o}jcik, for the magnetic properties of neutron stars, are studied. Specific model of dense matter, in which a small admixture of protons is completely polarized due to their interaction with neutrons, is considered. Magnetic field of neutron stars with a ferromagnetic core is calculated within the framework of general relativity.   Two types of boundary conditions at the ferromagnetic core edge are considered, corresponding to normal and superconducting liquid envelope, respectively. Numerical results for the neutron star magnetic dipole moment are confronted with pulsar timing. To be consistent with observations, ferromagnetic cores surrounded by a non-superconducting envelope, should consist of weakly ordered ferromagnetic domains. If domains are highly ordered, ferromagnetic core should be screened by a superconducting envelope.
In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely topological field equation from the metric-dependent constitutive law. We show here that GR allows for a premetric formulation, too. For this purpose, we apply the teleparallel approach of gravity, which represents GR as a gauge theory based on the translation group. We formulate the metric-free topological field equation and a general linear constitutive law between the basic field variables. The requirement of local Lorentz invariance turns the model into a full equivalent of GR. Our approach opens a way for a natural extension of GR to diverse geometrical structures of spacetime.
We consider the one-dimensional Glauber dynamics with coupling disorder in terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the spectrum gap of these latter are evaluated numerically by averaging over both binary and Gaussian disorder realizations. In the first case, these exponents are found to follow the non-universal values of those of plain dimerized chains. In the second situation their values are still non-universal and sub-diffusive below a critical variance above which, however, the relaxation time is suggested to grow as a stretched exponential of the equilibrium correlation length.
We present HST/WFPC2 high-spatial resolution images in the R and B bands of the close environment of the sightlines to seven quasars which spectra show either a damped Ly-alpha absorption line, 21cm absorption, or a very strong MgII/FeII absorption system at intermediate redshifts (0.4 < z < 1). Objects down to about 0.3", or 2.0 kpc at z=0.6 (H0 = 50 kms/s/Mpc, q0=0), and to a limiting magnitude m(702, lim)=25.9 could be detected for seven fields comprising eight absorbers (one at higher redshift z=1.78 towards MC 1331+170) with high HI column densities of at least 1x10^20 cm^-2. In each case, a candidate absorber with absolute magnitude Mb =-19.0 or much brighter has been detected. This small sample of gas-rich galaxies at intermediate redshifts covers a wide range in morphological types. There are three spiral galaxies of various sizes and luminosities (towards 3C 196, Q 1209+107 and MC 1331+170), three compact objects (towards EX 0302-223, PKS 0454+039 and, at high redshift, MC 1331+170), and two amorphous, low surface brightness galaxies (towards PKS 1229-021 and 3C 286). In the fields around 3C 196, PKS 1229-021 and Q 1209+107, there is an excess of galaxies in the PC2 images, suggestive of the presence of a group of galaxies associated with the damped Ly-alpha absorber, or maybe with the quasar itself for the two z = 1.0 cases. For 3C 196 and 3C 286, the quasar host galaxies have also tentatively been discovered.
Let $q$ be a prime power of a prime $p$, $n$ a positive integer and $\mathbb F_{q^n}$ the finite field with $q^n$ elements. The $k-$normal elements over finite fields were introduced and characterized by Huczynska et al (2013). Under the condition that $n$ is not divisible by $p$, they obtained an existence result on primitive $1-$normal elements of $\mathbb F_{q^n}$ over $\mathbb F_q$ for $q>2$. In this note, we extend their result to the excluded case $q=2$.
We consider the problem of self-adjoint extension of Hamilton operators for charged quantum particles in the pure Aharonov-Bohm potential (infinitely thin solenoid). We present a pragmatic approach to the problem based on the orthogonalization of the radial solutions for different quantum numbers. Then we discuss a model of a scalar particle with a magnetic moment which allows to explain why the self-adjoint extension contains arbitrary parameters and give a physical interpretation.