ShantanuT01/DACTYL-Pretraining huggingface dataset:
Entangled coherent states, which can in principle be created using strong Kerr non-linearities, allow the violation of Bell inequalities for very coarse-grained measurements. This seems to contradict a recent conjecture that observing quantum effects in macroscopic systems generally requires very precise measurements. However, here we show that both the creation of the required states and the required measurements rely on being able to control the phase of the necessary Kerr-nonlinearity based unitary operations with extreme precision. This lends support to the idea that there is a general principle that makes macroscopic quantum effects difficult to observe, even in the absence of decoherence.
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the energy. Here we consider the problem of scattering by the members of a family of potentials $V_a(x)=-{\rm sgn}(x)\,|x|^a$, where sgn represents the sign function and $a$ is a positive rational number. The scattering function and the phase shifts are obtained from global solutions of the Schr\"odinger equation. For the determination of the Gamow states, associated to resonances, we exploit their close relation with the eigenvalues of the $\mathcal{PT}$-symmetric Hamiltonians with potentials $V_a^{\mathcal{PT}}(x)=-{\rm i}\,{\rm sgn}(x)\,|x|^a$. Calculation of the time delay in the scattering at real energies is used to characterize the resonances. As an additional result, the breakdown of the $\mathcal{PT}$-symmetry of the family of potentials $V_a^{\mathcal{PT}}$ for $a<3$ may be conjectured.
This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine the "default term" apparent in risk-neutral option prices if the underlying stock exhibits a bubble modeled by a strict local martingale. Results for certain path dependent options and last passage time formulas are given.
We study the question of whether the blow-ups of toric surfaces of Picard number one at the identity point of the torus are Mori Dream Spaces. For some of these toric surfaces, the question whether the blow-up is a Mori Dream Space is equivalent to countably many planar interpolation problems. We state a conjecture which generalizes a theorem of Gonzalez and Karu. We give new examples and non-examples of Mori Dream Spaces among these blow-ups.
We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg triangular ladder using the density matrix renormalization group and Gutzwiller variational wave functions. Near an isotropic lattice regime, for moderate to large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea consisting of three partially filled bands. Going away from the triangular towards the square lattice regime, we find a staggered dimer phase with dimers in the transverse direction, while for small ring exchanges the system is in a featureless rung phase. We also discuss parent states and a possible phase diagram in two dimensions.
Zero modes of rotationally symmetric vortices in a hierarchy of generalized Abelian Higgs models are studied. Under the finite-energy and the smoothness condition, it is shown, that in all models, $n$ self-dual vortices superimposed at the origin have $2n$ modes. The relevance of these modes for vortex scattering is discussed, first in the context of the slow-motion approximation. Then a corresponding Cauchy problem for an all head-on collision of $n$ vortices is formulated. It is shown that the solution of this Cauchy problem has a $\frac{\pi}{n}$ symmetry.
Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gives a self-contained introduction to the algebro-geometric concepts underlying our framework.
We analyse $u-r$ colour distributions for several samples of galaxies in groups drawn from the Fourth Data Release of the Sloan Digital Sky Survey. For all luminosity ranges and environments considered the colour distributions are well described by the sum of two Gaussian functions. We find that the fraction of galaxies in the red sequence is an increasing function of group virial mass. We also study the evolution of the galaxy colour distributions at low redshift, $z\le0.18$ in the field and in groups for galaxies brighter than $M_r-5\log(h)=-20$, finding significant evidence of recent evolution in the population of galaxies in groups. The fraction of red galaxies monotonically increases with decreasing redshift, this effect implies a much stronger evolution of galaxies in groups than in the field.
We show that the differential-geometric description of matter by differential structures of spacetime leads to a unifying model of the three types of energy in the cosmos: matter, dark matter and dark energy. Using this model we are able to calculate the ratio of dark energy to the total energy of the cosmos.
We numerically solve the transport equations for a quark gas described by the the Nambu-Jona-Lasinio model. The mean field equations of motion, which consist of the Vlasov equation for the density and the gap equation for the mean field, are discussed, and energy and momentum conservation are proven. Numerical solutions of the partial differential equations are obtained by applying finite difference methods. For an expanding fireball of the light quark mass evolves from small values initially to the value of 350 MeV. This leads to a depletion of the high energy part of the quark spectrum and an enhancement at low momenta. When collisions are included one obtains an equation of the Boltzmann type, where the transition amplitudes depend on the properties of the medium. These equations are given for flavor SU(3), i. e. including strangeness. They are solved numerically in the relaxation time approximation and the time evolution of various observables is given. Medium effects in the relaxtion times do not significantly influence the shape of the spectra. The mass of the strange quark changes little during the expansion. The strangeness yield and the slope temperatures of the final spectra are studied as a function of the size of the initial fireball.
We calculate the specific heat of the ideal gas obeying the generalized exclusion statistics (GES) in the continuum model and the tight binding model numerically. In the continuum model of 3-d space, the specific heat increases with statistical parameter at low temperature whereas it decreases with statistical parameter at high temperature. We find that the critical temperature normalized by $\mu_f$ (Fermi energy) is 0.290. The specific heat of 2-d space was known to be independent of $g$ in the continuum model, but it varies with $g$ drastically in the tight-binding model. From its unique behavior, identification of GES particles will be possible from the specific heat.
In 1965, Erd\H{o}s and P\'{o}sa proved that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold for odd cycles, and Dejter and Neumann-Lara asked in 1988 to find all pairs ${(\ell, z)}$ of integers where such a duality holds for the family of cycles of length $\ell$ modulo $z$. We characterise all such pairs, and we further generalise this characterisation to cycles in graphs labelled with a bounded number of abelian groups, whose values avoid a bounded number of elements of each group. This unifies almost all known types of cycles that admit such a duality, and it also provides new results. Moreover, we characterise the obstructions to such a duality in this setting, and thereby obtain an analogous characterisation for cycles in graphs embeddable on a fixed compact orientable surface.
Long-lived high-energy (>100MeV) emission, a common feature of most Fermi-LAT detected gamma-ray burst, is detected up to \sim 10^2 s in the short GRB 090510. We study the origin of this long-lived high-energy emission, using broad-band observations including X-ray and optical data. We confirm that the late > 100 MeV, X-ray and optical emission can be naturally explained via synchrotron emission from an adiabatic forward shock propagating into a homogeneous ambient medium with low number density. The Klein-Nishina effects are found to be significant, and effects due to jet spreading and magnetic field amplification in the shock appear to be required. Under the constraints from the low-energy observations, the adiabatic forward shock synchrotron emission is consistent with the later-time (t>2s) high-energy emission, but falls below the early-time (t < 2s) high energy emission. Thus we argue that an extra high energy component is needed at early times. A standard reverse shock origin is found to be inconsistent with this extra component. Therefore, we attribute the early part of the high-energy emission (t< 2s) to the prompt component, and the long-lived high energy emission (t>2s) to the adiabatic forward shock synchrotron afterglow radiation. This avoids the requirement for an extremely high initial Lorentz factor.
We present a method to generate many automorphisms of a supersingular K3 surface in odd characteristic. As an application, we show that, if p is an odd prime less than or equal to 7919, then every supersingular K3 surface in characteristic p has an automorphism whose characteristic polynomial on the N\'eron-Severi lattice is a Salem polynomial of degree 22. For a supersingular K3 surface with Artin invariant 10, the same holds for odd primes less than or equal to 17389.
We investigate the full-counting statistics (FCS) of energy transport carried by electrons in molecular junctions for the Anderson-Holstein model in the polaronic regime. Using two-time quantum measurement scheme, generating function (GF) for the energy transport is derived and expressed as a Fredholm determinant in terms of Keldysh nonequilibrium Green's function in the time domain. Dressed tunneling approximation is used in decoupling the phonon cloud operator in the polaronic regime. This formalism enables us to analyze the time evolution of energy transport dynamics after a sudden switch-on of the coupling between the dot and the leads towards the stationary state. The steady state energy current cumulant GF in the long time limit is obtained in the energy domain as well. Universal relations for steady state energy current FCS are derived under finite temperature gradient with zero bias and this enables us to express the equilibrium energy current cumulant by a linear combination of lower order cumulants. Behaviors of energy current cumulants in steady state under temperature gradient and external bias are numerically studied and explained. Transient dynamics of energy current cumulants is numerically calculated and analyzed. The universal scaling of normalized transient energy cumulants is found under both temperature gradient and external bias.
In this manuscript, we calculate the scalar curvature of a two-dimensional thermodynamic space to study the properties of two thermodynamic systems. In particular, we study the stability and possible anyonic behavior of quantum group invariant systems and systems with fractal distribution functions.
It is shown that the magnetic current-driven (`kink-type') instability produces flow and field patterns with helicity and even with \alpha-effect but only if the magnetic background field possesses non-vanishing current helicity \bar{\vec{B}}\cdot curl \bar{\vec{B}} by itself. Fields with positive large-scale current helicity lead to negative small-scale kinetic helicity. The resulting \alpha-effect is positive. These results are very strict for cylindric setups without <i>z/I>-dependence of the background fields. The sign rules also hold for the more complicated cases in spheres where the toroidal fields are the result of the action of differential rotation (induced from fossil poloidal fields) at least for the case that the global rotation is switched off after the onset of the instability.
In this work we shall study the well-posedness and ill-posedness of the Cauchy problem associated to the equation \begin{equation*} u_{t}+a(u^{n})_{x}+(b\mathscr{H} u_{t}+u_{yy})_{x}=0, \end{equation*} in anisotropic weigthed Sobolev spaces. In particular, we examine the unique continuation property for solutions, of this, with polynomial decay.
This is the author's 2008 thesis from the University of Chicago. We generalize the notion of the Clifford index to an arbitrary very ample line bundle and show how it determines when a curve and its various secant varieties have determinantal equations. In particular we establish the scheme theoretic version of a conjecture of Eisenbud-Koh-Stillman. If $L_1$ and $L_2$ are line bundles of degree at least $2g+1+k$, then ${\rm Sec}^j(C)$ is determinantally presented for $j \leq k$ and for $j \leq k+1$ if $L_1 \neq L_2$. We also give a geometric characterization of the standard Clifford index in terms of which secant varieties of $C$ are determinantal in the bicanonical embedding. The relationship with Koszul cohomology and Green's conjecture is also discussed.
We study the role of rotating sunspots in relation to the evolution of various physical parameters characterizing the non-potentiality of the active region NOAA 11158 and its eruptive events using the magnetic field data from the Helioseismic and Magnetic Imager (HMI) and multi-wavelength observations from the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO). From the evolutionary study of HMI intensity and AIA channels, it is observed that the AR consists of two major rotating sunspots one connected to flare-prone region and another with CME. The constructed space-time intensity maps reveal that the sunspots exhibited peak rotation rates coinciding with the occurrence of the major eruptive events. Further, temporal profiles of twist parameters, viz., average shear angle, $\alpha_{\rm av}$, $\alpha_{\rm best}$, derived from HMI vector magnetograms and the rate of helicity injection, obtained from the horizontal flux motions of HMI line-of-sight magnetograms, corresponded well with the rotational profile of the sunspot in CME-prone region, giving predominant evidence of rotational motion to cause magnetic non-potentiality. Moreover, mean value of free-energy from the Virial theorem calculated at the photospheric level shows clear step down decrease at the on set time of the flares revealing unambiguous evidence of energy release, intermittently that is stored by flux emergence and/or motions in pre-flare phases. Additionally, distribution of helicity injection is homogeneous in CME prone region while it is not and often changes sign in flare-prone region. This study provides clear picture that both proper and rotational motions of the observed fluxes played significant role to enhance the magnetic non-potentiality of the AR, leading to favorable conditions for the observed transient activity.
We introduce version 2.0 of $Z'$-explorer, a software tool which provides a simple, fast and user-friendly test of models with an extra $U(1)$ gauge boson ($Z'$) against experimental LHC results. The main novelty of the second version is the inclusion of missing energy searches, as the first version only included final states into SM particles. Hence $Z'$-explorer 2.0 is able to test dark matter models where the $Z'$ acts as an s-channel mediator between the Standard Model and the dark sector, a widespread benchmark employed by the ATLAS and CMS experimental collaborations. To this end, we perform here the first public reinterpretation of the most recent ATLAS mono-jet search with 139 fb$^{-1}$. In addition, the corresponding searches in the visible final states have also been updated. We illustrate the power of our code by re-obtaining public plots, and also showing novel results. In particular, we study the cases where the $Z'$ couples strongly to top quarks (top-philic), where dark matter couples with a mixture of vector and axial-vector couplings, and also perform a scan in the parameter space of a string inspired St\"uckelberg model. $Z'$-explorer 2.0 is publicly available on GitHub.
We discuss the possibility of measuring generalized parton distributions in exclusive electroproduction of mesons off the nucleon and estimate the uncertainty from perturbatively induced higher-twist corrections. We find that, while the magnitude of the cross section changes significantly taking into account twist-four contributions modeled via renormalons, the transverse spin asymmetry is weakly sensitive to them and displays the precocious scaling.
For an affine variety $S$ we consider the ring $AK(S),$ which is the intersection of the rings of constants of all locally-nilpotent derivations of the ring $\Cal {O}(S).$ We show that $AK(S\times\Bbb {C}^n)=AK(S)$ for a smooth affine surface $S$ with $H^2(S,\Bbb {Z})=\{0\}.$
We study the existence, uniqueness and regularity of solutions of the equation $f_t = \Delta_p f = \text{div} (|Df|^{p-2} Df)$ under over-determined boundary conditions $f = 0$ and $|Df| = 1$. We show that if the initial data is concave and Lipschitz with a bounded and convex support, then the problem admits a unique solution which exists until it vanishes identically. Furthermore, the free-boundary of the support of $f$ is smooth for all positive time.
The central part of the globular cluster NGC 288 was surveyed in a search for short-period variable stars. We obtained the V-band light curves for 4 SX Phe stars and 2 RR Lyrae variables, five of which are new discoveries. All SX Phe stars belong to blue stragglers. We present a color-magnitude diagram including stars from the tip of red giant branch to the level of the main-sequence turnoff. Three likely hot subdwarfs were located on the extension of the blue horizontal branch of the cluster.
We give conditions on the rational numbers a,b,c which imply that there are infinitely many triples (x,y,z) of rational numbers such that x+y+z=a+b+c and xyz=abc. We do the same for the equations x+y+z=a+b+c and x^3+y^3+z^3=a^3+b^3+c^3. These results rely on exhibiting families of positive-rank elliptic curves.
We report far-infrared optical properties of YbRh$_{2}$Si$_{2}$ for photon energies down to 2 meV and temperatures 0.4 -- 300 K. In the coherent heavy quasiparticle state, a linear dependence of the low-energy scattering rate on both temperature and photon energy was found. We relate this distinct dynamical behavior different from that of Fermi liquid materials to the non-Fermi liquid nature of YbRh$_{2}$Si$_{2}$ which is due to its close vicinity to an antiferromagnetic quantum critical point.
Dust is commonly present in weakly radio emitting star-forming galaxies and this dust may obscure the signatures of accreting black holes in these objects. We aim to uncover weak active galactic nuclei, AGN, in the faint radio source population by means of deep high-resolution radio observations. VLBI observations with a world-wide array at unparallelled sensitivity are carried out to assess the nature of the faint radio source population in the Hubble Deep Field North and its flanking fields. Images of twelve compact, AGN-driven radio sources are presented. These represent roughly one quarter of the detectable faint radio source sample. Most, but not all of these low power AGN have X-ray detections. The majority of the faint radio source population must be star-forming galaxies. Faint AGN occur in a variety of (distant) host galaxies, and these are often accompanied by a dust-obscured starburst. Deep, high-resolution VLBI is a unique, powerful technique to assess the occurrence of faint AGN.
After a brief outline of general aspects of conformal field theories in coordinate space, in a first part we review the solution of the conformal constraints of three- and four-point functions in momentum space in dimensions $d\geq 2$, in the form of conformal Ward identities (CWI's). We center our discussion on the analysis of correlators containing stress-energy tensors $(T)$, conserved currents $(J)$, and scalar operators $(O)$. For scalar four-point functions, we briefly discuss our method for determining the dual conformal solutions of such equations, identified only by the CWI's, and related to the conformal Yangian symmetry, introduced by us in previous work. In correlation functions with $T$ tensors, evaluated around a flat spacetime, the conformal anomaly is characterized by the (non-local) exchange of massless poles in specific form factors, a signature that has been investigated both in free field theory and non-perturbatively, by solving the conformal constraints. We discuss the anomaly effective action, and illustrate the derivation of the CWI's directly from its path integral definition and its Weyl symmetry, which is alternative to the standard operatorial approach used in conformal field theories in flat space. For two- and three-point functions, we elaborate on the matching of these types of correlators to free-field theories. Perturbative realizations of CFTs at one-loop provide the simplest expressions of the general solutions identified by the CWI's, for generic operators $T$, $J$, and scalars of specific scaling dimensions, by an appropriate choice of their field content. In a technical appendix we offer details on the reconstruction of the $TTO$ and $TTT$ correlators in the approach of Bzowski, McFadden and Skenderis, and specifically on the secondary Ward identities of the method, in order to establish a complete match with the perturbative description.
An electron spin resonance (ESR) and photoluminescence signal is observed in the as grown single crystal of stishovite indicating the presence of defects in the non-irradiated sample. Photoluminescence of the as received stishovite single crystals exhibits two main bands - a blue at 3 eV and an UV at 4.75 eV. Luminescence is excited in the range of optical transparency of stishovite (below 8.75 eV) and, therefore, is ascribed to defects. A wide range of decay kinetics under a pulsed excitation is observed. For the blue band besides the exponential decay with a time constant of about 18 {\mu}s an additional ms component is revealed. For the UV band besides the fast component with a time constant of 1-3 ns a component with a decay in tens {\mu}s is obtained. The main components (18 {\mu}s and 1-3 ns) possess a typical intra-center transition intensity thermal quenching. The effect of the additional slow component is related to the presence of OH groups and/or carbon molecular defects modifying the luminescence center. The additional slow components exhibit wave-like thermal dependences. Photo-thermally stimulated creation-destruction of complex comprising host defect - interstitial modifiers explains slow luminescence wave-like thermal dependences.