ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this work an exactly solvable model of N two-level systems interacting with a single bosonic dephasing reservoir is considered to unravel the role played by collective non-Markovian dephasing. We show that phase estimation with entangled states for this model can exceed the standard quantum limit and demonstrate Heisenberg scaling with the number of atoms for an arbitrary temperature. For a certain class of reservoir densities of states decoherence can be suppressed in the limit of large number of atoms and the Heisenberg limit can be restored for arbitrary interrogation times. We identify the second class of densities when the Heisenberg scaling can be restored for any finite interrogation time. We also find the third class of densities when the standard quantum limit can be exceeded only on the initial stage of dynamics in the Zeno-regime.
We review the reasons why one might choose to seriously re-examine the traditional approach to nuclear theory where nucleons are treated as immutable. This examination leads us to argue that the modification of the structure of the nucleon when immersed in a nuclear medium is fundamental to how atomic nuclei are built. Consistent with this approach we suggest key experiments which should tell us unambiguously whether there is such a change in the structure of a bound nucleon. We also briefly report on extremely promising recent calculations of the structure of nuclei across the periodic table based upon this idea.
We present a method for measuring the masses of galaxy clusters using the imprint of their gravitational lensing signal on the cosmic microwave background (CMB) temperature anisotropies. The method first reconstructs the projected gravitational potential with a quadratic estimator and then applies a matched filter to extract cluster mass. The approach is well-suited for statistical analyses that bin clusters according to other mass proxies. We find that current experiments, such as Planck, the South Pole Telescope and the Atacama Cosmology Telescope, can practically implement such a statistical methodology, and that future experiments will reach sensitivities sufficient for individual measurements of massive systems. As illustration, we use simulations of Planck observations to demonstrate that it is possible to constrain the mass scale of a set of 62 massive clusters with prior information from X-ray observations, similar to the published Planck ESZ-XMM sample. We examine the effect of the thermal (tSZ) and kinetic (kSZ) Sunyaev-Zeldovich (SZ) signals, finding that the impact of the kSZ remains small in this context. The stronger tSZ signal, however, must be actively removed from the CMB maps by component separation techniques prior to reconstruction of the gravitational potential. Our study of two such methods highlights the importance of broad frequency coverage for this purpose. A companion paper presents application to the Planck data on the ESZ-XMM sample.
We find that the polarization field, B_chi, obtained by scaling the weak-parallel-field magnetoresistance at different electron densities in a dilute two-dimensional electron system in (111) silicon, corresponds to the spin susceptibility that grows strongly at low densities. The polarization field, B_sat, determined by resistance saturation, turns out to deviate to lower values than B_chi with increasing electron density, which can be explained by filling of the upper electron subbands in the fully spin-polarized regime.
We use a 3D Monte Carlo radiative transfer code to study the polarimetric and photometric variability from stationary corotating interaction regions (CIR) in the wind of massive stars. Our CIRs are approximated by Archimedean spirals of higher (or lower) density formed in a spherical wind originating from the star and we also made allowance for a bright gaussian spot at the base of the CIR. Comparing results from our code to previous analytical calculations in the optically thin case, we find differences which we attribute mainly to a better estimation of the total unpolarized flux reaching the observer. In the optically thick case, the differences with the analytical calculations are much larger, as multiple scattering introduces extra complexities including occultation effects. The addition of a gaussian spot does not alter the shape of the polarization curve significantly but does create a small excess in polarization. On the other hand, the effect can be larger on the light curve and can become dominant over the resulting CIR, depending on the spot parameters and density of the wind.
We consider the best constant in the Rellich-Hardy inequality (with a radial power weight) for curl-free vector fields on $\mathbb{R}^N$, originally found by Tertikas-Zographopoulos \cite{Tertikas-Z} for unconstrained fields. This inequality is considered as an intermediate between Hardy-Leray and Rellich-Leray inequalities. Under the curl-free condition, we compute the new explicit best constant in the inequality and prove the non-attainability of the constant. This paper is a sequel to \cite{CF_MAAN,CF_Re}.
A subset of type Ic supernovae (SNe Ic), broad-lined SNe Ic (SNe Ic-bl), show unusually high kinetic energies ($\sim 10^{52}$ erg) which cannot be explained by the energy supplied by neutrinos alone. Many SNe Ic-bl have been observed in coincidence with long gamma-ray bursts (GRBs) which suggests a connection between SNe and GRBs. A small fraction of core-collapse supernovae (CCSNe) form a rapidly-rotating and strongly-magnetized protoneutron star (PNS), a proto-magnetar. Jets from such magnetars can provide the high kinetic energies observed in SNe Ic-bl and also provide the connection to GRBs. In this work we use the jetted outflow produced in a 3D CCSN simulation from a consistently formed proto-magnetar as the central engine for full-star explosion simulations. We extract a range of central engine parameters and find that the extracted engine energy is in the range of $6.231 \times 10^{51}-1.725 \times 10^{52}$ erg, the engine time-scale in the range of $0.479-1.159$ s and the engine half-opening angle in the range of $\sim 9-19^{\circ}$. Using these as central engines, we perform 2D special-relativistic (SR) hydrodynamic (HD) and radiation transfer simulations to calculate the corresponding light curves and spectra. We find that these central engine parameters successfully produce SNe Ic-bl which demonstrates that jets from proto-magnetars can be viable engines for SNe Ic-bl. We also find that only the central engines with smaller opening angles ($\sim 10^{\circ}$) form a GRB implying that GRB formation is likely associated with narrower jet outflows and Ic-bl's without GRBs may be associated with wider outflows.
The Kondo lattice system CeZn_{0.66}Sb_{2} is studied by the electrical resistivity and ac magnetic susceptibility measurements at several pressures. At P=0 kbar, ferromagnetic and antiferromagnetic transitions appear at 3.6 and 0.8 K, respectively. The electrical resistivity at T_N dramatically changes from the Fisher-Langer type (ferromagnetic like) to the Suzaki-Mori type near 17 kbar, i.e., from a positive divergence to a negative divergence in the temperature derivative of the resistivity. The pressure-induced SM type anomaly, which shows thermal hysteresis, is easily suppressed by small magnetic field (1.9 kOe for 19.8 kbar), indicating a weakly first-order nature of the transition. By subtracting a low-pressure data set, we directly compare the resistivity anomaly with the SM theory without any assumption on backgrounds, where the negative divergence in d\rho/dT is ascribed to enhanced critical fluctuations in the presence of superzone gaps.
This paper presents deformable templates as a tool for segmentation and localization of biological structures in medical images. Structures are represented by a prototype template, combined with a parametric warp mapping used to deform the original shape. The localization procedure is achieved using a multi-stage, multi-resolution algorithm de-signed to reduce computational complexity and time. The algorithm initially identifies regions in the image most likely to contain the desired objects and then examines these regions at progressively increasing resolutions. The final stage of the algorithm involves warping the prototype template to match the localized objects. The algorithm is presented along with the results of four example applications using MRI, x-ray and ultrasound images.
We take an application of the Kernel Lemma by Kostochka and Yancey to its logical conclusion. The consequence is a sort of magical way to draw conclusions about list coloring (and online list coloring) just from the existence of an independent set incident to many edges. We use this to prove an Ore-degree version of Brooks' Theorem for online list-coloring. The Ore-degree of an edge $xy$ in a graph $G$ is $\theta(xy) = d_G(x) + d_G(y)$. The Ore-degree of $G$ is $\theta(G) = \max_{xy\in E(G)}\theta(xy)$. We show that every graph with $\theta\ge18$ and $\omega\le\frac{\theta}{2}$ is online $\left\lfloor \frac{\theta}{2}\right\rfloor $-choosable. In addition, we prove an upper bound for online list-coloring triangle-free graphs: $\chi_{OL}\le\Delta+1-\lfloor\frac{1}{4}\lg(\Delta)\rfloor$. Finally, we characterize Gallai trees as the connected graphs $G$ with no independent set incident to at least $|G|$ edges.
Ultraluminous X-ray (ULX) pulsars are a new class of object powered by apparent super-critical accretion onto magnetized neutron stars. Three sources in this class identified so far; M82 X-2, NGC 5907 ULX-1 and NGC 7793 P13, have been found to have two properties in common; $\sim1$-s spin periods, and for NGC 5907 ULX-1 and NGC 7793 P13 periodic X-ray flux modulations on timescales of $\sim60-80$ days. M82 X-2 resides in a crowded field that includes the ULX M82 X-1 separated from X-2 by 5", as well as other bright point sources. A 60-day modulation has been observed from the region but the origin has been difficult to identify; both M82 X-1 and X-2 have been suggested as the source. In this paper we present the analysis of a systematic monitoring campaign by Chandra, the only X-ray telescope capable of resolving the crowded field. From a simple Lomb-Scargle periodogram analysis and a more sophisticated Gaussian Process analysis we find that only X-2 exhibits a periodic signal around 60 days supporting previous claims that it is the origin. We also construct a phase-averaged flux profile of the modulations from higher cadence Swift/XRT data and find that the flux variations in the Chandra data are fully consistent with the flux profile. Since the orbit of the neutron star and its companion is known to be 2.5 days, the $\sim60$-day period must be super-orbital in origin. The flux of the modulations varies by a factor of $\sim$100 from minimum to maximum, with no evidence for spectral variations, making the origin difficult to explain.
"All misfortune of man comes from the fact that he does not stay peacefully in his room", has once asserted Blaise Pascal. In the present paper we evoke this statement as the "Pascal principle" in regard to the problem of survival of an "A" particle, which performs a lattice random walk in presence of a concentration of randomly moving traps "B", and gets annihilated upon encounters with any of them. We prove here that at sufficiently large times for both perfect and imperfect trapping reactions, for arbitrary spatial dimension "d" and for a rather general class of random walks, the "A" particle survival probability is less than or equal to the survival probability of an immobile target in the presence of randomly moving traps.
Let $Z = (Z_t)_{t\in[0,\infty)}$ be an ergodic Markov process and, for every $n\in\mathbb{N}$, let $Z^n = (Z_{n^2 t})_{t\in[0,\infty)}$ drive a process $X^n$. Classical results show under suitable conditions that the sequence of non-Markovian processes $(X^n)_{n\in\mathbb{N}}$ converges to a Markov process and give its infinitesimal characteristics. Here, we consider a general sequence $(Z^n)_{n\in\mathbb{N}}$. Using a general result on stochastic averaging from [Kur92], we derive conditions which ensure that the sequence $(X^n)_{n\in\mathbb{N}}$ converges as in the classical case. As an application, we consider the diffusion limit of a Wright-Fisher model with fluctuating selection.
Berstel proved that the Arshon sequence cannot be obtained by iteration of a morphism. An alternative proof of this fact is given here. The $\sigma$-sequence was constructed by Evdokimov in order to construct chains of maximal length in the n-dimensional unit cube. It turns out that the $\sigma$-sequence has a close connection to the Dragon curve. We prove that the $\sigma$-sequence can not be defined by iteration of a morphism.
In this master thesis I discuss how the weak three-body decay B^+ --> pi^- pi^+ K^+ is related to the strong interactions between the final-state particles. Current issues in hadron spectroscopy define a region of interest in a Dalitz plot of this decay. This region is roughly characterized by energies from 0 to 1.6 GeV of the pi^- pi^+ and the pi^- K^+ system, and energies from 3 to 5 GeV of the pi^+ K^+ system. Therefore I propose to use for the former two systems elastic unitarity (Watson's theorem) as an approximate ansatz, and a non-vanishing forward-peaked amplitude for the latter system. I introduce most basic concepts in detail with the intention that this be of use to non-experts interested in this topic.
We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we generalize known results on the Wong-Zakai type approximations.
The semi-classical conductance of a two-dimensional electron gas is calculated in the presence of a one-dimensional modulated magnetic field with zero average. In the limit of small magnetic field amplitudes (B) the contribution of the magnetic modulation to the magnetoresistance increases as $B^{3/2}$ in the diffusive limit, while the increase is linear in $B$ in the ballistic regime. Temperature does not influence the power law behavior but it decreases the prefactor of this functional behavior.
Numerous efforts have been devoted to reveal exotic semimetallic phases with topologically non-trivial bulk and/or surface states in materials with strong spin-orbit coupling. In particular, semimetals with nodal line Fermi surface (FS) exhibit novel properties, and searching for candidate materials becomes an interesting research direction. Here we provide a generic condition for a four-fold degenerate nodal line FS in non-symmorphic crystals with inversion and time-reversal symmetry (TRS). When there are two glide planes or screw axes perpendicular to each other, a pair of Bloch bands related by non-symmorphic symmetry become degenerate on a Brillouin Zone (BZ) boundary. There are two pairs of such bands, and they disperse in a way that the partners of two pairs are exchanged on other BZ boundaries. This enforces a nodal line FS on a BZ boundary plane protected by non-symmorphic symmetries. When TRS is broken, four-fold degenerate Dirac points or Weyl ring FS could occur depending on a direction of the magnetic field. On a certain surface double helical surface states exist, which become double Ferm arcs as TRS is broken.
In a relativistic Brueckner-Hartree-Fock calculation we include explicit negative-energy states in the two-body propagator. This is achieved by using the Gross spectator-equation, modified by medium effects. Qualitatively our results compare well with other RBHF calculations. In some details significant differences occur, e.g, our equation of state is stiffer and the momentum dependence of the self-energy components is stronger than found in a reference calculation without intermediate negative energy states.
To enhance our knowledge of the characteristics and distribution of the circumstellar dust associated with the individual components of the young hierarchical triple system T Tau, observations in the N-band with MIDI at the VLTI were performed. Our study is based on both the interferometric and the spectrophotometric measurements and is supplemented by new visual and infrared photometry. Also, the phases were investigated to determine the dominating mid-infrared source in the close southern binary. The data were fit with the help of a sophisticated physical disc model. This model utilises the radiative transfer code MC3D that is based on the Monte-Carlo method. Extended mid-infrared emission is found around all three components of the system. Simultaneous fits to the photometric and interferometric data confirm the picture of an almost face-on circumstellar disc around T Tau N. Towards this star, the silicate band is seen in emission. This emission feature is used to model the dust content of the circumstellar disc. Clear signs of dust processing are found. Towards T Tau S, the silicate band is seen in absorption. This absorption is strongly pronounced towards the infrared companion T Tau Sa as can be seen from the first individual N-band spectra for the two southern components. Our fits support the previous suggestion that an almost edge-on disc is present around T Tau Sa. This disc is thus misaligned with respect to the circumstellar disc around T Tau N. The interferometric data indicate that the disc around T Tau Sa is oriented in the north-south direction, which favours this source as launching site for the east-western jet. We further determine from the interferometric data the relative positions of the components of the southern binary.
The generating functionals for the local composite operators, $\Phi^2(x)$ and $\Phi^4(x)$, are used to study excitations in the scalar quantum field theory with $\lambda \Phi^4$ interaction. The effective action for the composite operators is obtained as a series in the Planck constant $\hbar$, and the two- and four-particle propagators are derived. The numerical results are studied in the space-time of one dimension, when the theory is equivalent to the quantum mechanics of an anharmonic oscillator. The effective potential and the poles of the composite propagators are obtained as series in $\hbar$, with effective mass and coupling determined by non-perturbative gap equations. This provides a systematic approximation method for the ground state energy, and for the second and fourth excitations. The results show quick convergence to the exact values, better than that obtained without including the operator $\Phi^4$.
A book embedding of a graph consists of an embedding of its vertices along the spine of a book, and an embedding of its edges on the pages such that edges embedded on the same page do not intersect. The pagenumber is the minimum number of pages in which the graph $G$ can be embedded. The main purpose of this paper is to study the book embedding of the complete expansion graph. This is the first work about it, and some exact pagenumbers of the complete expansion graphs of some special graphs are obtained.
We present the experimental phase diagram of LiHo$_x$Er$_{1-x}$F$_4$, a dilution series of dipolar-coupled model magnets.The phase diagram was determined using a combination of AC susceptibility and neutron scattering. Three unique phases in addition to the Ising ferromagnet LiHoF$_4$ and the XY anti-ferromagnet LiErF$_4$ have been identified. Below $x=0.86$ an embedded spin-glass phase is observed, where a spin-glass exists within the ferromagnetic structure. Below $x=0.57$ an Ising spin-glass is observed consisting of frozen needle-like clusters. For $x \sim 0.3 - 0.1$ an antiferromagnetically coupled spin-glass occurs. A reduction of $T_C(x)$ for the ferromagnet is observed which disobeys the mean-field predictions that worked for LiHo$_x$Y$_{1-x}$F$_4$.
Early-type stars generally tend to be fast rotators. In these stars, mode identification is very challenging as the effects of rotation are not well known. We consider here the example of $\alpha$ Ophiuchi, for which dozens of oscillation frequencies have been measured. We model the star using the two-dimensional structure code ESTER, and we compute both adiabatic and non-adiabatic oscillations using the TOP code. Both calculations yield very complex spectra, and we used various diagnostic tools to try and identify the observed pulsations. While we have not reached a satisfactory mode-to-mode identification, this paper presents promising early results.
We present an analysis of the galaxy distribution surrounding 15 of the most luminous (>10^{14} L_sun; M_1450 ~ -30) QSOs in the sky with z~2.7. Our data are drawn from the Keck Baryonic Structure Survey (KBSS). In this work, we use the positions and spectroscopic redshifts of 1558 galaxies that lie within ~3', (4.2 h^{-1} comoving Mpc; cMpc) of the hyperluminous QSO (HLQSO) sightline in one of 15 independent survey fields, together with new measurements of the HLQSO systemic redshifts. We measure the galaxy-HLQSO cross-correlation function, the galaxy-galaxy autocorrelation function, and the characteristic scale of galaxy overdensities surrounding the sites of exceedingly rare, extremely rapid, black hole accretion. On average, the HLQSOs lie within significant galaxy overdensities, characterized by a velocity dispersion sigma_v ~ 200 km s^{-1} and a transverse angular scale of ~25", (~200 physical kpc). We argue that such scales are expected for small groups with log(M_h/M_sun)~13. The galaxy-HLQSO cross-correlation function has a best-fit correlation length r_0_GQ = (7.3 \pm 1.3) h^{-1} cMpc, while the galaxy autocorrelation measured from the spectroscopic galaxy sample in the same fields has r_0_GG = (6.0 \pm 0.5) h^{-1} cMpc. Based on a comparison with simulations evaluated at z ~ 2.6, these values imply that a typical galaxy lives in a host halo with log(M_h/M_sun) = 11.9\pm0.1, while HLQSOs inhabit host halos of log(M_h/M_sun) = 12.3\pm0.5. In spite of the extremely large black hole masses implied by their observed luminosities [log(M_BH/M_sun) > 9.7], it appears that HLQSOs do not require environments very different from their much less luminous QSO counterparts. Evidently, the exceedingly low space density of HLQSOs (< 10^{-9} cMpc^{-3}) results from a one-in-a-million event on scales << 1 Mpc, and not from being hosted by rare dark matter halos.
We review a series of works where the fundamental master equation is used to develop a microscopical description of evolution of non-equilibrium atomic distributions in alloys. We describe exact equations for temporal evolution of local concentrations and their correlators as well as approximate methods to treat these equations, such as the kinetic mean-field and the kinetic cluster methods. We also describe an application of these methods to studies of kinetics of L1_0 type orderings in FCC alloys which reveal a number of peculiar microstructural effects, many of them agreeing well with experimental observations.
We describe special supersymmetric gauge theories in three, five, seven and nine dimensions, whose compactification on two-, four-, six- and eight-folds produces a supersymmetric quantum mechanics on moduli spaces of holomorphic bundles and/or solutions to the analogues of instanton equations in higher dimensions. The theories may occur on the worldvolumes of D-branes wrapping manifolds of special holonomy. We also discuss the theories with matter.
Shadowing and antishadowing of the electromagnetic nuclear structure functions are produced by the coherence of multiscattering quark nuclear processes. This picture leads to substantially different antishadowing for charged and neutral current processes, particularly in anti-neutrino reactions, thus affecting the extraction of the weak-mixing angle $\sin^2\theta_W$.