ShantanuT01/DACTYL-Pretraining huggingface dataset:
Complementarity relations for wave-particle duality are saturated only for pure, single-quanton, quantum states. For a completely incoherent state, it is known that wave and particle quantifiers can reach zero, and hence no information about the wave and particle aspects of the system can be obtained. This means that the information is being shared with another systems, and quantum correlations can be seen as responsible for the loss of purity of the quanton, provided that the quanton is part of a multipartite pure quantum system. In this paper, by exploring the purity of bi- and tri-partite pure quantum states, we show that it is possible to obtain complete complementarity relations. This procedure allows us to create a general framework for obtaining complete complementarity relations for a subsystem that belongs to an arbitrary multi-partite quantum system in a pure state. Besides, by some simple examples, we show that if the predictability measure is changed then the correlation measure must also be changed in order to obtain complete complementarity relations for pure cases.
The form factors of the semileptonic $B_{q}\to D_{q}(J^{P}=0^{-})\ell\nu$ with $q=s, u, d$ transitions are calculated in the framework of three point QCD sum rules. Using the $q^2$ dependencies of the relevant form factors, the total decay width and the branching ratio for these decays are also evaluated. A comparison of our results for the form factors of $B\to D\ell\nu$ with the lattice QCD predictions within heavy quark effective theory and zero recoil limit is presented. Our results of the branching ratio are in good agreement with the constituent quark meson model for ($q=s, u, d$) and experiment for ($q= u, d$). The result of branching ratio for $B_{s}\to D_{s}(1968)\ell\nu$ indicates that this transition can also be detected at LHC in the near future.
Recently proposed exceptional field theories (EFTs) making manifest the duality $E_{n(n)}$ symmetry, first observed as nonlinearly realized symmetries of the maximal $d=3,4,...,9$ supergravity ($n=11-d$) and containing 11D and type IIB supergravity as sectors, were formulated in enlarged spacetimes. In the case of $E_{7(7)}$ EFT such an enlarged spacetime can be identified with the bosonic body of the $d=4$ central charge superspace $\Sigma^{(60|32)}$, the ${\cal N}=8$ $d=4$ superspace completed by 56 additional bosonic coordinates associated to central charges of the maximal $d=4$ supersymmetry algebra.   In this paper we show how the hypothesis on the relation of all the known $E_{n(n)}$ EFTs, including $n=8$, with supersymmetry leads to the conjecture on existence of 11D exceptional field theory living in 11D tensorial central charge superspace $\Sigma^{(528|32)}$ and underlying all the $E_{n(n)}$ EFTs with $n=2,...,8$, and probably the double field theory (DFT). We conjecture the possible form of the section conditions of such an 11D EFT and show that quite generic solutions of these can be generated by superparticle models the ground states of which preserve from one half to all but one supersymmetry. The properties of these superparticle models are briefly discussed. We argue that, upon quantization, their quantum states should describe free massless non-conformal higher spin fields in D=11.   We also discuss some relevant representations of the M-theory superalgebra which, in the present context, describes supersymmetry of the 11D EFT.
We study the heat transport due to phonons in nanomechanical structures using a phase space representation of non-equilibrium Green's functions. This representation accounts for the atomic degrees of freedom making it particularly suited for the description of small (molecular) junctions systems. We show that for the steady state limit our formalism correctly recovers the heuristic Landauer-like heat conductance for a quantum coherent molecular system coupled to thermal reservoirs. We find general expressions for the non-stationary heat current due to an external periodic drive. In both cases we discuss the quantum thermodynamic properties of the systems. We apply our formalism to the case of a diatomic molecular junction.
The temporal magnetic correlations of the triangular lattice antiferromagnet NiGa$_2$S$_4$ are examined through thirteen decades ($10^{-13}-1$~sec) using ultra-high-resolution inelastic neutron scattering, muon spin relaxation, AC and nonlinear susceptibility measurements. Unlike the short-ranged {\it spatial} correlations, the temperature dependence of the {\it temporal} correlations show distinct anomalies. The spin fluctuation rate decreases precipitously upon cooling towards $T^{\ast}=8.5$~K, but fluctuations on the microsecond time scale then persist in an anomalous dynamical regime for 4 K $<T\le T^{\ast}$. As this time scale exceeds that of single site dynamics by six orders of magnitude, these fluctuations bear evidence of emergent degrees of freedom within the short-range correlated incommensurate state of NiGa$_2$S$_4$.
The present-day state of the Milky Way disk can tell us much about the history of our Galaxy and provide insights into its formation. We have constructed a high-precision catalogue of disk stars using data from the Sloan Digital Sky Survey (SDSS) and use these stars to probe the heating history as well as investigating the detailed phase-space distribution. We also show how this sample can be used to probe the global properties of the Milky Way disk, employing the Jeans equations to provide a simple model of the potential close to the disk. Our model is in excellent agreement with others in the literature and provides an indication that the disk, rather than the halo, dominates the circular speed at the solar neighborhood. The work presented in these proceedings has been published as "Slicing and dicing the Milky Way disc in SDSS" (Smith et al. 2012).
Deformable image registration is a very important field of research in medical imaging. Recently multiple deep learning approaches were published in this area showing promising results. However, drawbacks of deep learning methods are the need for a large amount of training datasets and their inability to register unseen images different from the training datasets. One shot learning comes without the need of large training datasets and has already been proven to be applicable to 3D data. In this work we present a one shot registration approach for periodic motion tracking in 3D and 4D datasets. When applied to 3D dataset the algorithm calculates the inverse of a registration vector field simultaneously. For registration we employed a U-Net combined with a coarse to fine approach and a differential spatial transformer module. The algorithm was thoroughly tested with multiple 4D and 3D datasets publicly available. The results show that the presented approach is able to track periodic motion and to yield a competitive registration accuracy. Possible applications are the use as a stand-alone algorithm for 3D and 4D motion tracking or in the beginning of studies until enough datasets for a separate training phase are available.
In this brief report, we attention to the system of two qubits modeled by Heisenberg XXZ chain with the Dzyaloshinskii Moriya interaction. The system exposed to bosonic baths with the Cauchy Lorentz distribution of frequency. We've got a new formula to calculate the specific heat of open systems using density and found that the specific heat at low temperatures can be negative. We observed that when the state of system is entangle, in contradiction with the third law of thermodynamics, the specific heat is diverge when the temperature goes to zero. The speed of divergence is depend to the amount of entanglement. These results may be useful to design solid quantum gate and quantum memories.
We study rationality properties of smooth complete intersections of three quadrics in $\mathbb{P}^7$. We exhibit a smooth family of such intersections with both rational and non-rational fibers.
Recently, Andrews, Chan, Kim and Osburn introduced a $q$-series $h(q)$ for the study of the first positive rank and crank moments for overpartitions. They conjectured that for all integers $m \geq 3$, \begin{equation*}\label{hqcon} \frac{1}{(q)_{\infty}} (h(q) - m h(q^{m})) \end{equation*} has positive power series coefficients for all powers of $q$. Byungchan Kim, Eunmi Kim and Jeehyeon Seo provided a combinatorial interpretation and proved it is asymptotically true by circle method. In this note, we show this conjecture is true if $m$ is any positive power of $2$, and we show that in order to prove this conjecture, it is only to prove it for all primes $m$. Moreover we give a stronger conjecture. Our method is very simple and completely different from that of Kim et al.
We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial $f$ defining a plane branch $(C,0)$, in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non equisingular) deformations of a plane branch $(C,0)$ supported on certain monomials in the approximate roots of $f$. As a consequence we find out a Kouchnirenko type formula for the Milnor number $(C,0)$. Our results provide a geometrical approach to Abhyankar's straight line conditions and its consequences. As an application we give an equisingularity criterion for a family of plane curves to be equisingular to a plane branch and we express it algorithmically.
We present the first metallicity distribution functions of the old field populations in the Magellanic Clouds. Our metallicities are based on the Fourier decomposition of Type ab RR Lyrae light curves from the Optical Gravitational Lensing Experiment (OGLE-III). On the metallicity scale of Zinn & West; we find a mean metallicity of [Fe/H] = -1.50 +/- 0.24 dex based on 16776 RR Lyrae stars in the Large Magellanic Cloud (LMC). For the Small Magellanic Cloud (SMC) we obtain -1.70 +/- 0.27 dex based on 1831 RR Lyrae stars. These uncertainties represent the intrinsic spread in the population rather than the standard deviation of the mean. Our results are in good agreement with the few existing spectroscopic metallicity determinations for LMC RR Lyrae stars from the literature. For both the LMC and the SMC the metallicity spread exceeds 1 dex in [Fe/H]. The distribution of metallicities in both Clouds is very uniform, and no significant metallicity gradient is detectable. We also do not find any pronounced populations of extremely metal-poor RR Lyrae candidates with metallicities well below -2 dex, although we need to caution that the photometric method used may overestimate the metallicities of metal-deficient stars. Moreover, because of stellar evolutionary effects one does not expect to observe many RR Lyrae stars among very metal-poor horizontal branch stars. We suggest that the Magellanic Clouds experienced fairly rapid and efficient early enrichment involving pre-enriched gas as well as possibly gas infall, while metal loss through outflows does not seem to have played a significant role. Moreover we suggest that the differences in the metallicities of the old population of LMC and SMC make an origin from a single, common progenitor unlikely, unless the separation happened very early on.
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field theories are derived. Several coordinates require as a novel feature the introduction of deformed plane waves.
Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components of the original random structure. In this paper we build up on previous work and derive results in the multivariate case and in situations where regular variation is not restricted to one particular direction or quadrant.
There exist a range of exciting scientific opportunities for Big Bang Nucleosynthesis (BBN) in the coming decade. BBN, a key particle astrophysics "tool" for decades, is poised to take on new capabilities to probe beyond standard model (BSM) physics. This development is being driven by experimental determination of neutrino properties, new nuclear reaction experiments, advancing supercomputing/simulation capabilities, the prospect of high-precision next-generation cosmic microwave background (CMB) observations, and the advent of 30m class telescopes.
The efficiency of recent star formation (SF) in galaxies increases with increasing projected distance from the centre of a cluster out to several times its virial radius (R_v). Using a complete sample of galaxies in 268 clusters from the SDSS DR4, we investigate how, at a given projected radius from the cluster centre, M* and SF properties of a galaxy depend on its absolute line-of-sight velocity in the cluster rest frame, |v_LOS|. We find that for R<0.5 R_v, the fraction of high mass non-BCG galaxies increases towards the centre for low |v_LOS|. At a given projected radius, the fraction of Galaxies with Ongoing or Recent (<1-3 Gyr) Efficient Star Formation (GORES, with EW(H_delta)>2 ang & D_4000>1.5) is slightly but significantly lower for low |v_LOS| galaxies than for their high velocity counterparts. We study these observational trends with the help of a dark matter (DM) cosmological simulation. We find that the backsplash particles account for at least one-third (half) of all particles at projected radii slightly greater than the virial radius and |v_LOS|<sigma_v. The deprojection of the GORES fraction leads to a saturated linear increase with radius. We fit simple models of the fraction of GORES as a function of class only or class and distance to the cluster centre (as in our deprojected fraction). In our best-fitting model GORES account for 13% of galaxies within the virial sphere, 11% of the virial population, 34% of the distant (for projected radii R<2 R_v) infall population and 19% of the backsplash galaxies. Given the 1-3 Gyr lookback time of our GORES indicators, these results suggest that SF in a galaxy is almost completely quenched in a single passage through the cluster.
We compare the gravitational collapse of homogeneous perfect fluid with various equations of state in the framework of General Relativity and in $R^2$ gravity. We make our calculations using dimensionless time with characteristic timescale $t_{g}\sim (G\rho)^{-1/2}$ where $\rho$ is a density of collapsing matter. The cases of matter, radiation and stiff matter are considered. We also account the possible existence of vacuum energy and its influence on gravitational collapse. In a case of $R^2$ gravity we have additional degree of freedom for initial conditions of collapse. For barotropic equation of state $p=w\rho$ the result depends from the value of parameter $w$: for $w>1/3$ the collapse occurs slowly in comparison with General Relativity while for $w<1/3$ we have opposite situation. Vacuum energy as expected slows down the rate of collapse and for some critical density gravitational contraction may change to expansion. It is interesting to note that for General Relativity such expansion is impossible. We also consider the collapse in the presence of so-called phantom energy. For description of phantom energy we use Lagrangian in the form $-X-V$ (where $X$ and $V$ are the kinetic and potential energy of the field respectively) and consider the corresponding Klein-Gordon equation for phantom scalar field.
Using hydrodynamical simulations of entire galactic discs similar to the Milky Way, reaching 4.6pc resolution, we study the origins of observed physical properties of giant molecular clouds (GMCs). We find that efficient stellar feedback is a necessary ingredient in order to develop a realistic interstellar medium (ISM), leading to molecular cloud masses, sizes, velocity dispersions and virial parameters in excellent agreement with Milky Way observations. GMC scaling relations observed in the Milky Way, such as the mass-size ($M$--$R$), velocity dispersion-size ($\sigma$--$R$), and the $\sigma$--$R\Sigma$ relations, are reproduced in a feedback driven ISM when observed in projection, with $M\propto R^{2.3}$ and $\sigma\propto R^{0.56}$. When analysed in 3D, GMC scaling relations steepen significantly, indicating potential limitations of our understanding of molecular cloud 3D structure from observations. Furthermore, we demonstrate how a GMC population's underlying distribution of virial parameters can strongly influence the scatter in derived scaling relations. Finally, we show that GMCs with nearly identical global properties exist in different evolutionary stages, where a majority of clouds being either gravitationally bound or expanding, but with a significant fraction being compressed by external ISM pressure, at all times.
We present proper motions for 21 bright main shell and 17 faint, higher-velocity, outer ejecta knots in the Cas A supernova remnant and use them to derive new estimates for the remnant's expansion center and age. Our study included 1951 - 1976 Palomar 5 m prime focus plates, 1988 - 1999 CCD images from the KPNO 4 m and MDM 2.4 m telescopes, and 1999 HST WFPC2 images. Measurable positions covered a 23 to 41 yr time span for most knots, with a few outer knots followed for almost 48 yr. We derive an expansion center of alpha = 23h 23m 27s.77 +- 0s.05, delta = 58d 48' 49".4 +- 0".4 (ICRS), with little difference between centers derived using outer or main shell knots. This position is 3.0 arcsec due north of that estimated by van den Bergh and Kamper (1983). It also lies 6.6 +- 1.5 arcsec almost due north (PA = 354 deg) of the remnant's recently-detected central X-ray point source, implying a transverse velocity for the X-ray point source of about 330 km/s at a distance of 3.4 kpc. Using the knots which lie out ahead of the remnant's forward blast wave, we estimate a knot convergent date of A.D. 1671.3 +- 0.9, assuming no deceleration. However, a deceleration of just approximately 1.6 km/(s yr) over a 300 yr time span would produce an explosion date A.D. 1680, consistent with the suspected sighting of the Cas A supernova by J. Flamsteed.
We consider a two-color P\'{o}lya urn in the case when a fixed number $S$ of balls is added at each step. Assume it is a large urn that is, the second eigenvalue $m$ of the replacement matrix satisfies $1/2<m/S\leq1$. After $n$ drawings, the composition vector has asymptotically a first deterministic term of order $n$ and a second random term of order $n^{m/S}$. The object of interest is the limit distribution of this random term. The method consists in embedding the discrete-time urn in continuous time, getting a two-type branching process. The dislocation equations associated with this process lead to a system of two differential equations satisfied by the Fourier transforms of the limit distributions. The resolution is carried out and it turns out that the Fourier transforms are explicitly related to Abelian integrals over the Fermat curve of degree $m$. The limit laws appear to constitute a new family of probability densities supported by the whole real line.
We establish a logarithmic stability inequality for the inverse problem of determining the non linear term, appearing in a semilinear BVP, from the corresponding Dirichlet-to-Neumann map (abbreviated to DtN map in the rest of this text). Our result can be seen as a stability inequality for an earlier uniqueness result by Isakov and Sylvester [Commun. Pure Appl. Math. 47 (1994), 1403-1410].
The Coulomb interaction between the two protons is included in the calculation of three-nucleon hadronic and electromagnetic reactions using screening and renormalization approach. Calculations are done using integral equations in momentum space. The reliability of the method is demonstrated. The Coulomb effect on observables is discussed.
In order to generate the baryon asymmetry of the Universe sufficiently strong CP violation is needed. It was therefore proposed that at finite temperature there might be spontaneous (transitional) CP violation within the bubble walls at the electroweak phase transition in supersymmetric models. We investigate this question in the MSSM.
For a left-compressed intersecting family \A contained in [n]^(r) and a set X contained in [n], let \A(X) = {A in \A : A intersect X is non-empty}. Borg asked: for which X is |\A(X)| maximised by taking \A to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r.
We describe square lattice spin liquids which break time-reversal symmetry, while preserving translational symmetry. The states are distinguished by the manner in which they transform under mirror symmetries. All the states have non-zero scalar spin chirality, which implies the appearance of spontaneous orbital charge currents in the bulk (even in the insulator); but in some cases, orbital currents are non-zero only in a formulation with three orbitals per unit cell. The states are formulated using both the bosonic and fermionic spinon approaches. We describe states with $\mathbb{Z}_2$ and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the N\'eel state.
We analyze the solution of the Schr\"odinger equation arising in the treatment of a geometric model introduced to explain the origin of the observed shallow levels in semiconductors threaded by a dislocation density. We show (contrary to what the authors claimed) that the model does not support bound states for any chosen set of model parameters. Assuming a fictitious motion in the $x-y$ plane there are bound states provided that $k\neq 0$ and not only for $k>0$ as the authors believed. The truncation condition proposed by the authors yields only one particular energy for a given value of a chosen model parameter and misses all the others (conditionally solvable problem)
Non-equilibrium radiation is addressed theoretically by means of a stochastic lattice-gas model. We consider a resonating transmission line composed of a chain of radiation resonators, each at a local equilibrium, whose boundaries are in thermal contact with two blackbody reservoirs at different temperatures. In the long chain limit, the stationary state of the non-equilibrium radiation is obtained in a closed form. The corresponding spectral energy density departs from the Planck expression, yet it obeys a useful scaling form. A macroscopic fluctuating hydrodynamic limit is obtained leading to a Langevin equation whose transport parameters are calculated. In this macroscopic limit, we identify a local temperature which characterises the spectral energy density. The generality of our approach is discussed and applications for the interaction of non-equilibrium radiation with matter are suggested.
We demonstrate coherent driving of a single electron spin using second harmonic excitation in a Si/SiGe quantum dot. Our estimates suggest that the anharmonic dot confining potential combined with a gradient in the transverse magnetic field dominates the second harmonic response. As expected, the Rabi frequency depends quadratically on the driving amplitude and the periodicity with respect to the phase of the drive is twice that of the fundamental harmonic. The maximum Rabi frequency observed for the second harmonic is just a factor of two lower than that achieved for the first harmonic when driving at the same power. Combined with the lower demands on microwave circuitry when operating at half the qubit frequency, these observations indicate that second harmonic driving can be a useful technique for future quantum computation architectures.