ShantanuT01/DACTYL-Pretraining huggingface dataset:
The ability to simulate one Hamiltonian with another is an important primitive in quantum information processing. In this paper, a simulation method for arbitrary $\sigma_z \otimes \sigma_z$ interaction based on Hadamard matrices (quant-ph/9904100) is generalized for any pairwise interaction. We describe two applications of the generalized framework. First, we obtain a class of protocols for selecting an arbitrary interaction term in an n-qubit Hamiltonian. This class includes the scheme given in quant-ph/0106064v2. Second, we obtain a class of protocols for inverting an arbitrary, possibly unknown n-qubit Hamiltonian, generalizing the result in quant-ph/0106085v1.
Modular curves like X_0(N) and X_1(N) appear very frequently in arithmetic geometry. While their complex points are obtained as a quotient of the upper half plane by some subgroups of SL_2(Z), they allow for a more arithmetic description as a solution to a moduli problem. This description turns out to be very useful in many applications. We wish to give such a moduli description for two modular curves: those associated to non-split Cartan subgroups and their normaliser in GL_2(F_p). These modular curves appear for instance in Serre's problem of classifying all possible Galois structures of p-torsion points on elliptic curves over number fields. Some classical results about the geometry of those curves can be proven using this moduli description. For instance, we can count the number of elliptic points, describe the cusps and the degeneracy maps. We also give a moduli-theoretic interpretation and a new proof of a result of Chen.
A $pseudo$-$oval$ of a finite projective space over a finite field of odd order $q$ is a configuration of equidimensional subspaces that is essentially equivalent to a translation generalised quadrangle of order $(q^n,q^n)$ and a Laguerre plane of order $q^n$ (for some $n$). In setting out a programme to construct new generalised quadrangles, Shult and Thas asked whether there are pseudo-ovals consisting only of lines of an elliptic quadric ${Q}^-(5,q)$, non-equivalent to the $classical$ $example$, a so-called $pseudo$-$conic$. To date, every known pseudo-oval of lines of ${Q}^-(5,q)$ is projectively equivalent to a pseudo-conic. Thas characterised pseudo-conics as pseudo-ovals satisfying the $perspective$ property, and this paper is on characterisations of pseudo-conics from an algebraic combinatorial point of view. In particular, we show that pseudo-ovals in $Q^-(5,q)$ and pseudo-conics can be characterised as certain Delsarte designs of an interesting five-class association scheme. These association schemes are introduced and explored, and we provide a complete theory of how pseudo-ovals of lines of $Q^-(5,q)$ can be analysed from this viewpoint.
We present multi-molecular line maps obtained with the Mopra Telescope towards the southern giant molecular cloud (GMC) complex G333, associated with the HII region RCW 106. We have characterised the GMC by decomposing the 3D data cubes with GAUSSCLUMPS, and investigated spatial correlations among different molecules with principal component analysis (PCA). We find no correlation between clump size and line width, but a strong correlation between emission luminosity and line width. PCA classifies molecules into high and low density tracers, and reveals that HCO+ and N2H+ are anti-correlated.
A neutron number dependence of the E1 0+ --> 1- reduced transition probability in spherical even--even nuclei is analysed within the Q--phonon approach in the fermionic space to describe the structure of collective states. Microscopic calculations of the E1 0+ --> 1- transition matrix elements are carried out for the Xe isotopes based on the RPA for the ground state wave function. A satisfactory description of the experimental data is obtained.
We prove that weak solutions of a slightly supercritical quasi-geostrophic equation become smooth for large time. We prove it using a De Giorgi type argument using ideas from a recent paper by Caffarelli and Vasseur.
We investigate exponential phase moments of the s-parametrized quasidistributions (smoothed Wigner functions). We show that the knowledge of these moments as functions of s provides, together with photon-number statistics, a complete description of the quantum state. We demonstrate that the exponential phase moments can be directly sampled from the data recorded in balanced homodyne detection and we present simple expressions for the sampling kernels. The phase moments are Fourier coefficients of phase distributions obtained from the quasidistributions via integration over the radial variable in polar coordinates. We performed Monte Carlo simulations of the homodyne detection and we demonstrate the feasibility of direct sampling of the moments and subsequent reconstruction of the phase distribution.
We try to gain an understanding of the recent Superkamiokande data on neutrino oscillations and several other important phenomenological issues within the framework of supersymmetric $SU(4)_c \times SU(2)_L \times SU(2)_R$ ($\equiv G_{422}$). By supplementing $G_{422}$ with a U(1)-${\cal R}$ symmetry, we can provide an explanation of the magnitude $M_G$ ($\sim 10^{16}$ GeV) of the $G_{422}$- symmetry breaking scale, resolve the MSSM $\mu $ problem, and understand why proton decay has not been seen ($\tau_p \gg 10^{34}$ yr). The family dependent ${\cal R}$ - symmetry also helps provide an explanation of the charged fermion mass hierarchies as well as the magnitudes of the CKM matrix elements. Several additional heavy states in the mass range $10^4-10^7$ GeV are predicted, and the MSSM parameter $\tan \beta $ turns out to be of order unity. The atmospheric neutrino problem is explained through $\nu_{\mu}-\nu_{\tau}$ mixing with $\sin^2 2\theta_{\mu \tau}\simeq 1$. The resolution of the solar neutrino puzzle is via the small angle MSW oscillations and necessarily requires a sterile neutrino $\nu_s$ which, thanks to the ${\cal R}$ - symmetry, has a tiny mass.
Through an optical campaign performed at 5 telescopes located in the northern and the southern hemispheres, plus archival data from two on line sky surveys, we have obtained optical spectroscopy for 17 counterparts of suspected or poorly studied hard X-ray emitting active galactic nuclei (AGNs) detected with Swift/BAT in order to determine or better classify their nature. We find that 7 sources of our sample are Type 1 AGNs, 9 are Type 2 AGNs, and 1 object is an X-ray bright optically normal galaxy; the redshifts of these objects lie in a range between 0.012 and 0.286. For all these sources, X-ray data analysis was also performed to estimate their absorption column and to search for possible Compton thick candidates. Among our type 2 objects, we did not find any clear Compton thick AGN, but at least 6 out of 9 of them are highly absorbed (N_H > 10^23 cm^-2), while one does not require intrinsic absorption; i.e., it appears to be a naked Seyfert 2 galaxy.
We compute the sum and number of eigenvalues for a certain class of magnetic Schrodinger operators in a domain with boundary. Functions in the domain of the operator satisfy a (magnetic) Robin condition. The calculations are valid in the semi-classical asymptotic limit and the eigenvalues concerned correspond to eigenstates localized near the boundary of the domain. The formulas we derive display the influence of the boundary and the boundary condition and are valid under a weak regularity assumption of the boundary function. Our approach relies on three main points: reduction to the boundary; construction of boundary coherent states; handling the boundary term as a surface electric potential and controlling the errors by various Lieb-Thirring inequalities.
Hot electron cooling rate P, due to acoustic phonons, is investigated in three-dimensional Dirac fermion systems at low temperature taking account of screening of electron-acoustic phonon interaction. P is studied as a function of electron temperature T_e and electron concentration n_e. Screening is found to suppress P very significantly for about T_e < 0.5 K and its effect reduces considerably for about T_e > 1K in Cd_3As_2 . In Bloch-Gruniesen (BG) regime, for screened (unscreened) case T_e dependence is P ~ T_e^ 9 (T_e^ 5) and ne dependence gives P ~ n_e ^-5/3(n_e^-1/3). The T_e dependence is characteristics of 3D phonons and n_e dependence is characteristics of 3D Dirac fermions. In BG regime, screening effect is found to enhance for larger n_e. Screening is found to reduce the range of validity of BG regime temperature. Plot of P / T_e^ 4 vs T_e shows a maximum at temperature T_e m which shifts to higher values for larger n_e. Interesting observation is that maximum of P / T_e^4 is nearly same for different n_e and T_em / n_e^ 1/3 appears to be nearly constant. More importantly, we propose, the n_e dependent measurements of P would provide a clearer signature to identify 3D Dirac semimetal phase.
In this work we present spectra of all $\gamma$-ray burst (GRB) afterglows that have been promptly observed with the X-shooter spectrograph until 31-03-2017. In total, we obtained spectroscopic observations of 103 individual GRBs observed within 48 hours of the GRB trigger. Redshifts have been measured for 97 per cent of these, covering a redshift range from 0.059 to 7.84. Based on a set of observational selection criteria that minimize biases with regards to intrinsic properties of the GRBs, the follow-up effort has been focused on producing a homogeneous sample of 93 afterglow spectra for GRBs discovered by the Swift satellite. We here provide a public release of all the reduced spectra, including continuum estimates and telluric absorption corrections. For completeness, we also provide reductions for the 18 late-time observations of the underlying host galaxies. We provide an assessment of the degree of completeness with respect to the parent GRB population, in terms of the X-ray properties of the bursts in the sample and find that the sample presented here is representative of the full Swift sample. We constrain the fraction of dark bursts to be < 28 per cent and we confirm previous results that higher optical darkness is correlated with increased X-ray absorption. For the 42 bursts for which it is possible, we provide a measurement of the neutral hydrogen column density, increasing the total number of published HI column density measurements by $\sim$ 33 per cent. This dataset provides a unique resource to study the ISM across cosmic time, from the local progenitor surroundings to the intervening universe.
Using the nonequilibrium Green's function (NEGF) formalism, we propose a microscopic theory for near-field radiative heat transfer between metal plates. Tight-binding models for the electrons are coupled to the electromagnetic field continuum. Our approach differs from the established ones based on fluctuational electrodynamics, in that it describes truly nonequilibrium steady states, and is nonlocal in system's dielectric properties. For a two quantum-dot model a new length scale emerges at which the heat current shows a peak. This length scale is related to the physics of parallel plate capacitors. The three-dimensional model results are consistent with the theory of Polder and van Hove except at very short distances.
We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped in the braneworld, for a wide variety of self-interaction potentials. We focus on Randall-Sundrum (RS) and on Dvali-Gabadadze-Porrati (DGP) braneworld models exclusively. These models are complementary to each other: while the RS brane produces ultra-violet (UV) corrections to general relativity, the DGP braneworld modifies Einstein's theory at large scales, i. e., produces infra-red (IR) modifications of general relativity. This study of the asymptotic properties of both braneworld models, shows -- in the phase space -- the way the dynamics of a scalar field trapped in the brane departs from standard general relativity behaviour.
In the first months after the launch in July 2019, eROSITA onboard Spektr-RG (SRG) performed long-exposure observations in the regions around SN 1987A and SNR N132D in the Large Magellanic Cloud (LMC). We analyse the distribution and the spectrum of the diffuse X-ray emission in the observed fields to determine the physical properties of the hot phase of the interstellar medium (ISM). The eROSITA data are complemented by newly derived column density maps for the Milky Way and the LMC, 888 MHz radio continuum map from the Australian Square Kilometer Array Pathfinder (ASKAP), and optical images of the Magellanic Cloud Emission Line Survey (MCELS). We detect significant emission from thermal plasma with kT=0.2 keV in all the regions. There is also an additional higher-temperature emission component from a plasma with kT = 0.7 keV. In addition, non-thermal X-ray emission is significantly detected in the superbubble 30 Dor C. The absorbing column density NH in the LMC derived from the analysis of the X-ray spectra taken with eROSITA is consistent with the NH obtained from the emission of the cold medium over the entire area. Neon abundance is enhanced in the regions in and around 30 Dor and SN 1987A, indicating that the ISM has been chemically enriched by the young stellar population. Emission from the stellar cluster RMC 136 and the Wolf-Rayet stars RMC 139 and RMC 140 is best modelled with a high-temperature (kT>1 keV) non-equilibrium ionisation plasma emission and a non-thermal component with a photon index of {\Gamma} =1.3. In addition, the optical SNR candidate J0529-7004 is also detected with eROSITA and we thus confirm the source as an SNR.
A personal feeling of where we stand theoretically in the puzzle of EWSB, faced with the impressive limits on new physics set at the summer conferences. Plenary talk at EPS HEP 2011.
Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication (LOCC), in the limit of many copies. While for two pure states a result of Walgate et al. shows that LOCC is just as powerful as global measurements, data hiding states (DiVincenzo et al.) show that locality can impose severe restrictions on the distinguishability of even orthogonal states. Here we determine the optimal error probability and measurement to discriminate many copies of particular data hiding states (extremal d x d Werner states) by a linear programming approach. Surprisingly, the single-copy optimal measurement remains optimal for n copies, in the sense that the best strategy is measuring each copy separately, followed by a simple classical decision rule. We also put a lower bound on the bias with which states can be distinguished by separable operations.
The low-mass dielectron signal from heavy-ion collisions at the CERN--SPS reported by the {\em CERES} collaboration is in excess of estimated hadronic decays suggestive of possible contribution from two-pion annihilation or other hadronic reactions. In the absence of dramatic medium modifications, annihilation alone is unable to account for the data. We explore the role of pion plus resonance scattering [$\pi\rho\to a_{1}(1260) \to \pi e^+e^-$] which has favorable kinematics to populate masses between $2m_{\pi}$ and $m_{\rho}$. While it seems to account for some of the remaining excess beyond annihilation, it fails to allow quantitative interpretation of data.
We analyze a measurement scheme that allows determination of the Berry curvature and the topological Chern number of a Hamiltonian with parameters exploring a two-dimensional closed manifold. Our method uses continuous monitoring of the gradient of the Hamiltonian with respect to one parameter during a quasi-adiabatic quench of the other. Measurement back-action leads to disturbance of the system dynamics, but we show that this can be compensated by a feedback Hamiltonian. As an example, we analyze the implementation with a superconducting qubit subject to time varying, near resonant microwave fields; equivalent to a spin 1/2 particle in a magnetic field.
We study the quantumness of correlations for ensembles of bi- and multi-partite systems and relate it to the task of quantum data hiding. Quantumness is here intended in the sense of minimum average disturbance under local measurements. We consider a very general framework, but focus on local complete von Neumann measurements as cause of the disturbance, and, later on, on the trace-distance as quantifier of the disturbance. We discuss connections with entanglement and previously defined notions of quantumness of correlations. We prove that a large class of quantifiers of the quantumness of correlations are entanglement monotones for pure bipartite states. In particular, we define an entanglement of disturbance for pure states, for which we give an analytical expression. Such a measure coincides with negativity and concurrence for the case of two qubits. We compute general bounds on disturbance for both single states and ensembles, and consider several examples, including the uniform Haar ensemble of pure states, and pairs of qubit states. Finally, we show that the notion of ensemble quantumness of correlations is most relevant in quantum data hiding. Indeed, while it is known that entanglement is not necessary for a good quantum data hiding scheme, we prove that ensemble quantumness of correlations is.
We construct density dependent Class $III$ charge symmetry violating (CSV) potential due to mixing of $\pi$-$\eta$ meson with off-shell corrections. The density dependence enters through the non-vanishing $\pi$-$\eta$ mixing driven by both the neutron-proton mass difference and their asymmetric density distribution. The contribution of density dependent CSV potential is found to be appreciably larger than the contribution of vacuum CSV potential.
We consider three directed walkers on the square lattice, which move simultaneously at each tick of a clock and never cross. Their trajectories form a non-crossing configuration of walks. This configuration is said to be osculating if the walkers never share an edge, and vicious (or: non-intersecting) if they never meet. We give a closed form expression for the generating function of osculating configurations starting from prescribed points. This generating function turns out to be algebraic. We also relate the enumeration of osculating configurations with prescribed starting and ending points to the (better understood) enumeration of non-intersecting configurations. Our method is based on a step by step decomposition of osculating configurations, and on the solution of the functional equation provided by this decomposition.
We report transport measurements through a single-molecule magnet, the Mn12 derivative [Mn12O12(O2C-C6H4-SAc)16(H2O)4], in a single-molecule transistor geometry. Thiol groups connect the molecule to gold electrodes that are fabricated by electromigration. Striking observations are regions of complete current suppression and excitations of negative differential conductance on the energy scale of the anisotropy barrier of the molecule. Transport calculations, taking into account the high-spin ground state and magnetic excitations of the molecule, reveal a blocking mechanism of the current involving non-degenerate spin multiplets.
We show that to every p-divisible group over a p-adic ring one can associate a display by crystalline Dieudonne theory. For an appropriate notion of truncated displays, this induces a functor from truncated Barsotti-Tate groups to truncated displays, which is a smooth morphism of smooth algebraic stacks. As an application we obtain a new proof of the equivalence between infinitesimal p-divisible groups and nilpotent displays over p-adic rings, and a new proof of the equivalence due to Berthelot and Gabber between commutative finite flat group schemes of p-power order and Dieudonne modules over perfect rings.
We suggest that the low viscosity in close binary accretion disks during quiescence is due to magnetic fields from the companion star. In very late evolutionary phase the companion stars become brown dwarfs and have cooled down to such low a temperature that this process cannot work anymore. The extremely low viscosity in WZ Sge stars supports this connection between companion stars and viscosity. We further suggest that magnetic activity in such very cool stars is cut off by their poor electric conductivity.
Using high-precision photometry from the \textit{Kepler} mission, we investigate patterns of spot activity on the K1-type subgiant component of KIC 11560447, a short-period late-type eclipsing binary. We tested the validity of maximum entropy reconstructions of starspots by numerical simulations. Our procedure successfully captures up to three large spot clusters migrating in longitude. We suggest a way to measure a lower limit for stellar differential rotation, using slopes of spot patterns in the reconstructed time-longitude diagram. We find solar-like differential rotation and recurrent spot activity with a long-term trend towards a dominant axisymmetric spot distribution during the period of observations.
The observed empirical relation between the star-formation rates (SFR) of low-redshift galaxies and their radio continuum luminosity offers a potential means of measuring SFR in high redshift galaxies that is unaffected by dust obscuration. In this study, we make the first test for redshift evolution in the SFR-radio continuum relation at high redshift using dust-corrected H$\alpha$ SFR. Our sample consists of 178 galaxies from the MOSFIRE Deep Evolution Field (MOSDEF) Survey at $1.4 < z < 2.6$ with rest-frame optical spectroscopy and deep 1.5 GHz radio continuum observations from the Karl G. Jansky Very Large Array (VLA) GOODS North field. Using a stacking analysis we compare the observed radio continuum luminosities with those predicted from the dust-corrected H$\alpha$ SFR assuming a range of $z\sim0$ relations. We find no evidence for a systematic evolution with redshift, when stacking the radio continuum as a function of dust-corrected H$\alpha$ SFR and when stacking both optical spectroscopy and radio continuum as a function of stellar mass. We conclude that locally calibrated relations between SFR and radio continuum luminosity remain valid out to $z\sim 2$.
The convex hull of several i.i.d. beta distributed random vectors in $\mathbb R^d$ is called the random beta polytope. Recently, the expected values of their intrinsic volumes, number of faces, normal and tangent angles and other quantities have been calculated, explicitly and asymptotically. In this paper, we aim to investigate the asymptotic behavior of the beta polytopes with extremal intrinsic volumes. We suggest a conjecture and solve it in dimension 2. To this end, we obtain some general limit relation for a wide class of $U$-$\max$ statistics whose kernels include the perimeter and the area of the convex hull of the arguments.
Advances in scaling down heterostructures and having an improved interface quality together with atomically-thin two-dimensional materials suggest a novel approach to systematically design materials. A given material can be transformed through proximity effects whereby it acquires properties of its neighbors, for example, becoming superconducting, magnetic, topologically nontrivial, or with an enhanced spin-orbit coupling. Such proximity effects not only complement the conventional methods of designing materials by doping or functionalization, but can also overcome their various limitations. In proximitized materials it is possible to realize properties that are not present in any constituent region of the considered heterostructure. While the focus is on magnetic and spin-orbit proximity effects with their applications in spintronics, the outlined principles provide also a broader framework for employing other proximity effects to tailor materials and realize novel phenomena.