ShantanuT01/DACTYL-Pretraining huggingface dataset:
Following Ref. [Oriols X 2007 Phys. Rev. Lett., 98 066803], an algorithm to deal with the exchange interaction in non-separable quantum systems is presented. The algorithm can be applied to fermions or bosons and, by construction, it exactly ensures that any observable is totally independent from the interchange of particles. It is based on the use of conditional Bohmian wave functions which are solutions of single-particle pseudo-Schr\"odinger equations. The exchange symmetry is directly defined by demanding symmetry properties of the quantum trajectories in the configuration space with a universal algorithm, rather than through a particular exchange-correlation functional introduced into the single-particle pseudo-Schr\"odinger equation. It requires the computation of N^2 conditional wave functions to deal with N identical particles. For separable Hamiltonians, the algorithm reduces to the standard Slater determinant for fermions, or permanent for bosons. A numerical test for a two-particle system, where exact solutions for non-separable Hamiltonians are computationally accessible, is presented. The numerical viability of the algorithm for quantum electron transport (in a far-from equilibrium time-dependent open system) is demonstrated by computing the current and fluctuations in a nano-resistor, with exchange and Coulomb interactions among electrons.
In this paper we solve combinatorial and algebraic problems associated with a multivariate identity first considered by S. Sherman wich he called an analog to the Witt identity. We extend previous results obtained for the univariante case.
We elaborate on s-confinement phases in three-dimensional $\mathcal{N}=2$ supersymmetric gauge theory, especially focusing on the $SU(N)$ and $USp(2N)$ gauge theories with anti-symmetric tensors and (anti-)fundamental matters. This will elucidate a quantum structure of the Coulomb moduli space of vacua. We stress the importance of so-called dressed Coulomb branch operators for describing these s-confinement phases. The 3d s-confinement phases are highly richer than the 4d ones since there is no chiral anomaly constraint on the matter contents.
It is well-known since the work of Pardoux and Peng [12] that Backward Stochastic Differential Equations provide probabilistic formulae for the solution of (systems of) second order elliptic and parabolic equations, thus providing an extension of the Feynman-Kac formula to semilinear PDEs, see also Pardoux and Rascanu [14]. This method was applied to the class of PDEs with a nonlinear Neumann boundary condition first by Pardoux and Zhang [15]. However, the proof of continuity of the extended Feynman-Kac formula with respect to x (resp. to (t,x)) is not correct in that paper. Here we consider a more general situation, where both the equation and the boundary condition involve the (possibly multivalued) gradient of a convex function. We prove the required continuity. The result for the class of equations studied in [15] is a Corollary of our main results.
Neutron stars have the strongest magnetic fields known anywhere in the Universe. In this review, I intend to give a pedagogical discussion of some of the related physics. Neutron stars exist because of Pauli's exclusion principle, in two senses: 1) It makes it difficult to squeeze particles too close together, in this way allowing a mechanical equilibrium state in the presence of extremely strong gravity. 2) The occupation of low-energy proton and electron states makes it impossible for low-energy neutrons to beta decay. A corollary of the second statement is that charged particles are necessarily present inside a neutron star, allowing currents to flow. Since these particles are degenerate, they collide very little, and therefore make it possible for the star to support strong, organized magnetic fields over long times. These show themselves in pulsars and are the most likely energy source for the high X-ray and gamma-ray luminosity ``magnetars''. I briefly discuss the possible origin of this field and some physical constraints on its equilibrium configurations.
Boltzmann codes are used extensively by several groups for constraining cosmological parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires from 10'000 to 100'000 Boltzmann code executions. The newly released code CLASS (Cosmic Linear Anisotropy Solving System) incorporates improved approximation schemes leading to a simultaneous gain in speed and precision. We describe here the three approximations used by CLASS for basic LambdaCDM models, namely: a baryon-photon tight-coupling approximation which can be set to first order, second order or to a compromise between the two; an ultra-relativistic fluid approximation which had not been implemented in public distributions before; and finally a radiation streaming approximation taking reionisation into account.
We present large field HI-line emission maps obtained with the single-dish Green Bank Telescope centered on the dwarf irregular galaxies Sextans A, NGC 2366, and WLM. We do not detect the extended skirts of emission associated with the galaxies that were reported from Effelsberg observations (Huchtmeier et al. 1981). The ratio of HI at 10^19 atoms cm^-2 to optical extents of these galaxies are instead 2--3, which is normal for this type of galaxy. There is no evidence for a truncation in the HI distribution >/=10^19 atoms cm^-2.
The Next Generation Virgo Cluster Survey is a deep (with a $2\sigma$ detection limit $\mu_g$ = 29~mag~arcsec$^{-2}$ in the $g-$band) optical panchromatic survey targeting the Virgo cluster from its core to virial radius, for a total areal coverage of 104 square degrees. As such, the survey is well suited for the study of galaxies' outskirts, haloes and low surface brightness features that arise from dynamical interactions within the cluster environment. We report the discovery of extremely faint ($\mu_g$ $>$ 25 mag arcsec$^{-2}$) shells in three Virgo cluster early-type dwarf galaxies, VCC~1361, VCC~1447 and VCC~1668. Among them, VCC~1447 has an absolute magnitude M$_{g}$ = -11.71 mag and is {\it the least massive galaxy with a shell system discovered to date}. We present a detailed study of these low surface brightness features. We detect between three and four shells in each of our galaxies. Within the uncertainties, we find no evidence of a color difference between the galaxy main body and shell features. The observed arcs of the shells are located upto several effective radii of the galaxies. We further explore the origin of these low surface brightness features with the help of idealized numerical simulations. We find that a near equal mass merger is best able to reproduce the main properties of the shells, including their quite symmetric appearance and their alignment along the major axis of the galaxy. The simulations provide support for a formation scenario in which a recent merger, between two near-equal mass, gas-free dwarf galaxies forms the observed shell systems.
I describe a semi-analytical model for the formation and evolution of galaxies in hierarchical clustering models, and its predictions for the properties of the galaxy population at high z. The predictions are found to agree well with the observed properties of the Lyman break galaxies found at z sim 3 by Steidel et al. The models predict that the star formation rate per comoving volume should have peaked at z sim 1-2, which also agrees well with recent observational data.
According to band structure calculations, the Fermi surface of the quasi-two dimensional metal $\theta$-(ET) 4 ZnBr 4 (C 6 H 4 Cl 2) illustrates the linear chain of coupled orbits model. Accordingly, de Haas-van Alphen oscillations spectra recorded in pulsed magnetic field of up to 55 T evidence many Fourier components, the frequency of which are linear combinations of the frequencies relevant to the closed $\alpha$ and the magnetic breakdown $\beta$ orbits. The field and temperature dependence of these component's amplitude are quantitatively accounted for by analytic calculations including, beyond the Lifshitz-Kosevich formula, second order terms in damping factors due to the oscillation of the chemical potential as the magnetic field varies. Whereas these second order terms are negligible for the orbits $\alpha$, $\beta$ and 2$\beta$ -- $\alpha$, they are solely responsible for the 'forbidden orbit' $\beta$ -- $\alpha$ and its harmonic and have a significant influence on Fourier components such as 2$\alpha$ and $\beta$ + $\alpha$, yielding strongly non-Lifshitz-Kosevich behaviour in the latter case.
A Doppler image of the ZAMS late-type rapidly rotating star LO Pegasi, based on spectra acquired between 12 and 15 September 2003, is presented. The Least Square Deconvolution technique is applied to enhance the signal-to-noise ratio of the mean rotational broadened line profiles extracted from the observed spectra. In the present application, a unbroadened spectrum is used as a reference, instead of a simple line list, to improve the deconvolution technique applied to extract the mean profiles. The reconstructed image is similar to those previously obtained from observations taken in 1993 and 1998, and shows that LO Peg photospheric activity is dominated by high-latitude spots with a non-uniform polar cap. The latter seems to be a persistent feature as it has been observed since 1993 with little modifications. Small spots, observed between ~ 10 and ~ 60 degrees of latitude, appears to be different with respect to those present in the 1993 and 1998 maps.
A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lema\^itre-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge independent quantities. We shall see that in the QM-scheme we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz et al that deals with perturbation in the standard Einstein framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting on particular choices of the perturbed variables as a combination of gauge dependent quantities.
Detailed magnetization measurements in La_{5/8-y}Pr_{y}Ca_{3/8} MnO_{3}, including magnetic relaxation properties, demonstrate the dynamic nature of the phase separated state in manganites. The difference between the field-cooled-cooling and zero-field-cooled magnetization curves signals the existence in the latter of blocked metastable states separated by high energy barriers. Results of the magnetic viscosity show that the system becomes unblocked in a certain temperature window, where large relaxation rates are observed. We propose a simple phenomenological model in which the system evolves through a hierarchy of energy barriers, which separates the coexisting phases. The calculated magnetization curves using this model reproduce all the qualitative features of the experimental data. The overall results allowed us to construct an H-T phase diagram, where frozen and dynamical phase separation regions are clearly distinguished.
Attention is paid to the fact that temperature of a classical black hole can be derived from the extremality condition of its free energy with respect to variation of the mass of a hole. For a quantum Schwarzschild black hole evaporating massless particles the same condition is shown to result in the following one-loop temperature $T=(8\pi M)^{-1} (1+\sigma (8\pi M^2)^{-1})$ and entropy $S = 4\pi M^2 - \sigma\log M$ expressed in terms of the effective mass $M$ of a hole together with its radiation and the integral of the conformal anomaly $\sigma$ that depends on the field species. Thus, in the given case quantum corrections to $T$ and $S$ turn out to be completely provided by the anomaly. When it is absent ($\sigma=0$), which happens in a number of supersymmetric models, the one-loop expressions of $T$ and $S$ preserve the classical form. On the other hand, if the anomaly is negative ($\sigma<0$) an evaporating quantum hole seems to cease to heat up when its mass reaches the Planck scales.
The experimental observation of a spin-gap in the antiferromagnetic spin-1/2 compound $CaV_4O_9$ has been attributed to the formation of a plaquette resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin-1/2 model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace of this parameter regime, the first excited state can be calculated exactly. In a different parameter regime, the dimer state is shown to be the exact ground state.
We revisit the model of the two-component plasma in a gravitational field, which mimics charged colloidal suspensions. We concentrate on the computation of the grand potential of the system. Also, a special sum rule for this model is presented.
Starting from $E_{11}$ and the space-time translations we construct an algebra that promotes the global $E_{11}$ symmetries to local ones, and consider all its possible massive deformations. The Jacobi identities imply that such deformations are uniquely determined by a single tensor that belongs to the same representation of the internal symmetry group as the $D-1$ forms specified by $E_{11}$. The non-linear realisation of the deformed algebra gives the field strengths of the theory which are those of any possible gauged maximal supergravity theory in any dimension. All the possible deformed algebras are in one to one correspondence with all the possible massive maximal supergravity theories. The hierarchy of fields inherent in the $E_{11}$ formulation plays an important role in the derivation. The tensor that determines the deformation can be identified with the embedding tensor used previously to parameterise gauged supergravities. Thus we provide a very efficient, simple and unified derivation of the bosonic sector, and in the absence of gravity, of all maximal gauged supergravities from $E_{11}$.
Accelerations of both the solar system barycenter (SSB) and stars in the Milky Way cause a systematic observational effect on the stellar proper motions, which was first studied in the early 1990s and developed by J. Kovalevsky (aberration in proper motions, 2003, A&A, 404, 743). This paper intends to extend that work and aims to estimate the magnitude and significance of the aberration in proper motions of stars, especially in the region near the Galactic center. We adopt two models for the Galactic rotation curve to evaluate the aberrational effect on the Galactic plane. Based on the theoretical developments, we show that the effect of aberration in proper motions depends on the galactocentric distance of stars; it is dominated by the acceleration of stars in the central region of the Galaxy. Within 200 pc from the Galactic center, the systematic proper motion can reach an amplitude larger than 1000 uas/yr by applying a flat rotation curve. With a more realistic rotation curve which is linearly rising in the core region of the Galaxy, the aberrational proper motions are limited up to about 150 uas/yr. Then we investigate the applicability of the theoretical expressions concerning the aberrational proper motions, especially for those stars with short period orbits. If the orbital period of stars is only a fraction of the light time from the star to the SSB, the expression proposed by Kovalevsky is not appropriate. With a more suitable formulation, we found that the aberration has no effect on the determination of the stellar orbits on the celestial sphere. The aberrational effect under consideration is small but not negligible with high-accurate astrometry in the future, particularly in constructing the Gaia celestial reference system realized by Galactic stars.
Phonon lifetime calculations from first principles usually rely on time consuming molecular dynamics calculations, or density functional perturbation theory (DFPT) where the zero temperature crystal structure is assumed to be dynamically stable. Here a new and effective method for calculating phonon lifetimes from first principles is presented, not limited to crystal structures stable at 0 K, and potentially much more effective than most corresponding molecular dynamics calculations. The method is based on the recently developed self consistent lattice dynamical method and is here tested by calculating the bcc phase phonon lifetimes of Li, Na, Ti and Zr, as representative examples.
Large scale Hartree-Fock-Bogoliubov (HFB) calculations with the finite-range   Gogny force D1S have been performed in order to extract the corresponding theoretical average mass dependence of the nuclear gap values. Good agreement with experimental data from the three-point filter   $\Delta^{(3)}$(N) with N odd has been found for both the neutron and proton gaps. The study confirms earlier findings [W. Satula,   J. Dobaczewski, and W. Nazarewicz, Phys. Rev. Lett. 81 3599 (1998)] that the mass dependence of the gap is much weaker than the so far accepted 12/$\sqrtA$ MeV law.
Let C \in P2 be a reduced, singular curve of degree d and equation f = 0. Let \Sigma denote the jacobian subscheme of C. We have 0 -> E -> 3.O -> I_\Sigma(d-1) -> 0 (the surjection is given by the partials of f). We study the relationships between the Betti numbers of the module H^0_*(E) and the integers, d; \tau, where \tau = deg(\Sigma). We observe that our results apply to any quasi-complete intersection of type (s; s; s).
It has been argued that the Nekrasov's partition function gives the generating function of refined BPS state counting in the compactification of M theory on local Calabi-Yau spaces. We show that a refined version of the topological vertex we proposed before (hep-th/0502061) is a building block of the Nekrasov's partition function with two equivariant parameters. Compared with another refined topological vertex by Iqbal-Kozcaz-Vafa (hep-th/0701156), our refined vertex is expressed entirely in terms of the specialization of the Macdonald symmetric functions which is related to the equivariant character of the Hilbert scheme of points on C^2. We provide diagrammatic rules for computing the partition function from the web diagrams appearing in geometric engineering of Yang-Mills theory with eight supercharges. Our refined vertex has a simple transformation law under the flop operation of the diagram, which suggests that homological invariants of the Hopf link are related to the Macdonald functions.
We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding $t_{1,2}-J_{1,2}$ Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.
We explore joint observations of the South-East limb made by Hinode, TRACE and SOHO/SUMER on April 12, 2008 as part of the Whole Heliosphere Interval (WHI) Quiet Sun Characterization targeted observing program. During the sequence a large, 10Mm long, macro-spicule was sent upward and crossed the line-of-sight of the SUMER slit, an event that affords us an opportunity to study the coupling of cooler chromospheric material to transition region emission formed as hot as 600,000K. This short article provides preliminary results of the data analysis.
We have studied the structural, magnetic properties, and electronic structure of the compound InCuPO5 synthesized by solid state reaction method. The structure of InCuPO5 comprises of S = 1/2 uniform spin chains formed by corner-shared CuO4 units. Magnetic susceptibility chi(T) data shows a broad maximum at about 65 K, a characteristic feature of one-dimensional (1D) magnetism. The chi(T) data is fitted to the coupled, S = 1/2 Heisenberg antiferromagnetic (HAFM) uniform chain model that gives the intra-chain coupling (J/kB) between nearest neighbour Cu2+ ions as -100 K and the ratio of inter-chain to intra-chain coupling (J'/J) as about 0.07. The exchange couplings estimated from the magnetic data analysis are in good agreement with the computed values from the electronic structure calculations based on density functional theory + Hubbard U (DFT+U) approach. The combination of theoretical and experimental analysis confirms that InCuPO5 is a candidate material for weakly coupled S = 1/2 uniform chains. A detailed theoretical analysis of the electronic structure further reveals that the system is insulating with a gap of 2.4 eV and a local moment of 0.70 muB /Cu.
Strong gravitational lensing effect is a powerful tool to probe cosmological models and gravity theories. Recently, the time-delay cosmography from strong lensing and the stellar kinematics of the deflector, which encode the Hubble constant and the post-Newtonian parameter via two distance ratios reflecting the lensing mass and dynamical mass respectively, have been proposed to investigate these two parameters simultaneously. Among strong lensing systems with different sources, strongly lensed fast radio bursts (FRBs) have been proposed as precision probes of the universe since the time delay $\sim$ 10 days between images could be measured extremely precisely because of their short duration of a few milliseconds. In this work, we investigate the ability of strongly lensed FRBs on simultaneously estimating these two parameters via simulations. Take the expected FRB detection rate of upcoming facilities and lensing probability into consideration, it is likely to accumulate 10 lensed FRBs in several years and we find that $H_0$ could be determined to a $\sim1.5\%$ precision and $\gamma_{\rm PPN}$ could be constrained to a $\sim8.7\%$ precision simultaneously from them. These simultaneous estimations will be helpful for properly reflecting the possible correlation between these two fundamental parameters.
We discuss two different types of issues concerning the quantization of Einstein-Rosen waves. First of all we study in detail the possibility of using the coherent states corresponding to the dynamics of the auxiliary, free Hamiltonian appearing in the description of the model to study the full dynamics of the system. For time periods of arbitrary length we show that this is only possible for states that are close, in a precise mathematical sense, to the vacuum. We do this by comparing the quantum evolutions defined by the auxiliary and physical Hamiltonians on the class of coherent states. In the second part of the paper we study the structure of n-point functions. As we will show their detailed behavior differs from the one corresponding to standard perturbative quantum field theories. We take this as a manifestation of the fact that the correct approximation scheme for physically interesting objects in these models does not lead to a power series expansion in the relevant coupling constant but to a more complicated asymptotic behavior.