ShantanuT01/DACTYL-Pretraining huggingface dataset:
Structural, magnetization and heat capacity studies were performed on Ce$_2$(Pd$_{1-x}$Ni$_x$)$_2$Sn ($0 \leq x \leq 1$) alloys. The substitution of Pd atoms by isoelectronic Ni leads to a change in the crystallographic structure from tetragonal (for $x \leq 0.3$) to centered orthorhombic lattice (for $x \geq 0.4$). The volume contraction thorough the series is comparable to the expected from the atomic size ratio between transition metal components. The consequent weak increase of the Kondo temperature drives the two transitions observed in Ce$_2$Pd$_2$Sn to merge at $x = 0.25$. After about a 1% of volume collapse at the structural modification, the system behaves as a weakly magnetic heavy fermion with an enhanced degenerate ground state. Notably, an incipient magnetic transition arises on the Ni-rich size. This unexpected behavior is discussed in terms of an enhancement of the density of states driven by the increase of the $4f$-conduction band hybridization and the incipient contribution of the first excited crystal field doublet on the ground state properties.
This paper is devoted to study the asymptotic properties for the solution of decoupled forward backward stochastic differential equations with delayed generator. As an application, we establish a large deviation principe for solution of the backward equation.
The singular part of the finite-size free energy density $f_s$ of the O(n) symmetric $\phi^4$ field theory in the large-n limit is calculated at finite cutoff for confined geometries of linear size L with periodic boundary conditions in 2 < d < 4 dimensions. We find that a sharp cutoff $\Lambda$ causes a non-universal leading size dependence $f_s \sim \Lambda^{d-2} L^{-2}$ near $T_c$ which dominates the universal scaling term $\sim L^{-d}$. This implies a non-universal critical Casimir effect at $T_c$ and a leading non-scaling term $\sim L^{-2}$ of the finite-size specific heat above $T_c$.
In this paper, we study the Igusa's local zeta functions of a class of hybrid polynomials with coefficients in a non-archimedean local field of positive characteristic. Such class of hybrid polynomial was first introduced by Hauser in 2003 to study the resolution of singularities in positive characteristic. We prove the rationality of these local zeta functions and describe explicitly their poles. The proof is based on Igusa's stationary phase formula.
The point-line geometry known as a \textit{partial quadrangle} (introduced by Cameron in 1975) has the property that for every point/line non-incident pair $(P,\ell)$, there is at most one line through $P$ concurrent with $\ell$. So in particular, the well-studied objects known as \textit{generalised quadrangles} are each partial quadrangles. An \textit{intriguing set} of a generalised quadrangle is a set of points which induces an equitable partition of size two of the underlying strongly regular graph. We extend the theory of intriguing sets of generalised quadrangles by Bamberg, Law and Penttila to partial quadrangles, which surprisingly gives insight into the structure of hemisystems and other intriguing sets of generalised quadrangles.
Some extensions of the standard model contain additional leptons which are vectorlike under weak isospin. A class of models is considered in which these leptons do not appreciably mix with the known leptons. In such models, the heavy charged lepton and the heavy neutrino are degenerate in mass, and the degeneracy is broken by radiative corrections. The mass splitting is calculated and found to be very weakly dependent on the lepton mass, varying from 250 to 330 MeV as the mass varies from 100 to 800 GeV. This result is {\it not} affected significantly by inclusion in a supersymmetric model in spite of the additional loops involving the superpartners. As a result, this fairly general class of models has a charged lepton whose lifetime varies in the narrow range from 0.5 to 2.0 nanoseconds, and which decays into neutrals plus a very low energy electron or muon.
We use a suite a cooling halo simulations to study a new mechanism for rapid accretion of hot halo gas onto star-forming galaxies. Correlated supernovae events create converging 'superbubbles' in the halo gas. Where these collide, the density increases, driving cooling filaments of low metallicity gas that feed the disc. At our current numerical resolution (20 pc) we are only able to resolve the most dramatic events; these could be responsible for the build-up of galaxy discs after the most massive gas-rich mergers have completed (z < 1). As we increase the numerical resolution, we find that the filaments persist for longer, driving continued late-time star formation. This suggests that SNe-driven accretion could act as an efficient mechanism for extracting cold gas from the hot halo, driving late-time star formation in disc galaxies. We show that such filament feeding leads to a peak star formation rate (SFR) of $\sim 3$ M$_{\rm sun}$ yr$^{-1}$, consistent with estimates for the Milky Way. By contrast, direct cooling from the hot halo ('hot-mode' accretion, not present in the simulations that show filament feeding) falls short of the SNe-driven SFR by a factor of 3-4, and is sustained over a shorter time period. The filaments we resolve extend to $\sim$ 50 kpc, reaching column densities of $\sim 10^{18}$ cm$^{-2}$. We show that such structures can plausibly explain the broad dispersion in Mg II absorption seen along sight lines to quasars. Our results suggest a dual role for stellar feedback in galaxy formation, suppressing hot-mode accretion while promoting cold-mode accretion along filaments. This ultimately leads to more star formation, suggesting that the positive feedback effect outweighs the negative. Finally, since the filamentary gas has higher angular momentum than that coming from hot-mode accretion, we show that this leads to the formation of substantially larger gas discs.
As proved recently in [PT], for varieties $X^{r+1}\subset \mathbb P^N$ such that through $n\geq 2$ general points there passes an irreducible curve $C$ of degree $\delta\geq n-1$ we have $N\leq \pi(r,n,\delta+r(n-1)+2)$, where $\pi(r,n,d)$ is the Castelnuovo-Harris bound function for the geometric genus of an irreducible non-degenerate variety $Y^r\subset\mathbb P^{n+r-1}$ of degree $d$. A lot of examples of varieties as in the title and attaining the previous bound for the embedding dimension are constructed from Castelnuovo varieties and were thus dubbed {\it of Castelnuovo type} in [PT], where it is also proved that all extremal varieties as above are of this kind, except possibly when $n>2$, $r>1$ and $\delta=2n-3$.   One of the main results of the paper is the classification of extremal varieties $X^{r+1}\subset \mathbb P^{2r+3}$ 3-covered by twisted cubics and not of Castelnuovo type. Interesting examples are provided by the so called {\it twisted cubics over complex Jordan algebras of rank 3}, as pointed out by Mukai. By relating to an extremal variety 3-covered by twisted cubics, via tangential projection, a quadro-quadric Cremona transformation in $\mathbb P^r$ we are able to classify all these object either for $r\leq 4$ or under the smoothness assumption. In the last case we obtain that they are either smooth rational normal scrolls (hence of Castelnuovo type) or the Segre embeddings of $\p^1\times Q^r$ or one of the four Lagrangian Grassmannians. We end by discussing some open problems pointing towards the equivalence of these apparently unrelated objects: extremal varieties 3-covered by twisted cubics, quadro-quadric Cremona transformations of $\mathbb P^r$ and complex Jordan algebras of dimension $r+1$ and of rank three.
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical and quantum), mathematical structures, and their consequences. These include the canonical form of classical correlation functionals, general definitions of separable (entangled) states, definition and analysis of quantumness of correlations, description of entanglement of formation, and PPT states. This work is intended both for physicists interested not only in collection of results but also in the mathematical methods justifying them, and mathematicians looking for an application of quantum probability to concrete new problems of quantum theory.
The approximate renormalized one-loop effective action of the quantized massive scalar, spinor and vector field in a large mass limit, i.e., the lowest order of the DeWitt-Schwinger expansion involves the coincidence limit of the Hadamard-DeWitt coefficient a3. Building on this and using Wald's approach we shall construct the general expression describing entropy of the spherically-symmetric static black hole being the solution of the semi-classical field equations. For the concrete case of the quantum-corrected Reissner-Nordstrom black hole this result coincides, as expected, with the entropy obtained by integration of the first law of black hole thermodynamics with a suitable choice of the integration constant. The case of the extremal quantum corrected black hole is briefly considered.
Following the spirit of S-matrix program, we proposed a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified BCFW recursion relation to compute or analyze color-ordered tree amplitudes without relying on any detail information of noncommutative Yang-Mills theory. After clarifying the color structure of noncommutative tree amplitudes, we wrote down the noncommutative analogies of U(1)-decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered tree amplitudes, and proved them using the modified BCFW recursion relation.
In this paper we use microscopic arguments to derive a nonlinear Schr\"{o}dinger equation for trapped Bose-condensed gases. This is made possible by considering the equations of motion of various anomalous averages. The resulting equation explicitly includes the effect of repeated binary interactions (in particular ladders) between the atoms. Moreover, under the conditions that dressing of the intermediate states of a collision can be ignored, this equation is shown to reduce to the conventional Gross-Pitaevskii equation in the pseudopotential limit. Extending the treatment, we show first how the occupation of excited (bare particle) states affects the collisions, and thus obtain the many-body T-matrix approximation in a trap. In addition, we discuss how the bare particle many-body T-matrix gets dressed by mean fields due to condensed and excited atoms. We conclude that the most commonly used version of the Gross-Pitaevskii equation can only be put on a microscopic basis for a restrictive range of conditions. For partial condensation, we need to take account of interactions between condensed and excited atoms, which, in a consistent formulation, should also be expressed in terms of the many-body T-matrix. This can be achieved by considering fluctuations around the condensate mean field beyond those included in the conventional finite temperature mean field, i.e. Hartree-Fock-Bogoliubov (HFB), theory.
The Klein-Gordon equation is a useful test arena for quantum cosmological models described by the Wheeler-DeWitt equation. We use the decoherent histories approach to quantum theory to obtain the probability that a free relativistic particle crosses a section of spacelike surface. The decoherence functional is constructed using path integral methods with initial states attached using the (positive definite) ``induced'' inner product between solutions to the constraint equation. The notion of crossing a spacelike surface requires some attention, given that the paths in the path integral may cross such a surface many times, but we show that first and last crossings are in essence the only useful possibilities. Different possible results for the probabilities are obtained, depending on how the relativistic particle is quantized (using the Klein-Gordon equation, or its square root, with the associated Newton-Wigner states). In the Klein-Gordon quantization, the decoherence is only approximate, due to the fact that the paths in the path integral may go backwards and forwards in time. We compare with the results obtained using operators which commute with the constraint (the ``evolving constants'' method).
We derive two-sided estimates on moments and tails of Gaussian chaoses, that is, random variables of the form $\sum a_{i_1,...,i_d}g_{i_1}... g_{i_d}$, where $g_i$ are i.i.d. ${\mathcal{N}}(0,1)$ r.v.'s. Estimates are exact up to constants depending on $d$ only.
The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing decoherence, and then the deletion of a subsystem. This description of the measuring process is a substantial generalization of current models in quantum measurement theory. In particular, no ancilla is needed. The final result is represented by a completely positive map of the quantum state $\rho$ (possibly with a change of the dimensions of $\rho$). A continuous limit of the above process leads to Lindblad's equation for the quantum dynamical semigroup.
In this paper we consider an alternative formulation of a class of stochastic wave and master equations with scalar noise that are used in quantum optics for modelling open systems and continuously monitored systems. The reformulation is obtained by applying J.M.C. Clark's pathwise reformulation technique from the theory of classical nonlinear filtering. The pathwise versions of the stochastic wave and master equations are defined for all driving paths and depend continuously on them. In the case of white noise equations, we derive analogs of Clark's robust approximations. The results in this paper may be useful for implementing filters for the continuous monitoring and measurement feedback control of quantum systems, and for developing new types of numerical methods for unravelling master equations. The main ideas are illustrated by an example.
We present analytical results concerning the magneto-roton instability in higher Landau levels evaluated in the single mode approximation. The roton gap appears at a finite wave vector, which is approximately independent of the LL index n, in agreement with numerical calculations in the composite-fermion picture. However, a large maximum in the static susceptibility indicates a charge density modulation with wave vectors $q_0(n)\sim 1/\sqrt{2n+1}$, as expected from Hartree-Fock predictions. We thus obtain a unified description of the leading charge instabilities in all LLs.
Massive stars play a significant role in the chemical and dynamical evolution of galaxies. However, much of their variability, particularly during their evolved supergiant stage, is poorly understood. To understand the variability of evolved massive stars in more detail, we present a study of the O9.2Ib supergiant $\zeta$ Ori Aa, the only currently confirmed supergiant to host a magnetic field. We have obtained two-color space-based BRIght Target Explorer photometry (BRITE) for $\zeta$ Ori Aa during two observing campaigns, as well as simultaneous ground-based, high-resolution optical CHIRON spectroscopy. We perform a detailed frequency analysis to detect and characterize the star's periodic variability. We detect two significant, independent frequencies, their higher harmonics, and combination frequencies: the stellar rotation period $P_{\mathrm{rot}} = 6.82\pm0.18$ d, most likely related to the presence of the stable magnetic poles, and a variation with a period of $10.0\pm0.3$ d attributed to circumstellar environment, also detected in the H$\alpha$ and several He I lines, yet absent in the purely photospheric lines. We confirm the variability with $P_{\mathrm{rot}}$/4, likely caused by surface inhomogeneities, being the possible photospheric drivers of the discrete absorption components. No stellar pulsations were detected in the data. The level of circumstellar activity clearly differs between the two BRITE observing campaigns. We demonstrate that $\zeta$ Ori Aa is a highly variable star with both periodic and non-periodic variations, as well as episodic events. The rotation period we determined agrees well with the spectropolarimetric value from the literature. The changing activity level observed with BRITE could explain why the rotational modulation of the magnetic measurements was not clearly detected at all epochs.
We define special Hamiltonian-paths and special permutations of the up-facing dark tiles on a checked triangular grid related to the generalized Sierpi\'{n}ski Gasket. Our definitions and observations make possible the generalization of the Sierpi\'{n}ski Arrowhead Curve for all orders. We produce these symmetric recursive curves in many ways by two kinds of asymmetric paths which are in a bijective relation and unambiguously transformable into each other in any order. These node-rewriting and edge-rewriting recursive curves keep their self-avoiding and simple properties after the transformation and their cardinality specifies a new integer sequence. We show a transformation table to change the curves into each other and we give another table to change them into Lindenmayer-system strings both by the absolute direction codes of their edges.
Magnetic structure evolution of multiferroic hexagonal $YMn_{1-x}Fe_{x}O_{3}$ (${x} = 0, 0.05,$ and $0.1$) has been studied by carrying out detailed temperature-dependent neutron diffraction at zero- and 5T-fields. Thermodynamic data confirm antiferromagnetic ordering at $T_{N}$ in all the compositions. Our sub-$T_{N}$ neutron diffraction results assign the magnetic structure of pure $YMnO_3$ to $\Gamma_{1}$ irreducible representation. Over the perturbative-doping range, the magnetic configuration changes via $\Gamma_{1}+\Gamma_{2}$ for $YMn_{0.95}Fe_{0.05}O_{3}$ on to $\Gamma_{2}$ for $YMn_{0.9}Fe_{0.1}O_{3}$, as the maiden compositional analogue of spin-reorientation; its occurrence in temperature-domain already reported for several manganites. Moreover, while the large thermal isostructural changes observed above ${T}_{N}$ are subdued in the ordered state, small alterations by the applied 5T-field are relatively uniform across, confirming strong magneto-elastic nature of the system. Decrease of the ordered magnetic moment ($\mu_{ord}$) and planar magnetic frustration noted with Fe-doping is enhanced by the applied field, apparently through canting.
Local models are schemes defined in terms of linear algebra which can be used to study the local structure of integral models of certain Shimura varieties, with parahoric level structure. We investigate the local models for groups of the form Res_{F/\Q_p} GL_n and Res_{F/\Q_p} GSp_2g where F/Q_p is a totally ramified extension, as defined by Pappas and Rapoport, and show that they are topologically flat. In the linear case, flatness can be deduced from this.
The heterobimetallic metallacrown (MC), (TMA)$_2${Mn(OAc)$_2$[12-MC$_{Mn(III)Cu(II)N(shi)}$-4](CH$_3$OH)}$\cdot$2.90CH$_3$OH, 1, where TMA$^+$ is tetramethylammonium, $^-$OAc is acetate, and shi$^{3-}$ is salicylhydroximate, consists of a Mn$^{II}$ ion captured in the central cavity and alternating unambiguous and ordered manganese(III) and copper(II) sites about the MC ring, a first for the archetypal MC structure design. DC-magnetometry characterization and subsequent simulation with the Spin Hamiltonian $$H = -J_1(\mathbf{s}_1+\mathbf{s}_3)\cdot\mathbf{s}_5-J_2(\mathbf{s}_2+\mathbf{s}_4)\cdot\mathbf{s}_5-J_3\sum_{i=1}^{4}\mathbf{s}_i\cdot\mathbf{s}_{i+1} + d(s_{z,1}^2 + s_{z,3}^2) + \mu_B\sum_{j=1}^5 g_j\mathbf{s}_j\cdot\mathbf{B}$$ indicates an S = 5/2 ground state and a sizable axial zero-field splitting on Mn$^{III}$. AC-susceptibility measurements reveal that 1 displays slow magnetization relaxation akin to single-molecule magnet (SMM) behavior.
We present late-time ($\sim$240-260 days after peak brightness) optical photometry and nebular (+236 and +264 days) spectroscopy of SN 2018oh, the brightest Type Ia supernova (SN Ia) observed by the Kepler telescope. The Kepler/K2 30-minute cadence observations started days before explosion and continued past peak brightness. For several days after explosion, SN 2018oh had blue "excess" flux in addition to a normal SN rise. The flux excess can be explained by the interaction between the SN and a Roche-lobe filling non-degenerate companion star. Such a scenario should also strip material from the companion star, that would emit once the SN ejecta become optically thin, imprinting relatively narrow emission features in its nebular spectrum. We search our nebular spectra for signs of this interaction, including close examination of wavelengths of hydrogen and helium transitions, finding no significant narrow emission. We place upper limits on the luminosity of these features of $2.6,\ 2.9\ \mathrm{and}\ 2.1\times10^{37}\ \mathrm{erg\ s^{-1}}$ for H$\alpha$, He I $\lambda$5875, and He I $\lambda$6678, respectively. Assuming a simple model for the amount of swept-up material, we estimate upper mass limits for hydrogen of $5.4\times10^{-4}\ \mathrm{M_{\odot}}$ and helium of $4.7\times10^{-4}\ \mathrm{M_{\odot}}$. Such stringent limits are unexpected for the companion-interaction scenario consistent with the early data. No known model can explain the excess flux, its blue color, and the lack of late-time narrow emission features.
It has long been claimed that the antisymmetric tensor field of the second rank is pure longitudinal after quantization. In my opinion, such a situation is quite unacceptable. I repeat the well-known procedure of the derivation of the set of Proca equations. It is shown that it can be written in various forms. Furthermore, on the basis of the Lagrangian formalism I calculate dynamical invariants (including the Pauli-Lubanski vector of relativistic spin for this field). Even at the classical level the Pauli-Lubanski vector can be equal to zero after applications of well-known constraints. The importance of the normalization is pointed out for the problem of the description of quantized fields of maximal spin 1. The correct quantization procedure permits us to propose a solution of this puzzle in the modern field theory. Finally, the discussion of the connection of the Ogievetskii-Polubarinov-Kalb-Ramond field and the electrodynamic gauge is presented.
Real Space Renormalization Group (RSRG) techniques and their applications, mainly to quantum mechanics and to partial differential equations, are discussed. Special emphasis is given to the theoretical insight and the reasons for the success of some techniques, specially DMRG. Applications to the spectrum of dendrimers and excitons on random media are considered. This work is the Ph.D. of the author. Almost all the results have already been published. The main interest of this text is paedagogical and as a review.
Two sides of cosmological constant problem are discussed: a mysterious compensation of all contributions to vacuum energy with the accuracy of 100-50 orders of magnitude and a surprising equality of a constant vacuum energy density to the present-day value of time dependent cosmological energy density.
Assuming the Generalized Riemann Hypothesis, the authors study when a character sum over all n <= x is o(x); they show that this holds if log x / log log q -> infinity and q -> infinity (q is the size of the finite field).