ShantanuT01/DACTYL-Pretraining huggingface dataset:
Since the quality factor of an acoustic wave resonator (AWR) reached $10^{11}$, AWRs have been regarded as a good carrier of quantum information. In this paper, we propose a scheme to construct a NOON state with two AWRs assisted by a nitrogen-vacancy-center ensemble (NVE). The two AWRs cross each other vertically, and the NVE is located at the center of the crossing. By considering the decoherence of the system and using resonant interactions between the AWRs and the NVE, and the single-qubit operation of the NVE, a NOON state can be achieved with a fidelity higher than $98.8\%$ when the number of phonons in the AWR is $N \le 3$.
In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs in short) under general settings without technical assumptions on the coefficients. For the solution of semi-linear degenerate BSPDE, we first give a proof for its existence and uniqueness, as well as regularity. Then the connection between semi-linear degenerate BSPDEs and forward backward stochastic differential equations (FBSDEs in short) is established, which can be regarded as an extension of Feynman-Kac formula to non-Markov frame.
Magnetic and electronic properties of NaTiSi$_2$O$_6$ in low temperature phase were studied in the framework of the LDA+U approximation. We stress that neglecting correlation effects in LSDA calculations one obtains not only several times smaller value of the band gap, but also fails to describe magnetic properties of NaTiSi$_2$O$_6$. Our LDA+U results confirm formation of singlet Ti-Ti dimers in low temperature phase of NaTiSi$_2$O$_6$ driven by corresponding orbital ordering [J. Phys. Soc. Jpn. 71, 1423 (2002)], but strongly disagree with the LSDA results and interpretations of Phys. Rev. Lett. 93, 036401 (2004).
The spin-Hall effect describes the interconversion of charge currents and spin currents, enabling highly efficient manipulation of magnetization for spintronics. Symmetry conditions generally restrict polarizations of these spin currents to be orthogonal to both the charge and spin flows. Spin polarizations can deviate from such direction in nonmagnetic materials only when the crystalline symmetry is reduced11. Here we experimentally show control of the spin polarization direction by using a non-collinear antiferromagnet Mn$_{3}$GaN, in which the triangular spin structure creates a low magnetic symmetry state while maintaining a high crystalline symmetry. We demonstrate that epitaxial Mn3GaN/Permalloy heterostructures can generate unique types of spinHall torques at room temperature corresponding to unconventional spin polarizations collinear to spin currents or charge currents which are forbidden in any sample with two-fold rotational symmetry. Our results demonstrate an approach based on spin-structure design for controlling spinorbit torque, paving the way for further progress in the emergent field of antiferromagnetic spintronics.
The mapping observations of CO $J=2-1$, CO $J=3-2$, $^{13}$CO $J=2-1$ and $^{13}$CO $J=3-2$ lines in the direction of IRAS 22506+5944 have been made. The results show that the cores in the $J=2-1$ transition lines have a similar morphology to those in the $J=3-2$ transition lines. Bipolar molecular outflows are verified. The prior IRAS 22506+5944 observations indicated that two IRAS sources and three H$_{2}$O masers were located close to the peak position of the core. One of the IRAS sources may be the driving source of the outflows. In addition, the H$_{2}$O masers may occur in relatively warm environments. The parameters of the dense core and outflow, obtained by the LTE method, indicate that IRAS 22506+5944 is a high-mass star formation region.
Large-scale fully interconnected ring carbon nanotube (CNT) networks were first prepared using thermo chemical vapor deposition in nano-channel network templates of porous anodic alumina. This conductive CNT network film consists of billions of nanotube segments with a single layer, and could be made as large as the centimeter size of the template, with a uniform two-dimensional ring topological structure. These CNT networks could be grown from tiny Fe/Co catalyst particles which were electro-deposited into the templates, or totally without additional metallic catalysts. The common interconnected ring topology suggests a both-tip growth mechanism in which the growth of every CNT should occurs at both ends by the incorporation of carbon clusters until they connect into other CNTs. Comparing the different morphology of CNT networks grown with and without catalyst particles, we found that the local concentration of carbon clusters should play the key role for the continued growth of CNTs.
We discuss B-meson signatures of a Supersymmetric U(2) flavor model, with relatively light (electroweak scale masses) third generation right-handed scalars. We impose current B and K meson experimental constraints on such a theory, and obtain expectations for B->X_s gamma, B->X_s glue, B->X_s l+ l-, B->phi K_s, B_s-B_sbar mixing, and the dilepton asymmetry in B_s. We show that such a theory is compatible with all current data, and furthermore, could reconcile the apparent deviations from Standard Model predictions that have been found in some experiments.
We consider a semi-linear parabolic problem in a model plane thick fractal junction $\Omega_{\varepsilon}$, which is the union of a domain $\Omega_{0}$ and a lot of joined thin trees situated $\varepsilon$-periodically along some interval on the boundary of $\Omega_{0}.$ The trees have finite number of branching levels. The following nonlinear Robin boundary condition $\partial_{\nu}v_{\varepsilon} + \varepsilon^{\alpha_i} \kappa_i(v_{\varepsilon}) = \varepsilon^{\beta_i} g^{(i)}_{\varepsilon}$ is given on the boundaries of the branches from the $i$-th branching layer; $\alpha_i$ and $\beta_i$ are real parameters. The asymptotic analysis of this problem is made as $\varepsilon\to0,$ i.e., when the number of the thin trees infinitely increases and their thickness vanishes. In particular, the corresponding homogenized problem is found and the existence and uniqueness of its solution in an anizotropic Sobolev space of multi-sheeted functions is proved. We construct the asymptotic approximation for the solution $v_\varepsilon$ and prove the corresponding asymptotic estimate in the space $C\big([0,T]; L^2(\Omega_\varepsilon) \big) \cap L^2\big(0, T; H^1(\Omega_\varepsilon)\big)$, which shows the influence of the parameters $\{\alpha_i\}$ and $\{\beta_i\}$ on the asymptotic behavior of the solution.
We present three-dimensional magnetohydrodynamic simulations of magnetized gas clouds accelerated by hot winds. We initialize gas clouds with tangled internal magnetic fields and show that this field suppresses the disruption of the cloud: rather than mixing into the hot wind as found in hydrodynamic simulations, cloud fragments end up co-moving and in pressure equilibrium with their surroundings. We also show that a magnetic field in the hot wind enhances the drag force on the cloud by a factor ~(1+v_A^2/v_wind^2)$, where v_A is the Alfven speed in the wind and v_wind measures the relative speed between the cloud and the wind. We apply this result to gas clouds in several astrophysical contexts, including galaxy clusters, galactic winds, the Galactic center, and the outskirts of the Galactic halo. Our results can explain the prevalence of cool gas in galactic winds and galactic halos and how such cool gas survives in spite of its interaction with hot wind/halo gas. We also predict that drag forces can lead to a deviation from Keplerian orbits for the G2 cloud in the galactic center.
Models of neutrino mass which attempt to describe the observed lepton mixing pattern are typically based on discrete family symmetries with a non-Abelian and one or more Abelian factors. The latter so-called shaping symmetries are imposed in order to yield a realistic phenomenology by forbidding unwanted operators. Here we propose a supersymmetric model of neutrino flavor which is based on the group T7 and does not require extra Z_N or U(1) factors, which makes it the smallest realistic family symmetry that has been considered so far. At leading order, the model predicts tribimaximal mixing which arises completely accidentally from a combination of the T7 Clebsch-Gordan coefficients and suitable flavon alignments. Next-to-leading order (NLO) operators break the simple tribimaximal structure and render the model compatible with the recent results of the Daya Bay and Reno collaborations which have measured a reactor angle of around 9 degrees. Problematic NLO deviations of the other two mixing angles can be controlled in an ultraviolet completion of the model.
We study scattering of the electroweak gauge bosons in 5D warped models. Within two different models we determine the precise manner in which the Higgs boson and the vector resonances ensure the unitarity of longitudinal vector boson scattering. We identify three separate scales that determine the dynamics of the scattering process in all cases. For a quite general background geometry of 5D, these scales can be linked to a simple functional of the warp factor. The models smoothly interpolate between a `composite' Higgs limit and a Higgsless limit. By holographic arguments, these models provide an effective description of vector boson scattering in 4D models with a strongly coupled electroweak breaking sector.
We consider random walks in a balanced i.i.d. random environment in $Z^d$ for $d\ge2$ and the corresponding discrete non-divergence form difference operators. We first obtain an exponential integrability of the heat kernel bounds. We then prove the optimal diffusive decay of the semigroup generated by the heat kernel for $d\ge3$. As a consequence, we deduce a functional central limit theorem for the environment viewed from the particle.
The magnetoresistance of a three-dimensional Rashba material placed on top of a ferromagnetic insulator is theoretically investigated. In addition to the intrinsic Rashba spin-orbit interaction, we also consider extrinsic spin-orbit coupling via side-jump and skew scattering, and the Elliott-Yafet spin relaxation mechanism. The latter is anisotropic due to the mass anisotropy which reflects the noncentrosymmetric crystal structure of three-dimensional Rashba metals. A quasiclassical approach is employed to derive a set of coupled spin-diffusion equations, which are supplemented by boundary conditions that account for the spin-transfer torque at the interface of the bilayer. The magnetoresistance is fully determined by the current-induced spin polarization, i.e., it cannot in general be ascribed to a single (bulk) spin Hall angle. Our theoretical results reproduce several features of the experiments, at least qualitatively, and contain established phenomenological results in the relevant limiting cases. In particular, the anisotropy of the Elliott-Yafet spin relaxation mechanism plays a major role for the interpretation of the observed magnetoresistance.
We introduce a variant to the Diffusion Monte Carlo algorithm that can be employed to study the effects of the Rashba interaction in a many electron systems. Because of the spin--orbit nature of Rashba interaction a standard algorithm cannot be applied and therefore a specific imaginary time spin dependent propagator has been developed and implemented following previous work developed in the framework of nuclear physics. We computed the ground state energy of the 2D electron gas at different densities for several values of the Rashba interaction strength as a function of "Rashba spin states" polarization. Comparison is given with analytically known Hartree-Fock results and for the system in absence of Coulomb interaction.
Based on Bhatnagar-Gross-Krook equation coupled with Maxwell equation, we investigate the spatial dependence of a chemical, an electrostatic and an electrochmeical potentials inside a specimen connected with reservoirs. We also confirm that a gap of the chemical potential between at a connection point is negligible.
Context. For the last thirty years, most of the studies on the relaxation of stressed magnetic fields in the solar environment have onlyconsidered the Lorentz force, neglecting plasma contributions, and therefore, limiting every equilibrium to that of a force-free field. Aims. Here we begin a study of the non-resistive evolution of finite beta plasmas and their relaxation to magnetohydrostatic states, where magnetic forces are balanced by plasma-pressure gradients, by using a simple 2D scenario involving a hydromagnetic disturbance to a uniform magnetic field. The final equilibrium state is predicted as a function of the initial disturbances, with aims to demonstrate what happens to the plasma during the relaxation process and to see what effects it has on the final equilibrium state. Methods. A set of numerical experiments are run using a full MHD code, with the relaxation driven by magnetoacoustic waves damped by viscous effects. The numerical results are compared with analytical calculations made within the linear regime, in which the whole process must remain adiabatic. Particular attention is paid to the thermodynamic behaviour of the plasma during the relaxation. Results. The analytical predictions for the final non force-free equilibrium depend only on the initial perturbations and the total pressure of the system. It is found that these predictions hold surprisingly well even for amplitudes of the perturbation far outside the linear regime. Conclusions. Including the effects of a finite plasma beta in relaxation experiments leads to significant differences from the force-free case.
GU Ori was observed with the 1m telescope at Yunnan Observatories in 2005. To determine its physical properties, the Wilson-Devinney program is used. The results reveal that GU Ori is a W-subtype shallow contact binary with a more massive but cooler star 2. The mass of its two component stars are estimated to be $M_1 = 0.45M_\odot$, $M_2 = 1.05M_\odot$. The O'Connell effect was reported to be negative on the light curves observed in 2005. However, it changed to a positive one on the light curves observed from 2011 to 2012. The mean surface temperatures of star 2 ($T_2$) determined by the two sets of light curves were different, which may result from stellar activities. The O - C diagram shows that the period of GU Ori is decreasing at a rate of $dP/dt=-6.24\times{10^{-8}}day\cdot year^{-1}$, which may be caused by mass transfer from star 2 to star 1 with a rate of $\frac{dM_{2}}{dt}= - 2.98\times{10^{-8}}M_\odot/year$. GU Ori is a contact binary with quite high metallicity.
Mortality introduces an intrinsic time scale into the scale-invariant Brownian motion. This fact has important consequences for different statistics of Brownian motion. Here we are telling three short stories, where spontaneous death, such as radioactive decay, puts a natural limit to "lifetime achievements" of a Brownian particle. In story 1 we determine the probability distribution of a mortal Brownian particle (MBP) reaching a specified point in space at the time of its death. In story 2 we determine the probability distribution of the area $A=\int_0^{T} x(t) dt$ of a MBP on the line. Story 3 addresses the distribution of the winding angle of a MBP wandering around a reflecting disk in the plane. In stories 1 and 2 the probability distributions exhibit integrable singularities at zero values of the position and the area, respectively. In story 3 a singularity at zero winding angle appears only in the limit of very high mortality. A different integrable singularity appears at a nonzero winding angle. It is inherited from the recently uncovered singularity of the short-time large-deviation function of the winding angle for immortal Brownian motion.
It is argued that the lesson we should learn from Bell's inequalities is not that quantum mechanics requires some kind of action at a distance, but that it leads us to believe in parallel worlds.
Due to the time reversal invariance of the angular momentum operator J^2, the average energies and variances at fixed J for random two-body Hamiltonians exhibit odd-even-J staggering, that may be especially strong for J=0. It is shown that upon ensemble averaging over random runs, this behaviour is reflected in the yrast states. Displaced (attractive) random ensembles lead to rotational spectra with strongly enhanced BE2 transitions for a certain class of model spaces. It is explained how to generalize these results to other forms of collectivity.
We study energy measures of canonical Dirichlet forms on inhomogeneous Sierpinski gaskets. We prove that the energy measures and suitable reference measures are mutually singular under mild assumptions.
In this paper we study the so-called large solutions of elliptic semilinear equations with non null sources term, thus solutions blowing up on the boundary of the domain for which reason they are greater than any other solution whenever Weak Maximum Principle holds. The main topic about large solutions is uniqueness results and their behavior near the boundary. It is much less than being simple. The structure of the semilinear equations considered includes the well known Keller-Osserman integral and an assumption on the ellipticity of the leading part of the differential operator. In our study an uniform ellipticity near the boundary is required. We consider source terms in the PDE whose boundary explosion is consistent with the Keller-Osserman condition. Extra Keller-Osserman explosions on the source are also studied, showing in particular that in some cases the PDE only admits large solutions.
Given a finite transitive group $G\leq \operatorname{Sym}(\Omega)$, a subset $\mathcal{F}$ of $G$ is \emph{intersecting} if any two elements of $\mathcal{F}$ agree on some element of $\Omega$. The \emph{intersection density} of $G$, denoted by $\rho(G)$, is the maximum of the rational number $|\mathcal{F}|\left(\frac{|G|}{|\Omega|}\right)^{-1}$ when $\mathcal{F}$ runs through all intersecting sets in $G$. In this paper, we prove that if $G$ is the group $\operatorname{Sym}(n)$ or $\operatorname{Alt}(n)$ acting on the $k$-subsets of $\{1,2,3\ldots,n\}$, for $k\in \{3,4,5\}$, then $\rho(G)=1$. Our proof relies on the representation theory of the symmetric group and the ratio bound.
Today, most application of time-dependent density functional theory (TDDFT) use adiabatic exchange-correlation (XC) potentials that do not take into account non-local temporal effects. Incorporating such "memory" terms into XC potentials is complicated by the constraint that the derived force and torque densities must integrate to zero at every instance. This requirement can be met by deriving the potentials from an XC action that is Galilean in-variant (GI). We develop a class of simple but flexible forms for an action that respect these constraints. The basic idea is to formulate the action in terms of the Eularian-Lagrangian transformation (ELT) metric tensor, which is itself GI. The general form of the XC potentials in this class is then derived and the linear response limit is derived as well.
Solar prominences are an important tool for studying the structure and evolution of the coronal magnetic field. Here we consider so-called "hedgerow" prominences, which consist of thin vertical threads. We explore the possibility that such prominences are supported by tangled magnetic fields. A variety of different approaches are used. First, the dynamics of plasma within a tangled field is considered. We find that the contorted shape of the flux tubes significantly reduces the flow velocity compared to the supersonic free fall that would occur in a straight vertical tube. Second, linear force-free models of tangled fields are developed, and the elastic response of such fields to gravitational forces is considered. We demonstrate that the prominence plasma can be supported by the magnetic pressure of a tangled field that pervades not only the observed dense threads but also their local surroundings. Tangled fields with field strengths of about 10 G are able to support prominence threads with observed hydrogen density of the order of 10^(11) cm^(-3). Finally, we suggest that the observed vertical threads are the result of Rayleigh-Taylor instability. Simulations of the density distribution within a prominence thread indicate that the peak density is much larger than the average density. We conclude that tangled fields provide a viable mechanism for magnetic support of hedgerow prominences.
For a prime $p$, we consider Kloosterman sums $$ K_{p}(a) = \sum_{x\in \F_p^*} \exp(2 \pi i (x + ax^{-1})/p), \qquad a \in \F_p^*, $$ over a finite field of $p$ elements. It is well known that due to results of Deligne, Katz and Sarnak, the distribution of the sums $K_{p}(a)$ when $a$ runs through $\F_p^*$ is in accordance with the Sato--Tate conjecture. Here we show that the same holds where $a$ runs through the sums $a = u+v$ for $u \in \cU$, $v \in \cV$ for any two sufficiently large sets $\cU, \cV \subseteq \F_p^*$.   We also improve a recent bound on the nonlinearity of a Boolean function associated with the sequence of signs of Kloosterman sums.
Inspired by the Weak Lefschetz Principle, we study when a smooth projective variety fully determines the birational geometry of some of its subvarieties. In particular, we consider the natural embedding of the space of complete quadrics into the space of complete collineations and we observe that their birational geometry, from the point of view of Mori theory, fully determines each other. When two varieties are related in this way, we call them birational twins. We explore this notion and its various flavors for other embeddings between Mori dream spaces.
We study the constraints on the contribution of new physics in the form of scalar/pseudoscalar operators to the average forward backward asymmetry <A_{FB}> of muons in B --> K mu+ mu- and the longitudinal polarization asymmetry A_{LP} of muons in B_s --> mu+ mu-. We find that the maximum possible value of <A_{FB}> allowed by the present upper bound on B(B_s --> mu+ mu-) is about 1% at 95% C.L. and hence will be very difficult to measure. On the other hand, the present bound on B(B_s --> mu+ mu-) fails to put any constraints on A_{LP}, which can be as high as 100% even if B(B_s --> mu+ mu-) is close to its standard model prediction. The measurement of A_{LP} will be a direct evidence for an extended Higgs sector, and combined with the branching ratio B(B_s --> mu+ mu-) it can even separate the new physics scalar and pseudoscalar contributions.
Classical Gon\v{c}arov polynomials arose in numerical analysis as a basis for the solutions of the Gon\v{c}arov interpolation problem. These polynomials provide a natural algebraic tool in the enumerative theory of parking functions. By replacing the differentiation operator with a delta operator and using the theory of finite operator calculus, Lorentz, Tringali and Yan introduced the sequence of generalized Gon\v{c}arov polynomials associated to a pair $(\Delta, Z)$ of a delta operator $\Delta$ and an interpolation grid $Z$. Generalized Gon\v{c}arov polynomials share many nice algebraic properties and have a connection with the theories of binomial enumeration and order statistics. In this paper we give a complete combinatorial interpretation for any sequence of generalized Gon\v{c}arov polynomials. First, we show that they can be realized as weight enumerators in partition lattices. Then, we give a more concrete realization in exponential families and show that these polynomials enumerate various enriched structures of vector parking functions.
The rank one Gross conjecture for Deligne-Ribet $p$-adic $L$-functions was solved in works of Darmon-Dasgupta-Pollack and Ventullo by the Eisenstein congruence among Hilbert modular forms. The purpose of this paper is to prove an analogue of the Gross conjecture for the Katz $p$-adic $L$-functions attached to imaginary quadratic fields via the congruences between CM forms and non-CM forms. The new ingredient is to apply the $p$-adic Rankin-Selberg method to construct a non-CM Hida family which is congruent to a Hida family of CM forms at the $1+\varepsilon$ specialization.