ShantanuT01/DACTYL-Pretraining huggingface dataset:
We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. The new representation is superior in practice to an earlier phase space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times several fold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse field Ising model in one and two dimensions
We revisit the work of Dhar and Majumdar [Phys. Rev. E 59, 6413 (1999)] on the limiting distribution of the temporal mean $M_{t}=t^{-1}\int_{0}^{t}du \sign y_{u}$, for a Gaussian Markovian process $y_{t}$ depending on a parameter $\alpha $, which can be interpreted as Brownian motion in the scale of time $t^{\prime}=t^{2\alpha}$. This quantity, for short the mean `magnetization', is simply related to the occupation time of the process, that is the length of time spent on one side of the origin up to time t. Using the fact that the intervals between sign changes of the process form a renewal process in the time scale t', we determine recursively the moments of the mean magnetization. We also find an integral equation for the distribution of $M_{t}$. This allows a local analysis of this distribution in the persistence region $(M_t\to\pm1)$, as well as its asymptotic analysis in the regime where $\alpha$ is large. We finally put the results thus found in perspective with those obtained by Dhar and Majumdar by another method, based on a formalism due to Kac.
The concept of relativistic scaling is applied to describe the most recent data from inclusive electron-deuteron scattering at large momentum transfer. We calculate the asymptotic scaling function f(y) of the deuteron using its relationship with the nucleon momentum distribution. The latter is obtained in the framework of the relativistic light-front dynamics (LFD) method, in which the deuteron is described by six invariant functions f_{i} (i=1,...,6) instead of two (S and D waves) in the nonrelativistic case. Comparison of the LFD asymptotic scaling function with other calculations using $S$ and $D$ waves corresponding to various nucleon-nucleon potentials, as well as with the Bethe-Salpeter result is made. It is shown that for |y|> 400 MeV/c the differences between the LFD and the nonrelativistic scaling functions become larger.
Carbon-rich grains are observed to condense in the ejecta of recent core-collapse supernovae, within a year after the explosion. Silicon carbide grains of type X are C-rich grains with isotpic signatures of explosive supernova nucleosynthesis have been found in primitive meteorites. Much rarer silicon carbide grains of type C are a special sub-group of SiC grains from supernovae. They show peculiar abundance signatures for Si and S, isotopically heavy Si and isotopically light S, which appear to to be in disagreement with model predictions. We propose that C grains are formed mostly from C-rich stellar material exposed to lower SN shock temperatures than the more common type X grains. In this scenario, extreme $^{32}$S enrichments observed in C grains may be explained by the presence of short-lived $^{32}$Si ($\tau$$_{1/2}$ = 153 years) in the ejecta, produced by neutron capture processes starting from the stable Si isotopes. No mixing from deeper Si-rich material and/or fractionation of Si from S due to molecular chemistry is needed to explain the $^{32}$S enrichments. The abundance of $^{32}$Si in the grains can provide constraints on the neutron density reached during the supernova explosion in the C-rich He shell material. The impact of the large uncertainty of the neutron capture cross sections in the $^{32}$Si region is discussed.
The most fundamental example of mirror symmetry compares the Fermat hypersurfaces in P^n and P^n/G, where G is a finite group that acts on P^n and preserves the Fermat hypersurface. We generalise this to hypersurfaces in Grassmannians, where the picture is richer and more complex. There is a finite group G that acts on the Grassmannian Gr(n,r) and preserves an appropriate Calabi-Yau hypersurface. We establish how mirror symmetry, toric degenerations, blow-ups and variation of GIT relate the Calabi-Yau hypersurfaces inside Gr(n,r) and Gr(n,r)/G. This allows us to describe a compactification of the Eguchi-Hori-Xiong mirror to the Grassmannian, inside a blow-up of the quotient of the Grassmannian by G.
Runaway O- and early B-type stars passing throughout the interstellar medium at supersonic velocities and characterized by strong stellar winds may produce bow shocks that can serve as particle acceleration sites. Previous theoretical models predict the production of high energy photons by non-thermal radiative processes, but their efficiency is still debated. We aim to test and explain the possibility of emission from the bow shocks formed by runaway stars traveling through the interstellar medium by using previous theoretical models. We apply our model to AE Aurigae, the first reported star with an X-ray detected bow shock, to BD+43 3654, in which the observations failed in detecting high energy emission, and to the transition phase of a supergiant star in the late stages of its life.From our analysis, we confirm that the X-ray emission from the bow shock produced by AE Aurigae can be explained by inverse Compton processes involving the infrared photons of the heated dust. We also predict low high energy flux emission from the bow shock produced by BD+43 3654, and the possibility of high energy emission from the bow shock formed by a supergiant star during the transition phase from blue to red supergiant.Bow shock formed by different type of runaway stars are revealed as a new possible source of high energy photons in our neighbourhood.
In this paper we study those generic intervals in the Bruhat order of the symmetric group that are isomorphic to the principal order ideal of a permutation w, and consider when the minimum and maximum elements of those intervals are related by a certain property of their reduced words. We show that the property does not hold when w is a decomposable permutation, and that the property always holds when w is the longest permutation.
The purpose of this paper is to obtain exact solutions of the Einstein field equations describing traversable wormholes supported by phantom energy. Their relationship to exact solutions in the literature is also discussed, as well as the conditions required to determine such solutions.
In this paper, we gives a complete classification of the global dynamics of two- species Lotka-Volterra competition models with nonlocal dispersals: where K, P represent nonlocal operators, under the assumptions that the nonlo- cal operators are symmetric, the models admit two semi-trivial steady states and 0<bc<1. In particular, when both semi-trivial steady states are locally stable, it is proved that there exist infinitely many steady states and the solution with non- negative and nontrivial initial data converges to some steady state. Furthermore, we generalize these results to the case that competition coefficients are location-dependent and dispersal strategies are mixture of local and nonlocal dispersals.
In this paper we study the Dirichlet problem corresponding to an open bounded set $D\subset \mathbb{R}^{d}$ and the operator \begin{equation*} A=\sum_{i=1}^{d}a\frac{\partial ^{2}}{\partial x_{i}^{2}} +\sum_{i=1}^{d}b_{i}\frac{\partial }{\partial x_{i}}, \end{equation*} where $a>0$ and $b\in \mathbb{R}^{d}$. We define a mean value property and prove that a function $u$ has such property in $D$ if and only if $Au=0$ in $D$. Using this characterization, and a drifted Brownian motion, we define a family of random variables that converges almost surely and the limit is used to give an explicit representation for the solutions to the Dirichlet problem, this immediately implies the uniqueness. On the other hand, the existence of the solution is proved imposing a regular condition on the boundary of $D$.
In this work we use a low order dynamo model and study under which conditions can it reproduce solar grand minima. We begin by building the phase space of a proxy for the toroidal component of the solar magnetic field and we develop a model, derived from mean field dynamo theory, that gives the time evolution of the toroidal field. This model is characterized by a non-linear oscillator whose coefficients retain most of the physics behind dynamo theory. In the derivation of the model we also include stochastic oscillations in the $\alpha$ effect. We found no evidences that stochastic fluctuations in a linear $\alpha$ effect can trigger grand minima episodes in this model. In contrast, the model used points out that possible mechanism that can trigger grand minima should involve the meridional circulation, magnetic diffusivity or field intensification by buoyancy driven instabilities.
On the basis of postulates for the holographic description of gravity and the introduction of entropic force, for static sources we derive the universal law: the entropy of a holographic screen is equal to quarter of its area in the Planck system of units.
The oxidation of the Ni(111) surface is studied experimentally with low energy electron microscopy and theoretically by calculating the electron reflectivity for realistic models of the NiO/Ni(111) surface with an ab-initio scattering theory. Oxygen exposure at 300 K under ultrahigh-vacuum conditions leads to the formation of a continuous NiO(111)-like film consisting of nanosized domains. At 750 K, we observe the formation of a nano-heterogeneous film composed primarily of NiO(111)-like surface oxide nuclei, which exhibit virtually the same energy-dependent reflectivity as in the case of 300 K and which are separated by oxygen-free Ni(111) terraces. The scattering theory explains the observed normal incidence reflectivity R(E) of both the clean and the oxidized Ni(111) surface. At low energies R(E) of the oxidized surface is determined by a forbidden gap in the k_parallel=0 projected energy spectrum of the bulk NiO crystal. However, for both low and high temperature oxidation a rapid decrease of the reflectivity in approaching zero kinetic energy is experimentally observed. This feature is shown to characterize the thickness of the oxide layer, suggesting an average oxide thickness of two NiO layers.
We study the spacetime structures which are described by the IIB matrix model with orientifolding. Matrix orientifolding that preserves supersymmetries yields the mirror image point with respect to a four-dimensional plane for each spacetime point that corresponds to the eigenvalue of the bosonic matrix. In order to consider the upper bound on the distance between two eigenvalues in this model, we calculate the effective action for the eigenvalues up to two-loop. The eigenvalues distribute in a tubular region around the four-dimensional plane.
The statistical distribution, when determined from an incomplete set of constraints, is shown to be suitable as host for encrypted information. We design an encoding/decoding scheme to embed such a distribution with hidden information. The encryption security is based on the extreme instability of the encoding procedure. The essential feature of the proposed system lies in the fact that the key for retrieving the code is generated by random perturbations of {\em {very small value}}. The security of the proposed encryption relies on the security to interchange the secret key. Hence, it appears as a good complement to the quantum key distribution protocol.
We have investigated the $Ln^{3+}$-substitution ($Ln$ = lanthanoid) effect of a quasi two-dimensional ferromagnet Sr$_3$Fe$_{2-x}$Co$_x$O$_{7-\delta}$ ($x$$ = $0.5). %$Ln^{3+}$-substitution creates antiferromagnetic insulating clusters around $Ln^{3+}$. With increasing $Ln^{3+}$-concentration, the ferromagnetism is gradually suppressed and the resistivity is increasing, which are ascribed to an increase in antiferromagnetic (AFM) clusters created by $Ln^{3+}$-substitution. In Sr$_{2.7}$Gd$_{0.3}$Fe$_{1.5}$Co$_{0.5}$O$_{7-\delta}$, the magnetoresistance (MR) is enhanced by about 20 % compared with that of Sr$_3$Fe$_{1.5}$Co$_{0.5}$O$_{7-\delta}$. Coexistence of ferromagnetic (FM) and AFM phases is essential for the enhancement of the MR\@. Applied magnetic fields align the FM clusters in the same direction, resulting in a reduction in the resistivity. A metamagnetic transition observed in the $Ln^{3+}$-doped samples also contributes to the enhancement of the MR.
Let d be a squarefree integer. Does there exist four squares in arithmetic progression over Q(sqrt{d})? We shall give a partial answer to this question, depending on the value of d. In the affirmative case, we construct explicit arithmetic progressions consisting of four squares over Q(sqrt{d}).
We review the different theoretical challenges concerning magnetism in interacting binary or multiple stars that will be studied in the BinaMIcS (Binarity and Magnetic Interactions in various classes of Stars) project during the corresponding spectropolarimetric Large Programs at CFHT and TBL. We describe how completely new and innovative topics will be studied with BinaMIcS such as the complex interactions between tidal flows and stellar magnetic fields, the MHD star-star interactions, and the role of stellar magnetism in stellar formation and vice versa. This will strongly modify our vision of the evolution of interacting binary and multiple stars.
Energy conversion is most efficient for micro or nano machines with tight coupling between input and output power. To reach meaningful amounts of power, ensembles of $N$ such machines must be considered. We use a model system to demonstrate that interactions between $N$ tightly coupled nanomachines can enhance the power output per machine. Furthermore, while interactions break tight coupling and thus lower efficiency in finite ensembles, the macroscopic limit ($N \rightarrow \infty$) restores it and enhances both the efficiency and the output power per nanomachine.
We present dynamical mean field theory (DMFT) results for the local spectral densities of the one- and two-particle response functions for the infinite dimensional Hubbard model in a magnetic field. We look at the different regimes corresponding to half-filling, near half-filling and well away from half-filling, for intermediate and strong values of the local interaction $U$. The low energy results are analyzed in terms of quasiparticles with field dependent parameters. The renormalized parameters are determined by two different methods, both based on numerical renormalization group (NRG) calculations, and we find good agreement. Away from half-filling the quasiparticle weights, $z_\sigma(H)$, differ according to the spin type $\sigma=\uparrow$ or $\sigma=\downarrow$. Using the renormalized parameters, we show that DMFT-NRG results for the local longitudinal and transverse dynamic spin susceptibilities in an arbitrary field can be understood in terms of repeated scattering of these quasiparticles. We also check Luttinger's theorem for the Hubbard model and find it to be satisfied in all parameter regimes and for all values of the magnetic field.
We estimate the masses of elliptical galaxies out to five effective radii using planetary nebulae and globular clusters as tracers. A sample of 15 elliptical galaxies with a broad variation in mass is compiled from the literature. A distribution function-maximum likelihood analysis is used to estimate the overall potential slope, normalisation and velocity anisotropy of the tracers. We assume power-law profiles for the potential and tracer density and a constant velocity anisotropy. The derived potential power-law indices lie in between the isothermal and Keplerian regime and vary with mass: there is tentative evidence that the less massive galaxies have steeper potential profiles than the more massive galaxies. We use stellar mass-to-light ratios appropriate for either a Chabrier/KTG (Kroupa, Tout & Gilmore) or Salpeter initial mass function to disentangle the stellar and dark matter components. The fraction of dark matter within five effective radii increases with mass, in agreement with several other studies. We employ simple models to show that a combination of star formation efficiency and baryon extent are able to account for this trend. These models are in good agreement with both our measurements out to five effective radii and recent SLACS measurements within one effective radii when a universal Chabrier/KTG initial mass function is adopted.
We report a detection of the baryon acoustic oscillation (BAO) feature in the three-dimensional correlation function of the transmitted flux fraction in the \Lya forest of high-redshift quasars. The study uses 48,640 quasars in the redshift range $2.1\le z \le 3.5$ from the Baryon Oscillation Spectroscopic Survey (BOSS) of the third generation of the Sloan Digital Sky Survey (SDSS-III). At a mean redshift $z=2.3$, we measure the monopole and quadrupole components of the correlation function for separations in the range $20\hMpc<r<200\hMpc$. A peak in the correlation function is seen at a separation equal to $(1.01\pm0.03)$ times the distance expected for the BAO peak within a concordance $\Lambda$CDM cosmology. This first detection of the BAO peak at high redshift, when the universe was strongly matter dominated, results in constraints on the angular diameter distance $\da$ and the expansion rate $H$ at $z=2.3$ that, combined with priors on $H_0$ and the baryon density, require the existence of dark energy. Combined with constraints derived from Cosmic Microwave Background (CMB) observations, this result implies $H(z=2.3)=(224\pm8){\rm km\,s^{-1}Mpc^{-1}}$, indicating that the time derivative of the cosmological scale parameter $\dot{a}=H(z=2.3)/(1+z)$ is significantly greater than that measured with BAO at $z\sim0.5$. This demonstrates that the expansion was decelerating in the range $0.7<z<2.3$, as expected from the matter domination during this epoch. Combined with measurements of $H_0$, one sees the pattern of deceleration followed by acceleration characteristic of a dark-energy dominated universe.
We revisit and extend realizations of Minimal Flavor Violation (MFV) in theories with strongly coupled electro-weak symmetry breaking. MFV requires that some chiralities of light SM quarks are strongly composite leading, depending on the scenario, to bounds from compositeness searches, precision electro-weak tests or even flavor physics. Within the framework of partial compositeness we show how to extend the MFV paradigm allowing the treat the top quark differently. This can be realized if for example the strong sector has an U(2) symmetry. In this case the light generations can be mostly elementary and all the bounds are easily satisfied.
We investigate experimentally the statistics of the free volume inside bidimensional granular packings, for two different kinds of grains and two levels of compaction. With the aim to gain new insight into the statistical description of granular media, we measure the free volume distribution in clusters of increasing size. Our main result is that the logarithm of the free volume distribution scales in a nonextensive way with the cluster size, while still enabling the extraction of two intensive parameters. We discuss the interpretation of these parameters, and the consequences of the nonextensivity on the possible measurements of Edwards' ''compactivity''.
Color transparency CT depends on the formation of a wavepacket of small spatial extent. It is useful to interpret experimental searches for CT with a multiple scattering scattering series based on wavepacket-nucleon scattering instead of the standard one using nucleon-nucleon scattering. We develop several new techniques which are valid for differing ranges of energy. These techniques are applied to verify some early approximations; study new forms of the wave-packet-nucleon interaction; examine effects of treating wave packets of non-zero size; and predict the production of $N^*$'s in electron scattering experiments.
Assuming the dark matter halo of the Milky Way as a non-spherical potential (i.e. triaxial, prolate, oblate), we show how the assembling process of the Milky Way halo, may have left long lasting stellar halo kinematic fossils only due to the shape of the dark matter halo. In contrast with tidal streams, associated with recent satellite accretion events, these stellar kinematic groups will typically show inhomogeneous chemical and stellar population properties. However, they may be dominated by a single accretion event for certain mass assembling histories. If the detection of these peculiar kinematic stellar groups is confirmed, they would be the smoking gun for the predicted triaxiality of dark halos in cosmological galaxy formation scenarios.
The gravitating matter is studied within the framework of the non-commutative geometry. The non-commutative Einstein-Hilbert action on the product of a four dimensional manifold with a discrete space gives the models of matter fields coupled to the standard Einstein gravity.The matter multiplet is encoded in the Dirac operator which yields the representation of the algebra of the universal forms. The general form of the Dirac operator depends on a choice of the grading of the corresponding spinor bundle. A choice is given, which leads to the nonlinear vector sigma-model coupled to the Einstein gravity.
We show how to prepare a variety of cavity field states for multiple cavities. The state preparation technique used is related to the method of stimulated adiabatic Raman passage or STIRAP. The cavity modes are coupled by atoms, making it possible to transfer an arbitrary cavity field state from one cavity to another, and also to prepare non-trivial cavity field states. In particular, we show how to prepare entangled states of two or more cavities, such as an EPR state and a W state, as well as various entangled superpositions of coherent states in different cavities, including Schrodinger cat states. The theoretical considerations are supported by numerical simulations.
The micromotion of ion crystals confined in Paul traps is usually considered an inconvenient nuisance, and is thus typically minimised in high-precision experiments such as high-fidelity quantum gates for quantum information processing. In this work, we introduce a particular scheme where this behavior can be reversed, making micromotion beneficial for quantum information processing. We show that using laser-driven micromotion sidebands, it is possible to engineer state-dependent dipole forces with a reduced effect of off-resonant couplings to the carrier transition. This allows one, in a certain parameter regime, to devise entangling gate schemes based on geometric phase gates with both a higher speed and a lower error, which is attractive in light of current efforts towards fault-tolerant quantum information processing. We discuss the prospects of reaching the parameters required to observe this micromotion-enabled improvement in experiments with current and future trap designs.
In this paper we consider the weak formulation of the inverse anisotropic mean curvature flow, in the spirit of Huisken-Ilmanen. By using approximation method involving Finsler-p-Laplacian, we prove the existence and uniqueness of weak solutions.