ShantanuT01/DACTYL-Pretraining huggingface dataset:
Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations. As prototypes we study three variants of a generic time-fractional Fokker-Planck equation with constant force. Type A generates superdiffusion, type B subdiffusion and type C both super- and subdiffusion depending on parameter variation. Furthermore type C obeys a fluctuation-dissipation relation whereas A and B do not. We calculate analytically the position PDFs for all three cases and explore numerically their strongly non-Gaussian shapes. While for type C we obtain the conventional transient work fluctuation relation, type A and type B both yield deviations by featuring a coefficient that depends on time and by a nonlinear dependence on the work. We discuss possible applications of these types of dynamics and fluctuation relations to experiments.
By exactly analyzing the spin-1/2 Luttinger liquid (LL) and numerically solving a model of a mobile impurity electron in the LL, we obtain the one-electron spectral function $A(p,\omega)$ in a one-dimensional (1D) metal in an entire range of $p$ at zero temperature. For $|p|$ near the Fermi point $p_{\rm F}$, $A(p,\omega)$ is featured by two prominent peaks of spinon and (anti)holon representing spin-charge separation, but we also find an additional cusp structure between them. For $|p| \gg p_{\rm F}$, this structure evolves as a main peak in $A(p,\omega)$ by swallowing the antiholon mode and its dispersion relation approaches the one of a free electron, implying the existence of an electron excitation in the whole region, but not quite a quasiparticle in the Fermi liquid due to ever existing power-law decay of the excitation.
We study the joint laws of a continuous, uniformly integrable martingale, its maximum, and its minimum. In particular, we give explicit martingale inequalities which provide upper and lower bounds on the joint exit probabilities of a martingale, given its terminal law. Moreover, by constructing explicit and novel solutions to the Skorokhod embedding problem, we show that these bounds are tight. Together with previous results of Az\'ema & Yor, Perkins, Jacka and Cox & Ob{\l}\'oj, this allows us to completely characterise the upper and lower bounds on all possible exit/no-exit probabilities, subject to a given terminal law of the martingale. In addition, we determine some further properties of these bounds, considered as functions of the maximum and minimum.
Based on the notion of strong modular form developed in Part I, we propose to structure the family of cuspidal modular form spaces $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ and to determine bases for each of these spaces, once known bases for the first values of $k$.   We then apply these theoretical results to explicitly determine bases for space families $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ when $1\leq N \leq 10$.
The difference of quantum mutual information for bipartite system of qubits and minimum taken with respect to local unitary transformation group is introduced as a characteristic of quantum correlations.The two qubits example (and specifically the two qubits X state) is studied in some details.
We study quantitative estimates of compactness in $\mathbf{W}^{1,1}_{loc}$ for the map $S_t$, $t>0$ that associates to every given initial data $u_0\in \mathrm{Lip}(\mathbb{R}^N)$ the corresponding solution $S_t u_0$ of a Hamilton-Jacobi equation $$ u_t+H\big(x, \nabla_{\!x} u\big)=0\,, \qquad t\geq 0,\quad x\in \mathbb{R}^N, $$ with a convex and coercive Hamiltonian $H=H(x,p)$. We provide upper and lower bounds of order $1/\varepsilon^N$ on the the Kolmogorov $\varepsilon$-entropy in $\mathbf{W}^{1,1}$ of the image through the map $S_t$ of sets of bounded, compactly supported initial data. Quantitative estimates of compactness, as suggested by P.D. Lax, could provide a measure of the order of "resolution" and of "complexity" of a numerical method implemented for this equation. We establish these estimates deriving accurate a-priori bounds on the Lipschitz, semiconcavity and semiconvexity constant of a viscosity solution when the initial data is semiconvex. The derivation of a small time controllability result is also fundamental to establish the lower bounds on the $\varepsilon$-entropy.
We investigate the non-Gaussian features of the IGM at redshift $z\sim 5 - 6$ using Ly$\alpha$ transmitted flux of quasar absorption spectra and cosmological hydrodynamic simulation of the concordance $\Lambda$CDM universe. We show that the neutral hydrogen mass density field and Ly$\alpha$ transmitted flux fluctuations possess all the non-Gaussian features predicted by the log-Poisson hierarchy, which depends only on two dimensionless parameters $\beta$ and $\gamma$, describing, respectively, the intermittence and singularity of the random fields. We find that the non-Gaussianity of the Ly$\alpha$ transmitted flux of quasars from $z=4.9$ to $z=6.3$ can be well reconstructed by the hydrodynamical simulation samples. Although the Gunn-Peterson optical depth and its variance underwent a significant evolution in the redshift range of $5 - 6$, the intermittency measured by $\beta$ is almost redshift-independent in this range. More interesting, the intermittency of quasar's absorption spectra on physical scales $0.1-1$ h$^{-1}$Mpc in redshift $5 - 6$ are found to be about the same as that on physical scales $1-10$ h$^{-1}$Mpc at redshifts $2 - 4$. Considering the Jeans length is less than 0.1 h$^{-1}$Mpc at $z\sim 5$, and $1$ h$^{-1}$Mpc at $z\sim 2$, these results imply that the nonlinear evolution in high and low redshifts will lead the cosmic baryon fluid to a state similar to fully developed turbulence. The log-Poisson high order behavior of current high redshift data of quasar's spectrum can be explained by uniform UV background in the redshift range considered. We also studied the log-Poisson non-Gaussianity by considering inhomogeneous background. With several simplified models of inhomogeneous background, we found the effect of the inhomogeneous background on the log-Poisson non-Gaussianity is not larger than 1-sigma.
We investigate effects of finite core-spin in two-neutron halos in the three-body model consisting of two neutrons and a core. The states in the neutron-core subsystem can then have an additional splitting due to the coupling of the neutron and core spins. The connection between the structure of the total system and the states of the neutron-core subsystem depends strongly on this spin splitting. However, the spatial structure is essentially unchanged. The neutron momentum distribution in a nuclear dissociation reaction will consist of a broad and a narrow distribution arising from the two spin split neutron-core virtual states. The large distance behavior is investigated and the conditions for the Efimov effect turn out to be more restrictive. The magnetic moment is equal to the core-value independent of spin splitting and energies of the neutron-core states. The excited states of opposite parity depend strongly on the spin splitting. The parameters in our numerical examples are chosen to be appropriate for $^{11}$Li and $^{19}$B.
Surveys of faint galaxies at high redshifts often result in a "pencil-beam" geometry that is much longer along the line-of-sight than across the sky. We explore the effects of this geometry on the abundance and clustering of Lyman-break galaxies (LBGs) and Lyman-alpha emitters (LAEs) in current and future surveys based on cosmological N-body simulations which adequately describe the nonlinear growth of structure on small scales and compare to linear theory. We find that the probability distribution of the LBG abundance is skewed toward low values since the narrow transverse dimension of the survey is more likely to probe underdense regions. Over a range that spans 1--2 orders of magnitude in galaxy luminosities, the variance in the number of objects differs from the commonly used analytic prediction and is not dominated by Poisson noise. Additionally, nonlinear bias on small scales results in a one-dimensional power spectrum of LAEs using a James Webb Space Telescope field-of-view that is relatively flat, markedly different from the expectation of linear perturbation theory. We discuss how these results may affect attempts to measure the UV background at high redshifts, estimate the relationship between halo mass and galaxy luminosity, and probe reionization by measuring the power-modulating effect of ionized regions.
In this paper we explore the possibility that recent results by ATLAS and CMS searching for heavy resonances decaying into bosons could be a first hint of a new sector of pure-gauge confining physics, possibly linked to the origin of the Higgs as a Composite Higgs. The lightest resonances (glueballs) of this new sector would be neutral, spin-zero and -two, and their behaviour would resemble that of a radion and a massive graviton of extra-dimensions. We outline how LHC8 data could be used to improve sensitivity on this scenario, as well as future characterization during the LHC13 run.
We analize the non-cyclic geometric phase for neutrinos. We find that the geometric phase and the total phase associated to the mixing phenomenon provide a tool to distinguish between Dirac and Majorana neutrinos. Our results hold for neutrinos propagating in vacuum and through the matter. Future experiments, based on interferometry, could reveal the nature of neutrinos.
Here we report on the formation of two and three magnon bound states in the quasi-one-dimensional antiferromagnet $\alpha$-NaMnO$_2$, where the single-ion, uniaxial anisotropy inherent to the Mn$^{3+}$ ions in this material provides a binding mechanism capable of stabilizing higher order magnon bound states. While such states have long remained elusive in studies of antiferromagnetic chains, neutron scattering data presented here demonstrate that higher order $n>2$ composite magnons exist, and, specifically, that a weak three-magnon bound state is detected below the antiferromagnetic ordering transition of NaMnO$_2$. We corroborate our findings with exact numerical simulations of a one-dimensional Heisenberg chain with easy-axis anisotropy using matrix-product state techniques, finding a good quantitative agreement with the experiment. These results establish $\alpha$-NaMnO$_2$ as a unique platform for exploring the dynamics of composite magnon states inherent to a classical antiferromagnetic spin chain with Ising-like single ion anisotropy.
In this work, we examine critically the relation between orbital magnetic dipole (scissors mode) strength and quadrupole deformation properties. Assuming a simple K=0 ground state band in an even-even nucleus, the quantities Q(2^+_1) (i.e., the static quadrupole moment) and B(E2)_{0_1 \to 2_1} both are described by a single parameter--the intrinsic quadrupole moment Q_0. In the shell model, we can operationally define Q_0(Static) and Q_0(BE2) and see if they are the same. Following a brief excursion to the sd shell, we perform calculations in the fp shell. The nuclei we consider ({44,46,48}Ti and {48,50}Cr) are far from being perfect rotors, but we find that the calculated ratio Q_0(Static)/Q_0(BE2) is in many cases surprisingly close to one. We also discuss the collectivity of orbital magnetic dipole transitions. We find that the large orbital B(M1) strength in {44}Ti relative to {46}Ti and {48}Ti cannot be explained by simple deformation arguments.
Zeckendorf's Theorem states that every positive integer can be uniquely represented as a sum of non-adjacent Fibonacci numbers, indexed from $1, 2, 3, 5,\ldots$. This has been generalized by many authors, in particular to constant coefficient fixed depth linear recurrences with positive (or in some cases non-negative) coefficients. In this work we extend this result to a recurrence with non-constant coefficients, $a_{n+1} = n a_{n} + a_{n-1}$. The decomposition law becomes every $m$ has a unique decomposition as $\sum s_i a_i$ with $s_i \le i$, where if $s_i = i$ then $s_{i-1} = 0$. Similar to Zeckendorf's original proof, we use the greedy algorithm. We show that almost all the gaps between summands, as $n$ approaches infinity, are of length zero, and give a heuristic that the distribution of the number of summands tends to a Gaussian. Furthermore, we build a game based upon this recurrence relation, generalizing a game on the Fibonacci numbers. Given a fixed integer $n$ and an initial decomposition of $n= na_1$, the players alternate by using moves related to the recurrence relation, and whoever moves last wins. We show that the game is finite and ends at the unique decomposition of $n$, and that either player can win in a two-player game. We find the strategy to attain the shortest game possible, and the length of this shortest game. Then we show that in this generalized game when there are more than three players, no player has the winning strategy. Lastly, we demonstrate how one player in the two-player game can force the game to progress to their advantage.
We consider the question of when points in tropical affine space uniquely determine a tropical hypersurface. We introduce a notion of multiplicity of points so that this question may be meaningful even if some of the points coincide. We give a geometric/combinatorial way and a tropical linear-algebraic way to approach this question. First, given a fixed hypersurface, we show how one can determine whether points on the hypersurface determine it by looking at a corresponding marking of the dual complex. With a regularity condition on the dual complex and when the number of points is minimal, we show that our condition is equivalent to the connectedness of an appropriate sub-complex. Second, we introduce notions of non-singularity of tropical matrices and solutions to tropical linear equations that take into account our notion of multiplicity and prove a Cramer's Rule type theorem relating them.
Given a variation of Hodge structures on a quasi-projective base $S$, whose generic Mumford-Tate group is non-product, we prove that the (countable) union of positive components of the Hodge locus is either an algebraic subvariety of $S$, or is Zariski-dense in $S$.
We present a systematic analysis of the constraints $\sigma_\gamma$ on the mass profile slope $\gamma$ obtainable when fitting a singular power-law ellipsoid model to a typical strong lensing observation of an extended source. These results extend our previous analysis of circular systems, Paper I. We draw our results from 676 mock observations covering a range of image configurations, each created with a fixed signal to noise ratio $S=100$ in the images. We analyse the results using a combination of theory and a simplified model which identifies the contribution to the constraints of the individual fluxes and positions in each of the lensed images. The main results are: 1. For any lens ellipticity, the constraints $\sigma_\gamma$ for two image systems are well described by the results of Paper I, transformed to elliptical coordinates; 2. We derive an analytical expression for $\sigma_\gamma$ for systems with the source aligned with the axis of the lens; 3. For both two-image systems and aligned systems, $\sigma_\gamma$ is limited by the flux uncertainties; 4. The constraints for off-axis four-image systems are a factor of two to eight better, depending on source size, than for two-image systems, and improve with increasing lens ellipticity. We show that the constraints on $\gamma$ in these systems derive from the complementary positional information of the images alone, without using flux. The complementarity improves as the offset of the source from the axis increases, such that the best constraints $\sigma_\gamma<0.01$, for $S=100$, occur when the source approaches the caustic.
An analytic study is presented of the E-e Jahn-Teller (JT) polaron. The Hamiltonian is mapped onto a new Hilbert space, which is isomorphic to an eigenspace of the angular momentum operator J, belonging to a fixed eigenvalue j of J. In this representation, the Hamiltonian decomposes into a Holstein term and a residual JT interaction. While the ground state of the JT polaron is shown to belong to j=1/2, the Holstein polaron is obtained for the "unphysical" value j=0. This is the optimal form of the Hamiltonian, which can be achieved by purely analytic means, allowing the JT and the Holstein polaron to be treated in a unified framework. The new Hamiltonian is then subjected to a variational treatment, yielding the dispersion relations and effective masses for both polarons.
Flicker (1/f^gamma) voltage noise spectrum is derived from finite-temperature quantum electromagnetic fluctuations produced by elementary charge carriers in external electric field. It is suggested that deviations of the frequency exponent \gamma from unity, observed in thin metal films, can be attributed to quantum backreaction of the conducting medium on the fluctuating field of the charge carrier. This backreaction is described phenomenologically in terms of the effective momentum space dimensionality, D. Using the dimensional continuation technique, it is shown that the combined action of the photon heat bath and external field results in a 1/f^gamma-contribution to the spectral density of the two-point correlation function of electromagnetic field. The frequency exponent is found to be equal to 1 + delta, where delta = 3 - D is a reduction of the momentum space dimensionality. This result is applied to the case of a biased conducting sample, and a general expression for the voltage power spectrum is obtained which possesses all characteristic properties of observed flicker noise spectra. The range of validity of this expression covers well the whole measured frequency band. Gauge independence of the power spectrum is proved. It is shown that the obtained results naturally resolve the problem of divergence of the total noise power. A detailed comparison with the experimental data on flicker noise measurements in metal films is given.
Whether in the Standard Model or beyond it, neutrinos contribute to the invisible decay mode of orthopositronium but practically not at all to that of parapositronium. Although this remark does not resolve the orthopositronium decay puzzle, it allows for upper bounds to be set on neutrino magnetic moments.
We propose and analyze a new method for manipulation of a heavy hole spin in a quantum dot. Due to spin-orbit coupling between states with different orbital momenta and opposite spin orientations, an applied rf electric field induces transitions between spin-up and spin-down states. This scheme can be used for detection of heavy-hole spin resonance signals, for the control of the spin dynamics in two-dimensional systems, and for determining important parameters of heavy-holes such as the effective $g$-factor, mass, spin-orbit coupling constants, spin relaxation and decoherence times.
Interacting boson models provide an elegant and powerful method to describe collective excitations of complex systems by introducing a set of effective degrees of freedom. We review the interacting boson model of nuclear structure and discuss a recent extension to the nucleon and its excited states.
We present tentative H-alpha emission line detections of four submillimetre-detected galaxies at z>3.5: the radio galaxies 8C1909+722 and 4C60.07 at signal-to-noise ratios (SNRs) of 3.1 and 2.5, and two submillimetre-selected galaxies (SMGs) near the first of these at SNRs of 10.0 and 2.4, made with the AKARI Space Telescope as part of the FUHYU mission program. These are the highest-redshift H-alpha detections in such galaxies, made possible by AKARI's unique near-infrared spectroscopic capability. The two radio galaxies had known redshifts and surrounding structure, and we have detected broad H-alpha components indicating the presence of dust-shrouded quasars. We conclude that powerful AGNs at z>3.5 occur in peaks of the star-formation density fields, supporting a close connection between stellar mass build-up and black hole mass assembly at this redshift. We also show that 4C60.07 is a binary AGN. The H-alpha detections of the two SMGs are the first redshift determinations for these sources, confirming their physical association around their companion radio galaxy. The H-alpha-derived star formation rates (SFRs) for the SMGs are lower than their far-infrared derived SFRs by a factor of ~10, suggesting a level of dust obscuration similar to that found in studies at ~1<z<2.7.
The Paschos-Wolfenstein (PW) relation joins neutral- and charged-current neutrino- and antineutrino-induced cross sections into an expression that depends on the weak mixing angle $\sin^2 \theta_W$. Contrary to the traditional approach with partonic degrees of freedom, we adopt a model built on hadronic degrees of freedom to perform a study of the PW relation at intermediate energies (100 MeV to 2 GeV). With upcoming high-statistics scattering experiments such as MINER$\nu$A and FINeSSE, a scrutiny of the PW relation is timely. Employing a relativistic Glauber nucleon knockout model for the description of quasielastic neutrino-nucleus reactions, the influence of nuclear effects on the PW relation is investigated. We discuss nuclear-model dependences and show that the PW relation is a robust ratio, mitigating the effect of final-state interactions, for example to the 1% level. The role played by a possible strangeness content of the nucleon is investigated. It appears that the uncertainties arising from the poorly known strangeness parameters and the difficulties in nuclear modelling seriously limit the applicability of the PW relation as an intermediate-energy electroweak precision tool. On the other hand, we show that nuclear effects may be sufficiently well under control to allow the extraction of new information on the axial strangeness parameter. Results are presented for $^{16} {O}$ and $^{56} {Fe}$.
In this paper, we focus on the limb-brightened, prolate spheroidal cavity of the radio galaxy Cygnus A, as revealed by the Chandra X-ray Observatory. We use the shock heated, thermal intracluster medium around the expanding cavity to infer the properties of the radio synchrotron-emitting gas inside the cavity. The gas along the N and S edges of the cavity is found to have an average temperature of 6.0 keV, which is hotter than the temperature (4.6 keV) of the adjacent intracluster gas. It is proposed that this hotter gas is intracluster gas shocked by the expanding cavity. The shock is thus inferred to be weak (Mach number 1.3, a value also inferred from the density jump at the cavity edge) and its velocity 1,460 km/s. The total kinetic power of the expansion is found to be 1.2 x 10^{46} erg/s, which is larger than both the total radio power and the power emitted by the entire intracluster medium in the 2 -- 10 keV band. It appears that most of the power of the jets in Cygnus A is currently going into heating the intracluster medium. From the derived pressure inside the cavity, there is no conclusive evidence for a component contributing pressure additional to the magnetic fields and relativistic particles responsible for the synchrotron radio emission. Further, the ratio of energy densities in positive to negative cosmic rays in Cygnus A is between 1 and 100 (the value in our Galaxy).