ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider heat transfer across an arbitrary harmonic network connected to two heat baths at different temperatures. The network has $N$ positional degrees of freedom, of which $N_L$ are connected to a bath at temperature $T_L$ and $N_R$ are connected to a bath at temperature $T_R$. We derive an exact formula for the cumulant generating function for heat transfer between the two baths. The formula is valid even for $N_L \ne N_R$ and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.
It is investigated why the root mean square radius of the point neutron distribution is smaller by about 0.1 fm in non-relativistic mean field models than in relativistic ones. The difference is shown to stem from the different values of the product of the effective mass and the strength of the one-body potential in the two frameworks. The values of those quantities are constrained by the Hugenholtz-Van Hove theorem. The neutron skin is not a simple function of the symmetry potential, but depends on the nucleon effective mass.
The S-matrix Bootstrap originated on the idea that the S-matrix might be fully constrained by global symmetries, crossing, unitarity, and analyticity without relying on an underlying dynamical theory that may or may not be a quantum field theory. Recently this approach was revived from a somewhat different point of view. Using the same constraints, one numerically maps out the (infinite-dimensional) space of allowed S-matrices that should contain all consistent quantum field theories (and quantum theories of gravity). Moreover, in the best case scenario one finds special points in the space that can be identified with a certain quantum field theory of interest. In that case, the approach allows the numerical computation of the S-matrix without relying on the particular Lagrangian of the theory.   In this white paper we summarize the state of the art and discuss the future of the topic.
We prove an asymptotic formula for the mean-square average of $L$- functions associated to subgroups of characters of sufficiently large size. Our proof relies on the study of certain character sums ${\cal A}(p,d)$ recently introduced by E. Elma. We obtain an asymptotic formula for ${\cal A}(p,d)$ which holds true for any divisor $d$ of $p-1$ removing previous restrictions on the size of $d$. This anwers a question raised in Elma's paper. Our proof relies both on estimates on the frequency of large character sums and techniques from the theory of uniform distribution. As an application we deduce the following bound $h_{p,d}^- \leq 2\left (\frac{(1+o(1))p}{24}\right )^{m/4}$ on the relative class numbers of the imaginary number fields of conductor $p\equiv 1\mod d$ and degree $m=(p-1)/d$.
Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of measures, when the sequence $\xi_n$ is assumed to be stationary. In this respect, the limit variable is naturally described as a certain canonical conditional distribution. Then, given some functional $\tau$ defined on a space of laws, the consistency of the estimators $\tau(m_n)$ is investigated. Hence, a criterion for a refined notion of robustness, that applies when considering random measures, is provided in terms of the modulus of continuity of $\tau$.
We consider the inverse Stefan type free boundary problem, where information on the boundary heat flux and density of the sources are missing and must be found along with the temperature and the free boundary. We pursue optimal control framework where boundary heat flux, density of sources, and free boundary are components of the control vector. The optimality criteria consists of the minimization of the $L_2$-norm declinations of the temperature measurements at the final moment, phase transition temperature, and final position of the free boundary. We prove the Frechet differentiability in Besov spaces, and derive the formula for the Frechet differential under minimal regularity assumptions on the data. The result implies a necessary condition for optimal control and opens the way to the application of projective gradient methods in Besov spaces for the numerical solution of the inverse Stefan problem.
We propose a phase factor of the worldsheet S-matrix for strings on AdS_5 x S^5 apparently solving Janik's crossing relation.
A quantum-mechanical 1/3 magnetization plateau and magnetic long-range order appear in the large-spin (5/2) substance SrMn3P4O14. Magnetization results of SrMn3P4O14 can be explained by the spin-5/2 isolated antiferromagnetic linear trimer with the intra-trimer interaction ($J_1$) value of 4.0 K. In the present study, to confirm the spin system, we performed inelastic neutron scattering (INS) experiments of SrMn3P4O14 powders. We observed plural magnetic excitations. The peak positions are 0.46, 0.68, and 1.02 meV. Constant-Q-scan spectra at several Q values (magnitude of the scattering vector) indicate that the dispersion is weak. The weak dispersion indicates that the excitations are transitions between discrete energy levels. Our INS results are consistent with results expected in the trimer model. We evaluated the J1 value as 0.29 meV (3.4 K) without considering the other interactions.
We systematically study the spectrum of open strings attached to half BPS giant gravitons in the N=4 SYM AdS/CFT setup. We find that some null trajectories along the giant graviton are actually null geodesics of AdS_5x S^5, so that we can study the problem in a plane wave limit setup. We also find the description of these states at weak 't Hooft coupling in the dual CFT. We show how the dual description is given by an open spin chain with variable number of sites. We analyze this system in detail and find numerical evidence for integrability. We also discover an interesting instability of long open strings in Ramond-Ramond backgrounds that is characterized by having a continuum spectrum of the string, which is separated from the ground state by a gap. This instability arises from accelerating the D-brane on which the strings end via the Ramond-Ramond field. From the integrable spin chain point of view, this instability prevents us from formulating the integrable structure in terms of a Bethe Ansatz construction.
Isospin and flavor SU(3) relations in charmless hadronic B decays $B\to \pi \pi, \pi K$ are investigated in detail with paying attention to the SU(3) symmetry breaking effects in both amplitudes and strong phases. In general, the isospin and the flavor SU(3) structure of the effective Hamiltonian provide several relations among the amplitudes and strong phases. Whereas a global fit to the latest data shows that some relation seems not to be favorable for a consistent explanation to the current data within the standard model (SM). By considering several patterns of SU(3) breaking, the amplitudes and the corresponding strong phases are extracted and compared with the theoretical estimations. It is found that in the case of SU(3) limits and also the case with SU(3) breaking only in amplitudes, the fitting results lead to an unexpected large ratio between two isospin amplitudes $a^{c}_{3/2}/a^{u}_{3/2}$, which is about an order of magnitude larger than the SM prediction. The results are found to be insensitive to the weak phase $\gamma$. By including SU(3) breaking effects on the strong phases, one is able to obtain a consistent fit to the current data within the SM, which implies that the SU(3) breaking effect on strong phases may play an important role in understanding the observed charmless hadronic B decay modes $B\to \pi \pi$ and $\pi K$. It is possible to test those breaking effects in the near future from more precise measurements of direct CP violation in B factories.
Since its discovery more than half a century ago Przybylski's star (HD101065) continues to excite the astronomical community by the unusual nature of its spectrum, exhibiting exotic element abundances. This star was also the first magnetic chemically peculiar A-type star for which the presence of rapid oscillations was established. Our analysis of newly acquired and historic longitudinal magnetic field measurements indicates that Przybylski's star is also unusual with respect to its extremely slow rotation. Adopting a dipolar structure for the magnetic field and using a sine wave fit to all reported longitudinal magnetic field values over the last 43yr, we find a probable rotation period P_rot ~ 188yr, which however has to be considered tentative as it does not represent a unique solution and has to be verified by future observations. Additionally, based on our own spectropolarimetric material obtained with HARPSpol, we discuss the impact of the anomalous structure of its atmosphere, in particular of the non-uniform horizontal and vertical distributions of chemical elements on the magnetic field measurements and the pulsational variability. Anomalies related to the vertical abundance stratification of Pr and Nd are for the first time used to establish the presence of a radial magnetic field gradient.
Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.
The competition number k(G) of a graph G is the smallest number k such that G together with k isolated vertices added is the competition graph of an acyclic digraph. A chordless cycle of length at least 4 of a graph is called a hole of the graph. The number of holes of a graph is closely related to its competition number as the competition number of a graph which does not contain a hole is at most one and the competition number of a complete bipartite graph $K_{\lfloor \frac{n}{2} \rfloor, \lceil \frac{n}{2} \rceil}$ which has so many holes that no more holes can be added is the largest among those of graphs with n vertices. In this paper, we show that even if a connected graph G has many holes, the competition number of G can be as small as 2 under some assumption. In addition, we show that, for a connected graph G with exactly h holes and at most one non-edge maximal clique, if all the holes of G are pairwise edge-disjoint and the clique number $\omega = \omega (G)$ of G satisfies $2 \leq \omega \leq h+1$, then the competition number of G is at most $h - \omega + 3$.
Measuring the volume weighted velocity power spectrum suffers from a severe systematic error, due to imperfect sampling of the velocity field from inhomogeneous distribution of dark matter particles/halos in simulations or galaxies with velocity measurement. This "sampling artifact" depends on both the mean particle number density $\bar{n}_P$ and the intrinsic large scale structure (LSS) fluctuation in the particle distribution. (1) We report robust detection of this sampling artifact in N-body simulations. It causes $\sim 12$% underestimation of the velocity power spectrum at $k=0.1$h/Mpc for samples with $\bar{n}_P=6\times10^{-3}$ (Mpc/h)$^{-3}$. This systematic underestimation increases with decreasing $\bar{n}_P$ and increasing $k$. Its dependence on the intrinsic LSS fluctuations is also robustly detected. (2) All these findings are expected by our theoretical modelling in paper I \cite{Zhang14}. In particular, the leading order theoretical approximation agrees quantitatively well with simulation result for $\bar{n}_P\gtrsim6\times 10^{-4}$(Mpc/h)$^{-3}$. Furthermore, we provide an ansatz to take high order terms into account. It improves the model accuracy to $\lesssim1$% at $k\lesssim0.1$h/Mpc over 3 orders of magnitude in $\bar{n}_P$ and over typical LSS clustering from $z=0$ to $z=2$. (3) The sampling artifact is determined by the deflection ${\bf D}$ field, which is straightforwardly available in both simulations and data of galaxy velocity. Hence the sampling artifact in the velocity power spectrum measurement can be self-calibrated within our framework. By applying such self-calibration in simulations, it becomes promising to determine the {\it real} large scale velocity bias of $10^{13}M_\odot$ halos with $\sim 1$% accuracy, and that of lower mass halos by better accuracy. ...[abridged]
We argue that through the Wilson lines, gauge invariance has as an effect that the hard functions in weighted spin-asymmetries in hadronic scattering processes are given by gluonic pole cross sections, rather than the usual partonic cross sections.
The hydrodynamical models used to describe the evolution of heavy-ion collisions are briefly reviewed and their results compared with recent RHIC data.
This work puts forward a generalization of the well-known rocking Markovian Brownian ratchets to the realm of antipersistent non-Markovian subdiffusion in viscoelastic media. A periodically forced subdiffusion in a parity-broken ratchet potential is considered within the non-Markovian generalized Langevin equation (GLE) description with a power-law memory kernel $\eta(t)\propto t^{-\alpha}$ ($0<\alpha<1$). It is shown that subdiffusive rectification currents, defined through the mean displacement and subvelocity $v_{\alpha}$, $<\delta x(t)>\sim v_{\alpha} t^{\alpha}/ \Gamma(1+\alpha)$, emerge asymptotically due to the breaking of the detailed balance symmetry by driving. The asymptotic exponent is $\alpha$, the same as for free subdiffusion, $<\delta x^2(t)>\propto t^\alpha$.   However, a transient to this regime with some time-dependent $\alpha_{\rm eff}(t)$ gradually decaying in time, $\alpha\leq \alpha_{\rm eff}(t)\leq 1$, can be very slow depending on the barrier height and the driving field strength. In striking contrast to its normal diffusion counterpart, the anomalous rectification current is absent asymptotically in the limit of adiabatic driving with frequency $\Omega\to 0$, displaying a resonance like dependence on the driving frequency. However, an anomalous current inversion occurs for a sufficiently fast driving, like in the normal diffusion case. In the lowest order of the driving field, such a rectification current presents a quadratic response effect. Beyond perturbation regime it exhibits a broad maximum versus the driving field strength. Moreover, anomalous current exhibits a maximum versus the potential amplitude.
We apply a simple analytical method based on a unitary transformation to calculate the Bloch-Siegert (BS) shift over the entire driving-strength range. In quantitative comparison with the numerically exact BS shift obtained by Floquet formalism as well as the previous BS results, we confirm that our calculated results are not only accurate in the weak-driving regime but also correct in strong-driving limit. In the intermediate strong-driving regime, the calculated values of the BS shift are nearly the same as the exact ones. It turns out that our calculation for the BS shift is beyond perturbation. Meanwhile, we demonstrate the signatures caused by the BS shift by monitoring the excited-state population and the probe-pump spectrum under the experiment accessible conditions. In particular, we find that when the driving frequency is fixed at the transition frequency of the system, the lineshape of the probe-pump spectrum becomes asymmetric with the increase of the driving strength, which may be verified experimentally.
We determine the expectation value of the gauge invariant operator Tr [F^2+... ] for N=4 SU(N) SYM, in the presence of an infinitely heavy static particle in the symmetric representation of SU(N). We carry out the computation in the context of the AdS/CFT correspondence, by considering the perturbation of the dilaton field caused by the presence of a D3 brane dual to such an external probe. We find that the effective chromo-electric charge of the probe has exactly the same expression as the one recently found in the computation of energy loss by radiation.
Detailed structural and magnetotransport properties of the monophosphate tungsten bronze K$_{x}$P$_4$W$_{8}$O$_{32}$ single crystals are reported. Both galvanomagnetic and thermal properties are shown to be consistent with a charge density wave electronic transition due to hidden nesting of quasi - 1D portion of the Fermi surface. We also observe the enhancement of electronic anisotropy due to reconstruction of the Fermi surface at the Peierls transition. The resistivity presents a thermal hysteresis suggesting a first order nature characteristics of a strong coupling scenario. However, other measurements such as the change of carriers density demonstrate a second order Peierls scenario with weak coupling features. We suggest that the structural transition driven by the residual strain in the K - P - O environment is responsible for the resistivity hysteresis and modifes the Fermi surface which then helps the rise to the second order Peierls instability.
We show that the baryon asymmetry produced by the out of equilibrium decay of heavy $GUT$ scalars can be the baryon asymmetry that is observed today. No restrictions need be imposed on the initial values of $B$, $L$ and $B-L$, nor on the neutrino masses; no new symmetries need be gauged nor new fermions introduced. We find two mechanisms that can bring this about for any $GUT$ gauge group. Two illustrative models are discussed that are robust, and need just two (at most four) more $GUT$ scalar fields than the minimum model. The additional scalar fields can also help in generating an adequately large value of the CP violation parameter and in efficiently annihilating the monopoles. Our work should firmly re-establish heavy $GUT$ scalars as probable progenitors of today's baryon asymmetry.
We prove a new Morse-Sard type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for $C^2$ mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the $t$-regularity and its bridge toward the $\rho$-regularity which implies topological triviality at infinity.
We describe an end-to-end generative approach for the segmentation and recognition of human activities. In this approach, a visual representation based on reduced Fisher Vectors is combined with a structured temporal model for recognition. We show that the statistical properties of Fisher Vectors make them an especially suitable front-end for generative models such as Gaussian mixtures. The system is evaluated for both the recognition of complex activities as well as their parsing into action units. Using a variety of video datasets ranging from human cooking activities to animal behaviors, our experiments demonstrate that the resulting architecture outperforms state-of-the-art approaches for larger datasets, i.e. when sufficient amount of data is available for training structured generative models.
We present a systematic study of the cosmic variance that existed in the formation of first stars and galaxies. We focus on the cosmic variance induced by the large-scale density and velocity environment engraved at the epoch of recombination. The density environment is predominantly determined by the dark-matter overdensity, and the velocity environment by the dark matter-baryon streaming velocity. Toward this end, we introduce a new cosmological initial condition generator BCCOMICS, which solves the quasi-linear evolution of small-scale perturbations under the large-scale density and streaming-velocity environment and generates the initial condition for dark matter and baryons, as either particles or grid data at a specific redshift. We also describe a scheme to simulate the formation of first galaxies inside density peaks and voids, where a local environment is treated as a separate universe. The resulting cosmic variance in the minihalo number density and the amount of cooling mass are presented as an application. Density peaks become a site for enhanced formation of first galaxies, which compete with the negative effect from the dark matter-baryon streaming velocity on structure formation.
The gravity-related model of spontaneous wave function collapse, a longtime hypothesis, damps the massive Schr\"odinger Cat states in quantum theory. We extend the hypothesis and assume that spontaneous wave function collapses are responsible for the emergence of Newton interaction. Superfluid helium would then show significant and testable gravitational anomalies.
A combination of the X-ray imaging and SZ measurements of clusters permits an indirect determination of the radial temperature profiles of intracluster gas, which requires no assumption about the dynamical properties and the equation of state for clusters. A comparison of such a derived gas temperature with that given by the X-ray spectral analysis constitutes an effective probe of properties of intracluster gas. Using the available data of 31 clusters in literature, we have performed the first comparison of the central gas temperatures provided by the two methods. The good agreement between these two independent temperature estimates suggests that the distribution of intracluster gas is essentially consistent with isothermality characterized by a mean polytropic index of gamma=0.9+-0.1.
We address the problem of the determination of the images of three-dimensional geometric and modular Galois representations. In the modular case the existence of these representations is only conjectural. We give conditions to ensure that the images are as large as possible for almost every prime. We compute some examples and stress the applications to inverse Galois theory.
I describe the use of chiral effective theory (ChiET) to compute electromagnetic reactions in two- and three-nucleon systems. I first explain how chiral perturbation theory can be extended to the few-nucleon sector. I then explain the predictions of the resulting ChiET for electron-deuteron scattering, and how they will be tested by forthcoming data from BLAST. I conclude by displaying predictions for elastic Compton scattering from deuterium and Helium-3 nuclei. These computations, in concert with future data from MAX-Lab and HIGS, should give significant new information on neutron polarizabilities, and hence yield insight into the structure of the nucleon.