ShantanuT01/DACTYL-Pretraining huggingface dataset:
Neutrinoless double-beta decay nuclear transition matrix elements are generated by an effective two-body transition operator and it consists of Gamow-Teller like and Fermi like (also tensor) operators. Spectral distribution method for the corresponding transition strengths (squares of the transition matrix elements) involves convolution of the transition strength density generated by the non-interacting particle part of the Hamiltonian with a spreading function generated by the two-body part of the Hamiltonian. Extending the binary correlation theory for spinless embedded $k$-body ensembles to ensembles with proton-neutron degrees of freedom, we establish that the spreading function is a bivariate Gaussian for transition operators $\co(k_\co)$ that change $k_\co$ number of neutrons to $k_\co$ number of protons. Towards this end, we have derived the formulas for the fourth-order cumulants of the spreading function and calculated their values for some heavy nuclei; they are found to vary from $\sim -0.4$ to -0.1. Also for nuclei from $^{76}$Ge to $^{238}$U, the bivariate correlation coefficient is found to vary from $\sim 0.6 - 0.8$ and these values can be used as a starting point for calculating nuclear transition matrix elements using the spectral distribution method.
Following previous work (JCP 134, 201103 (2011)), the replica exchange Monte Carlo technique is used to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. Here, in addition to the analytical approximation of the overlap distance given by Berne and Pechukas (BP) and the exact numerical solution of Perram and Wertheim, we tested a simple modification of the original BP approximation (MBP) which corrects the known T-shape mismatch of BP for all aspect-ratios. We found that the MBP equation of state shows a very good quantitative agreement with the exact solution. The MBP analytical expression allowed us to study size effects on the previously reported results. For the thermodynamic limit, we estimated the exact 1:5 hard ellipsoid isotropic-nematic transition at the volume fraction 0.343(3), and the nematic-solid transition in the volume fraction interval 0.592(6)-0.634(8).
In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named Spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to the famous Geroch's theorem concerning to the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all the three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-K\"ahler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle (CB)) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of a RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.
We present optical observations and Monte Carlo radiative transfer modeling of the Type Ia supernova SN 2011aa. With a $\Delta m_{15} (B)$ of $0.59 \pm 0.07$ mag and a peak magnitude $M_{\rm B}$ of $-19.30 \pm 0.27$ mag, SN 2011aa has the slowest decline rate among SNe Ia. The secondary maximum in the $I$-band is absent or equally bright as the primary maximum. The velocity of C II is lower than the velocity of Si II. This indicates either presence of C at lower velocities than Si or a line of sight effect. Application of Arnett's radiation diffusion model to the bolometric light curve indicates a massive ejecta $M_{\rm{ej}} ~ 1.8 - 2.6~M_{\odot}$. The slow decline rate and large ejecta mass, with a normal peak magnitude, are well explained by double degenerate, violent merger explosion model. The synthetic spectra and light curves generated with SEDONA considering a violent merger density profile match the observations.
Within the Bose-Einstein statistics it is shown that the blackbody radiation contains coalescent photons along with single photons. Coalescent photons were first observed in the famous Hong-Ou-Mandel experiment of 1987. For the sake of convenience, $N$ coalescent photons are referred to as the $N$-photon cluster. In this work, statistics of photon clusters and probability that a photon cluster contains $N$ photons are found versus radiation frequency and temperature. Spectra of photon-cluster radiation are calculated as functions of blackbody temperature for different cluster ranks. Derivation of the Planck's radiation law is discussed in view of the existence of photon clusters in blackbody radiation.
We systematically surveyed period variations of superhumps in SU UMa-type dwarf novae based on newly obtained data and past publications. In many systems, the evolution of superhump period are found to be composed of three distinct stages: early evolutionary stage with a longer superhump period, middle stage with systematically varying periods, final stage with a shorter, stable superhump period. During the middle stage, many systems with superhump periods less than 0.08 d show positive period derivatives. Contrary to the earlier claim, we found no clear evidence for variation of period derivatives between superoutburst of the same object. We present an interpretation that the lengthening of the superhump period is a result of outward propagation of the eccentricity wave and is limited by the radius near the tidal truncation. We interpret that late stage superhumps are rejuvenized excitation of 3:1 resonance when the superhumps in the outer disk is effectively quenched. Many of WZ Sge-type dwarf novae showed long-enduring superhumps during the post-superoutburst stage having periods longer than those during the main superoutburst. The period derivatives in WZ Sge-type dwarf novae are found to be strongly correlated with the fractional superhump excess, or consequently, mass ratio. WZ Sge-type dwarf novae with a long-lasting rebrightening or with multiple rebrightenings tend to have smaller period derivatives and are excellent candidate for the systems around or after the period minimum of evolution of cataclysmic variables (abridged).
The topological charge $\epsilon$ of AdS black hole is introduced in Ref.[1,2], where a complete thermodynamic first law is obtained. In this paper, we investigate a new phase transition related to the topological charge in Einstein-Maxwell theory. Firstly, we derive the explicit solutions corresponding to the divergence of specific heat $C_{\epsilon}$ and determine the phase transition critical point. Secondly, the $T-r$ curve and $T-S$ curve are investigated and they exhibit an interesting van der Waals system's behavior. Critical physical quantities are also obtained which are consistent with those derived from the specific heat analysis. Thirdly, a van der Waals system's swallow tail behavior is observed when $\epsilon>\epsilon_{c}$ in the $F-T$ graph. What's more, the analytic phase transition coexistence lines are obtained by using the Maxwell equal area law and free energy analysis, the results of which are consistent with each other.
Among recently introduced new notions in real algebraic geometry is that of regulous functions. Such functions form a foundation for the development of regulous geometry. Several interesting results on regulous varieties and regulous sheaves are already available. In this paper, we define and investigate regulous vector bundles. We establish algebraic and geometric properties of such vector bundles, and identify them with stratified-algebraic vector bundles. Furthermore, using new results on curve-rational functions, we characterize regulous vector bundles among families of vector spaces parametrized by an affine regulous variety. We also study relationships between regulous and topological vector bundles.
Let G be a simple and simply connected complex linear algebraic group. In this paper, we discuss the generalization of the parabolic construction of holomorphic principal G-bundles over a smooth elliptic curve to the case of a singular curve of arithmetic genus one and to a fibration of Weierstrass cubics over a base B. Except for G of type E_8, the method gives a family of weighted projective spaces associated to a sum of line bundles over B. Working with the universal family of Weierstrass curves over affine two-space and its natural C^*-action, we determine the line bundles that arise in the direct sum in terms of the Casimir weights of the group. We show that in the case of a cuspidal or nodal curve C, provided that G is not of type E_8 or C is not cuspidal, the parabolic construction is closely related to constructions of Kostant and Steinberg of sections for the adjoint quotient morphism of the group G or its Lie algebra, and that moreover it gives a compactification of the adjoint quotient. We describe how the construction may be modified for E_8. Finally, given an irreducible representation of G, we characterize the G-bundles arising from the parabolic construction such that the associated vector bundle is unstable.
We give a necessary and sufficient condition for the integrality of the Taylor coefficients at the origin of formal power series $q_i({\mathbf z})=z_i\exp(G_i({\mathbf z})/F({\mathbf z}))$, with ${\mathbf z}=(z_1,...,z_d)$ and where $F({\mathbf z})$ and $G_i({\mathbf z})+\log(z_i)F({\mathbf z})$, $i=1,...,d$ are particular solutions of certain A-systems of differential equations. This criterion is based on the analytical properties of Landau's function (which is classically associated with the sequences of factorial ratios) and it generalizes the criterion in the case of one variable presented in "Crit\`ere pour l'int\'egralit\'e des coefficients de Taylor des applications miroir" [J. Reine Angew. Math.]. One of the techniques used to prove this criterion is a generalization of a version of a theorem of Dwork on the formal congruences between formal series, proved by Krattenthaler and Rivoal in "Multivariate $p$-adic formal congruences and integrality of Taylor coefficients of mirror maps" [arXiv:0804.3049v3, math.NT]. This criterion involves the integrality of the Taylor coefficients of new univariate mirror maps listed in "Tables of Calabi--Yau equations" [arXiv:math/0507430v2, math.AG] by Almkvist, van Enckevort, van Straten and Zudilin.
In this paper we obtain a new family of identities for random measures on the unit ball of a separable Hilbert space which arise as the asymptotic analogues of the Gibbs measures in the Sherrington-Kirkpatrick and $p$-spin models and which are known to satisfy the Ghirlanda-Guerra identities. We give several applications of the new identities to structural results for such measures.
We present a quantum algorithm for data classification based on the nearest-neighbor learning algorithm. The classification algorithm is divided into two steps: Firstly, data in the same class is divided into smaller groups with sublabels assisting building boundaries between data with different labels. Secondly we construct a quantum circuit for classification that contains multi control gates. The algorithm is easy to implement and efficient in predicting the labels of test data. To illustrate the power and efficiency of this approach, we construct the phase transition diagram for the metal-insulator transition of $VO_2$, using limited trained experimental data, where $VO_2$ is a typical strongly correlated electron materials, and the metallic-insulating phase transition has drawn much attention in condensed matter physics. Moreover, we demonstrate our algorithm on the classification of randomly generated data and the classification of entanglement for various Werner states, where the training sets can not be divided by a single curve, instead, more than one curves are required to separate them apart perfectly. Our preliminary result shows considerable potential for various classification problems, particularly for constructing different phases in materials.
We consider bosonized $QCD_2$, and prove that after rewritting the theory in terms of gauge invariant fields, there exists an integrability condition valid for the quantum theory as well. Furthermore, performing a duality type transformation we obtain an appropriate action for the description of the strong coupling limit, which is still integrable. We also prove that the model displays a complicated set of constraints, restricting the dynamics of part of the theory, but which are necessary to maintain the positive metric Hilbert space.
Local and global properties of the moduli space of Calabi--Yau type compactifications determine the low energy parameters of the string effective action. We show that the moduli space geometry is entirely encoded in the Picard--Fuchs equations for the periods of the Calabi--Yau $H^{(3)}$--cohomology.
In this paper, we study the fattening effect of points over the complex numbers for del Pezzo surfaces $\mathbb{S}_r$ arising by blowing-up of $\mathbb{P}^2$ at $r$ general points, with $ r \in \{1, \dots, 8 \}$. Basic questions when studying the problem of points fattening on an arbitrary variety are what is the minimal growth of the initial sequence and how are the sets on which this minimal growth happens characterized geometrically. We provide complete answer for del Pezzo surfaces.
In order to understand the possible physical nature of the newly observed resonance $d^*(2380)$, we calculate the real photo-absorption cross section on deuteron contributed by the resonance $d^*(2380)$ by considering the electromagnetic transition amplitude of $\gamma +d\rightarrow d^*(2380)$. In our interpretation, the $d^*(2380)$ is regarded as a compact six-quark system with mainly two components of $\Delta\Delta$ and hidden-color clusters $C_8C_8$. We find that only the next-to-leading terms contribute the $\gamma +d\rightarrow d^*(2380)$ and the obtained photo-absorption cross section is quite small which is in the order of 10 $nb$. Compared with data measured at ELPH and Mainz recently, it is almost about 20 times smaller.
The aim of this two-part paper is to investigate the stability properties of a special class of solutions to a coagulation-fragmentation equation. We assume that the coagulation kernel is close to the diagonal kernel, and that the fragmentation kernel is diagonal. We construct a two-parameter family of stationary solutions concentrated in Dirac masses. We carefully study the asymptotic decay of the tails of these solutions, showing that this behaviour is stable. In a companion paper we prove that for initial data which are sufficiently concentrated, the corresponding solutions approach one of these stationary solutions for large times.
We have developed a subtractive renormalization method with which we can evaluate nucleon-nucleon (NN) scattering phase shifts produced by the NN potential obtained at leading, next-to-leading, and next-to-next-to-leading order (NNLO) in chiral effective theory ($\chi$ET). In this method the low-energy constants associated with short-distance NN physics are eliminated from the Lippmann-Schwinger equation (LSE) for the NN t-matrix, in favor of physical observables. This allows us to straightforwardly compute scattering phase shifts for ultra-violet cutoffs of at least 10 GeV. We then perform detailed analyses of the maximum cutoff at which the use of a $\chi$ET NN potential in the LSE makes sense.
The "Breakthrough Starshot" program is planning to send transrelativistic probes to travel to nearby stellar systems within decades. Since the probe velocity is designed to be a good fraction of the light speed, \citet{zha18} recently proposed that these transrelativistic probes can be used to study astronomical objects and to test special relativity. In this work, we further propose some methods to test special relativity and constrain photon mass using the Doppler effect with the images and spectral features of astronomical objects as observed in the transrelativistic probes. We introduce more general theories to set up the framework of testing special relativity, including a parametric general Doppler effect and Doppler effect with massive photon. We find that by comparing the spectra of a certain astronomical object, one can test Lorentz invariance and constrain photon mass. Besides, using imaging and spectrograph capabilities of transrelativistic probes, one can test time dilation and constrain photon mass. For a transrelativistic probe with velocity $v\sim0.2c$, aperture $D\sim3.5~{\rm cm}$ and spectral resolution $R\sim100$ (or $1000$), we find that the probe velocity uncertainty can be constrained to $\sigma_v\sim0.01c$ (or $0.001c$), and the time dilation factor uncertainty can be constrained to $\Delta\gamma=|\hat\gamma-\gamma|\lesssim0.01$ (or $0.001$), where $\hat\gamma$ is the time dilation factor and $\gamma$ is the Lorentz factor. Meanwhile, the photon mass limit is set to $m_\gamma\lesssim10^{-33}~{\rm g}$, which is slightly lower than the energy of the optical photon.
In this paper, we consider a data matrix $X\in\mathbb{C}^{N\times M}$ where all the columns are i.i.d. samples being $N$ dimensional complex Gaussian of mean zero and covariance $\Sigma\in\mathbb{C}^{N\times N}$. Here the population matrix $\Sigma$ is of finite rank perturbation of the identity matrix. This is the "spiked population model" first proposed by Johnstone in \cite{21}. As $M, N\to\infty$ but $M/N = \gamma\in(1, \infty)$, we first establish in this paper the asymptotic distribution of the smallest eigenvalue of the sample covariance matrix $S:= XX^*/M$. It also exhibits a phase transition phenomenon proposed in \cite{1} --- the local fluctuation will be the generalized Tracy-Widom or the generalized Gaussian to be defined in the paper. Moreover we prove that the largest and the smallest eigenvalue are asymptotically independent as $M, N\to\infty$.
Numerical simulations of domain wall propagation in thin nanotubes when an external magnetic field is applied along the nanotube axis have shown an unexpected behavior described as a transition from a linear to a magnonic regime. As the applied magnetic field increases, the initial regime of linear growth of the speed with the field is followed by a sudden change in slope accompanied by the emission of spin waves. In this work an analytical formula for the speed of the domain wall that explains this behavior is derived by means of an asymptotic study of the Landau Lifshitz Gilbert equation for thin nanotubes. We show that the dynamics can be reduced to a one dimensional hyperbolic reaction diffusion equation, namely, the damped double Sine Gordon equation, which shows the transition to the magnonic regime as the domain wall speed approaches the speed of spin waves. This equation has been previously found to describe domain wall propagation in weak ferromagnets with the mobility proportional to the Dzyaloshinskii-Moriya interaction constant, for Permalloy nanotubes the mobility is proportional to the nanotube radius.
A stochastic description of solutions of the Navier-Stokes equation is investigated. These solutions are represented by laws of finite dimensional semi-martingales and characterized by a weak Euler- Lagrange condition. A least action principle, related to the relative entropy, is provided. Within this stochastic framework, by assuming further symmetries, the corresponding invariances are expressed by martingales, stemming from a weak Noether's theorem.
The aim of this thesis is to investigate the absence of pulses in pulsar, a phenomena also know as pulsar nulling. The motivation for the work done in thesis is listed in Chapter 2. A detailed discussion on the previous work carried out to investigate pulsar nulling phenomena is also included in Chapter 2. Chapter 3 discusses in details all the observations carried out for the thesis. In Chapter 4, details regarding the nulling behaviour of various pulsars are listed. Chapter 4 highlights the fact that nulling is unpredictable. Chapter 5 presents a comparison between two pulsars with high NFs. It is shown that both the pulsars exhibit similar bursting behaviour, but strikingly different quasi-periodicities and emission properties. Chapter 6 discusses the details regarding the simultaneous observations of two nulling pulsars at four different frequencies. These observations suggest that nulling is a frequency independent phenomena simultaneous occuring over a decade of frequency. Chapter 7 summaries the results obtained in three different studies along with their implications. The future work to extend the work carried out in the thesis is also listed in Chapter 7. The main conclusions of the thesis are as follow, (1) NF is not an ideal parameter to quantify nulling behaviour, confirmed firmly by comparing low NF pulsars as well as high NF pulsars, (2) Nulling occurs randomly with unpredictable length durations. Quasi-periodicities seen in the high NF pulsars can also be explained by the Markov models with a forcing function, (3) Nulling is an extreme form of mode-changing phenomena which occurs on a global magnetospheric scale, (4) Geometric reasons are less favoured as a likely cause of nulling phenomena due to the randomness and broadband behaviour reported in this thesis.
We calculate the in-medium $D$ meson self-energies in a hot pion gas induced by resonance interactions with pions. The appropriate resonances in the {\it s},~ {\it p} and {\it d} waves of the $D$ meson-pion pair are represented by low lying scalar, vector and tensor $D^*$ mesons. At temperatures around 200 MeV the D-meson mass drops by $30~ \rm {MeV}$ and the scattering width grows up to $60~ \rm {MeV}$. Similar medium effects are found for the $D^*$ vector mesons. This opens and/or enhances the decay and/or dissociation channels of the charmonium states $\Psi^\prime$, $\chi_c$ and $J/\Psi$ to $D \bar D,~D^* \bar D,~D \bar D^* ,~D^* \bar D^*$ pairs in pion matter.
We analyse the low-energy physics of nearly ferromagnetic metals in two spatial dimensions using the functional renormalization group technique. We find a new low-energy fixed point, at which the fermionic (electron-like) excitations are non-Fermi-liquid ($z_f = 13/10$) and the magnetic fluctuations exhibit an anomalous Landau damping whose rate vanishes as $\Gamma_{\bf q} \sim \vert {\bf q} \vert^{3/5}$ in the low-$\vert {\bf q} \vert$ limit. We discuss this renormalization of the Landau-damping exponent, which is the major novel prediction of our work, and highlight the possible link between that renormalization and neutron-scattering data on UGe$_2$ and related compounds. Implications of our analysis for YFe$_2$Al$_{10}$ are also discussed.
Development of steady state thermodynamics and statistical mechanics depends crucially on our ability to develop notions of equilibrium thermodynamics for nonequilibrium steady states (NESS). The present paper considers the development of heat capacity. A modified definition is proposed which continues to maintain the same relation to steady state Shannon entropy as in equilibrium, thus providing a thermodynamically consistent treatment of NESS heat capacity.