ShantanuT01/DACTYL-Pretraining huggingface dataset:
We construct a massive non-abelian N= 1 SYM theory on R^3. This is achieved by using a non-local gauge and Poincare invariant mass term for gluons due to Nair. The underlying supersymmetry algebra is shown to be a non-central extension of the Poincare algebra by the spacetime rotation group so(3). The incorporation of Chern-Simons couplings in the formalism is also presented. The dimensional reduction of the gauge theory and the SUSY algebra is related to a massive N=2 massive matrix quantum mechanics based on euclidean $Clifford_2(R)$.
From a Bayesian analysis of the electric dipole polarizability, the constrained energy of isovector giant dipole resonance, the peak energy of isocalar giant quadrupole resonance and the constrained energy of isocalar giant monopole resonance in $^{208}$Pb, we extract the isoscalar and isovector effective masses in nuclear matter at saturation density $\rho_0$ as $m_{s,0}^{\ast}/m=0.87_{-0.04}^{+0.04}$ and $m_{v,0}^{\ast}/m = 0.78_{-0.05}^{+0.06}$ at $90\%$ confidence level. The obtained constraints on $m_{s,0}^{\ast}$ and $m_{v,0}^{\ast}$ lead to a positive isospin splitting of nucleon effective mass in asymmetric nuclear matter of isospin asymmetry $\delta$ at $\rho_0$ as $m_{n-p}^* / m=(0.20^{+0.15}_{-0.14})\delta$. In addition, the symmetry energy at the subsaturation density $\rho^{\ast}=0.05~\mathrm{fm}^{-3}$ is determined to be $E_{\mathrm{sym}}(\rho^{\ast})=16.7\pm1.3$ MeV at $90\%$ confidence level.
We study parabolic equations in variable H\"older spaces on domains of Euclidean spaces. The existence and uniqueness of solutions is proved.
We show how the stratification method, introduced by Vezzosi in his study of PGL_3, provides a unified approach to the known computations of the Chow rings of the classifying spaces of GL_n, SL_n, Sp_n, O_n and SO_n.
A family of proper smooth curves of genus $\geq 2$, parametrised by an open dense subset $U$ of a normal variety $S$, extends to $S$ if the natural map $\pi_1(U) \to \pi_1(S)$ on fundamental groups is an isomorphism. The criterion of this note is actually more precise.
This thesis is about the study of Diophantine equations involving binary recurrent sequences with arithmetic functions. Various Diophantine problems are investigated and new results are found out of this study. Firstly, we study several questions concerning the intersection between two classes of non-degenerate binary recurrence sequences and provide, whenever possible, effective bounds on the largest member of this intersection. Our main study concerns Diophantine equations of the form $\varphi(|au_n |)=|bv_m|,$ where $\varphi$ is the Euler totient function, $\{u_n\}_{n\geq 0}$ and $\{v_m\}_{m\geq 0}$ are two non-degenerate binary recurrence sequences and $a,b$ some positive integers. More precisely, we study problems involving members of the recurrent sequences being rep-digits, Lehmer numbers, whose Euler's function remain in the same sequence. We particularly study the case when $\{u_n\}_{n\geq 0}$ is the Fibonacci sequence $\{F_n\}_{n\geq 0}$, the Lucas sequences $\{L_n\}_{n\geq 0}$ or the Pell sequence $\{P_n\}_{n\geq 0}$ and its companion $\{Q_n\}_{n\geq 0}$. Secondly, we look of Lehmer's conjecture on some recurrence sequences. Recall that a composite number $N$ is said to be Lehmer if $\varphi(N)\mid N-1$. We prove that there is no Lehmer number neither in the Lucas sequence $\{L_n\}_{n\geq 0}$ nor in the Pell sequence $\{P_n\}_{n\geq 0}$. The main tools used in this thesis are lower bounds for linear forms in logarithms of algebraic numbers, the so-called Baker-Davenport reduction method, continued fractions, elementary estimates from the theory of prime numbers and sieve methods.
The possibilities of the proposed statistical approach are shown in the task of investigating the post-scission transformation of mass and charge yields of fission fragments with considering the emission of different length of chains of elementary particles as the beta particles and neutrons fission. Using as the example the 232 Th isotope, which is located on the border between pre-actinide and actinides nuclei, the changes in the topology of fission fragments yields, the role of emission of nuclear particles in the competition of symmetric and asymmetric modes in fission processes are investigated. The proposed method allows one to determine the most probable two fission's fragments clusters, obtained in considering the different chain's length of emitted nuclear particles and the parameters of their stability. All these results are essential when interpreting the experimental data.
Three-body photodisintegration of 3He is calculated in the photon energy range 200 - 400 MeV assuming quasifree absorption on np pairs both in initial quasideuteron and singlet configurations. The model includes the normal nucleonic current, explicit meson exchange currents and the Delta(1232)-isobar excitation. The total cross section is increased by a factor of about 1.5 compared with free deuteron photodisintegration. Well below and above the Delta region also some spin observables differ significantly from the ones of free deuteron disintegration due to the more compressed wave function of the correlated np pairs in 3He compared to the deuteron. The initial singlet state causes a significant change in the analyzing power Ay. These differences could presumably be seen at the conjugate angles where two-body effects are maximized and where photoreactions could complement similar pion absorption experiments. Figures by fax or post from janiskanen@phcu.helsinki.fi
Let $\mathcal{T}_n$ be the cover time of two-dimensional discrete torus $\mathbb{Z}^2_n=\mathbb{Z}^2/n\mathbb{Z}^2$. We prove that $\mathbb{P}[\mathcal{T}_n\leq \frac{4}{\pi}\gamma n^2\ln^2 n]=\exp(-n^{2(1-\sqrt{\gamma})+o(1)})$ for $\gamma\in (0,1)$. One of the main methods used in the proofs is the decoupling of the walker's trace into independent excursions by means of soft local times.
We consider M-theory and type IIA reductions to four dimensions with N=2 and N=1 supersymmetry and discuss their interconnection. Our work is based on the framework of Exceptional Generalized Geometry (EGG), which extends the tangent bundle to include all symmetries in M-theory and type II string theory, covariantizing the local U-duality group E7. We describe general N=1 and N=2 reductions in terms of SU(7) and SU(6) structures on this bundle and thereby derive the effective four-dimensional N=1 and N=2 couplings, in particular we compute the Kahler and hyper-Kahler potentials as well as the triplet of Killing prepotentials (or the superpotential in the N=1 case). These structures and couplings can be described in terms of forms on an eight-dimensional tangent space where SL(8) contained in E7 acts, which might indicate a description in terms of an eight-dimensional internal space, similar to F-theory. We finally discuss an orbifold action in M-theory and its reduction to O6 orientifolds, and show how the projection on the N=2 structures selects the N=1 ones. We briefly comment on new orientifold projections, U-dual to the standard ones.
We consider the nodal length $L(\lambda)$ of the restriction to a ball of radius $r_\lambda$ of a {\it Gaussian pullback monochromatic random wave} of parameter $\lambda>0$ associated with a Riemann surface $(\mathcal M,g)$ without conjugate points. Our main result is that, if $r_\lambda$ grows slower than $(\log \lambda)^{1/25}$, then (as $\lambda\to \infty$) the length $L(\lambda)$ verifies a Central Limit Theorem with the same scaling as Berry's random wave model -- as established in Nourdin, Peccati and Rossi (2019). Taking advantage of some powerful extensions of an estimate by B\'erard (1986) due to Keeler (2019), our techniques are mainly based on a novel intrinsic bound on the coupling of smooth Gaussian fields, that is of independent interest, and moreover allow us to improve some estimates for the nodal length asymptotic variance of pullback random waves in Canzani and Hanin (2016). In order to demonstrate the flexibility of our approach, we also provide an application to phase transitions for the nodal length of arithmetic random waves on shrinking balls of the $2$-torus.
We searched for thermonuclear X-ray bursts from Galactic neutron stars in all event mode data of the Neil Gehrels Swift Observatory collected until March 31, 2018. In particular, we are interested in the intermediate-duration bursts (shell flashes fueled by thick helium piles) with the ill-understood phenomenon of strong flux fluctuations. Nine such bursts have been discussed in the literature to date. Swift is particularly suitable for finding additional examples. We find and list a total of 134 X-ray bursts; 44 are detected with BAT only, 41 with XRT only, and 49 with both. Twenty-eight bursts involve automatic slews. We find 12 intermediate-duration bursts, all detected in observations involving automatic slews. Five show remarkably long Eddington-limited phases in excess of 200 s. Five show fluctuations during the decay phase; four of which are first discussed in the present study. We discuss the general properties of the fluctuations, considering also 7 literature cases. In general two types of fluctuations are observed: fast ones, with a typical timescale of 1 s and up and downward fluctuations of up to 70%, and slow ones, with a typical timescale of 1 min and only downward fluctuations of up to 90%. The latter look like partial eclipses because the burst decay remains visible in the residual emission. We revisit the interpretation of this phenomenon in the context of the new data set and find that it has not changed fundamentally despite the expanded data set. It is thought to be due to a disturbance of the accretion disk by outflowing matter and photons, causing obscuration and reflection due to Thompson scattering in an orbiting highly ionized cloud or structure above or below the disk. We discuss in detail the most pronounced burster SAX J1712.6-3739. One of the bursts from this source is unusual in that it lasts longer than 5600 s, but does not appear to be a superburst.
Halved monotone triangles are a generalisation of vertically symmetric alternating sign matrices (VSASMs). We provide a weighted enumeration of halved monotone triangles with respect to a parameter which generalises the number of $-1$s in a VSASM. Among other things, this enables us to establish a generating function for vertically symmetric alternating sign trapezoids. Our results are mainly presented in terms of constant term expressions. For the proofs, we exploit Fischer's method of operator formulae as a key tool.
The recent detection of the gravitational wave event GW170817, produced by the coalescence of two neutron stars, and of its optical-infrared counterpart, powered by the radioactive decay of r-process elements, has opened a new window to gamma-ray astronomy: the direct detection of photons coming from such decays. Here we calculate the contribution of kilonovae to the diffuse gamma-ray background in the MeV range, using recent results on the spectra of the gamma-rays emitted in individual events, and we compare it with that from other sources. We find that the contribution from kilonovae is not dominant in such energy range, but within current uncertainties, its addition to other sources might help to fit the observational data.
Let C be a smooth projective curve defined over a number field and let C' be a twist of C. In this article we relate the l-adic representations attached to the l-adic Tate modules of the Jacobians of C and C' through an Artin representation. This representation induces global relations between the local factors of the respective Hasse-Weil L-functions. We make these relations explicit in a particularly illustrating situation. For every Qbar-isomorphism class of genus 2 curves defined over Q with automorphism group isomorphic to D_8 or D_{12}, except for a finite number, we choose a representative curve C/Q such that, for every twist C' of C satisfying some mild condition, we are able to determine either the local factor L_p(C'/Q,T) or the product L_p(C'/Q,T)L_p(C'/Q,-T) from the local factor L_p(C/Q,T).
An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such sub-period is not expected for non-interacting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges ("backscattering"). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward- and back-scattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.
The Polyakov loop is included in the SU(2)_L x SU(2)_R chiral quark-meson model by considering the propagation of the constituent quarks, coupled to the (sigma,pi) meson multiplet, on the homogeneous background of a temporal gauge field, diagonal in color space. The model is solved at finite temperature and quark baryon chemical potential both in the chiral limit and for the physical value of the pion mass by using an expansion in the number of flavors N_f. Keeping the fermion propagator at its tree-level, a resummation on the pion propagator is constructed which resums infinitely many orders in 1/N_f, where O(1/N_f) represents the order at which the fermions start to contribute in the pion propagator. The influence of the Polyakov loop on the tricritical or the critical point in the mu_q-T phase diagram is studied for various forms of the Polyakov loop potential.
We present ab-initio calculations of the quasi-harmonic temperature dependent elastic constants. The isothermal elastic constants are calculated at each temperature as second derivatives of the Helmholtz free energy with respect to strain and corrected for finite pressure effects. This calculation is repeated for a grid of geometries and the results interpolated at the minimum of the Helmholtz free energy. The results are compared with the quasi-static elastic constants. Thermodynamic relationships are used to derive the adiabatic elastic constants that are compared with the experimental measurements. These approaches are implemented for cubic solids in the $\texttt{thermo_pw}$ code and are validated by applications to silicon, aluminum, and silver.
We propose a quantum memory for a single-photon wave packet in a superposition of two different colors, i.e., two different frequency components, using the electromagnetically induced transparency technique in a double-{\Lambda} system. We examine a specific configuration in which the two frequency components are able to exchange energy through a four-wave mixing process as they propagate, so the state of the incident photon is recovered periodically at certain positions in the medium. We investigate the propagation dynamics as a function of the relative phase between the coupling beams and the input single-photon frequency components. Moreover, by considering time-dependent coupling beams, we numerically simulate the storage and retrieval of a two-frequency-component single-photon qubit.
The cosmic first order phase transition from quarks to hadrons, occurring a few microseconds after the Big Bang, would lead to the formation of quark nuggets which would be stable on a cosmological time scale, if the associated baryon number is larger than a critical value. We examine the possibility that these surviving quark nuggets may not only be viable candidates for cold dark matter but even close the universe.
Metastable dynamics of a hyperbolic variation of the Allen-Cahn equation with homogeneous Neumann boundary conditions are considered. Using the "dynamical approach" proposed by Carr-Pego [10] and Fusco-Hale [19] to study slow-evolution of solutions in the classic parabolic case, we prove existence and persistence of metastable patterns for an exponentially long time. In particular, we show the existence of an "approximately invariant" $N$-dimensional manifold $\mathcal{M}_0$ for the hyperbolic Allen-Cahn equation: if the initial datum is in a tubular neighborhood of $\mathcal{M}_0$, the solution remains in such neighborhood for an exponentially long time. Moreover, the solution has $N$ transition layers and the transition points move with exponentially small velocity. In addition, we determine the explicit form of a system of ordinary differential equations describing the motion of the transition layers and we analyze the differences with the corresponding motion valid for the parabolic case.
Creation of quantum computer is outstanding fundamental and practical problem. The quantum computer could be used for execution of very complicated tasks which are not solvable with the classical computers. The first prototype of solid state quantum computer was created in 2009 with superconducting qubits. However, it suffers from the decoherent processes and it is desirable to find more practical encoding of qubits with long-lived coherence. It could be single impurity or vacancy centers in solids, but their interaction with electromagnetic radiation is rather weak. So, here, ensembles of atoms were proposed for the qubit encoding by using the dipole blockade mechanism in order to turn multilevel systems in two level ones. But dipole-dipole based blockade introduces an additional decoherence that limits its practical significance. Recently, the collective blockade mechanism has been proposed for the system of three-level atoms by using the different frequency shifts for the Raman transitions between the collective atomic states characterized by a different number of the excited atoms. Here, we propose two qubit gate by using another collective blockade mechanism in the system of two level atoms based on exchange interaction via the virtual photons between the multi-atomic ensembles in the resonator. Also we demonstrate the possibility of three qubit gate (Controlled SWAP gate) using a suppression of the swap-process between two multi-atomic ensembles due to dynamical shift of the atomic levels controlled by the states of photon encoded qubit.
We study the visible compression of a source E of pure quantum signal states, or, more formally, the minimal resources per signal required to represent arbitrarily long strings of signals with arbitrarily high fidelity, when the compressor is given the identity of the input state sequence as classical information. According to the quantum source coding theorem, the optimal quantum rate is the von Neumann entropy S(E) qubits per signal.   We develop a refinement of this theorem in order to analyze the situation in which the states are coded into classical and quantum bits that are quantified separately. This leads to a trade--off curve Q(R), where Q(R) qubits per signal is the optimal quantum rate for a given classical rate of R bits per signal.   Our main result is an explicit characterization of this trade--off function by a simple formula in terms of only single signal, perfect fidelity encodings of the source. We give a thorough discussion of many further mathematical properties of our formula, including an analysis of its behavior for group covariant sources and a generalization to sources with continuously parameterized states. We also show that our result leads to a number of corollaries characterizing the trade--off between information gain and state disturbance for quantum sources. In addition, we indicate how our techniques also provide a solution to the so--called remote state preparation problem. Finally, we develop a probability--free version of our main result which may be interpreted as an answer to the question: ``How many classical bits does a qubit cost?'' This theorem provides a type of dual to Holevo's theorem, insofar as the latter characterizes the cost of coding classical bits into qubits.
We present a method of noise level estimation that is valid even for high noise levels. The method makes use of the functional dependence of coarse grained correlation entropy $K_2(\eps)$ on the threshold parameter $\eps$. We show that the function $K_2(\eps)$ depends in a characteristic way on the noise standard deviation $\sigma$. It follows that observing $K_2(\eps)$ one can estimate the noise level $\sigma$. Although the theory has been developed for the gaussian noise added to the observed variable we have checked numerically that the method is also valid for the uniform noise distribution and for the case of Langevine equation corresponding to the dynamical noise. We have verified the validity of our method by applying it to estimate the noise level in several chaotic systems and in the Chua electronic circuit contaminated by noise.
With a special Lorentz-M{\o}ller-Nelson (LMN) transformation found transformation of velocity from the laboratory system S to an accelerated, rotating frame of reference s. The physical sense of parameter entering into the LMN special transformation is established. For small distances, and their proper smooth motion without jerks suggested the inverse special LMN transformation. The main consequences of this transformation is considered, namely, a) the desync in moving frame of reference s of proper clocks of the pre-synchronized in the laboratory frame S and b) the Lorentz contraction of proper rulers of frame s in the frame S. The applicability of the inverse LMN transformation for real frames with maximum rigidity is established. Equations for the rotation matrix is obtained. It is shown that the intrinsic rotation of the axes s, considered with respect to S is not rigid. Found the direct and inverse transformation of affine "angular" velocity in the S to the comoving, but not rotating frame s. Also shown that for the non-inertial motion of rigidly rotating frame of reference her the kinematic deformation of coordinates system is absent in two planes. The application of this transformation to a rotating rigid body is considered. The matrice and angle of proper Wigner rotation is calculated. We find differential equations for the inverse problem of relativistic kinematics, and their decision in the case of uniformly accelerated motion. The close connection between the proper Thomas precession and the proper Wigner rotation and their mutual compensation for the case uniformly accelerated motion has shown. The difference of the uniformly accelerated motion from the hyperbolic one has been shown. Also, the basic formulas are expressed in terms of the parameter, which is solution of the equation for the inverse problem of relativistic kinematics.
This paper reviews work, largely due to W. Simon and the author, on multipole theory of static spacetimes. The main purpose is to make this work, which lies at the interface of potential theory, conformal geometry and general relativity, known to mathematicians and to perhaps motivate them to look at the open problems which still remain.