ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is a well known fact that in $\mathbb{R}^n$ a subset of minimal perimeter $L$ among all sets of a given volume is also a set of maximal volume among all sets of the same perimeter $L$. This is called the reciprocity principle for isoperimetric problems. The aim of this note is to prove this relation in the case where the class of admissible sets is restricted to the subsets of some subregion $G\subsetneq\mathbb{R}^n$. Furthermore, we give a characterization of those (unbounded) convex subsets of $\mathbb{R}^2$ in which the isoperimetric problem has a solution. The perimeter that we consider is the one relative to $\mathbb{R}^n$.
We extend the Poincar\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Cs\"{o}rg\H{o} et al. (2003). Some notes on spheres with respect to $\ell_p$-norms are given.
A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and by a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. In contrast, the evolution of these quantities at shorter times reflect the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems.
The distribution of the spectral numbers of an isolated hypersurface singularity is studied in terms of the Bernoulli moments. These are certain rational linear combinations of the higher moments of the spectral numbers. They are related to the generalized Bernoulli polynomials. We conjecture that their signs are alternating and prove this in many cases. One motivation for the Bernoulli moments comes from the comparison with compact complex manifolds.
In this report, we simulate practical feature of Yuen-Kim protocol for quantum key distribution with unconditional secure. In order to demonstrate them experimentally by intensity modulation/direct detection(IMDD) optical fiber communication system, we use simplified encoding scheme to guarantee security for key information(1 or 0). That is, pairwise M-ary intensity modulation scheme is employed. Furthermore, we give an experimental implementation of YK protocol based on IMDD.
In this paper we study quasilinear elliptic equations driven by the so-called double phase operator and with a nonlinear boundary condition. Due to the lack of regularity, we prove the existence of multiple solutions by applying the Nehari manifold method along with truncation and comparison techniques and critical point theory. In addition, we can also determine the sign of the solutions (one positive, one negative, one nodal). Moreover, as a result of independent interest, we prove for a general class of such problems the boundedness of weak solutions.
Using the Kuga-Satake correspondence we provide an effective algorithm for the computation of the Picard and Brauer groups of K3 surfaces of degree 2 over number fields.
Stellar conditions leading to a possible semi-convective mixing are discussed in three relevant cases: (1) low mass MS stars in which the CNO cycle takes progressively the lead over the PP chain due to the increase in temperature as core hydrogen burning proceeds, (2) massive MS stars which experience a large contri- bution of the radiation pressure to the total pressure and (3) core helium burning stars for which the production of carbon in the core increases the opacity. A short discussion of semi-convection in terms of instability of non radial modes follows.
The constraints on the mixing angles of the standard fermions with new heavy particles that can appear in many extensions of the electroweak theory are reviewed. Some emphasis is put in distinguishing the effects of a mixing with new states which transform in a non-canonical way with respect to $SU(2)\times U(1)$ (left-handed singlets or right-handed doublets), from the effects of a mixing with new states with standard quantum number assignments. Constraints from flavor changing neutral current processes, as well as from flavor diagonal and charged current experimental data are considered. New limits for lepton flavor violating mixings are presented. By using the most recent results on the $\tau$ mass, lifetime and branching ratios, updated limits on the mixing parameters of the $\tau$ neutrino are derived. These limits are improved up to a factor of 3, and no signals of deviation from the standard model predictions are found. Limits on the mass of a $Z_1$ gauge boson from E$_6$, from the absence of muon number violating processes are briefly discussed as well.
In this contribution we solve the following problem. Let H_{nm} be a Hilbert space of dimension nm, and let A be a positive semidefinite self-adjoint linear operator on H_{nm}. Under which conditions on the spectrum has A a positive partial transpose (is PPT) with respect to any partition H_n \otimes H_m of the space H_{nm} as a tensor product of an n-dimensional and an m-dimensional Hilbert space? We show that the necessary and sufficient conditions can be expressed as a set of linear matrix inequalities on the eigenvalues of A.
We give a new proof of the renormalizability of a class of matter field theories on a space-time lattice; in particular we consider $\phi^4$ and massive Yukawa theories with Wilson fermions. We use the Polchinski approach to renormalization, which is based on the Wilson flow equation; this approach is substantially simpler than the BPHZ method, applied to the lattice by Reisz. We discuss matter theories with staggered fermions. In particular we analyse a simple kind of staggered fermions with minimal doubling, using which we prove the renormalizability of a chiral sigma model with exact chiral symmetry on the lattice.
Some time ago it was conjectured that the coefficients of an expansion of the Jones polynomial in terms of the cosmological constant could provide an infinite string of knot invariants that are solutions of the vacuum Hamiltonian constraint of quantum gravity in the loop representation. Here we discuss the status of this conjecture at third order in the cosmological constant. The calculation is performed in the extended loop representation, a generalization of the loop representation. It is shown that the the Hamiltonian does not annihilate the third coefficient of the Jones polynomal ($J_3$) for general extended loops. For ordinary loops the result acquires an interesting geometrical meaning and new possibilities appear for $J_3$ to represent a quantum state of gravity.
In the semi-conductor double quantum dot singlet-triplet qubit architecture, the decoherence caused by the qubit's charge environment poses a serious obstacle in the way towards large scale quantum computing. The effects of the charge decoherence can be mitigated by operating the qubit in the so called sweet spot regions where it is insensitive to electrical noise. In this paper, we propose singlet-triplet qubits based on two quantum dots of different sizes. Such asymmetric double dot systems allow the implementation of exchange gates with controllable exchange splitting $J$ operated in the doubly occupied charge region of the larger dot, where the qubit has high resilience to charge noise. In the larger dot, $J$ can be quenched to a value smaller than the intra-dot tunneling using magnetic fields, while the smaller dot and its larger splitting can be used in the projective readout of the qubit.
Micro-/nanomechanical mass sensors are capable to quantitatively determine molecule mass from only first three (two) measured cantilever (bridge) resonant frequencies. However, in liquid solutions that are relevant to most of the biological systems, the mass determination is challenging because the Q-factor due to fluid damping decreases and, as a result, usually just the fundamental resonant frequencies can be correctly identified. Moreover, for higher modes the resonance coupling, noise and internal damping have been proven to strongly affect the measured resonant frequencies and, correspondingly, the accuracy of the estimated masses. Here, we derive the easy accessible expressions enabling the quantitative mass(es) determination just from the fundamental resonant frequencies of the micro/nanomechanical mass sensor under intentionally applied axial tension, which can be easily created and controlled by the electrostatic or magnetostatic forces. We also show that typically achievable force resolution has a negligible impact on the mass determination and the mass sensitivity.
A general approach to simulate the mechanical behavior of textile materials by taking into account all their constitutive elementary fibers and contacts between them is presented in this paper. A finite element code, based on an implicit solver, is develop to model samples of woven fabrics as assemblies of beams submitted to large displacements and developing contactfriction interactions between themselves. Special attention is paid to the detection and modeling of the numerous contacts occurring in this kind of structures. Robust models and efficient algorithms allow to consider samples made of few hundreds of fibers. The unknown initial configuration of the woven fabric is obtained by simulation according to the chosen weaving pattern, providing useful informations on fibers trajectories and tows crosssections shapes. Various loading cases can then be applied to the textile sample, in presence of an elastic matrix, so as to identify its mechanical behavior under different solicitations. Results of simulations performed on coated fabric samples are given to illustrate the approach.
We discuss prospects for stabilizing the volume modulus of N=1 supersymmetric type IIB orientifold compactifications using only perturbative corrections to the Kahler potential. Concretely, we consider the known string loop corrections and tree-level alpha' corrections. They break the no-scale structure of the potential, which otherwise prohibits stabilizing the volume modulus. We argue that when combined, these corrections provide enough flexibility to stabilize the volume of the internal space without non-perturbative effects, although we are not able to present a completely explicit example within the limited set of currently available models. Furthermore, a certain amount of fine-tuning is needed to obtain a minimum at large volume.
The problem of controlling a finite state Markov chain in the presence of an adversary so as to ensure desired performance levels for a vector of objectives is cast in the framework of Blackwell approachability. Relying on an elementary two time scale construction a control scheme is proposed which ensures almost sure convergence to the desired set regardless of the adversarial actions.
A light singlino is a promising candidate for dark matter, and a light higgsino is natural in the parameter space of the NMSSM. We study the combined constraints on this scenario resulting from the dark matter relic density, the most recent results from direct detection experiments, LEP and the LHC. In particular limits from a recent search for electroweak production of charginos and neutralinos at $\sqrt{s}=13$ TeV after 35.9 fb$^{-1}$ by CMS and constraints on spin-independent dark matter-nucleon cross sections from XENON1T after one tonne$\times$year exposure are considered. We find that scenarios with higgsino masses below $\sim 250$ GeV as well as singlino masses below $\sim 100$ GeV are strongly constrained depending, however, on assumptions on the bino mass parameter $M_1$. Benchmark points and branching fractions for future searches at the LHC are proposed.
A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node-distance, betweenness, and loop distributions are all very narrow. Also, they are characterized by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community-structure. This family of nets exhibits an excellent performance with respect to other flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc. These remarkable features convert entangled networks in a useful concept, optimal or almost-optimal in many senses, and with plenty of potential applications computer science or neuroscience.
We propose two methods that enable us to obtain approximate solutions of the lens equation near a fold caustic with an arbitrary degree of accuracy. We obtain "post-linear" corrections to the well-known formula in the linear caustic approximation for the total amplification of two critical images of a point source. In this case, in order to obtain the nontrivial corrections we had to go beyond the approximation orders earlier used by Keeton et al. and to take into account the Taylor expansion of the lens equation near caustic up to the fourth order. Corresponding analytical expressions are derived for the amplification in cases of the Gaussian and power-law extended source models; the amplifications depend on three additional fitting parameters. Conditions of neglecting the correction terms are analysed. The modified formula for the amplification is applied to the fitting of light curves of the Q2237+0305 gravitational lens system in a vicinity of the high amplification events (HAEs). We show that the introduction of some "post-linear" corrections reduces chi^2 by 30% in the case of known HAE on the light curve of image C (1999). These corrections can be important for a precise comparison of different source models with regard for observational data. Key words: gravitational lensing: micro - quasars: individual (Q2237+0305) - gravitational lensing: strong - methods: analytical
The dissociation of heavy quarkonia in the constrained space is calculated at leading order compared with that in infinitely large medium. To deal with the summation of the discrete spectrum, a modified Euler-Maclaurin formula is developed as our numerical algorithm. We find that with the constraint in space, the dissociation of quarkonia at early time becomes negligible.
We present the discovery of rotation in quenched, low-mass early-type galaxies that are isolated. This finding challenges the claim that (all) rotating dwarf early-type galaxies in clusters were once spiral galaxies that have since been harassed and transformed into early-type galaxies. Our search of the Sloan Digital Sky Survey data within the Local volume ($z<0.02$) has yielded a sample of 46 galaxies with a stellar mass $M_\star \lesssim 5\times10^9$ M$_\odot$ (median $M_\star \sim 9.29 \times 10^8$ M$_\odot$), a low H$\alpha$ equivalent width EW$_{{\rm H}\alpha}< 2$ \AA, and no massive neighbour ($M_{\star}\gtrsim3 \times 10^{10}$ M$_{\odot}$) within a velocity interval of $\Delta V = 500$ km s$^{-1}$ and a projected distance of $\sim$1 Mpc. Nine of these galaxies were subsequently observed with Keck ESI and their radial kinematics are presented here. These extend out to the half-light radius $R_e$ in the best cases, and beyond $R_e/2$ for all. They reveal a variety of behaviours similar to those of a comparison sample of early-type dwarf galaxies in the Virgo cluster observed by Toloba et al. Both samples have similar frequencies of slow and fast rotators, as well as kinematically decoupled cores. This, and especially the finding of rotating quenched low-mass galaxies in isolation, reveals that the early-type dwarfs in galaxy clusters need not be harassed or tidally stirred spiral galaxies.
We employ gauge/gravity duality to study the effects of Lifshitz scaling on the holographic $p$ wave superconductors in the presence of Born-Infeld (BI) nonlinear electrodynamics. By using the shooting method in the probe limit, we calculate the relation between critical temperature $T_{c}$ and $\rho^{z/d}$ numerically for different values of mass, nonlinear parameter $b$ and Lifshitz critical exponent $z$ in various dimensions. We observe that critical temperature decreases by increasing $b$, $z$ or the mass parameter $m$ which makes conductor/superconductor phase transition harder to form. In addition, we analyze the electrical conductivity and find the behavior of real and imaginary parts as a function of frequency which depend on the model parameters. However, some universal behaviors are seen. For instance at low frequencies, real part of conductivity shows a delta function behavior while the imaginary part has a pole which means that these two parts are connected to each other through Kramers-Kronig relation. The behavior of real part of conductivity in the large frequency regime can be achieved by $Re[\sigma]=\omega^{D-4}$. Furthermore, with increasing the Lifshitz scaling $z$, the energy gap and the minimum values of the real and imaginary parts become unclear.
The motion of a free quantum particle in a thermal environment is usually described by the quantum Langevin equation, where the effect of the bath is encoded through a dissipative and a noise term, related to each other via the fluctuation dissipation theorem. The quantum Langevin equation can be derived starting from a microscopic model of the thermal bath as an infinite collection of harmonic oscillators prepared in an initial equilibrium state. The spectral properties of the bath oscillators and their coupling to the particle determine the specific form of the dissipation and noise. Here we investigate in detail the well-known Rubin bath model, which consists of a one-dimensional harmonic chain with the boundary bath particle coupled to the Brownian particle. We show how in the limit of infinite bath bandwidth, we get the Drude model and a second limit of infinite system-bath coupling gives the Ohmic model. A detailed analysis of relevant correlation functions, such as the mean squared displacement, velocity auto-correlation functions, and the response function are presented, with the aim of understanding of the various temporal regimes. In particular, we discuss the quantum to classical crossover time scales where the mean square displacement changes from a $\sim \ln t$ to a $\sim t$ dependence. We relate our study to recent work using linear response theory to understand quantum Brownian motion.
This is the third of a series of papers that presents an algorithm to search for close binaries with massive, possibly compact, unseen secondaries. The detection of such a binary is based on identifying a star that displays a large ellipsoidal periodic modulation, induced by tidal interaction with its companion. In the second paper of the series we presented a simple approach to derive a robust modified minimum mass ratio (mMMR), based on the observed ellipsoidal amplitude, without knowing the primary mass and radius, assuming the primary fills its Roche lobe. The newly defined mMMR is always smaller than the actual mass ratio. Therefore, a binary with an mMMR larger than unity is a good candidate for having a massive secondary, which might be a black hole or a neutron star. This paper considers 10,956 OGLE short-period ellipsoidals observed towards the Galactic Bulge. We re-analyse their modulation and identify 136 main-sequence systems with mMMR significantly larger than unity as candidates for having compact-object secondaries, assuming their observed periodic modulations reflect indeed the ellipsoidal effect. Obviously, one needs follow-up observations to find out the true nature of these companions.
In this paper, we present the application of a new method measuring Hubble parameter $H(z)$ by using the anisotropy of luminosity distance($d_{L}$) of the gravitational wave(GW) standard sirens of neutron star(NS) binary system. The method has never been put into practice so far due to the lack of the ability of detecting GW. However, LIGO's success in detecting GW of black hole(BH) binary system merger announced the potential possibility of this new method. We apply this method to several GW detecting projects, including Advanced LIGO(aLIGO), Einstein Telescope(ET) and DECIGO, and evaluate its constraint ability on cosmological parameters of $H(z)$. It turns out that the $H(z)$ by aLIGO and ET is of bad accuracy, while the $H(z)$ by DECIGO shows a good one. We simulate $H(z)$ data at every 0.1 redshift span using the error information of $H(z)$ by DECIGO, and put the mock data into the forecasting of cosmological parameters. Compared with the previous data and method, we get an obviously tighter constraint on cosmological parameters by mock data, and a concomitantly higher value of Figure of Merit(FoM, the reciprocal of the area enclosed by the $2\sigma$ confidence region). For a 3-year-observation by standard sirens of DECIGO, the FoM value is as high as 170.82. If a 10-year-observation is launched, the FoM could reach 569.42. For comparison, the FoM of 38 actual observed $H(z)$ data(OHD) is 9.3. We also investigate the undulant universe, which shows a comparable improvement on the constraint of cosmological parameters. These improvement indicates that the new method has great potential in further cosmological constraints.
In the context of the interacting boson model with $s$, $d$ and $g$ bosons, the conditions for obtaining an intrinsic shape with octahedral symmetry are derived for a general Hamiltonian with up to two-body interactions.
In this work we study rapidly rotating stars by considering the Rastall theory of gravity. We obtain and solve the equations by numerical methods for two usual parametrization of polytropic stars. Then the mass-radius relations, moments of inertia and other results of interest are obtained and compared with the ones for non-rotating stars.
We ask several questions about substitution maps in the Robba ring. These questions are motivated by $p$-adic Hodge theory and the theory of $p$-adic dynamical systems. We provide answers to those questions in special cases, thereby generalizing results of Kedlaya, Colmez, and others.
We analyse the proposal of sliding phases (SP) in layers hosting global U(1) symmetric variables with finite inter-layer Josephson coupling. Based on the Kosterlitz-Thouless renormalization group (RG) approach, such phases were predicted to exist in various layered (or 1D quantum coupled) systems. The key in the RG argument is treating the coupling as though the variables are non-compact. Large scale Monte Carlo simulations of a layered model, where the SP is supposed to exist, finds no indication of such a phase. Instead, 3D behavior is observed. This result is consistent with the asymptotically exact analytical solution. A generic argument against SP in translationally invariant systems with short range interactions is provided. We have also suggested an alternative model for the SP -- adding long-range interactions to the inter-layer Josephson term.
We study the electronic phase diagram of the excitonic insulator candidates Ta$_2$Ni(Se$_{1-x}$S$_x$)$_5$ [x=0, ... ,1] using Raman spectroscopy. Critical excitonic fluctuations are observed, that diminish with $x$ and ultimately shift to high energies, characteristic of a quantum phase transition. Nonetheless, a symmetry-breaking transition at finite temperatures is detected for all $x$, exposing a cooperating lattice instability that takes over for large $x$. Our study reveals a failed excitonic quantum phase transition, masked by a preemptive structural order.