ShantanuT01/DACTYL-Pretraining huggingface dataset:
A closed-form exact analytical solution for the q-state Potts model on a ladder 2 x oo with arbitrary two-, three-, and four-site interactions in a unit cell is presented. Using the obtained solution it is shown that the finite-size internal energy equation yields an accurate value of the critical temperature for the triangular Potts lattice with three-site interactions in alternate triangular faces. It is argued that the above equation is exact at least for self-dual models on isotropic lattices.
An introduction into the fundamental quests addressed in space missions is given. These quests are the exploration of the relativistic gravitational field, the Universality of Free Fall, the Universality of the Gravitational Redshift, Local Lorentz Invariance, the validity of Einstein's field equations, etc. In each case, the correspoding missions take advantage of the space conditions which are essential for the improvement of the accuracy of the experiments as compared to experiments on ground. A list and a short description of past, current and planned projects is given. Also the key technologies employed in space missions are addressed.
As a general rule, differential equations driven by a multi-dimensional irregular path $\Gamma$ are solved by constructing a rough path over $\Gamma$. The domain of definition ? and also estimates ? of the solutions depend on upper bounds for the rough path; these general, deterministic estimates are too crude to apply e.g. to the solutions of stochastic differential equations with linear coefficients driven by a Gaussian process with H\"older regularity $\alpha < 1/2$. We prove here (by showing convergence of Chen's series) that linear stochastic differential equations driven by analytic fractional Brownian motion [7, 8] with arbitrary Hurst index $\alpha \in (0, 1)$ may be solved on the closed upper halfplane, and that the solutions have finite variance.
We study the evolution of bound pairs of star clusters by means of direct N-body simulations. Our simulations include mass loss by stellar evolution. The initial conditions are selected to mimic the observed binary star cluster NGC 2136 and NGC 2137 in the Large Magellanic Cloud. Based on the rather old ages ($\sim 100$ Myr), masses, sizes of the two clusters and their projected separation, we conclude that the cluster pair must have been born with an initial separation of 15--20 pc. Clusters with a smaller initial separation tend to merge in $\aplt 60$ Myr due to loss of angular momentum from escaping stars. Clusters with a larger initial separation tend to become even more widely separated due to mass loss from the evolving stellar populations. The early orbital evolution of a binary cluster is governed by mass loss from the evolving stellar population and by loss of angular momentum from escaping stars. Mass loss by stellar winds and supernovae explosions in the first $\sim 30$ Myr causes the binary to expand and the orbit to become eccentric. The initially less massive cluster expands more quickly than the binary separation increases, and is therefore bound to initiate mass transfer to the more massive cluster. This process is quite contrary to stellar binaries in which the more massive star tends to initiate mass transfer. Since mass transfer proceeds on a thermal timescale from the less massive to the more massive cluster, this semi-detached phase is quite stable, even in an eccentric orbit until the orbital separation reaches the gyration radius of the two clusters, at which point both clusters merge to one.
We derive practical three-body equations for the equal-time three-body Green function in matter. Our equations describe both bosons and fermions at finite density and temperature, and take into account all possible two-body sub-processes allowed by the underlying Hamiltonian.
We analyze a recently proposed supersymmetry breaking mass deformation of the $E_1$ superconformal fixed point in five dimensions which, at weak gauge coupling, leads to pure $SU(2)$ Yang-Mills and which was conjectured to lead to an interacting CFT at strong coupling. We provide an explicit geometric construction of the deformation using brane-web techniques and show that for large enough gauge coupling a global symmetry is spontaneously broken and the theory enters a new phase which, at infinite coupling, displays an instability. The Yang-Mills and the symmetry broken phases are separated by a phase transition. Depending on the structure of the potential, this can be first or second order.
We identify the twisted sectors of a compact simplicial toric variety. We do the same for a generic nondegenerate Calabi-Yau hypersurface of an $n$-dimensional simplicial Fano toric variety and then explicitly compute $h^{1,1}_{orb}$ and $h^{n-2,1}_{orb}$ for the hypersurface. We give applications to the orbifold string theory conjecture and orbifold mirror symmetry.
In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which is a Gaussian noise, white in time and correlated in space. The differential operator is a fractional derivative operator. We prove a large deviations principle for our equation, using a weak convergence approach based on a variational representation of functionals of infinite-dimensional Brownian motion. This approach reduces the proof of LDP to establishing basic qualitative properties for controlled analogues of the original stochastic system.
We have completed a 350 MHz drift scan survey using the Robert C. Byrd Green Bank Telescope with the goal of finding new radio pulsars, especially millisecond pulsars that can be timed to high precision. This survey covered ~10300 square degrees and all of the data have now been fully processed. We have discovered a total of 31 new pulsars, seven of which are recycled pulsars. A companion paper by Boyles et al. (2012) describes the survey strategy, sky coverage, and instrumental set-up, and presents timing solutions for the first 13 pulsars. Here we describe the data analysis pipeline, survey sensitivity, and follow-up observations of new pulsars, and present timing solutions for 10 other pulsars. We highlight several sources---two interesting nulling pulsars, an isolated millisecond pulsar with a measurement of proper motion, and a partially recycled pulsar, PSR J0348+0432, which has a white dwarf companion in a relativistic orbit. PSR J0348+0432 will enable unprecedented tests of theories of gravity.
We report a new spin manipulation protocol for periodically reversing the sample magnetization for Magnetic Resonance Force Microscopy. The protocol modulates the microwave excitation frequency synchronously with the position of the oscillating detection cantilever, thus allowing manipulation of the spin magnetization independent of both magnetic field gradient strength and cantilever response time. This allows continuous variation of the detected sample volume and is effective regardless of spin relaxation rate. This enhanced flexibility improves the utility of MRFM as a generally applicable imaging and characterization tool.
We have discovered an unexpected and surprising fact: a 2D axially symmetric short-range potential contains {\it infinite} number of the levels of negative energy {\it if one takes into account the spin-orbit (SO) interaction.} For a shallow well ($m_eU_0R^2/\hbar^2 \ll 1$, where $m_e$ is the effective mass, $U_0$ and $R$ are the depth and the radius of the well, correspondingly) and weak SO coupling ($|\alpha|m_eR/\hbar \ll 1$, $\alpha$ is the SO coupling constant) exactly one two-fold degenerate bound state exists for each value of the half-integer moment $j=m+1/2$, and the corresponding binding energy $E_m$ extremely rapidly decreases with increasing $m$.
Brown dwarfs and giant planets orbiting close to a host star are subjected to significant irradiation that can modify the properties of their atmospheres. In order to test the atmospheric models that are used to describe these systems, it is necessary to obtain accurate observational estimates of their physical properties (masses, radii, temperatures, albedos). Interacting compact binary systems provide a natural laboratory for studying strongly irradiated sub-stellar objects. As the mass-losing secondary in these systems makes a critical, but poorly understood transition from the stellar to the sub-stellar regime, it is also strongly irradiated by the compact accretor. In fact, the internal and external energy fluxes are both expected to be comparable in these objects, providing access to an unexplored irradiation regime. However, the atmospheric properties of such donors have so far remained largely unknown. Here, we report the direct spectroscopic detection and characterisation of an irradiated sub-stellar donor in an accreting white dwarf binary system. Our near-infrared observations allow us to determine a model-independent mass estimate for the donor of $M_2=0.055\pm0.008M_{\odot}$ and an average spectral type of ${\rm L1}\pm{\rm1}$, supporting both theoretical predictions and model-dependent observational constraints. Our time-resolved data also allow us to estimate the average irradiation-induced temperature difference between the day and night sides on the sub-stellar donor, $\Delta{\rm T}\simeq57$~K, and the maximum difference between the hottest and coolest parts of its surface, of $\Delta{\rm T}_{max}\simeq200$~K. The observations are well described by a simple geometric reprocessing model with a bolometric (Bond) albedo of $A_B<0.54$ at 2-$\sigma$ confidence level, consistent with high reprocessing efficiency, but poor lateral heat redistribution in the donor's atmosphere.
We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential $\mu$ for the spin-three current. For the CFT on the infinite spatial line, we calculate the finite temperature entanglement entropy of a single interval perturbatively to second order in $\mu$ in each of the theories. We find that the result in each case is given by the same non-trivial function of temperature and interval length. Remarkably, we further obtain the same formula using a recent Wilson line proposal for the holographic entanglement entropy, in holomorphically factorized form, associated to the spin-three black hole in SL(3, R) x SL(3, R) Chern-Simons theory. Our result suggests that the order $\mu^2$ correction to the entanglement entropy may be universal for W-algebra CFTs with spin-three chemical potential, and constitutes a check of the holographic entanglement entropy proposal for higher spin theories of gravity in AdS_3.
We present high-resolution X-ray spectra of the multiple T Tauri star system Hen 3-600, obtained with the High Energy Transmission Grating Spectrograph on the Chandra X-ray Observatory. Two binary components were detected in the zeroth-order image. Hen 3-600-A, which has a large mid-infrared excess, is a 2-3 times fainter in X-rays than Hen 3-600-B, due to a large flare on B. The dispersed X-ray spectra of the two primary components overlap spatially; spectral analysis was performed on the combined system. Analysis of the individual spectra was limited to regions where the contributions of A and B can be disentangled. This analysis results in two lines of evidence indicating that the X-ray emission from Hen 3-600 is derived from accretion processes: line ratios of O VII indicate that the characteristic density of its X-ray-emitting plasma is large; a significant component of low-temperature plasma is present and is stronger in component A. These results are consistent with results obtained from X-ray gratings spectroscopy of more rapidly accreting systems. All of the signatures of Hen 3-600 that are potential diagnostics of accretion activity -- X-ray emission, UV excess, H-alpha emission, and weak infrared excess -- suggest that its components represent a transition phase between rapidly accreting, classical T Tauri stars and non-accreting, weak-lined T Tauri stars.
If the interaction rates between the visible and the dark sectors were never strong enough, the observed dark matter relic abundance could have been produced in the early Universe by non-thermal processes. This is what occurs in the so-called freeze-in mechanism. In the simplest version of the freeze-in paradigm, after dark matter is produced from the standard model thermal bath, its abundance is frozen and remains constant. However, thermalization and number-changing processes in the dark sector can have strong impacts, in particular enhancing the dark matter relic abundance by several orders of magnitude. Here we show that this enhancement can be computed from general arguments as the conservation of energy and entropy, independently from the underlying particle physics details of the dark sector. We also note that this result is quite general, and applies to FIMP production independently of being UV- or IR-dominated.
The subject of topological defects has become a very attractive field of study given its apparent relevance to as diverse systems as the early universe and condensed matter. As usually envisaged the topology of the manifold M of the minima of the relevant to our physical system effective potential V, provides reliable information about the capacity of that system to accommodate topological defects. Here we will examine the premises for that statement to be true.
Recently, many graph matching methods that incorporate pairwise constraint and that can be formulated as a quadratic assignment problem (QAP) have been proposed. Although these methods demonstrate promising results for the graph matching problem, they have high complexity in space or time. In this paper, we introduce an adaptively transforming graph matching (ATGM) method from the perspective of functional representation. More precisely, under a transformation formulation, we aim to match two graphs by minimizing the discrepancy between the original graph and the transformed graph. With a linear representation map of the transformation, the pairwise edge attributes of graphs are explicitly represented by unary node attributes, which enables us to reduce the space and time complexity significantly. Due to an efficient Frank-Wolfe method-based optimization strategy, we can handle graphs with hundreds and thousands of nodes within an acceptable amount of time. Meanwhile, because transformation map can preserve graph structures, a domain adaptation-based strategy is proposed to remove the outliers. The experimental results demonstrate that our proposed method outperforms the state-of-the-art graph matching algorithms.
Considered a unified field theory approach describing matter and space (metric tensor) by means of a 3-index tensor $P^{i}_{jk}$. It is shown that if the Lagrangian has partial U(1) gauge (semi-gauge) of the type $P^{i}_{jk}->P^{i}_{jk}+a \delta{^i_j} \phi{_{,k}}+b \delta{^i_k} \phi{_{,j}}+cg_{jk}g^{mi} \phi{_{,m}}$ where a,b,c are constants, then the Euler equations of motion contain the covariant low of conservation in the form $J^{k}_{;k}=0$.
We present a new approach to study the magnetic phase stability of magnetic overlayers on nonmagnetic substrates. The exchange integrals among magnetic atoms in the overlayer are estimated in the framework of the adiabatic approximation and used to construct the effective classical two-dimensional Heisenberg Hamiltonian. Its stability is then studied with respect to a large number of collinear and non-collinear magnetic arrangements which include, as special cases, not only ferromagnetic and various antiferromagnetic configurations, but also possible incommensurate spin-spiral structures. This allows us to investigate a broader class of systems than a conventional total energy search based on few, subjectively chosen configurations. As a case study we consider the Fe-monolayer on the random nonmagnetic bcc-Ta(x)W(1-x) (001) surface which was studied recently by a conventional approach. We have found a crossover of the ground state of the Fe monolayer from the ferromagnet on the Ta surface to the c(2x2) antiferromagnet on the W surface and that at the composition with about 20 % of Ta an incommensurate magnetic configuration might exist.
We perform a field-theoretical study of possible deuteron-like molecules with both open charm and bottom, using the Heavy-Meson Effective Theory. In this approach, we analyze the parameter space of the coupling constants and discuss the formation of loosely-bound $D^{(*)} B^{(*)} $-states. We estimate their masses and other properties.
We consider the sparticle spectra that arise when anomaly mediation is the source of supersymmetry-breaking and the tachyonic slepton problem is solved by a Fayet-Iliopoulos D-term. We also show how this can lead to a minimal viable extension of anomaly mediation, in which the gauge symmetry associated with this D-term is broken at very high energies, leaving as its footprint in the low energy theory only the required D-terms and seesaw neutrino masses.
We analyze the asymptotic behavior of discrete-time, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing the system in pure states or subspace codes. We provide a linear-algebraic characterization of the dynamical properties leading to invariance and attractivity of a given quantum subspace. We then construct a design algorithm for discrete-time feedback control that allows to stabilize a target subspace, proving that if the control problem is feasible, then the algorithm returns an effective control choice. In order to prove this result, a canonical QR matrix decomposition is derived, and also used to establish the control scheme potential for the simulation of open-system dynamics.
Given an effective action of an (n-1)-dimensional torus on an n-dimensional normal affine variety, Mumford constructs a toroidal embedding, while Altmann and Hausen give a description in terms of a polyhedral divisor on a curve. We compare the fan of the toroidal embedding with this polyhedral divisor.
Nanocrystalline ribbons of inverse Heusler alloy Mn2Ni1.6Sn0.4 have been synthesised by melt spinning of the arc melted bulk precursor. The single phase ribbons crystallize into a cubic structure and exhibit very fine crystallite size of < 2 nm. Temperature dependent magnetization (M-T) measurements reveal that austenite (A)-martensite (M) phase transition begins at T~248 K and finishes at T~238 K during cooling cycle and these values increase to T~267 K and T~259 K while warming. In cooling cycle, the A-phase shows ferromagnetic (FM) ordering with a Curie temperature T~267 K, while both the FM-antiferromagnetic (AFM) and M-transitions occur at T~242 K. The M-phase undergoes FM transition at T~145 K. These transitions are also confirmed by temperature dependent resistivity measurements. The observed hysteretic behaviour of magnetization and resistivity in the temperature regime spanned by the A-M transition is a manifestation of the first order phase transition. Magnetization and susceptibility data also provide unambiguous evidence in favour of spin glass . The scaling of the glass freezing temperature (Tf) with frequency, extracted from the frequency dependent AC susceptibility measurements, confirms the existence of canonical spin glass at T<145 K. The occurrence of canonical spin glass has been explained in terms of the nanostructuring modified interactions between the FM correlations in the martensitic phase and the coexisting AFM.
Distinguishing different quantum states is a fundamental task having practical applications for information processing. Despite the efforts devoted so far, however, strategies for optimal discrimination are known only for specific examples. We here consider the problem of minimum-error quantum state discrimination where the average error is attempted to be minimized. We show the general structure of minimum-error state discrimination as well as useful properties to derive analytic solutions. Based on the general structure, we present a geometric formulation of the problem, which can be applied to cases where quantum state geometry is clear. We also introduce equivalent classes of sets of quantum states in terms of minimum-error discrimination: sets of quantum states in an equivalence class share the same guessing probability. In particular, for qubit states where the state geometry is found with the Bloch sphere, we illustrate that for an arbitrary set of qubit states, the minimum-error state discrimination with equal prior probabilities can be analytically solved, that is, optimal measurement and the guessing probability are explicitly obtained.
We investigate how entangled states can be created by considering collections of point-particles arranged at different spatial configurations, i.e., Fock states with spatial constraints. This type of states can be realized in Hubbard chains of spinless hard-core bosons, at different fillings, which have gapped energy spectrum with a highly degenerate ground state. We calculate the bipartite entanglement entropy for superpositions of such Fock states and show that their entanglement can be controlled via the spatial freedom of the particles, determined by the system filling. In addition we study the effect of confinement/boundary conditions on the Fock states and show that edge modes appear at the ends of the system, when open boundary conditions are considered. Our result is an example of entangled many-body states in 1D systems of strongly interacting particles, without requiring the spin, long-range microscopic interactions or external fields. Instead, the entanglement can be tuned by the empty space in the system, which determines the spatial freedom of the interacting particles.
The double perovskite Y_2NiMnO_6 displays ferromagnetic transition at Tc = 81 K. The ferromagnetic order at low temperature is confirmed by the saturation value of magnetization (M_s) and also, validated by the refined ordered magnetic moment values extracted from neutron powder diffraction data at 10 K. This way, the dominant Mn4+ and Ni2+ cationic ordering is confirmed. The cation-ordered P 21/n nuclear structure is revealed by neutron powder diffraction studies at 300 and 10 K. Analysis of frequency dependent dielectric constant and equivalent circuit analysis of impedance data takes into account the bulk contribution to total dielectric constant. This reveals an anomaly which coincides with the ferromagnetic transition temperature (T_c). Pyrocurrent measurements register a current flow with onset near Tc and a peak at 57 K that shifts with temperature ramp rate. The extrinsic nature of the observed pyrocurrent is established by employing a special protocol measurement. It is realized that the origin is due to re-orientation of electric dipoles created by the free charge carriers and not by spontaneous electric polarization at variance with recently reported magnetism-driven ferroelectricity in this material
We report the discovery of four doubly imaged quasar lenses. All the four systems are selected as lensed quasar candidates from the Sloan Digital Sky Survey data. We confirm their lensing hypothesis with additional imaging and spectroscopic follow-up observations. The discovered lenses are SDSS J0743+2457 with the source redshift z_s=2.165, the lens redshift z_l=0.381, and the image separation theta=1.034", SDSS J1128+2402 with z_s=1.608 and theta=0.844", SDSS J1405+0959 with z_s=1.810, z_l~0.66, and theta=1.978", and SDSS J1515+1511 with z_s=2.054, z_l=0.742, and theta=1.989". It is difficult to estimate the lens redshift of SDSS J1128+2402 from the current data. Two of the four systems (SDSS J1405+0959 and SDSS J1515+1511) are included in our final statistical lens sample to derive constraints on dark energy and the evolution of massive galaxies.