ShantanuT01/DACTYL-Pretraining huggingface dataset:
Here, we study a minimal model, the three-level V system coupled to two heat baths, and investigate the role of quantum coherences in heat transport in both the transient regime and in the nonequilibrium steady-state. In our model, energy is exchanged between the baths through two parallel pathways, which can be made distinct through the nondegeneracy of excited levels (energy splitting $\Delta$) and a control parameter $\alpha$, which adjusts the strength of one of the arms. Using a nonsecular quantum master equation of Redfield form, we succeed in deriving closed-form expressions for the quantum coherences and the heat current in the steady state limit for closely degenerate excited levels. By including three ingredients in our analysis: nonequilibrium baths, nondegeneracy of levels, and asymmetry of pathways, we show that quantum coherences are generated and sustained in the V model in the steady-state limit if three conditions, conjoining thermal and coherent effects are simultaneously met: (i) The two baths are held at different temperatures. (ii) Bath-induced pathways do not interfere destructively. (iii) Thermal rates do not mingle with the control parameter $\alpha$ to destroy interferences through an effective local equilibrium condition. We find that coherences are maximized when the heat current is suppressed. On the other hand, the secular Redfield quantum master equation is shown to fail in a broad range of parameters. Although we mainly focus on analytical results in the steady state limit, numerical simulations reveal that the transient behavior of coherences contrasts the steady-state limit, suggesting that different mechanisms are at play in these two regimes. Enhancing either the lifetime of transient coherences or their magnitude at steady state thus requires the control and optimization of different physical parameters.
We present 1/N Schwinger boson and quantum Monte Carlo calculations of the magnetization and NMR relaxation rate for the two-dimensional ferromagnetic Heisenberg model representing a quantum Hall system at filling factor nu=1. Comparing the analytic and numerical calculations, we find that the SU(N) version of Schwinger boson theory gives accurate results for the magnetization at low temperatures, whereas the O(N) model works well at higher temperatures.
The Ni-base superalloy 718 is the most widely used material for turbomachinery in the aerospace industry and land-based turbines. Although the relationship between processing and the resulting properties is well known, an understanding of the specific deformation mechanisms activated across its application temperature range is required to create more mechanistically accurate property models. Direct atomic-scale imaging observations with high angle annular dark-field scanning transmission electron microscopy, complemented by phase-field modeling informed by generalized stacking fault surface calculations using density functional theory, were employed to understand the shear process of ${\gamma}''$ and ${\gamma}'/{\gamma}''$ co-precipitates after 1 \% macroscopic strain at lower temperature (ambient and $427 {\deg}C$). Experimentally, intrinsic stacking faults were observed in the ${\gamma}''$, whereas the ${\gamma}'$ was found to exhibit anti-phase boundaries or superlattice intrinsic stacking faults. Additionally, the atomically flat ${\gamma}'/{\gamma}''$ interfaces in the co-precipitates were found to exhibit offsets after shearing, which can be used as tracers for the deformation events. Phase-field modeling shows that the developing fault-structure is dependent on the direction of the Burgers vector of the $a/2 \langle110\rangle$ matrix dislocation (or dislocation group) due to the lower crystal symmetry of the ${\gamma''}$ phase. The interplay between ${\gamma}'$ and ${\gamma}''$ phases results in unique deformation pathways of the co-precipitate and increases the shear resistance. Consistent with the experimental observations, the simulation results indicate that complex shearing mechanisms are active in the low-temperature deformation regime and that multiple $a/2 \langle110\rangle$ dislocations of non-parallel Burgers vectors may be active on the same slip plane.
In this work we deal with a scalar spectral mixed boundary value problem in a spacial junction of thin rods and a plate. Constructing asymptotics of the eigenvalues, we employ two equipollent asymptotic models posed on the skeleton of the junction, that is, a hybrid domain. We, first, use the technique of self-adjoint extensions and, second, we impose algebraic conditions at the junction points in order to compile a problem in a function space with detached asymptotics. The latter problem is involved into a symmetric generalized Green formula and, therefore, admits the variational formulation. In comparison with a primordial asymptotic procedure, these two models provide much better proximity of the spectra of the problems in the spacial junction and in its skeleton. However, they exhibit the negative spectrum of finite multiplicity and for these "parasitic" eigenvalues we derive asymptotic formulas to demonstrate that they do not belong to the service area of the developed asymptotic models.
Let C be an irreducible projective curve of degree d in Pn(K), where K is an algebraically closed field, and let I be the associated homogeneous prime ideal. We wish to compute generators for I, assuming we are given sufficiently many points on the curve C. In particular if I can be generated by polynomials of degree at most m and we are given md + 1 points on C, then we can find a set of generators for I. We will show that a minimal set of generators of I can be constructed in polynomial time. Our constructions are completely independent of any notion of term ordering; this allows us the maximal freedom in performing our constructions in order to improve the numerical stability. We also summarize some classical results on bounds for the degrees of the generators of our ideal in terms of the degree and genus of the curve.
We present a comprehensive analysis of the structural properties and luminosities of the 23 dwarf spheroidal galaxies that fall within the footprint of the Pan-Andromeda Archaeological Survey (PAndAS). These dwarf galaxies represent the large majority of Andromeda's known satellite dwarf galaxies and cover a wide range in luminosity ($-11.6<M_V<-5.8$ or $10^{4.2}< L <10^{6.5} L_\odot$) and surface brightness ($25.1<\mu_0<29.3$ mag/arcsec$^2$). We confirm most previous measurements, but find And XIX to be significantly larger than before ($r_h=3065^{+1065}_{-935}$ pc, $M_V=-10.1^{+0.8}_{-0.4}$) and cannot derive parameters for And XXVII as it is likely not a bound stellar system. We also significantly revise downward the luminosities of And~XV and And~XVI, which are now $M_V\sim-7.5$ or $L\sim10^5 L_\odot$. Finally, we provide the first detailed analysis of Cas II/And XXX, a fairly faint system ($M_V=-8.0^{+0.4}_{-0.3}$) of typical size ($r_h=270\pm50$ pc), located in close proximity to the two bright elliptical dwarf galaxies NGC 147 & 185. Combined with the set of homogeneous distances published in an earlier contribution, our analysis dutifully tracks all relevant sources of uncertainty in the determination of the properties of the dwarf galaxies from the PAndAS photometric catalogue. We further publish the posterior probability distribution functions of all the parameters we fit for in the form of MCMC chains available online; these inputs should be used in any analysis that aims to remain truthful to the data and properly account for covariance between parameters.
We show how the nature of the the phase transition in the two-dimensional bimodal Ising spin glass model can be understood in terms of elementary excitations. Although the energy gap with the ground state is expected to be 4J in the ferromagnetic phase, a gap 2J is in fact found if the finite lattice is wound around a cylinder of odd circumference $L$. This 2J gap is really a finite size effect that should not occur in the thermodynamic limit of the ferromagnet. The spatial influence of the frustration must be limited and not wrap around the system if $L$ is large enough. In essence, the absence of 2J excitations defines the ferromagnetic phase without recourse to calculating magnetisation or investigating the system response to domain wall defects. This study directly investigates the response to temperature. We also estimate the defect concentration where the phase transition to the spin glass glass state occurs. The value $p_c = 0.1045(11)$ is in reasonable agreement with the literature.
The Infrared Space Observatory (ISO) was an extremely successful european space mission that gave us an unparallel view of the Universe in the infrared, and provided us with hundreds of observations of star forming regions and bipolar outflows. Three of the instrument teams, in charge of the infrared camera (CAM) and the two spectrometers at short and long wavelengths (SWS and LWS respectively), used a significant fraction of their guarantee time to study YSOs and outflows spectroscopically. In here, I will briefly review some of their main findings, particularly the detection of water, H2 rotational emission lines and the presence of other complex molecules. I will present new spectroscopic results on HH 1-2, HH 7-11 and Cep E, and their sources. And finally, I will discuss some of the general trends derived from these observations and their relevance in understanding the emission from these objects using J and C shock models.
Temperature-dependent dynamical spin correlations, which can be readily accessed via a variety of experimental techniques, hold the potential of offering a unique fingerprint of quantum spin liquids and other intriguing dynamical states. In this work we present an in-depth study of the temperature-dependent dynamical spin structure factor $S({\bf q}, \omega)$ of the antiferromagnetic (AFM) Heisenberg spin-1/2 model on the kagome lattice with additional Dzyaloshinskii--Moriya (DM) interactions. Using the finite-temperature Lanczos method on lattices with up to $N = 30$ sites we find that even without DM interactions, chiral low-energy spin fluctuations of the $120^\circ$ AFM order parameter dominate the dynamical response. This leads to a nontrivial frequency dependence of $S({\bf q}, \omega)$ and the appearance of a pronounced low-frequency mode at the M point of the extended Brillouin zone. Adding an out-of-plane DM interactions $D^z$ gives rise to an anisotropic dynamical response, a softening of in-plane spin fluctuations, and, ultimately, the onset of a coplanar AFM ground-state order at $D^z > 0.1 J$. Our results are in very good agreement with existing inelastic neutron scattering and temperature-dependent NMR spin-lattice relaxation rate ($1/T_1$) data on the paradigmatic kagome AFM herbertsmithite, where the effect of its small $D^z$ on the dynamical spin correlations is shown to be rather small, as well as with $1/T_1$ data on the novel kagome AFM YCu$_3$(OH)$_6$Cl$_3$, where its substantial $D^z \approx 0.25 J$ interaction is found to strongly affect the spin dynamics.
Topological insulators (TIs) have been found in strained binary HgTe and ternary I-III-VI2 chalcopyrite compounds such as CuTlSe2 which have inverted band structures. However, the non-trivial band gaps of these existing binary and ternary TIs are limited to small values, usually around 10 meV or less. In this work, we reveal that a large non-trivial band gap requires the material having a large negative crystal field splitting $\Delta_{CF}$ at top of the valence band and a moderately large negative $s-p$ band gap $E_g^{s-p}$. These parameters can be better tuned through chemical ordering in multinary compounds. Based on this understanding, we show that a series of quaternary I2-II-IV-VI4 compounds, including Cu2HgPbSe4, Cu2CdPbSe4, Ag2HgPbSe4 and Ag2CdPbTe4 are TIs, in which Ag2HgPbSe4 has the largest TI band gap of 47 meV because it combines the optimal values of $\Delta_{CF}$ and $E_g^{s-p}$.
Using a high resolution hydrodynamical cosmological simulation of the formation of a massive spheroidal galaxy we show that elliptical galaxies can be very compact and massive at high redshift in agreement with recent observations. Accretion of stripped in-falling stellar material increases the size of the system with time and the central concentration is reduced by dynamical friction of the surviving stellar cores. In a specific case of a spheroidal galaxy with a final stellar mass of $1.5 \times 10^{11} M_{\odot}$ we find that the effective radius $r_e$ increases from $0.7 \pm 0.2 \rm kpc$ at z = 3 to $r_e = 2.4 \pm 0.4 \rm kpc$ at z = 0 with a concomitant decrease in the effective density of an order of magnitude and a decrease of the central velocity dispersion by approximately 20% over this time interval. A simple argument based on the virial theorem shows that during the accretion of weakly bound material (minor mergers) the radius can increase as the square of the mass in contrast to the usual linear rate of increase for major mergers. By undergoing minor mergers compact high redshift spheroids can evolve into present-day systems with sizes and concentrations similar to observed local ellipticals. This indicates that minor mergers may be the main driver for the late evolution of sizes and densities of early-type galaxies.
We consider the Higgs boson mass in a class of the UMSSM models in which the MSSM gauge group is extended by an additional U(1)' group. Implementing the universal boundary conditions at the GUT scale we target phenomenologically interesting regions of UMSSM where the necessary radiative contributions to the lightest CP-even Higgs boson mass are significantly small and LSP is always the lightest neutralino. We find that the smallest amount of radiative contributions is about 50 GeV in UMSSM, this result is much lower than that obtained in MSSM, which is around 90 GeV. Additionally, we examine the Higgs boson properties in these models to check if it can behave similar to the SM Higgs boson under the current experimental constraints. We find that enforcement of smaller radiative contribution mostly restricts the U(1)' breaking scale as v_S <~ 10 TeV. Besides, such low contributions demand h_S ~ 0.2 - 0.45. Because of the model dependency in realizing these radiative contributions theta_E_6 < 0 are more favored, if one seeks for the solutions consistent with the current dark matter constraints. As to the mass spectrum, we find that stop and stau can be degenerate with the LSP neutralino in the range from 300 GeV to 700 GeV; however, the dark matter constraints restrict this scale as m_stop, m_stau >~ 500$ GeV. Such degenerate solutions also predict stop-neutralino and stau-neutralino coannihilation channels, which are effective to reduce the relic abundance of neutralino down to the ranges consistent with the current dark matter observations. Finally, we discuss the effects of heavy M_Z' in the fine-tuning. Even though the radiative contributions are significantly low, the required fine-tuning can still be large. We comment about reinterpretation of the fine-tuning measure in the UMSSM framework, which can yield efficiently low results for the fine-tuning at the electroweak scale.
Two aspects of the widely accepted heuristic picture of the final state of gravitational collapse are the so-called Price law tails, describing the asymptotics of the exterior region of the black hole that forms, and Israel-Poisson's mass inflation scenario, describing the internal structure of the black hole. (The latter scenario, if valid, would indicate that the maximal development of initial data is extendible as a C^0 metric, putting into question the validity of Penrose's strong cosmic censorship conjecture.) In this talk, I shall discuss a series of rigorous results proving both Price's law and the mass inflation scenario in an appropriate spherically symmetric setting. The proof of Price's law is joint work with I. Rodnianski.
This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst parameter greater than $1/4$. In order to ensure the positiveness of the volatility, the coefficients of that equation satisfy a viability condition. The absence of arbitrages, the completeness of the market and a pricing formula are established.
We report transient electron paramagnetic resonance (trEPR) measurements with sub-microsecond time resolution performed on a P3HT:PCBM blend at low temperature. The trEPR spectrum immediately following photoexcitation reveals signatures of spin-correlated polaron pairs. The pair partners (positive polarons in P3HT and negative polarons in PCBM) can be identified by their characteristic g-values. The fact that the polaron pair states exhibit strong non-Boltzmann population unambiguously shows that the constituents of each pair are geminate, i.e. originate from one exciton. We demonstrate that coupled polaron pairs are present even several microseconds after charge transfer and suggest that they embody the intermediate charge transfer complexes which form at the donor/acceptor interface and mediate the conversion from excitons into free charge carriers.
In general relativity, the Mercury's orbit becomes approximately elliptical and the its perihelion has thus an additional advance. We demonstrate, meanwhile, that in comparison of those given by the Newton's theory of gravitation for the orbit of the Mercury, the circumference and the area are reduced by $40.39$ km and $2.35\ast10^{9}$ km$^{2}$, respectively, beside the major-axis contraction pointed out recently, and all are produced by the curved space within the Einstein's theory of gravitation. Since the resolution power of present astronomical distance measurement technology reaches $one$ kilometer, the shrinkage of Mercury's orbit can then be observable.
The analysis of the cluster environment is a valuable instrument to investigate the origin of AGN and star-forming galaxies gas fuelling and trigger mechanisms. To this purpose, we present a detailed analysis of the point-like X-ray sources in the Bullet cluster field. Thanks to $\sim600$ ks Chandra observations, we produced a catalogue of 381 X-ray point sources up to a distance of $\sim$1.5 virial radius and with flux limits $\sim1\times10^{-16}$ and $\sim8\times10^{-16}$ erg cm$^{-2}$ s$^{-1}$ in the 0.5-2 keV and 2-10 keV bands, respectively. We found a strong (up to a factor 1.5-2) and significant ($\ge$4$\sigma$) over-density in the full region studied $0.3R_{200}<R<1.5R_{200}$. We identified optical and infrared counterparts for $\sim$84% and $\sim$48% of the X-ray sources, respectively. We obtained new spectroscopic redshifts for 106 X-ray sources. Spectroscopic and photometric redshifts of optical and infrared sources have been also collected, and these sources were used as ancillary samples. We find that the over-density in the region $0.3R_{200}<R<R_{200}$ is likely due to X-ray AGN (mostly obscured) and star-forming galaxies both associated to the cluster, while in the more external region it is likely mostly due to background AGN. The fraction of cluster galaxies hosting an X-ray detected AGN is 1.0$\pm$0.4$\%$, nearly constant with the radius, a fraction similar to that reported in other clusters of galaxies at similar redshift. The fraction of X-ray bright AGN (L$_{2-10keV}$$>$10$^{43}$ ergs s$^{-1}$) in the region $0.3R_{200}<R<R_{200}$ is $0.5^{+0.6}_{-0.2}$$\%$, higher than that in other clusters at similar redshift and more similar to the AGN fraction in the field. Finally, the spatial distributions of AGN and star-forming galaxies, selected also thanks to their infrared emission, appear similar, thus suggesting that both are triggered by the same mechanism.
We investigate when the independence complex of $G[H]$, the lexicographical product of two graphs $G$ and $H$, is either vertex decomposable or shellable. As an application, we construct an infinite family of graphs with the property that every graph in this family has the property that the independence complex of each graph is shellable, but not vertex decomposable.
The Standard-Model Extension (SME) parameterizes all possible Lorentz-violating contributions to the Standard Model and General Relativity. It can be considered as an effective framework to describe possible quantum-gravity effects for energies much below the Planck energy. In the current paper, the spin-nondegenerate operators of the SME fermion sector are the focus. The propagators, energies, and solutions to the modified Dirac equation are obtained for several families of coefficients including nonminimal ones. The particle energies and spinors are computed at first order in Lorentz violation and, with the optical theorem, they are shown to be consistent with the propagators. The optical theorem is then also used to derive the matrices formed from a spinor and its Dirac conjugate at all orders in Lorentz violation. The results are the first explicit ones derived for the spin-nondegenerate operators. They will prove helpful for future phenomenological calculations in the SME that rely on the footing of quantum field theory.
Quantum entanglement effects between the electronic spin and charge degrees of freedom are examined in an organic molecular solid, termed a dimer-Mott insulating system, in which molecular dimers are arranged in a crystal as fundamental units. A low energy effective model includes an antisymmetric exchange interaction, as one of the dominant magnetic interactions. This interaction favors a 90 degree spin configuration, and competes with the Heisenberg-type exchange interaction. Stabilities of the magnetic ordered phases are examined by using the spin-wave theory, as well as the Schwinger-boson theory. It is found that the spin-charge interaction promotes an instability of the long-range magnetic ordered state around a parameter region where two spin-spiral phases are merged. Implication for the quantum spin liquid state observed in $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ is discussed.
We present recent results on elastic deuteron Compton scattering calculations for polarised beans and targets up to next-to-leading order within Chiral Effective Field Theory in the Small Scale Expansion variant to implement a dynamical \Delta(1232) degree of freedom. A simple power-counting argument discloses that np-intermediate rescattering states must be explicitly included at leading order already. This automatically results in the correct Thomson limit and guarantees current conservation. In view of ongoing effort at MAXlab, proposals at HIGS and plans at MAMI, we address in detail single- and double-polarised observables with linearly or circularly polarised photons on both unpolarised and vector-polarised deuterons. Our results indicate that several of the polarisation observables can be instrumental to extract not only spin-independent nucleon polarisabilities, but also the so-far practically un-determined spin-dependent polarisabilities which parameterise the stiffness of the nucleon spin in external electro-magnetic fields. Amongst the questions addressed are: convergence of the expansion for including the \Delta, the role of the np-rescattering contributions, and sensitivity to the deuteron wave function. An interactive Mathematica 7.0 notebook of these findings is available from the authors.