ShantanuT01/DACTYL-Pretraining huggingface dataset:
We exploit the knowledge of the nonequilibrium potential in a model for the modulated class A laser. We analyse both, the deterministic and the stochastic dynamics of such a system in terms of the Lyapunov potential. Furthermore, we analyse the stochastic response of such a system and explain it again using the potential in a wide range of parameters and for small values of the noise. Such a response is quantified by means of the amplification factor, founding stochastic resonance within specific parameter's ranges.
We study the Kondo effect in two crossed Luttinger liquids, using Boundary Conformal Field Theory. We predict two types of critical behaviors: either a two-channel Kondo fixed point with a nonuniversal Wilson ratio, or a new theory with an anomalous response identical to that found by Furusaki and Nagaosa (for the Kondo effect in a single Luttinger liquid). Moreover, we discuss the relevance of perturbations like channel anisotropy, and we make links with the Kondo effect in a two-band Hubbard system modeled by a channel-dependent Luttinger Hamiltonian. The suppression of backscattering off the impurity produces a model similar to the four-channel Kondo theory.
We present results from our ALMA Cycle 0 observations, at the frequencies around the HCN, HCO+, and HNC J=4-3 transition lines, of the luminous infrared galaxy IRAS 20551-4250 at z=0.043, which is known to host an energetically important obscured AGN. In addition to the targeted HCN, HCO+, and HNC J=4-3 emission lines, two additional strong emission lines are seen, which we attribute to H2S and CH3CN(+CCH). The HCN-to-HCO+ J=4-3 flux ratio (~0.7) is higher than in the other starburst-dominated galaxy (~0.2) observed in our ALMA Cycle 0 program. We tentatively (~5 sigma) detected the vibrationally excited (v2=1) HCN J=4-3 (l=1f) emission line, which is important for testing an infrared radiative pumping scenario for HCN. This is the second detection of this molecular transition in external galaxies. The most likely reason for this detection is not only the high flux of this emission line, but also the small molecular line widths observed in this galaxy, suggesting that vibrational excitation of HCN may be relatively common in AGN-hosting galaxies.
We analyze {\it K2} light curves for 794 low-mass ($1 > M_* > 0.1$ $M_{\odot}$) members of the $\approx$650-Myr-old open cluster Praesepe, and measure rotation periods ($P_{rot}$) for 677 of these stars. We find that half of the rapidly rotating $>$0.3 $M_{\odot}$ stars are confirmed or candidate binary systems. The remaining $>0.3$ $M_{\odot}$ fast rotators have not been searched for companions, and are therefore not confirmed single stars. We found previously that nearly all rapidly rotating $>$0.3 $M_{\odot}$ stars in the Hyades are binaries, but we require deeper binary searches in Praesepe to confirm whether binaries in these two co-eval clusters have different $P_{rot}$ distributions. We also compare the observed $P_{rot}$ distribution in Praesepe to that predicted by models of angular-momentum evolution. We do not observe the clear bimodal $P_{rot}$ distribution predicted by Brown (2014) for $>$0.5 $M_{\odot}$ stars at the age of Praesepe, but 0.25$-$0.5 $M_{\odot}$ stars do show stronger bimodality. In addition, we find that $>$60\% of early M dwarfs in Praesepe rotate more slowly than predicted at 650 Myr by Matt et al. (2015), which suggests an increase in braking efficiency for these stars relative to solar-type stars and fully convective stars. The incompleteness of surveys for binaries in open clusters likely impacts our comparison with these models, since the models only attempt to describe the evolution of isolated single stars.
Most models for the connection between galaxies and their haloes ignore the possibility that galaxy properties may be correlated with halo properties other than mass, a phenomenon known as galaxy assembly bias. Yet, it is known that such correlations can lead to systematic errors in the interpretation of survey data. At present, the degree to which galaxy assembly bias may be present in the real Universe, and the best strategies for constraining it remain uncertain. We study the ability of several observables to constrain galaxy assembly bias from redshift survey data using the decorated halo occupation distribution (dHOD), an empirical model of the galaxy--halo connection that incorporates assembly bias. We cover an expansive set of observables, including the projected two-point correlation function $w_{\mathrm{p}}(r_{\mathrm{p}})$, the galaxy--galaxy lensing signal $\Delta \Sigma(r_{\mathrm{p}})$, the void probability function $\mathrm{VPF}(r)$, the distributions of counts-in-cylinders $P(N_{\mathrm{CIC}})$, and counts-in-annuli $P(N_{\mathrm{CIA}})$, and the distribution of the ratio of counts in cylinders of different sizes $P(N_2/N_5)$. We find that despite the frequent use of the combination $w_{\mathrm{p}}(r_{\mathrm{p}})+\Delta \Sigma(r_{\mathrm{p}})$ in interpreting galaxy data, the count statistics, $P(N_{\mathrm{CIC}})$ and $P(N_{\mathrm{CIA}})$, are generally more efficient in constraining galaxy assembly bias when combined with $w_{\mathrm{p}}(r_{\mathrm{p}})$. Constraints based upon $w_{\mathrm{p}}(r_{\mathrm{p}})$ and $\Delta \Sigma(r_{\mathrm{p}})$ share common degeneracy directions in the parameter space, while combinations of $w_{\mathrm{p}}(r_{\mathrm{p}})$ with the count statistics are more complementary. Therefore, we strongly suggest that count statistics should be used to complement the canonical observables in future studies of the galaxy--halo connection.
We propose two methods for generating non-Gaussian maps with fixed power spectrum and bispectrum. The first makes use of a recently proposed rigorous, non-perturbative, Bayesian framework for generating non-Gaussian distributions. The second uses a simple superposition of Gaussian distributions. The former is best suited for generating mildly non-Gaussian maps, and we discuss in detail the limitations of this method. The latter is better suited for the opposite situation, i.e. generating strongly non-Gaussian maps. The ensembles produced are isotropic and the power spectrum can be jointly fixed; however we cannot set to zero all other higher order cumulants (an unavoidable mathematical obstruction). We briefly quantify the leakage into higher order moments present in our method. We finally present an implementation of our code within the HEALPIX package
The dynamics of atom-molecule conversion system subject to dephasing noises is studied in this paper. With the dephasing master equation and the mean-field theory, we drive a Bloch equation for the system, this equation is compared with the Bloch equation derived by the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy truncation approach. Fixed points of the system are calculated by solving both the Bloch equations and the master equation, comparison between these two calculations suggests that while in a short time the mean-field theory is a good approximation for the atom-molecule conversion system, a high order hierarchy truncation approach is necessary for the system in a long time scale. Although the MFT can not predict correctly the fixed points, its prediction on the stability of the fixed points are consistent with the BBGKY theory for a wide range of parameters.
We perform global three-dimensional (3D) radiation-hydrodynamic (RHD) simulations of out- flow from supercritical accretion flow around a 10 Msun black hole. We only solve the outflow part, starting from the axisymmetric 2D simulation data in a nearly steady state but with small perturbations in a sinusoidal form being added in the azimuthal direction. The mass accretion rate onto the black hole is ~10^2 L_E/c^2 in the underlying 2D simulation data and the outflow rate is ~10 L_E/c^2 (with LE and c being the Eddington luminosity and speed of light, respectively). We first confirm the emergence of clumpy outflow, which was discovered by the 2D RHD simulations, above the photosphere located at a few hundreds of Schwarzschild radii (r_S) from the central black hole. As prominent 3D features we find that the clumps have the shape of a torn sheet, rather than a cut string, and that they are rotating around the central black hole with a sub-Keplerian velocity at a distance of ~10^3 r_S from the center. The typical clump size is ~30 r_S or less in the radial direction, and is more elongated in the angular directions, ~hundreds of r_S at most. The sheet separation ranges from 50 to 150 r_S. We expect stochastic time variations when clumps pass across the line of the sight of a distant observer. Variation timescales are estimated to be several seconds for a black hole with mass of ten to several tens of Msun, in rough agreement with the observations of some ultra-luminous X-ray sources.
We briefly explain the notion of exclusion statistics and in particular discuss the concept of an ideal exclusion statistics gas. We then review a recent work where it is demonstrated that a {\em two-dimensional} Bose gas with repulsive delta function interactions obeys ideal exclusion statistics, with a fractional parameter related to the interaction strength.
In this paper we provide an algorithm to classify groups of points on abelian threefolds over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $\mathbb{F}_q$-isogeny class. This work completes partial classification given by S.Rybakov.
The monochromatic tree partition number of an $r$-edge-colored graph $G$, denoted by $t_r(G)$, is the minimum integer $k$ such that whenever the edges of $G$ are colored with $r$ colors, the vertices of $G$ can be covered by at most $k$ vertex-disjoint monochromatic trees. In general, to determine this number is very difficult. For 2-edge-colored complete multipartite graph, Kaneko, Kano, and Suzuki gave the exact value of $t_2(K(n_1,n_2,...,n_k))$. In this paper, we prove that if $n\geq 3$, and K(n,n) is 3-edge-colored such that every vertex has color degree 3, then $t_3(K(n,n))=3.$
We report on the controllable response of the lasing frequency to the cavity round-trip path change. This is achieved by modifying the dispersion of the intracavity medium in the four-wave mixing regime in Rb. We can either increase the response by at least a factor of $2.7$ or drastically reduce it. The former regime is useful for sensitive measurements tracking the cavity round trip length and the latter regime is useful for precision metrology.
We study the spin-1 Ising model with non-local constraints imposed by the Bak-Tang-Wiesenfeld sandpile model of self-organized criticality (SOC). The model is constructed as if the sandpile is being built on a (honeycomb) lattice with Ising interactions. In this way we combine two models that exhibit power-law decay of correlation functions characterized by different exponents. We discuss the model properties through an order parameter and the mean energy per node, as well as the temperature dependence of their fourth-order Binder cumulants. We find (i) a thermodynamic phase transition at a finite T_c between paramagnetic and antiferromagnetic phases, and (ii) that above T_c the correlation functions decay in a way typical of SOC. The usual thermodynamic criticality of the two-dimensional Ising model is not affected by SOC constraints (the specific heat critical exponent \alpha \approx 0), nor are SOC-induced correlations affected by the interactions of the Ising model. Even though the constraints imposed by the SOC model induce long-range correlations, as if at standard (thermodynamic) criticality, these SOC-induced correlations have no impact on the thermodynamic functions.
In the framework of R-parity violating (\rpv) supersymmetry, we try to find a consistent explanation for both recently measured CP asymmetry in B^0 --> phi K_S decay and the large branching ratio of B^{+/-} --> eta' K^{+/-} decay, which are inconsistent with the Standard Model (SM) prediction. We also investigate other charmless hadronic B --> PP and B --> VP decay modes whose experimental data favor the SM: for instance, recently measured CP asymmetries in B^0 --> eta^{prime} K_S and B^0 --> J / Psi K_S. We find that all the observed data can be accommodated for certain values of \rpv couplings.
Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study fluctuations, large deviations and moderate deviations nonlinear Hawkes processes in a new asymptotic regime, the large intensity function and the small exciting function regime. It corresponds to the large baseline intensity asymptotics for the linear case, and can also be interpreted as the asymptotics for the mean process of Hawkes processes on a large network.
We investigate some necessary and sufficient conditions for an exceptional divisor to contribute jumping numbers of an effective divisor on a variety of arbitrary dimension, inspired by the results for curves on surfaces by Smith and Thompson and Tucker. In particular, we construct an example of an exceptional divisor that is not contracted in the log canonical model, and does not contribute any jumping numbers.
Coupling constants of $S_{11}(1535)$ and $S_{11}(1650)$ resonances to meson-baryon ($\pi N$, $\eta N$, $\eta^\prime N$, $KY$) are investigated in a chiral quark model, complemented by inclusion of five-quark components in those resonances. The known strong decay partial widths of both resonances are well reproduced, provided sizeable strangeness components in the relevant wave functions. %to excellent description for the strong decays of the above two resonances, which %cannot be reproduced very well in the traditional chiral quark model with or without %$SU(6)\otimes O(3)$ breaking. Finally, we find that $S_{11}(1535)$ and $S_{11}(1650)$ %couple strongly to the channels with strangeness.
A brief review of recent advances in neutron scattering studies of low-dimensional quantum magnets is followed by a particular example. The separation of single-particle and continuum states in the weakly-coupled $S=1/2$ chains system BaCu2Si2O7 is described in some detail.
The notion of $(k,m)$-agreeable society was introduced by Deborah Berg et al.: a family of convex subsets of $\R^d$ is called $(k,m)$-agreeable if any subfamily of size $m$ contains at least one non-empty $k$-fold intersection. In that paper, the $(k,m)$-agreeability of a convex family was shown to imply the existence of a subfamily of size $\beta n$ with non-empty intersection, where $n$ is the size of the original family and $\beta\in[0,1]$ is an explicit constant depending only on $k,m$ and $d$. The quantity $\beta(k,m,d)$ is called the minimal \emph{agreement proportion} for a $(k,m)$-agreeable family in $\R^d$.   If we only assume that the sets are convex, simple examples show that $\beta=0$ for $(k,m)$-agreeable families in $\R^d$ where $k<d$. In this paper, we introduce new techniques to find positive lower bounds when restricting our attention to families of $d$-boxes, i.e. cuboids with sides parallel to the coordinates hyperplanes. We derive explicit formulas for the first non-trivial case: the case of $(2,3)$-agreeable families of $d$-boxes with $d\geq 2$.
We theoretically demonstrate that the transport inefficiency recently found experimentally for branched-out mesoscopic networks can also be observed in a quantum ring of finite width with an attached central horizontal branch. This is done by investigating the time evolution of an electron wave packet in such a system. Our numerical results show that the conductivity of the ring does not necessary improves if one adds an extra channel. This ensures that there exists a quantum analogue of the Braess Paradox, originating from quantum scattering and interference.
We consider the bosonic and fermionic symmetries of five-dimensional Maxwell- and Yang-Mills-Einstein supergravity theories on a spacetime with boundaries (isomorphic to M x S1/Z2). Due to the appearance of the "Chern-Simons" term, the classical action is not generally invariant under gauge and supersymmetries. Once bulk vector fields are allowed to propagate on the boundaries, there is an "inflow" governed by the rank-3 symmetric tensor that defines the five-dimensional theories. We discuss the requirements that invariance of the action imposes on new matter content and boundary conditions.
We use a model of the Galactic fountain to simulate the neutral-hydrogen emission of the Milky Way Galaxy. The model was developed to account for data on external galaxies with sensitive HI data. For appropriate parameter values, the model reproduces well the HI emission observed at Intermediate Velocities. The optimal parameters imply that cool gas is ionised as it is blasted out of the disc, but becomes neutral when its vertical velocity has been reduced by ~30 per cent. The parameters also imply that cooling of coronal gas in the wakes of fountain clouds transfers gas from the virial-temperature corona to the disc at ~2 Mo/yr. This rate agrees, to within the uncertainties with the accretion rate required to sustain the Galaxy's star formation without depleting the supply of interstellar gas. We predict the radial profile of accretion, which is an important input for models of Galactic chemical evolution. The parameter values required for the model to fit the Galaxy's HI data are in excellent agreement with values estimated from external galaxies and hydrodynamical studies of cloud-corona interaction. Our model does not reproduce the observed HI emission at High Velocities, consistent with High Velocity Clouds being extragalactic in origin. If our model is correct, the structure of the Galaxy's outer HI disc differs materially from that used previously to infer the distribution of dark matter on the Galaxy's outskirts.
We prove that the partition function for tripartite double-dimer configurations of a planar bipartite graph satisfies a recurrence related to the Desnanot-Jacobi identity from linear algebra. A similar identity for the dimer partition function was established nearly 20 years ago by Kuo and has applications to random tiling theory and the theory of cluster algebras. This work was motivated in part by the potential for applications in these areas. Additionally, we discuss an application to Donaldson-Thomas and Pandharipande-Thomas theory which will be the subject of a forthcoming paper. The proof of our recurrence requires generalizing work of Kenyon and Wilson; specifically, lifting their assumption that the nodes of the graph are black and odd or white and even.
As a refinement of the celebrated recent work of Yitang Zhang we show that any admissible k-tuple of integers contains at least two primes and almost primes in each component infinitely often if k is at least 181000. This implies that there are infinitely many gaps between consecutive primes of size at most 2530338, with an improved admissible k-tuple of Andrew W. Sutherland to 2326476.
Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the underlying sources. Furthermore, the phaseless far field pattern is also invariant if the source is multiplied by any complex number with modulus one. Therefore, the source can not be uniquely determined, even the multifrequency phaseless far field patterns are considered. By adding a reference point source into the model, we propose a simple and stable phase retrieval method and establish several uniqueness results with phaseless far field data. We proceed to introduce a novel direct sampling method for shape and location reconstruction of the source by using broadband sparse phaseless data directly. We also propose a combination method with the novel phase retrieval algorithm and the classical direct sampling methods with phased data. Numerical examples in two dimensions are also presented to demonstrate their feasibility and effectiveness.
The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived.
We investigate classes of quantum Heisenberg spin systems which have different coupling constants but the same energy spectrum and hence the same thermodynamical properties. To this end we define various types of isospectrality and establish conditions for their occurence. The triangle and the tetrahedron whose vertices are occupied by spins 1/2 are investigated in some detail. The problem is also of practical interest since isospectrality presents an obstacle to the experimental determination of the coupling constants of small interacting spin systems such as magnetic molecules.
We consider the Ramond sector of the $N=1$ superconformal algebra and find expressions for the singular vectors in reducible highest weight Verma module representations by the fusion principle of Bauer et al.
Within a nonperturbative dynamical two-body approach - based on coupled equations of motion for the one-body density matrix and the two-body correlation function - we study the distribution of occupation numbers in a correlated system close to the groundstate, the relaxation of single-particle excitations and the damping of collective modes. For this purpose the nonlinear equations of motion are solved numerically within a finite oscillator basis for the first time adopting short-range repulsive and long-range attractive two-body forces. We find in all cases that the formation of long- and short-range correlations and their mixing is related to the long- and short-range part of the nucleon-nucleon interaction which dominate the resummation of loop or ladder diagrams, respectively. However, the proper description of relaxation or damping phenomena is found to require both types of diagrams as well as the mixed terms simultaneously.
The statistical mechanics of quarks and gluons are investigated within the context of the canonical ensemble. Recursive techniques are developed which enforce the exact conservation of baryon number, total isospin, electric charge, strangeness, and color. Bose and Fermi-Dirac statistics are also accounted for to all orders. The energy, entropy and particle number densities are shown to be significantly reduced for volumes less than 5 cubic fm.
We have explained in detail why the canonical partition function of Interacting Self Avoiding Walk (ISAW), is exactly equivalent to the configurational average of the weights associated with growth walks, such as the Interacting Growth Walk (IGW), if the average is taken over the entire genealogical tree of the walk. In this context, we have shown that it is not always possible to factor the the density of states out of the canonical partition function if the local growth rule is temperature-dependent. We have presented Monte Carlo results for IGWs on a diamond lattice in order to demonstrate that the actual set of IGW configurations available for study is temperature-dependent even though the weighted averages lead to the expected thermodynamic behavior of Interacting Self Avoiding Walk (ISAW).