ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate experimentally and theoretically the Coherent Population Trapping (CPT) effect occurring in 87Rb D1 line due to the interaction with linearly polarized laser light (lin||lin CPT). In this configuration the coherence has a quadrupol like nature and is strongly influenced by the hyperfine structure of the excited state; consequently the quantum interference between CPT states is an essential feature of this interaction scheme. We study the lin||lin CPT signal as a function of the laser optical detuning. The comparison between experimental and theoretical results allows us to quantify the contribution from different CPT states to the total signal. Based on these results we investigate the signal depending on both the pressure broadening of the optical transition and the laser linewidth, and we find in which conditions the laser linewidth does not degrade the amplitude of the lin||lin CPT.
A promising trend in plasmonics involves shrinking the size of plasmon-supporting structures down to a few nanometers, thus enabling control over light-matter interaction at extreme-subwavelength scales. In this limit, quantum mechanical effects, such as nonlocal screening and size quantization, strongly affect the plasmonic response, rendering it substantially different from classical predictions. For very small clusters and molecules, collective plasmonic modes are hard to distinguish from other excitations such as single-electron transitions. Using rigorous quantum mechanical computational techniques for a wide variety of physical systems, we describe how an optical resonance of a nanostructure can be classified as either plasmonic or nonplasmonic. More precisely, we define a universal metric for such classification, the generalized plasmonicity index (GPI), which can be straightforwardly implemented in any computational electronic-structure method or classical electromagnetic approach to discriminate plasmons from single-particle excitations and photonic modes. Using the GPI, we investigate the plasmonicity of optical resonances in a wide range of systems including: the emergence of plasmonic behavior in small jellium spheres as the size and the number of electrons increase; atomic-scale metallic clusters as a function of the number of atoms; and nanostructured graphene as a function of size and doping down to the molecular plasmons in polycyclic aromatic hydrocarbons. Our study provides a rigorous foundation for the further development of ultrasmall nanostructures based on molecular plasmonics
We perform a thorough analysis of the relationship between discrete and series representation path integral methods, which are the main numerical techniques used in connection with the Feynman-Kac formula. First, a new interpretation of the so-called standard discrete path integral methods is derived by direct discretization of the Feynman-Kac formula. Second, we consider a particular random series technique based upon the Levy-Ciesielski representation of the Brownian bridge and analyze its main implementations, namely the primitive, the partial averaging, and the reweighted versions. It is shown that the n=2^k-1 subsequence of each of these methods can also be interpreted as a discrete path integral method with appropriate short-time approximations. We therefore establish a direct connection between the discrete and the random series approaches. In the end, we give sharp estimates on the rates of convergence of the partial averaging and the reweighted Levy-Ciesielski random series approach for sufficiently smooth potentials. The asymptotic rates of convergence are found to be O(1/n^2), in agreement with the rates of convergence of the best standard discrete path integral techniques.
We study the regularity of the solutions of the oblique derivative problem for linear uniformly parabolic equations with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized Morrey space than the strong solution belongs to the corresponding generalized Sobolev-Morrey space.
From state-of-the-art density-functional calculations using hybrid functionals we show that, persistent $n$-type conductivity in ZnO is due to defect complexes formed between H with intrinsic and extrinsic defects. H exhibits cationic, anionic, and electrically-inactive character on interacting with defects in ZnO. The electrically-inactive molecular hydrogen can contribute to $n$-type conductivity in ZnO by activating deep donor levels into shallow levels. By calculating local vibrational mode frequencies, we have identified origins of many H-related Raman and infra-red frequencies and thus confirmed the amphoteric behavior of H.
Status of tau lepton decay Monte Carlo generator TAUOLA, and its main recent applications are reviewed. It is underlined, that in recent efforts on development of new hadronic currents, the multi-dimensional nature of distributions of the experimental data must be taken with a great care. Studies for H to tau tau; tau to hadrons indeed demonstrate that multi-dimensional nature of distributions is important and available for evaluation of observables where tau leptons are used to constrain experimental data. For that part of the presentation, use of the TAUOLA program for phenomenology of H and Z decays at LHC is discussed, in particular in the context of the Higgs boson parity measurements with the use of Machine Learning techniques. Some additions, relevant for QED lepton pair emission and electroweak corrections are mentioned as well.
Using the almost all-sky 2MASS Photometric Redshift catalogue (2MPZ) we perform for the first time a tomographic analysis of galaxy angular clustering in the local Universe ($z<0.24$). We estimate the angular auto- and cross-power spectra of 2MPZ galaxies in three photometric redshift bins, and use dedicated mock catalogues to assess their errors. We measure a subset of cosmological parameters, having fixed the others at their Planck values, namely the baryon fraction $f_{b}=0.14^{+0.09}_{-0.06}$, the total matter density parameter $\Omega_{\rm m}=0.30\pm 0.06$, and the effective linear bias of 2MPZ galaxies $b_{\rm eff}$, which grows from $1.1^{+0.3}_{-0.4}$ at $\langle z \rangle=0.05$ up to $2.1^{+0.3}_{-0.5}$ at $\langle z\rangle=0.2$, largely because of the flux-limited nature of the dataset. The results obtained here for the local Universe agree with those derived with the same methodology at higher redshifts, and confirm the importance of the tomographic technique for next-generation photometric surveys such as Euclid or LSST.
We construct two Lefschetz decompositions of the derived category of coherent sheaves on the Grassmannian of $k$-dimensional subspaces in a vector space of dimension $n$. Both of them admit a Lefschetz basis consisting of equivariant vector bundles. We prove fullness of the first decomposition and conjecture it for the second one. In the case when $n$ and $k$ are coprime these decompositions coincide and are minimal. In general, we conjecture minimality of the second decomposition.
In this paper we study existence and asymptotic behavior of solitary-wave solutions for the generalized Shrira equation, a two-dimensional model appearing in shear flows. The method used to show the existence of such special solutions is based on the mountain pass theorem. One of the main difficulties consists in showing the compact embedding of the energy space in the Lesbesgue spaces; this is dealt with interpolation theory. Regularity and decay properties of the solitary waves are also established.
Within the framework of the perturbative QCD approach, we calculate the time-like $B_cB_c(B_c^*)$ form factors $F(Q^2)$ and $A_2(Q^2)$. We include relativistic corrections and QCD corrections, either of which can give about $20\%$ correction to the leading-order contribution, but there are cancellation effects between them. We calculate the cross sections of the $e^+e^-\to B_c^-B_c^+(B_c^{*+})$ processes. The cross sections are enhanced at the $Z$ pole to be $\sigma^{PP}(Q=m_Z) \sim 1.3\times10^{-5}\text{pb}$ and $\sigma^{PV}(Q=m_Z) \sim 2.5\times10^{-5}\text{pb}$, which are still too small to be detected by proposed $e^+e^-$ colliders such as the Circular Electron Positron Collider.
Recent observations with the Chandra X-ray telescope continue to detect X-ray emission from the transient GW170817. In a total exposure of 96.6 ks, performed between March 9 and March 16 2020 (935 d to 942 d after the merger), a total of 8 photons are measured at the source position, corresponding to a significance of about 5 sigma. Radio monitoring with the Australian Telescope Compact Array (ATCA) shows instead that the source has faded below our detection threshold (<33 uJy, 3 sigma). By assuming a constant spectral index beta=0.585, we derive an unabsorbed X-ray flux of approximately 1.4E-15 erg/cm^2/s, higher than earlier predictions, yet still consistent with a simple structured jet model. We discuss possible scenarios that could account for prolonged emission in X-rays. The current dataset appears consistent both with energy injection by a long-lived central engine and with the onset of a kilonova afterglow, arising from the interaction of the sub-relativistic merger ejecta with the surrounding medium. Long-term monitoring of this source will be essential to test these different models.
Let $X$ be a non-singular quasi-projective variety over a field, and let $\mathcal E$ be a vector bundle over $X$. Let $\mathbb G_X({d}, \mathcal E)$ be the Grassmann bundle of $\mathcal E$ over $X$ parametrizing corank $d$ subbundles of $\mathcal E$ with projection $\pi : {\mathbb G_X({d}, \mathcal E)} \to X$, and let $ \mathcal Q \gets \pi^*\mathcal E$ be the universal quotient bundle of rank $d$. In this article, a closed formula for $\pi_{*}\operatorname{ch} (\det \mathcal Q)$, the push-forward of the Chern character of the Pl\"ucker line bundle $\det \mathcal Q$ by $\pi$ is given in terms of the Segre classes of $\mathcal E$. Our formula yields a degree formula for $\mathbb G_X({d}, \mathcal E)$ with respect to $\det \mathcal Q$ when $X$ is projective and $\wedge ^d \mathcal E$ is very ample. To prove the formula above, a push-forward formula in the Chow rings from a partial flag bundle of $\mathcal E$ to $X$ is given.
The flavor structure in unified theory is probed with superparticle mass spectrum observed in future particle experiments. A key ingredient is the generation dependence of scalar mass non-degeneracy. The observed non-degeneracy in low-energy regime is shown to provide a direct imprint of flavor structure in high-energy fundamental theory. The implication from flavor-violating rare process is also discussed.
A grand canonical system of hard-core bosons, subject to thermal fluctuations, is studied on a lattice. Starting from the slave-boson representation with fields for occupied and unoccupied sites, an effective field theory is derived in which a complex field corresponds with the order parameter of the condensate and a real field with the total density of bosons. Near the boundary between the normal and the superfluid phase we obtain the Ginzburg-Landau functional for the superfluid order parameter. A mean-field calculation shows that the critical temperature $T_c$ increases with increasing density up to a maximum and decreases with further increasing density.
The ionizing background of cosmic hydrogen is an important probe of the sources and absorbers of ionizing radiation in the post-reionization universe. Previous studies show that the ionization rate should be very sensitive to changes in the source population: as the emissivity rises, absorbers shrink in size, increasing the ionizing mean free path and, hence, the ionizing background. By contrast, observations of the ionizing background find a very flat evolution from z~2-5, before falling precipitously at z~6. We resolve this puzzling discrepancy by pointing out that, at z~2-5, optically thick absorbers are associated with the same collapsed halos that host ionizing sources. Thus, an increasing abundance of galaxies is compensated for by a corresponding increase in the absorber population, which moderates the instability in the ionizing background. However, by z~5-6, gas outside of halos dominates the absorption, the coupling between sources and absorbers is lost, and the ionizing background evolves rapidly. Our halo based model reproduces observations of the ionizing background, its flatness and sudden decline, as well as the redshift evolution of the ionizing mean free path. Our work suggests that, through much of their history, both star formation and photoelectric opacity in the universe track halo growth.
We study the thermal and curvature effect to spontaneous symmetry breaking in phi^4 theory. The effective potential is evaluated in D-dimensional static universe with positive curvature R X S^{D-1} or negative curvature R X H^{D-1}. It is shown that temperature and positive curvature suppress the symmetry breaking, while negative curvature enhances it. To consider the back-reaction we numerically solve the gap equation and the Einstein equation simultaneously. The solution gives the relationship between the temperature and the scale factor.
The generating function for $p_N(n)$, the number of partitions of $n$ into at most $N$ parts, may be written as a product of $N$ factors. We find the behavior of coefficients in the partial fraction decomposition of this product as $N \to \infty$ by applying the saddle-point method, where the saddle-point we need is associated to a zero of the analytically continued dilogarithm. Our main result disproves a conjecture of Rademacher.
Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation. The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings.
The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model defined on the stacked triangular lattice. We consider all models at fixed d=3 and analyze the resummation procedures currently used to compute the critical exponents. We first show that, for the O(N) model, the resummation does not eliminate all non-physical (spurious) fixed points (FPs). Then the dependence of spurious as well as of the Wilson-Fisher FPs on the resummation parameters is carefully studied. The critical exponents at the Wilson-Fisher FP show a weak dependence on the resummation parameters. On the contrary, the exponents at the spurious FP as well as its very existence are strongly dependent on these parameters. For the cubic model, a new stable FP is found and its properties depend also strongly on the resummation parameters. It appears to be spurious, as expected. As for the frustrated models, there are two cases depending on the value of the number of spin components. When N is greater than a critical value Nc, the stable FP shows common characteristic with the Wilson-Fisher FP. On the contrary, for N<Nc, the results obtained at the stable FP are similar to those obtained at the spurious FPs of the O(N) and cubic models. We conclude from this analysis that the stable FP found for N<Nc in frustrated models is spurious. Since Nc>3, we conclude that the transitions for XY and Heisenberg frustrated magnets are of first order.
Artificially constructed van der Waals heterostructures (vdWHs) provide an ideal platform for realizing emerging quantum phenomena in condensed matter physics. Two methods for building vdWHs have been developed: stacking two-dimensional (2D) materials into a bilayer structure with different lattice constants, or with different orientations. The interlayer coupling stemming from commensurate or incommensurate superlattice pattern plays an important role in vdWHs for modulating the band structures and generating new electronic states. In this article, we review a series of novel quantum states discovered in two model vdWH systems -- graphene/hexagonal boron nitride (hBN) hetero-bilayer and twisted bilayer graphene (tBLG), and discuss how the electronic structures are modified by such stacking and twisting. We also provide perspectives for future studies on hetero-bilayer materials, from which an expansion of 2D material phase library is expected.
We have observed the composite active galactic nucleus (AGN)-starburst galaxy NGC 6764 with the Very Long Baseline Array at 1.6 and 4.9 GHz. These observations have detected a "core-jet" structure and a possible weak counterjet component at 1.6 GHz. The upper limits to the core and jet (1.6-4.9 GHz) spectral index are 0.6 and 0.3, respectively. Taken together with the high brightness temperature of ~10^7 K for the core region, the radio emission appears to be coming from a synchrotron jet. At a position angle of 25 degrees, the parsec-scale jet seems to be pointing closely toward the western edge of the southern kpc-scale bubble in NGC 6764. A real connection between the parsec- and sub-kpc-scale emission would not only suggest the presence of a curved jet, but also a close link between the AGN jet and the radio bubbles in NGC 6764. We demonstrate that a precessing jet model can explain the radio morphology from parsec- to sub-kpc scales, and the model best-fit parameters of jet speed and orientation are fully consistent with the observed jet-to-counterjet surface brightness ratio. The jet however appears to be disrupted on scales of hundreds of parsecs, possibly due to interaction with and entrainment of the interstellar medium gas, which subsequently leads to the formation of bubbles. The jet energetics in NGC 6764 suggest that it would take 12-21 Myr to inflate the (southern) bubble. This timescale corresponds roughly to the starburst episode that took place in NGC 6764 about 15-50 Myr ago, and could be indicative of a close connection between jet formation and the starburst activity in this galaxy.
In this paper, we are concerned with the effective elastic property of a two-phase high-contrast periodic composite with densely packed inclusions. The equations of linear elasticity are assumed. We first give a novel proof of the Flaherty-Keller formula for elliptic inclusions, which improves a recent result of Kang and Yu (Calc.Var.Partial Differential Equations, 2020). We construct an auxiliary function consisting of the Keller function and an additional corrected function depending on the coefficients of Lam\'e system and the geometry of inclusions, to capture the full singular term of the gradient. On the other hand, this method allows us to deal with the inclusions of arbitrary shape, even with zero curvature. An extended Flaherty-Keller formula is proved for m-convex inclusions, m > 2, curvilinear squares with round off angles, which minimize the elastic modulus under the same volume fraction of hard inclusions.
In this paper we present and discuss results of Monte Carlo numerical simulations of the two-dimensional Ising ferromagnet in contact with a heat bath that intrinsically has a thermal gradient. The extremes of the magnet are at temperatures $T_1<T_c<T_2$, where $T_c$ is the Onsager critical temperature. In this way one can observe a phase transition between an ordered phase ($T<T_c$) and a disordered one ($T>T_c$) by means of a single simulation. By starting the simulations with fully disordered initial configurations with magnetization $m\equiv 0$ corresponding to $T=\infty$, which are then suddenly annealed to a preset thermal gradient, we study the short-time critical dynamic behavior of the system. Also, by setting a small initial magnetization $m=m_0$, we study the critical initial increase of the order parameter. Furthermore, by starting the simulations from fully ordered configurations, which correspond to the ground state at T=0 and are subsequently quenched to a preset gradient, we study the critical relaxation dynamics of the system. Additionally, we perform stationary measurements ($t\rightarrow\infty$) that are discussed in terms of the standard finite-size scaling theory. We conclude that our numerical simulation results of the Ising magnet in a thermal gradient, which are rationalized in terms of both dynamic and standard scaling arguments, are fully consistent with well established results obtained under equilibrium conditions.
Bimonotone subdivisions in two dimensions are subdivisions all of whose sides are either vertical or have nonnegative slope. They correspond to statistical estimates of probability distributions of strongly positively dependent random variables. The number of bimonotone subdivisions compared to the total number of subdivisions of a point configuration provides insight into how often the random variables are positively dependent. We give recursions as well as formulas for the numbers of bimonotone and total subdivisions of $2\times n$ grid configurations in the plane. Furthermore, we connect the former to the large Schr\"oder numbers. We also show that the numbers of bimonotone and total subdivisions of a $2\times n$ grid are asymptotically equal. We then provide algorithms for counting bimonotone subdivisions for any $m \times n$ grid. Finally, we prove that all bimonotone triangulations of an $m \times n$ grid are connected by flips. This gives rise to an algorithm for counting the number of bimonotone (and total) triangulations of an $m\times n$ grid.