ShantanuT01/DACTYL-Pretraining huggingface dataset:
Gravitational lensing can happen not only for null signal but also timelike signals such as neutrinos and massive gravitational waves in some theories beyond GR. In this work we study the time delay between different relativistic images formed by signals with arbitrary asymptotic velocity $v$ in general static and spherically symmetric spacetimes. A perturbative method is used to calculate the total travel time in the strong field limit, which is found to be in quasi-series of the small parameter $a=1-b_c/b$ where $b$ is the impact parameter and $b_c$ is its critical value. The coefficients of the series are completely fixed by the behaviour of the metric functions near the particle sphere $r_c$ and only the first term of the series contains a weak logarithmic divergence. The time delay $\Delta t_{n,m}$ to the leading non-trivial order was shown to equal the particle sphere circumference divided by the local signal velocity and multiplied by the winding number and the redshift factor. By assuming the Sgr A* supermassive black hole is a Hayward one, we were able to validate the quasi-series form of the total time, and reveal the effects of the spacetime parameter $l$, the signal velocity $v$ and the source/detector coordinate difference $\Delta\phi_{sd}$ on the time delay. It is found that as $l$ increase from 0 to its critical value $l_c$, both $r_c$ and $\Delta t_{n,m}$ decrease. The variation of $\Delta t_{n+1,n}$ for $l$ from 0 to $l_c$ can be as large as $7.2\times 10^1$ [s], whose measurement then can be used to constrain the value of $l$. While for ultra-relativistic neutrino or gravitational wave, the variation of $\Delta t_{n,m}$ is too small to be resolved. The dependence of $\Delta t_{n,-n}$ on $\Delta \phi_{sd}$ shows that to temporally resolve the two sequences of images from opposite sides of the lens, $|\Delta \phi_{sd}-\pi|$ has to be larger than certain value.
Representations that can compactly and effectively capture the temporal evolution of semantic content are important to computer vision and machine learning algorithms that operate on multi-variate time-series data. We investigate such representations motivated by the task of human action recognition. Here each data instance is encoded by a multivariate feature (such as via a deep CNN) where action dynamics are characterized by their variations in time. As these features are often non-linear, we propose a novel pooling method, kernelized rank pooling, that represents a given sequence compactly as the pre-image of the parameters of a hyperplane in a reproducing kernel Hilbert space, projections of data onto which captures their temporal order. We develop this idea further and show that such a pooling scheme can be cast as an order-constrained kernelized PCA objective. We then propose to use the parameters of a kernelized low-rank feature subspace as the representation of the sequences. We cast our formulation as an optimization problem on generalized Grassmann manifolds and then solve it efficiently using Riemannian optimization techniques. We present experiments on several action recognition datasets using diverse feature modalities and demonstrate state-of-the-art results.
We introduce Gutzwiller-correlated wave functions for the variational investigation of general multi-band Hubbard models. We set up a diagrammatic formalism which allows us to evaluate analytically ground-state properties in the limit of infinite spatial dimensions. In this limit recent results obtained within the Gutzwiller approximation are seen to become exact for these wave functions. We further show that the Slave Boson mean-field theory for degenerate bands becomes variationally controlled at zero temperature in infinite dimensions. Lastly, we briefly comment on the variational approach to the Anderson transition in strongly correlated electron systems.
The inert Zee model is an extension of the Zee model for neutrino masses to allow for a solution to the dark matter problem that involves two vector-like fields, a doublet and a singlet of $SU(2)_L$, and two scalars, also a doublet and a singlet of $SU(2)_L$, all of them being odd under an exact $Z_2$ symmetry. The introduction of the $Z_2$ guarantees one-loop neutrino masses, forbids tree-level Higgs-mediated flavor changing neutral currents and ensures the stability of the dark matter candidate. Due to the natural breaking of lepton numbers in the inert Zee model and encouraged by the ambitious experimental program designed to look for charged lepton flavor violation signals and the electron electric dipole moment, we study the phenomenology of the processes leading to these kind of signals, and establish which are the most promising experimental perspectives on that matter.
We identify that quantum coherence is a valuable resource in the quantum heat engine, which is designed in a quantum thermodynamic cycle assisted by a quantum Maxwell's demon. This demon is in a superposed state. The quantum work and heat are redefined as the sum of coherent and incoherent parts in the energy representation. The total quantum work and the corresponding efficiency of the heat engine can be enhanced due to the coherence consumption of the demon. In addition, we discuss an universal information heat engine driven by quantum coherence. The extractable work of this heat engine is limited by the quantum coherence, even if it has no classical thermodynamic cost. This resource-driven viewpoint provides a direct and effective way to clarify the thermodynamic processes where the coherent superposition of states cannot be ignored.
The large branching ratios for $B \to K\pi$ decays as observed by the CLEO Collaboration indicate that penguin interactions contribute a major part to the decay rates and provide an interference between the Cabibbo-suppressed tree and penguin contributions resulting in a CP-asymmetry between the $B \to K\pi$ and its charge conjugate mode. The CP-averaged decay rates depend also on the weak phase $\gamma$ and give us a determination of this phase. In this talk, I would like to report on a recent analysis of $B \to K\pi$ decays using factorisation model with final state interaction phase shift included. We find that factorisation seems to describe qualitatively the latest CLEO data. We also obtain a relation for the branching ratios independent of the strength of the strong penguin interactions. This relation gives a central value of $0.60 \times 10^{-5}$ for ${\mathcal B}(\bar{B}^{0} \to \bar{K}^{0}\pi^{0})$, somewhat smaller than the latest CLEO measurement. We also find that a ratio obtained from the CP-averaged $B \to K\pi$ decay rates could be used to test the factorisation model and to determine the weak angle $\gamma$ with more precise data, though the latest CLEO data seem to favor $\gamma$ in the range $90^{\circ}-120^{\circ}$.
In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree functions. Here we provide an alternative proof for general low-degree functions, with no constraints on the influences. We show that any real-valued function on the slice, whose degree when written as a harmonic multi-linear polynomial is $o(\sqrt{n})$, has approximately the same distribution under the slice and cube measure.   Our proof is based on a novel decomposition of random increasing paths in the cube in terms of martingales and reverse martingales. While such decompositions have been used in the past for stationary reversible Markov chains, ours decomposition is applied in a non-reversible non-stationary setup. We also provide simple proofs for some known and some new properties of harmonic functions which are crucial for the proof.   Finally, we provide independent simple proofs for the facts that 1) one cannot distinguish between the slice and the cube based on functions of $o(n)$ coordinates and 2) Boolean symmetric functions on the cube cannot be approximated under the uniform measure by functions whose sum of influences is $o(\sqrt{n})$.
An approach is suggested for modeling quark and lepton masses and mixing in the context of grand unified theories that explains the curious fact that m_u ~ m_d even though m_t >> m_b. The structure of the quark mass matrices is such as to allow a non-Peccei-Quinn solution of the Strong CP Problem.
Given a standard Brownian motion $B^{\mu}=(B_t^{\mu})_{0\le t\le T}$ with drift $\mu \in \mathbb{R}$ and letting $S_t^{\mu}=\max_{0\le s\le t}B_s^{\mu}$ for $0\le t\le T$, we consider the optimal prediction problem: \[V=\inf_{0\le \tau \le T}\mathsf{E}(B_{\tau}^{\mu}-S_T^{\mu})^2\] where the infimum is taken over all stopping times $\tau$ of $B^{\mu}$. Reducing the optimal prediction problem to a parabolic free-boundary problem we show that the following stopping time is optimal: \[\tau_*=\inf \{t_*\le t\le T\mid b_1(t)\le S_t^{\mu}-B_t^{\mu}\le b_2(t)\}\] where $t_*\in [0,T)$ and the functions $t\mapsto b_1(t)$ and $t\mapsto b_2(t)$ are continuous on $[t_*,T]$ with $b_1(T)=0$ and $b_2(T)=1/2\mu$. If $\mu>0$, then $b_1$ is decreasing and $b_2$ is increasing on $[t_*,T]$ with $b_1(t_*)=b_2(t_*)$ when $t_*\ne 0$. Using local time-space calculus we derive a coupled system of nonlinear Volterra integral equations of the second kind and show that the pair of optimal boundaries $b_1$ and $b_2$ can be characterized as the unique solution to this system. This also leads to an explicit formula for $V$ in terms of $b_1$ and $b_2$. If $\mu \le 0$, then $t_*=0$ and $b_2\equiv +\infty$ so that $\tau_*$ is expressed in terms of $b_1$ only. In this case $b_1$ is decreasing on $[z_*,T]$ and increasing on $[0,z_*)$ for some $z_*\in [0,T)$ with $z_*=0$ if $\mu=0$, and the system of two Volterra equations reduces to one Volterra equation. If $\mu=0$, then there is a closed form expression for $b_1$. This problem was solved in [Theory Probab. Appl. 45 (2001) 125--136] using the method of time change (i.e., change of variables). The method of time change cannot be extended to the case when $\mu \ne 0$ and the present paper settles the remaining cases using a different approach.
We analyze implementations of bipartite unitaries by means of local operations and classical communication (LOCC) assisted by shared entanglement. We employ concepts and techniques developed in quantum Shannon theory to study an asymptotic scenario, in which two distant parties perform the same bipartite unitary on infinitely many pairs of inputs. We analyze minimum cost of entanglement and classical communication per copy. For two-round LOCC protocols, we derive a single-letter formula for the minimum cost of entanglement and classical communication, under an additional requirement that the error converges to zero faster than $1/n^4$, where $n$ is the number of input pairs. The formula is given by the "Markovianizing cost" of a tripartite state associated with the unitary, which can be computed by a finite-step algorithm. We also derive a lower bound on the minimum cost of resources, which applies for protocols with arbitrary number of rounds.
We propose a generalization of the classical point-line Cremona-Richmond configuration to a configuration of points and more dimensional subspaces of a projective space, and present them as geometric realizations of some interesting abstract incidence structures.
We present details about an experimental method based on the Landau Zener model which allows to measure very small tunnel splittings $\Delta$ in molecular clusters Fe8. The measurements are performed with an array of micro-SQUIDs. The observed oscillations of Delta as a function of the magnetic field applied along the hard anisotropy axis are explained in terms of topological quantum interference of two tunnel paths of opposite windings. Transitions between M = -S and (S - n), with n even or odd, revealed a parity (symmetry) effect which is analogous to the suppression of tunneling predicted for half integer spins. This observation is the first direct evidence of the topological part of the quantum spin phase (Berry phase) in a magnetic system. The influence of intermolecular dipole interactions on the measured tunnel splittings $\Delta$ are shown.
The frog model is a branching random walk on a graph in which particles branch only at unvisited sites. Consider an initial particle density of $\mu$ on the full $d$-ary tree of height $n$. If $\mu= \Omega( d^2)$, all of the vertices are visited in time $\Theta(n\log n)$ with high probability. Conversely, if $\mu = O(d)$ the cover time is $\exp(\Theta(\sqrt n))$ with high probability.
This paper shows that ordinary quantum mechanics is not consistent with the superluminal transmission of classical information.
In this work, we investigate whether the Kitaev honeycomb model can serve as a starting point to realize the intriguing physics of the Sachdev-Ye-Kitaev (SYK) model. The starting point is to strain the system, which leads to flat bands reminiscent of Landau levels, thereby quenching the kinetic energy. The presence of weak residual perturbations, such as Heisenberg interactions and the $\gamma$-term, creates effective interactions between the Majorana modes when projected into the flux-free sector. We assume the resulting interactions to be effectively random. This leads to a bipartite Sachdev-Ye-Kitaev model (b-SYK) with very similar properties as the SYK model. We also hypothesize under which conditions one would expect the standard SYK model in such a setup.
We propose a Ginzburg-Landau theory for the elastic properties of shape memory polycrystals. A single crystal elastic free energy for a system that undergoes a square-to-rectangle transformation is generalized to a polycrystal by introducing a crystal orientational field that is determined from a continuum phase field model. The coupled system is used to study domain morphology and mechanical properties of shape memory alloys in different temperature regimes.
These notes describe some applications of the analysis of ordinary differential equations to the study of the viscous approximation of conservation laws in one space dimension. The exposition mostly focuses on the analysis of invariant manifolds like the center manifold and the stable manifold. The last section addresses a more specific issue and describes a possible way of extending the notions of center and stable manifold to some classes of singular ordinary differential equations arising in the study of the Navier-Stokes equation in one space variable.
We use the TESIS EUV telescope to study the current sheet signatures observed during flux rope eruption. The special feature of the TESIS telescope was its ability to image the solar corona up to a distance of 2 $R_\odot$ from the Sun's center in the Fe 171 \AA\ line. The Fe 171 \AA\ line emission illuminates the magnetic field lines, and the TESIS images reveal the coronal magnetic structure at high altitudes. The analyzed CME had a core with a spiral-flux rope-structure. The spiral shape indicates that the flux rope radius varied along its length. The flux rope had a complex temperature structure: cold legs (70 000 K, observed in He 304 \AA\ line) and a hotter core (0.7 MK, observed in Fe 171 \AA\ line). Such structure contradicts the common assumption that the CME core is a cold prominence. When the CME impulsively accelerated, a dark double Y-structure appeared below the flux rope. The Y-structure timing, location, and morphology agree with the previously performed MHD simulations of the current sheet. We interpreted the Y-structure as a hot envelope of the current sheet and hot reconnection outflows. The Y-structure had a thickness 6.0 Mm. Its length increased over time from 79 Mm to more than 411 Mm.
The effects of strong Coulomb correlations in dense three-dimensional electron-hole plasmas are studied by means of unbiased direct path integral Monte Carlo simulations. The formation and dissociation of bound states, such as excitons and bi-excitons is analyzed and the density-temperature region of their appearance is identified. At high density, the Mott transition to the fully ionized metallic state (electron-hole liquid) is detected. Particular attention is paid to the influence of the hole to electron mass ratio $M$ on the properties of the plasma. Above a critical value of about M=80 formation of a hole Coulomb crystal was recently verified [Phys. Rev. Lett. {\bf 95}, 235006 (2005)] which is supported by additional results. Results are related to the excitonic phase diagram of intermediate valent Tm[Se,Te], where large values of $M$ have been observed experimentally.
The spatial distribution of the HI gas in galaxies holds important clues on the physical processes that shape the structure and dynamics of the interstellar medium (ISM). In this work, we quantify the structure of the HI gas in a sample of 33 nearby galaxies taken from the THINGS Survey using the delta-variance spectrum. The THINGS galaxies display a large diversity in their spectra, however, there are a number of recurrent features. In many galaxies, we observe a bump in the spectrum on scales of a few to several hundred pc. We find the characteristic scales associated with the bump to be correlated with galactic SFR for values of the SFR > 0.5 M$_{sol}$ yr$^{-1}$ and also with the median size of the HI shells detected in those galaxies. On larger scales, we observe the existence of two self-similar regimes. The first one, on intermediate scales is shallow and the power law that describes this regime has an exponent in the range [0.1-1] with a mean value of 0.55 which is compatible with the density field being generated by supersonic turbulence in the cold phase of the HI gas. The second power law is steeper, with a range of exponents between [0.5-1.5] and a mean value of 1.5. These values are associated with subsonic turbulence which is characteristic of the warm phase of the HI gas. The spatial scale at which the transition between the two regimes occurs is found to be $\approx 0.5 R_{25}$ which is similar to the size of the molecular disk in the THINGS galaxies. Overall, our results suggest that on scales < $0.5 R_{25}$, the structure of the ISM is affected by the effects of supernova explosions. On larger scales (> 0.5 $R_{25}$), stellar feedback has no significant impact, and the structure of the ISM is determined by large scale processes that govern the dynamics of the gas in the warm neutral medium such as the flaring of the HI disk and the effects of ram pressure stripping.
This paper proposes a novel graph-constrained generative adversarial network, whose generator and discriminator are built upon relational architecture. The main idea is to encode the constraint into the graph structure of its relational networks. We have demonstrated the proposed architecture for a new house layout generation problem, whose task is to take an architectural constraint as a graph (i.e., the number and types of rooms with their spatial adjacency) and produce a set of axis-aligned bounding boxes of rooms. We measure the quality of generated house layouts with the three metrics: the realism, the diversity, and the compatibility with the input graph constraint. Our qualitative and quantitative evaluations over 117,000 real floorplan images demonstrate that the proposed approach outperforms existing methods and baselines. We will publicly share all our code and data.
A recent scientific debate has arisen: Which processes underlie the actual ground of the valley Hall effect (VHE) in two-dimensional materials? The original VHE emerges in samples with ballistic transport of electrons due to the anomalous velocity terms resulting from the Berry phase effect. In disordered samples though, alternative mechanisms associated with electron scattering off impurities have been suggested: (i) asymmetric electron scattering, called skew scattering, and (ii) a shift of the electron wave packet in real space, called a side jump. It has been claimed that the side jump not only contributes to the VHE but fully offsets the anomalous terms regardless of the drag force for fundamental reasons and, thus, the side-jump together with skew scattering become the dominant mechanisms. However, this claim is based on equilibrium theories without any external valley-selective optical pumping, which makes the results fundamentally interesting but incomplete and impracticable. We develop in this paper a microscopic theory of the photoinduced VHE using the Keldysh nonequilibrium diagrammatic technique and find that the asymmetric skew scattering mechanism is dominant in the vicinity of the interband absorption edge. This allows us to explain the operation of optical transistors based on the VHE.
Let $S(a,b)$ denote the normalized Dedekind sum. We study the range of possible values for $S(a,b)=\frac{k}{q}$ with $\gcd(k,q)=1$. Girstmair proved local restrictions on $k$ depending on $q\pmod{12}$ and whether $q$ is a square and conjectured that these are the only restrictions possible. We verify the conjecture in the cases $q$ even, $q$ a square divisible by $3$ or $5$, and $2\le q\le 200$ (the latter by computer), and provide progress towards a general approach.
We extend the formalism of Leibovich, Ligeti, Stewart and Wise in the 1/m_Q expansion of Heavy Quark Effective Theory for the B semileptonic decays into excited D[(3/2)^+] mesons to the opposite parity states D[(3/2)^-]. For D[(3/2)^+] the 1/m_Q current perturbation dominates over the leading term at zero recoil, while for D[(3/2)^-] the 1/m_Q perturbation due to L_mag dominates also at zero recoil. We show that the corresponding 1/m_Q magnetic coupling is proportional to the mixing between the states D[(3/2)^-] and D[(1/2)^-] induced by the tensor force. We point out some subtleties that appear in this respect in HQET.
We compute the remaining amounts of hydrogen in red giant donors to see whether the conflict between theory and observations can be overcome. By considering the mass-stripping effect from an optically thick wind and the effect of thermally unstable disk, we systematically carried out binary evolution calculation for WD + MS and WD + RG systems. Here, we focus on the evolution of WD + RG systems. We found that some donor stars at the time of the supernova explosion contain little hydrogen-rich material on top of the helium core (as low as 0.017 $M_{\odot}$), which is smaller than the upper limit to the amount derived from observations of material stripped-off by explosion ejecta. Thus, no hydrogen line is expected in the nebular spectra of these SN Ia. We also derive the distributions of the envelope mass and the core mass of the companions from WD + RG channel at the moment of a supernova explosion by adopting a binary population synthesis approach. We rarely find a RG companion with a very low-mass envelope. Furthermore, our models imply that the remnant of the WD + RG channel emerging after the supernova explosion is a single low-mass white dwarf (0.15 $M_{\odot}$ - 0.30 $M_{\odot}$). The absence of a hydrogen line in nebular spectra of SNe Ia provides support to the proposal that the WD + RG system is the progenitor of SNe Ia.
We present a self-similar model of spherically symmetric collapse of a massless scalar field with a parameter $p$. The black hole formation is explicitly shown to occur only in the strong-field implosion of $p >1$. The field evolution in the critical limit $ p \rightarrow 1 $ is compared with numerical results found by Choptuik.