ShantanuT01/DACTYL-Pretraining huggingface dataset:
In a recent study, Cohen and Glashow argue that superluminal neutrinos of the type recently reported by OPERA should be affected by anomalous Cherenkov-like processes. This causes them to loose much of their energy before reaching the OPERA detectors. Related concerns were reported also by Gonzalez-Mestres and Bi et. al., who argued that pions cannot decay to superluminal neutrinos over part of the energy range studied by OPERA. We observe here that these arguments are set within a framework in which Lorentz symmetry is broken, by the presence of a preferred frame. We further show that these anomalous processes are forbidden if Lorentz symmetry is instead "deformed", preserving the relativity of inertial frames. These deformations add non-linear terms to energy momentum relations, conservation laws and Lorentz transformations in a way that is consistent with the relativity of inertial observers.
The switching dynamics of a single-domain BiFeO$_3$ thin films is investigated through combining the dynamics of polarization and Neel vector. The evolution of the ferroelectric polarization is described by the Landau-Khalatnikov (LK) equation, and the Landau-Lifshitz-Gilbert (LLG) equations for spins in two sublattices to model the time evolution of the antiferromagnetic order (Neel vector) in a G-type antiferromagnet. This work theoretically demonstrates that due to the rotation of the magnetic hard axis following the polarization reversal, the Neel vector can be switched by 180 degrees, while the weak magnetization can remain unchanged. The simulation results are consistent with the ab initio calculation, where the Neel vector rotates during polarization rotation, and also match our calculation of the dynamics of order parameter using Landau-Ginzburg theory. We also find that the switching time of the Neel vector is determined by the speed polarization switching and is predicted to be as short as 30 ps.
We propose an idea to investigate persistent current in individual arms of a multi-arm mesoscopic ring. Following a brief description of persistent current in a traditional Aharonov-Bohm (AB) ring, we examine the behavior of persistent currents in separate arms of a three-arm mesoscopic ring. Our analysis may be helpful in studying magnetic response of any complicated quantum network.
As part of the Transient UV Objects project, we have discovered a new outburst (at the beginning of October 2020) of the candidate cataclysmic variable (CV) ASASSN-18eh using the UV/Optical Telescope aboard the Neil Gehrels Swift Observatory. During the outburst its brightness increased by about 6 mag in UV compared to its brightness in the quiescent state. The properties of this outburst are consistent with it being a dwarf nova, strongly supporting the CV nature of ASASSN-18eh.
In analyzing a simple random walk on the Heisenberg group we encounter the problem of bounding the extreme eigenvalues of an $n\times n$ matrix of the form $M=C+D$ where $C$ is a circulant and $D$ a diagonal matrix. The discrete Schr\"odinger operators are an interesting special case. The Weyl and Horn bounds are not useful here. This paper develops three different approaches to getting good bounds. The first uses the geometry of the eigenspaces of $C$ and $D$, applying a discrete version of the uncertainty principle. The second shows that, in a useful limit, the matrix $M$ tends to the harmonic oscillator on $L^2(\mathbb{R})$ and the known eigenstructure can be transferred back. The third approach is purely probabilistic, extending $M$ to an absorbing Markov chain and using hitting time arguments to bound the Dirichlet eigenvalues. The approaches allow generalization to other walks on other groups.
In this paper, the Joule-Thomson expansion of the higher dimensional nonlinearly AdS black hole with power Maxwell invariant source is investigated. The results show the Joule-Thomson coefficient has a zero point and a divergent point, which are coincide with the inversion temperature $T_i$ and the zero point of Hawking temperature, respectively. The inversion temperature increases monotonously with inversion pressure. For high-pressure region, the inversion temperature decreases with the dimensionality $D$ and the nonlinearity parameter $s$, whereas it increases with the charge $Q$. However, $T_i$ for low-pressure region increase with $D$ and $s$, while it decreases with $Q$. The ratio ${\eta _{\rm{BH}}}$ between the minimum of inversion temperature and the critical temperature does not depend on $Q$, it recovers the higher dimensional Reissner-N\"{o}rdstrom AdS black hole case when $s=1$. However, for $s>1$, it becomes smaller and smaller as $D$ increase and approaches a constant when $D\rightarrow\infty$. Finally, we found that increase of mass $M$ and $s$, or reduce the charge $Q$ and $D$ can enhance the isenthalpic curve, and the effect of $s$ on the isenthalpic curve is much greater than other parameters.
We study the diagonalizability of the Atkin $U_t$-operator acting on Drinfeld cusp forms for $\Gamma_0(t)$: starting with the slopes of eigenvalues and then moving to the space of cusp forms for $\Gamma_1(t)$ to use Teitelbaum's interpretation as harmonic cocycles which makes computations more explicit. We prove $U_t$ is diagonalizable in odd characteristic for (relatively) small weights and explicitly compute the eigenvalues. In even characteristic we show that it is not diagonalizable when the weight is odd (except for the trivial cases) and prove some cases of non diagonalizability in even weight as well. We also formulate a few conjectures, supported by numerical search, about diagonalizability of $U_t$ and the slopes of its eigenforms.
We consider the nonlinear Schr{\"o}dinger-Langevin equation for both signs of the logarithmic nonlinearity. We explicitly compute the dynamics of Gaussian solutions for large times, which is obtained through the study of a particular nonlinear differential equation of order 2. We then give the asymptotic behavior of general energy weak solutions under some regularity assumptions. Some numerical simulations are performed in order to corroborate the theoretical results.
Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by $T_{rev} = 9 \mu a^2/4\hbar \pi$ where $a$ and $\mu$ are the length of one side and the mass of the point particle respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral ($60^{\circ}-60^{\circ}-60^{\circ}$) triangle, such as the half equilateral ($30^{\circ}-60^{\circ}-90^{\circ}$) triangle and other `foldings', which have related energy spectra and revival structures.
We calculate the ground--state energy and other physical properties of the hydrogen atom inside a spherical box with an impenetrable wall. We apply the variational method and perturbation theory and compare both approximate results. We show that the total, kinetic and potential energies for the moving--nucleus model are greater than those for the case in which the nucleus is clamped at the box center.
We deal with the problem of reconstructing material coefficients from the farfields they generate. By embedding small (single) inclusions to these media, located at points $z$ in the support of these materials, and measuring the farfields generated by these deformations we can extract the values of the total field generated by these media at the points $z$. The second step is to extract the values of the material coefficients from these internal values of the total field. The main difficulty in using internal fields is the treatment of their possible zeros.   In this work, we propose to deform the medium using multiple (precisely double) and close inclusions instead of only single ones. By doing so, we derive from the asymptotic expansions of the farfields the internal values of the Green function, in addition to the internal values of the total fields. This is possible because of the deformation of the medium with multiple and close inclusions which generates scattered fields due to the multiple scattering between these inclusions. Then, the values of the index of refraction can be extracted from the singularities of the Green function. Hence, we overcome the difficulties arising from the zeros of the internal fields.   We test these arguments for the acoustic scattering by a refractive index in presence of inclusions modeled by the impedance type small obstacles.
We study generalized Hermite polynomials with rectangular matrix arguments arising in multivariate statistical analysis and the theory of zonal polynomials. We show that these are well-suited for expressing the Wiener-Ito chaos expansion of functionals of the spectral measure associated with Gaussian matrices. In particular, we obtain the Wiener chaos expansion of Gaussian determinants of the form $\det(XX^T)^{1/2}$ and prove that, in the setting where the rows of $X$ are i.i.d. centred Gaussian vectors with a given covariance matrix, its projection coefficients admit a geometric interpretation in terms of intrinsic volumes of ellipsoids, thus extending the content of Kabluchko and Zaporozhets (2012) to arbitrary chaotic projection coefficients. Our proofs are based on a crucial relation between generalized Hermite polynomials and generalized Laguerre polynomials. In a second part, we introduce the matrix analog of the classical Mehler's formula for the Ornstein-Uhlenbeck semigroup and prove that matrix-variate Hermite polynomials are eigenfunctions of these operators. As a byproduct, we derive an orthogonality relation for Hermite polynomials evaluated at correlated Gaussian matrices. We apply our results to vectors of independent arithmetic random waves on the three-torus, proving in particular a CLT in the high-energy regime for a generalized notion of total variation on the full torus.
The cryptographic protocol of coin tossing consists of two parties, Alice and Bob, that do not trust each other, but want to generate a random bit. If the parties use a classical communication channel and have unlimited computational resources, one of them can always cheat perfectly. Here we analyze in detail how the performance of a quantum coin tossing experiment should be compared to classical protocols, taking into account the inevitable experimental imperfections. We then report an all-optical fiber experiment in which a single coin is tossed whose randomness is higher than achievable by any classical protocol and present some easily realisable cheating strategies by Alice and Bob.
The role of the Equivalence Principle (EP) in classical and quantum mechanics is reviewed. It is shown that the weak EP has a counterpart in quantum theory, a Quantum Equivalence Principle (QEP). This implies that also in the quantum domain the geometrisation of the gravitational interaction is an operational procedure similar to the procedure in classical physics. This QEP can be used for showing that it is only the usual Schr\"odinger equation coupled to gravito--inertial fields which obeys our equivalence principle. In addition, the QEP applied to a generalised Pauli equation including spin results in a characterisation of the gravitational fields which can be identified with the Newtonian potential and with torsion. Also, in the classical limit it is possible to state beside the usual EP for the path an EP for the spin which again may be used for introducing torsion as a gravitational field.
Fix a module M over a local ring R and a group action G on M, not necessarily R-linear. To understand how large is the G-orbit of an element z\in M one looks for the large submodules of M lying in Gz. We provide the corresponding (necessary/sufficient) conditions in terms of the tangent space to the orbit, T_{(Gz,z)}.   This question originates from the classical finite determinacy problem of Singularity Theory. Our treatment is rather general, in particular we extend the classical criteria of Mather (and many others) to a broad class of rings, modules and group actions.   When a particular `deformation space' is prescribed, \Sigma\subseteq M, the determinacy question is translated into the properties of the tangent spaces, T_{(Gz,z)}, T_{(\Si,z)}, and in particular to the annihilator of their quotient.
Recently, virtual reality, augmented reality, robotics, autonomous driving et al attract much attention of both academic and industrial community, in which image based camera localization is a key task. However, there has not been a complete review on image-based camera localization. It is urgent to map this topic to help people enter the field quickly. In this paper, an overview of image based camera localization is presented. A new and complete kind of classifications for image based camera localization is provided and the related techniques are introduced. Trends for the future development are also discussed. It will be useful to not only researchers but also engineers and other people interested.
Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the estimation error of $O(1/ \sqrt{N})$. Recently, Johnston introduced quantum supersampling (QSS) into rendering as a numerical integration method that can run on quantum computers. QSS breaks the fundamental limitation of the $O(1/ \sqrt{N})$ convergence rate of Monte Carlo integration and achieves the faster convergence rate. We introduce yet another quantum numerical integration algorithm, quantum coin (QCoin), and provide numerical experiments that are unprecedented in the fields of both quantum computing and rendering. We show that QCoin's convergence rate is equivalent to QSS's. We additionally show that QCoin is fundamentally more robust under the presence of noise in actual quantum computers due to its simpler quantum circuit and the use of fewer qubits. Considering various aspects of quantum computers, we discuss how QCoin can be a more practical alternative to QSS in quantum computers in the future.
Controlling the interplay between localized spins and itinerant electrons at the oxide interfaces can lead to exotic magnetic states. Here we devise SrTiO3/LaTiO3/SrTiO3 heterostructures with varied thickness of the LaTiO3 layer (n monolayers) to investigate the magnetic interactions in the two-dimensional electron gas system. The heterostructures exhibit significant Kondo effect when the LaTiO3 layer is rather thin (n = 2, 10), manifesting the strong interaction between the itinerant electrons and the localized magnetic moments at the interfaces, while the Kondo effect is greatly inhibited when n = 20. Notably, distinct Shubnikov-de Haas oscillations are observed and a nonzero Berry phase of {\pi} is extracted when the LaTiO3 layer is rather thin (n = 2, 10), which is absent in the heterostructure with thicker LaTiO3 layer (n = 20). The observed phenomena are consistently interpreted as a result of sub-band splitting and symmetry breaking due to the interplay between the interfacial Rashba spin-orbit coupling and the magnetic orderings in the heterostructures. Our findings provide a route for exploring and manipulating nontrivial electronic band structures at complex oxide interfaces.
This chapter aims at identifying what is specific to femtosecond laser ablation. It reviews the essential basic processes which contribute to femtosecond laser ablation of various materials : energy absorption by the material's electrons, electronic relaxation processes involving either electron-electron or electron-lattice interactions. A number of widely used models are briefly discussed, as well as some pending questions.
At which height will a prominence inclined to be unstable, or where is the most probable critical height for the prominence destabilization? This question is statistically studied based on 362 solar limb prominences well-recognized by SLIPCAT from 2007 April to the end of 2009. We found that there are about 71% disrupted prominences (DPs), among which about 42% of them did not erupt successfully and about 89% of them experienced a sudden destabilization (SD) process. After a comprehensive analysis of the DPs, the following findings are discovered. (1) Most DPs become unstable at the height of 0.06 -- 0.14 R$_\odot$ from the solar surface, and there are two most probable critical heights, at which a prominence is much likely to get unstable; the primary one is 0.13 R$_\odot$ and the secondary one is 0.19 R$_\odot$. (2) There exists upper limit for the erupting velocity of eruptive prominences (EPs), which decreases following a power law with increasing height and mass; the kinetic energy of EPs accordingly has an upper limit too, which decreases as critical height increases. (3) Stable prominences (SPs) are generally longer and heavier than DPs, and not higher than 0.4 R$_\odot$. (4) About 62% of EPs were associated with CMEs; but there is no difference in apparent properties between EPs associated with and without CMEs.
It is shown that Extensive Air Shower (EAS) longitudinal development has a critical point where an equilibrium between the main hadronic component and the secondary electromagnetic one exhibits a brake. This results in a change of slope in quasi-power law function $N_{e}(Eo)$. The latter leads to a knee in the EAS size spectrum at primary energy of about 100 TeV/nucleon. Many ``strange'' experimental results can be successfully explained in the frames of current approach.
We present a formalism for the matter effects in the Earth on low energy neutrino fluxes which is both accurate and has all advantages of a full analytic treatment. The oscillation probabilities are calculated up to second order term in $\epsilon(x) \equiv 2V(x)E/\Delta m^2$ where $V(x)$ is the neutrino potential at position $x$. We show the absence of large undamped phases which makes the expansion in $\epsilon$ well behaved. An improved expansion is presented in terms of the variation of $V(x)$ around a suitable mean value which allows to treat energies up to those relevant for Supernova neutrinos. We discuss also the case of three-neutrino mixing.
We present the status and update of a new approach to quantum general relativity as formulated by Feynman from the Einstein-Hilbert action wherein amplitude-based resummation techniques are applied to the theory's loop corrections to yield results (superficially) free of ultraviolet(UV) divergences. Recent applications are summarized.
A resonator can be effectively used as a cooler for another linear oscillator with a much smaller frequency. A huge cooling effect, which could be used to cool a mechanical oscillator below the energy of quantum fluctuations, has been predicted by several authors. However, here we show that there is a lower limit T* on the achievable temperature that was not considered in previous works and can be higher than the quantum limit in realistic experimental realizations. We also point out that the decay rate of the resonator, which previous studies stress should be small, must be larger than the decay rate of the cooled oscillator for effective cooling.
We introduce a formalism that exploits the many-input many-output nature of nodes in quantum circuits. There is a diagrammatic and an algebraic version, the latter similar to the spinor formalism of general relativity. This allows us to work in truly basis independent ways, clarifying and simplifying many aspects of quantum state processing. The narrative is at times interrupted by antics of characters from quantum age fairy tales.
Recently a nonuniversal character of the leading spatial behavior of the thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys. Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this observation and show that there is no such leading nonuniversal term in systems with short-ranged interactions if one treats properly the effects generated by a sharp momentum cutoff in the Fourier transform of the interaction potential. We also conclude that lattice and continuum models then produce results in mutual agreement independent of the cutoff scheme, contrary to the aforementioned report. All results are consistent with the {\em universal} character of the Casimir force in systems with short-ranged interactions. The effects due to dispersion forces are discussed for systems with periodic or realistic boundary conditions. In contrast to systems with short-ranged interactions, for $L/\xi \gg 1$ one observes leading finite-size contributions governed by power laws in $L$ due to the subleading long-ranged character of the interaction, where $L$ is the finite system size and $\xi$ is the correlation length.
Facial micro-expressions are subtle and involuntary expressions that can reveal concealed emotions. Micro-expressions are an invaluable source of information in application domains such as lie detection, mental health, sentiment analysis and more. One of the biggest challenges in this field of research is the small amount of available spontaneous micro-expression data. However, spontaneous data collection is burdened by time-consuming and expensive annotation. Hence, methods are needed which can reduce the amount of data that annotators have to review. This paper presents a novel micro-expression spotting method using a recurrent neural network (RNN) on optical flow features. We extract Histogram of Oriented Optical Flow (HOOF) features to encode the temporal changes in selected face regions. Finally, the RNN spots short intervals which are likely to contain occurrences of relevant facial micro-movements. The proposed method is evaluated on the SAMM database. Any chance of subject bias is eliminated by training the RNN using Leave-One-Subject-Out cross-validation. Comparing the spotted intervals with the labeled data shows that the method produced 1569 false positives while obtaining a recall of 0.4654. The initial results show that the proposed method would reduce the video length by a factor of 3.5, while still retaining almost half of the relevant micro-movements. Lastly, as the model gets more data, it becomes better at detecting intervals, which makes the proposed method suitable for supporting the annotation process.
The lighter group-V element phosphorus forms the As-type (hR2) structure under pressure, above 5 GPa, and at 10 GPa transforms to the simple cubic structure (cP1), similar to arsenic. Despite of its low packing density, the simple cubic structure is stable in phosphorus over a very wide pressure range up to 103 GPa. On further pressure increase, the simple cubic structure transforms to a simple hexagonal structure (hP1) via a complex phase that was solved recently as incommensurately modulated. Structural transformations of phosphorus are connected with the changes of physical properties. Above 5 GPa phosphorus shows superconductivity with Tc reaching ~9.5K at 32GPa. The crystal structures and properties of high-pressure phases for phosphorus are discussed within the model of the Fermi sphere and Brillouin zone interactions.