ShantanuT01/DACTYL-Pretraining huggingface dataset:
The bilayer systems exhibit the Bose-Einstein condensation of excitons that emerge due to Coulomb pairing of electrons belonging to one layer with the holes belonging to the other layer. Here we present the microscopic derivation of the dynamic equation for the condensate wave function at a low density of electron-hole ($e-h$) pairs in a strong magnetic field perpendicular to the layers and an electric field directed along the layers. From this equation we obtain the dispersion law for collective excitations of the condensate and calculate the electric charge of the vortex in the exciton condensate. The critical interlayer spacing, the excess of which leads to a collapse of the superfluid state, is estimated. In bilayer systems with curved conducting layers, the effective mass of the $e-h$ pair becomes the function of the $e-h$ pair coordinates, the regions arise, where the energy of the $e-h$ pair is lowered (exciton traps), and lastly $e-h$ pairs can gain the polarization in the basal plane. This polarization leads to the appearance of quantized vortices even at zero temperature.
Let f be a hypersurface surface local singularity whose zero set has 1-dimensional singular locus. We develop an explicit procedure that provides the boundary of the Milnor fibre of f as an oriented plumbed 3-manifold. The method provides the characteristic polynomial of the algebraic monodromy as well. Moreover, for any analytic germ g such that the pair (f,g) is an isolated complete intersection singularity, the (multiplicity system of the) open book decomposition of the boundary with binding determined by g and pages determined by the argument of g is also computed. In order to do this, we have to establish key results regarding the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g).   The theory is supported by many examples. E.g. the case of homogeneous singularities (including the case of arrangements) is detailed completely. A list of especially peculiar examples, and also a list of related open problems is given.
Ba2Ti2Fe2As4O is a self-doped superconductor exhibiting a Tc ~ 21.5 K and containing, distinctively with respect to other Fe-based superconductors, not only [Fe2As2] layers but also conducting [Ti2O] sheets. This compound exhibits a transition at T* ~ 125 K which has tentatively been assigned in the literature to a possible density-wave order. However, the nature of this density wave (whether it is a charge- or spin-induced) is still under debate. Magnetism in Ba2Ti2Fe2As4O has never been experimentally confirmed, which raises the question whether this superconductor might be non-magnetic or exhibiting a very weak magnetism. Here, we report evidence from inelastic neutron scattering (INS) measurements and ab initio calculations of phonon spectra pointing towards absence of magnetism in Ba2Ti2Fe2As4O. The INS measurements did not reveal any noticeable change of the phonon spectra across Tc, neither could magnetic effects be observed within the accessible (Q, E) space, setting Ba2Ti2Fe2As4O as an unconventional superconductor. The effect of magnetism on describing phonon spectra was further investigated by performing ab initio calculations. In this context, non-magnetic calculations reproduced well the measured phonon spectra. Therefore, our results indicate a non-magnetic and unconventional character of the superconductor Ba2Ti2Fe2As4O.
We present t$|$ket$\rangle$, a quantum software development platform produced by Cambridge Quantum Computing Ltd. The heart of t$|$ket$\rangle$ is a language-agnostic optimising compiler designed to generate code for a variety of NISQ devices, which has several features designed to minimise the influence of device error. The compiler has been extensively benchmarked and outperforms most competitors in terms of circuit optimisation and qubit routing.
The average Doppler shift shown by spectral lines formed from the chromosphere to the corona reveals important information on the mass and energy balance of the solar atmosphere, providing an important observational constraint to any models of the solar corona. Previous spectroscopic observations of vacuum ultra-violet (VUV) lines have revealed a persistent average wavelength shift of lines formed at temperatures up to 1 MK. At higher temperatures, the behaviour is still essentially unknown. Here we analyse combined SUMER/SoHO and EIS/Hinode observations of the quiet Sun around disk centre to determine, for the first time, the average Doppler shift of several spectral lines formed between 1 and 2 MK, where the largest part of the quiet coronal emission is formed. The measurements are based on a novel technique applied to EIS spectra to measure the difference in Doppler shift between lines formed at different temperatures. Simultaneous wavelength-calibrated SUMER spectra allow establishing the absolute value at the reference temperature of 1 MK. The average line shifts at 1 MK < T < 1.8 MK are modestly, but clearly bluer than those observed at 1 MK. By accepting an average blue shift of about (-1.8+/-0.6) km/s at 1 MK (as provided by SUMER measurements), this translates into a maximum Doppler shift of (-4.4+/-2.2) km/s around 1.8 MK. The measured value appears to decrease to about (-1.3+/-2.6) km/s at the Fe XV formation temperature of 2.1 MK. The measured average Doppler shift between 0.01 and 2.1 MK, for which we provide a parametrisation, appears to be qualitatively and roughly quantitatively consistent with what foreseen by 3-D coronal models where heating is produced by dissipation of currents induced by photospheric motions and by reconnection with emerging magnetic flux.
We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions and provide a full proof of existence and uniqueness through stochastic invariance of the canonical state space. Existence of exponential moments and the full range of validity of the affine transform formula are established. This is applied to the pricing of bond and stock options, which is illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models.
A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correlations is developed here by an extension of the hypernetted chain approximation, developed for bulk fluids, to the confined charges. The results reproduce all of the qualitative features observed in molecular dynamics simulations and experiments. These predictions are then tested quantitatively by comparison with new benchmark Monte Carlo simulations. Quantitative accuracy of the theory is obtained for the selected conditions by correcting the hypernetted chain approximation with a representation for the associated bridge functions.
Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and several ground state orders have been obtained. Dimer order and string orders are found to coexist in the ground state. Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain. This spin gap along with the string orders attribute to the Haldane phase. The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.
In this paper we prove global existence and uniqueness of solutions to the stochastic logarithmic Schr\"odinger equation with linear multiplicative noise. Our approach is mainly based on the rescaling approach and the method of maximal monotone operators. In addition, uniform estimates of solutions in the energy space $H^1(\mathbb{R}^d)$ and in an appropriate Orlicz space are also obtained here.
We observe a dependence of the damping of a confined mode of precessing ferromagnetic magnetization on the size of the mode. The micron-scale mode is created within an extended, unpatterned YIG film by means of the intense local dipolar field of a micromagnetic tip. We find that damping of the confined mode scales like the surface-to-volume ratio of the mode, indicating an interfacial damping effect (similar to spin pumping) due to the transfer of angular momentum from the confined mode to the spin sink of ferromagnetic material in the surrounding film. Though unexpected for insulating systems, the measured intralayer spin-mixing conductance $g_{\uparrow \downarrow} = 5.3 \times 10^{19} {\rm m}^{-2}$ demonstrates efficient intralayer angular momentum transfer.
We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind the application to the post-bounce phase of core-collapse supernovae (CCSNe). Such non-spherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch & Ott (2013) demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without the fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solved as an initial and boundary value problem with the use of Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15 $\mathrm{M_\odot}$ progenitor model by Woosley & Heger (2007), which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically showed that the growth rate is proportional to $l$, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.
In this paper we calculated the relativistic corrections to transition frequencies (q factors) of Fe I for the transitions from the even- and odd-parity states to the ground state. We also carried out isotope shift calculations in Fe I and Fe II. To the best of our knowledge, the isotope shift in Fe I was calculated for the first time.
Given a vector bundle $E$ on a tree of smooth rational curves $C$, we give necessary and sufficient conditions for a vector bundle $E'$ on $\mathbb{P}^1$ to specialize to $E$ on $C$, generalizing the rank 2 case, due to Coskun.
We verify the finite time fluctuation theorem for a linear Ising chain at its ends in contact with heat reservoirs. Analytic results are derived for a chain consisting of only two spins. The system can be mapped onto a model for particle transport, namely the symmetric exclusion process, in contact with thermal and particle reservoirs. We modify the symmetric exclusion process to represent a thermal engine and reproduce universal features of the efficiency at maximum power.
Long-lived coherences, emerging under periodic pulse driving in the disordered ensembles of strongly interacting spins, offer immense advantages for future quantum technologies, but the physical origin and the key properties of this phenomenon remain poorly understood. We theoretically investigate this effect in ensembles of different dimensionality, and predict existence of the long-lived coherences in two-dimensional and infinite-dimensional (where every spin is coupled to all others) systems, which are of particular importance for quantum sensing and quantum information processing. We explore the transition from two to infinite dimensions, and show that the long-time coherence dynamics in all dimensionalities is qualitatively similar, although the short-time behavior is drastically different, exhibiting dimensionality-dependent singularity. Our study establishes the common physical origin of the long-lived coherences in different dimensionalities, and suggests that this effect is a generic feature of the strongly coupled spin systems with positional disorder. Our results lay out foundation for utilizing the long-lived coherences in a range of application, from quantum sensing with two-dimensional spin ensembles, to quantum information processing with the infinitely-dimensional spin systems in the cavity-QED settings.
The possible conditions for hadron-quark phase transition in hybrid star cores are investigated in the present work. For the hadronic matter part the effective chiral model is adopted. Exotic baryonic degrees like hyperons and the delta baryons are also taken into account. As $\Delta$s posses Breit-Wigner mass distribution ($1232 \pm 120$ MeV), the hadronic equation of state is obtained by varying the mass of the delta baryons in this range. For the quark phase the MIT bag model is chosen with repulsive effects of the unpaired quarks. Phase transition is achieved using Gibbs construction and the gross properties of the resultant hybrid star are calculated in both static and rotating conditions and compared with the various constraints on them from different observational and empirical perspectives. The work presents a thorough study of the phase transition properties like the critical density of appearance of quarks, the density range for the persistence of the mixed phase and the population of different hadrons and quarks in hybrid star matter. The hybrid star properties, calculated in both static and rotating conditions, are found to be consistent with the bounds on them from different perspectives.
Let $f$ be a half-integral weight cusp form of level $4N$ for odd and squarefree $N$ and let $a(n)$ denote its $n^{\rm th}$ normalized Fourier coefficient. Assuming that all the coefficients $a(n)$ are real, we study the sign of $a(n)$ when $n$ runs through an arithmetic progression. As a consequence, we establish a lower bound for the number of integers $n\le x$ such that $a(n)>n^{-\alpha}$ where $x$ and $\alpha$ are positive and $f$ is not necessarily a Hecke eigenform.
Inspired by the inductive proof of LYM-inequality given by P. Frankl, we provide an inductive proof of the Bollob\'{a}s two family theorem.
We describe our procedure to determine effective temperatures, rotational velocities, microturbulent velocities, and chemical abundances in the atmospheres of Sun-like stars. We use independent determinations of iron abundances using the fits to the observed Fe I and Fe II atomic absorption lines. We choose the best solution from the fits to these spectral features for the model atmosphere that provides the best confidence in the determined log N(Fe), Vt, and vsini. First, we compute the abundance of iron for a set of adopted microturbulent velocities. To determine the most self-consistent effective temperature and microturbulent velocity in any star's atmosphere, we used an additional constraint where we minimise the dependence of the derived abundances of Fe I and Fe II on the excitation potential of the corresponding lines. We analyse the spectra of the Sun and two well known solar type stars, HD1835 and HD10700 to determine their abundances, microturbulent velocity and rotational velocity. For the Sun abundances of elements obtained from the fits of their absorption features agree well enough (+/- 0.1 dex) with the known values for the Sun. We determined a rotational velocity of vsini = 1.6 +/- 0.3 km/s for the spectrum of the Sun as a star. For HD1835 the self-consistent solution for Fe I and Fe II lines log N(Fe)=+0.2 was obtained with a model atmosphere of 5807/4.47/+0.2 andmicroturbulent velocity Vt = 0.75 km/s, and leads to vsini = 7.2 $\pm$ 0.5 km/s. For HD10700 the self-consistent solution log N(Fe) = -4.93 was obtained using a model atmosphere of 5383/4.59/-0.6and microturbulent velocity Vt = 0.5 km/s. The Fe I and Fe II lines give rise to a vsini = 2.4 +/- 0.4 km/s. Using the Teff found from the ionisation equilibrium parameters for all three stars, we found abundances of a number of other elements: Ti, Ni, Ca, Si, Cr. ... Abriged.
We consider the behavior of the Gaussian concentration bound (GCB) under stochastic time evolution. More precisely, we consider a Markovian diffusion process on $\mathbb{R}^d$ and start the process from an initial distribution $\mu$ that satisfies GCB. We then study the question whether GCB is preserved under the time-evolution, and if yes, how the constant behaves as a function of time. In particular, if for the constant we obtain a uniform bound, then we can also conclude properties of the stationary measure(s) of the diffusion process. This question, as well as the methodology developed in the paper allows to prove Gaussian concentration via semigroup interpolation method, for measures which are not available in explicit form.   We provide examples of conservation of GCB, loss of GCB in finite time, and loss of GCB at infinity. We also consider diffusions ``coming down from infinity'' for which we show that, from any starting measure, at positive times, GCB holds. Finally we consider a simple class of non-Markovian diffusion processes with drift of Ornstein-Uhlenbeck type, and general bounded predictable variance.
We have measured temperature and magnetic field dependences of the thermal conductivity along the c-axis, kc, and that along the [110] direction, k110, of CuB2O4 single crystals in zero field and magnetic fields along the c-axis and along the [110] direction. It has been found that the thermal conductivity is nearly isotropic and very large in zero field and that the thermal conductivity due to phonons is dominant in CuB2O4. The temperature and field dependences of kc and k110 have markedly changed at phase boundaries in the magnetic phase diagram, which has been understood to be due to the change of the mean free path of phonons caused by the change of the phonon-spin scattering rate at the phase boundaries. It has been concluded that thermal conductivity measurements are very effective for detecting magnetic phase boundaries.
The starting point of any general relativistic numerical simulation is a solution of the Hamiltonian and momentum constraints that (ideally) represents an astrophysically realistic scenario. We present a new method to produce initial data sets for binary neutron stars with arbitrary spins and orbital eccentricities. The method only provides approximate solutions to the constraints. However, we show that the corresponding constraint violations subside after a couple of orbits, becoming comparable to those found in evolutions of standard conformally flat, helically symmetric binary initial data. We evolve in time three data sets, corresponding to binaries with spins aligned, zero and anti-aligned with the orbital angular momentum. These simulations show the orbital "hang-up" effect previously seen in binary black holes. Additionally, all three show orbital eccentricities up to one order of magnitude smaller than those found in helically symmetric initial sets evolutions.
In order to provide an accurate theoretical description of current density voltage (J-V) characteristics of an organic heterojunction device over a wide range of electric fields at various temperatures, it is proposed that an accumulation of charge carriers at the heterojunction will lead to a reduction in the barrier height across the heterojunction. Two well-known hole transporting materials, 4,4,4-Tris(N-3-methylphenyl-N-phenyl-amino) triphenylamine (MTDATA) and N,N-diphenyl-N,N-bis(1-naphthyl)(1,1-biphenyl)-4,4diamine (NPB) were used to fabricate unipolar heterojunction devices. It is found that the J-V characteristics depends strongly on applied bias. The simulated J-V characteristics of the heterojunction device, with the modified injection model, are found to be in excellent agreement with the experimental data.
We investigate the limitations arising from atomic collisions on the storage and delay times of probe pulses in EIT experiments. We find that the atomic collisions can be described by an effective decay rate that limits storage and delay times. We calculate the momentum and temperature dependence of the decay rate and find that it is necessary to excite atoms at a particular momentum depending on temperature and spacing of the energy levels involved in order to minimize the decoherence effects of atomic collisions.
Recently proposed Capsule Network is a brain inspired architecture that brings a new paradigm to deep learning by modelling input domain variations through vector based representations. Despite being a seminal contribution, CapsNet does not explicitly model structured relationships between the detected entities and among the capsule features for related inputs. Motivated by the working of cortical network in human visual system, we seek to resolve CapsNet limitations by proposing several intuitive modifications to the CapsNet architecture. We introduce, (1) a novel routing weight initialization technique, (2) an improved CapsNet design that exploits semantic relationships between the primary capsule activations using a densely connected Conditional Random Field and (3) a Cholesky transformation based correlation module to learn a general priority scheme. Our proposed design allows CapsNet to scale better to more complex problems, such as the multi-label classification task, where semantically related categories co-exist with various interdependencies. We present theoretical bases for our extensions and demonstrate significant improvements on ADE20K scene dataset.
The measurement of time durations or instants of ocurrence of events has been frequently modelled ``operationally'' by coupling the system of interest to a ``clock''. According to several of these models the operational approach is limited at low energies because the perturbation of the clock does not allow to reproduce accurately the corresponding ideal time quantity, defined for the system in isolation. We show that, for a time-of-flight measurement model that can be set to measure dwell or arrival times, these limitations may be overcome by extending the range of energies where the clock works properly using pulsed couplings rather than continuous ones.