ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present high-quality numerical calculations of the exciton center-of-mass dispersion for GaAs/AlGaAs quantum wells of widths in the range 2-20 nm. The k.p-coupling of the heavy- and light-hole bands is fully taken into account. An optimized center-of-mass transformation enhances numerical convergence. We derive an easy-to-use semi-analytical expression for the exciton groundstate mass from an ansatz for the exciton wavefunction at finite momentum. It is checked against the numerical results and found to give very good results. We also show multiband calculations of the exciton groundstate dispersion using a finite-differences scheme in real space, which can be applied to rather general heterostructures.
In this paper we prove an incidence bound for points and cubic curves over prime fields. The methods generalise those used by Mohammadi, Pham, and Warren (2021).
We have developed a theoretical model to analyze the anomalous cooling of radiative quantum dot (QD) excitons by THz radiation reported by Yusa et al [Proc. 24th ICPS, 1083 (1998)]. We have made three-dimensional (3D) modeling of the strain and the piezoelectric field and calculated the 3D density of states of strain induced quantum dots. On the basis of this analysis we have developed a spin dependent Monte Carlo model, which describes the carrier dynamics in QD's when the intraband relaxation is modulated by THz radiation. We show that THz radiation causes resonance transfer of holes from dark to radiative states in strain-induced QD's. The transition includes a spatial transfer of holes from the piezoelectric potential mimima to the deformation potential minimum. This phenomenon strongly enhances the QD ground state luminescence at the expense of the luminescence from higher states. Our model also reproduces the delayed flash of QD ground state luminescence, activated by THz radiation even $\sim1$ s after the carrier generation. Our simulations suggest a more general possibility to cool the radiative exciton subsystem in optoelectronic devices.
In Brukner and Zeilinger's interpretation of quantum mechanics, information is introduced as the most fundamental notion and the finiteness of information is considered as an essential feature of quantum systems. They also define a new measure of information which is inherently different from the Shannon information and try to show that the latter is not useful in defining the information content in a quantum object.   Here, we show that there are serious problems in their approach which make their efforts unsatisfactory. The finiteness of information does not explain how objective results appear in experiments and what an instantaneous change in the so-called information vector (or catalog of knowledge) really means during the measurement. On the other hand, Brukner and Zeilinger's definition of a new measure of information may lose its significance, when the spin measurement of an elementary system is treated realistically. Hence, the sum of the individual measures of information may not be a conserved value in real experiments.
We study the existence of minimal supersolutions of BSDEs under a family of mutually singular probability measures. We consider generators that are jointly lower semicontinuous, positive, and either convex in the control variable and monotone in the value variable, or that fulfill a specific normalization property.
We consider a class of jump processes in euclidean space which are associated to a certain non-local symmetric Dirichlet form. We prove a lower bound on the occupation times of sets, and that a support theorem holds for these processes.
A central open problem of quantum physics is to reconcile theory with experience. In this work I present a framework for studying distinct modes of experience in a superposed world. A modes of experience is characterized by how the world, experiences, and options relate to each other by the perceptions, decisions, and actions, as well as by probabilistic rules encoding probabilistic or deterministic correlations among first person experiences. In a toy model, the life expectancies of beings in different candidate modes of experience are compared. It is found that the quantum mode without macroscopic superposition outlives that with macroscopic superposition and that with real amplitudes. These highlight the prospect to explain a mode of experience by its evolutionary advantages.
This paper deals with the controllability of the second grade fluids, a class of non-Newtonian of differentiel type, on a two-dimensional torus. Using the method of Agrachev-Sarychev [1], [2] and of Sirikyan [26], we prove that the system of second grade fluids is approximately controllable by a finite-dimensional control force.
The influence of the mass difference between the charged and neutral pions on the low-energy characteristics of nucleon-nucleon interaction in the $^{1}S_{0}$ spin-singlet state is studied within the framework of the effective-range approximation. By making use of the experimental singlet neutron-proton scattering parameters and the experimental value of neutron-neutron virtual-state energy, the following values were obtained for the neutron-neutron scattering length and effective range: $a_{nn}=-16.59(117)$fm, $r_{nn}=2.83(11)$fm. The calculated neutron-neutron scattering length $a_{nn}$ is in good agreement with one of the two well known and differing experimental values of this quantity, and the calculated effective range $r_{nn}$ is also in good agreement with present-day experimental results.
We propose an intersection-theoretic method to reduce questions in genus zero logarithmic Gromov-Witten theory to questions in the Gromov-Witten theory of smooth pairs, in the presence of positivity. The method is applied to the enumerative geometry of rational curves with maximal contact orders along a simple normal crossings divisor and to recent questions about its relationship to local curve counting. Three results are established. We produce counterexamples to the local/logarithmic conjectures of van Garrel-Graber-Ruddat and Tseng-You. We prove that a weak form of the conjecture holds for product geometries. Finally, we explicitly determine the difference between local and logarithmic theories, in terms of relative invariants for which efficient algorithms are known. The polyhedral geometry of the tropical moduli of maps plays an essential and intricate role in the analysis.
The quadratic curvature lagrangians having metric field equations with second order trace are constructed relative to an orthonormal coframe. In $n>4$ dimensions, pure quadratic curvature lagrangian having second order trace constructed contains three free parameters in the most general case. The fourth order field equations of some of these models, in arbitrary dimensions, are cast in a particular form using the Schouten tensor. As a consequence, the field equations for the New massive gravity theory are related to those of the Topologically massive gravity. In particular, the conditions under which the latter is "square root" of the former are presented.
To clarify the ultrafast temporal interplay of the different photocurrent mechanisms occurring in single InAs-nanowire-based circuits, an on-chip photocurrent pump-probe spectroscopy based on coplanar striplines was utilized. The data are interpreted in terms of a photo-thermoelectric current and the transport of photogenerated holes to the electrodes as the dominating ultrafast photocurrent contributions. Moreover, it is shown that THz radiation is generated in the optically excited InAs-nanowires, which is interpreted in terms of a dominating photo-Dember effect. The results are relevant for nanowire-based optoelectronic and photovoltaic applications as well as for the design of nanowire-based THz sources.
We discuss the relation between the highest energy cosmic rays   (UHECR) and UHE neutrinos. The neutrinos produced in the sources of optically thin astrophysical sources have been linked to the UHECR emissivity of the Universe. The fluxes of cosmogenic neutrinos, generated in propagation by UHECR, also reflect the acceleration of these particles, the maximum acceleration energy, and the cosmological evolution of their sources.
We study the energy spectrum and the persistent current in an ideal one-dimensional mesoscopic ring coupled to an external fermionic reservoir. The contact between ring and reservoir is described by a tunneling operator, which causes an indirect coupling between different ring states via states in the reservoir. For strong coupling to the reservoir new quasistates with sharp eigenenergies develop inside the ring. The formation of long-living states at strong tunnel coupling to the reservoir is analogous to the Dicke effect in optics, that was recently investigated in context of resonant scattering and resonant tunneling in solid state systems. Our model reproduces the results obtained in previous work based on the scattering matrix approach and furthermore it describes a new stable energy spectrum in the limit of strong coupling.
The evolution of intermediate-mass and massive stars speeds up considerably after they finish their hydrogen core-burning. Due to this accelerated evolution, the probability to observe stars during this episode is small. In suitable stellar aggregates, in particular star clusters of appropriate ages, the fast evolutionary phase causes a depopulated area~--~referred to as the Hertzsprung gap~--~in color-magnitude diagrams and derivatives therefrom. The explanation of the speed-up usually resorts to the star's Kelvin-Helmholtz timescale and the Sch\"onberg-Chandrasekhar instability is called upon. This exposition challenges this viewpoint with counterexamples and argues that a suitably defined nuclear timescale is enough to explain the fast evolution. A thermal instability, even though it develops in stars evolving through the Hertzsprung gap, is not a necessary condition to trigger the phenomenon.
NLTE radiative transfer calculations of differentially expanding supernovae atmospheres are computationally intensive and are almost universally performed in time-independent snapshot mode. The validity of the steady-state approximation in the rate equations has recently been questioned. We calculate the effective recombination time of hydrogen in SN II using our general purpose model atmosphere code PHOENIX. While we find that the recombination time for the conditions of SNe II at early times is increased over the classical value for the case of a simple hydrogen model atom with energy levels corresponding to just the first 2 principle quantum numbers, the classical value of the recombination time is recovered in the case of a multi-level hydrogen atom. We also find that the recombination time at most optical depths is smaller in the case of a multi-level atom than for a simple two-level hydrogen atom. We find that time dependence in the rate equations is important in the early epochs of a supernova's lifetime. The changes due to the time dependent rate equation (at constant input luminosity) are manifested in physical parameters such as the level populations which directly affects the spectra. The H-alpha profile is affected by the time dependent rate equations at early times. At later times time dependence does not significantly modify the level populations and therefore the H-alpha profile is roughly independent of whether the steady-state or time-dependent approach is used.
We consider various problems related to the persistence probability of fractional Brownian motion (FBM), which is the probability that the FBM $X$ stays below a certain level until time $T$. Recently, Oshanin et al. study a physical model where persistence properties of FBM are shown to be related to scaling properties of a quantity $J_N$, called steady-state current. It turns out that for this analysis it is important to determine persistence probabilities of FBM with a moving boundary. We show that one can add a boundary of logarithmic order to a FBM without changing the polynomial rate of decay of the corresponding persistence probability which proves a result needed in Oshanin et al. Moreover, we complement their findings by considering the continuous-time version of $J_N$. Finally, we use the results for moving boundaries in order to improve estimates by Molchan concerning the persistence properties of other quantities of interest, such as the time when a FBM reaches its maximum on the time interval $(0,1)$ or the last zero in the interval $(0,1)$.
Photon-photon linear colliders can be realized by laser back-scattering technique on the next generation linear $e^+e^-$ colliders. Here the associated productions of an intermediate mass Higgs (IMH) or Z-boson with $t \bar t$ pair in $\gamma\gamma$ collisions are studied. Since IMH is very unlikely to decay into $t\bar t$ pair, $t\bar tH$ production is the only direct channel to probe the Higgs-top Yukawa coupling in case of an IMH. $t\bar tZ$ production can be a potential background to $t\bar tH$ if the Higgs mass is close to $m_Z$. As an alternative to its parent $e^+e^-$ collider, $\gamma\gamma \to t\bar tH(Z)$ productions are compared with the corresponding productions in the $e^+e^-$ collisions.
We consider the problem of enumerating the permutations containing exactly $k$ occurrences of a pattern of length 3. This enumeration has received a lot of interest recently, and there are a lot of known results. This paper presents an alternative approach to the problem, which yields a proof for a formula which so far only was conjectured (by Noonan and Zeilberger). This approach is based on bijections from permutations to certain lattice paths with ``jumps'', which were first considered by Krattenthaler.
We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum gravity and string theory.
This paper is devoted to study some expressions of the type $\prod_{p} p^{\lfloor\frac{x}{f(p)}\rfloor}$, where $x$ is a nonnegative real number, $f$ is an arithmetic function satisfying some conditions, and the product is over the primes $p$. We begin by proving that such expressions can be expressed by using the $\mathrm{lcm}$ function, without any reference to prime numbers; we illustrate this result with several examples. The rest of the paper is devoted to study the two particular cases related to $f(m) = m$ and $f(m) = m - 1$. In both cases, we found arithmetic properties and analytic estimates for the underlying expressions. We also put forward an important conjecture for the case $f(m) = m - 1$, which depends on the counting of the prime numbers of a special form.
The main goal of this research is to determine the angular size and the atmospheric structures of cool giant stars and to compare them with hydrostatic stellar model atmospheres, to estimate the fundamental parameters, and to obtain a better understanding of the circumstellar environment.   We conducted spectro-interferometric observations of epsilon Oct, beta Peg, NU Pav, and psi Peg in the near-infrared K band (2.13-2.47 microm), and gamma Hya (1.9-2.47 microm) with the VLTI/AMBER instrument at medium spectral resolution. To obtain the fundamental parameters, we compared our data with hydrostatic atmosphere models (PHOENIX).   We estimated the Rosseland angular diameters of epsilon Oct, beta Peg, NU Pav, psi Peg, and gamma Hya. Together with distances and bolometric fluxes, we estimated radii, effective temperatures, and luminosities of our targets. In the beta Peg visibility, we observed a molecular layer of CO with a size similar to that modeled with PHOENIX. However, there is an additional slope in absorption starting around 2.3 microm. This slope is possibly due to a shell of water that is not modeled with PHOENIX. The visibility of psi Peg shows a low increase in the CO bands, compatible with the modeling of the PHOENIX model. The visibility data of the other sources show no increase in molecular bands.   The spectra and visibilities predicted by the PHOENIX atmospheres agree with the spectra and the visibilities observed in our stars (except for beta Peg). This indicates that the opacity of the molecular bands is adequately included in the model, and the atmospheres of our targets have an extension similar to the modeled atmospheres. The atmosphere of beta Peg is more extended than that predicted by the model. The targets are located close to the red limits of the evolutionary tracks of the STAREVOL model.
We present a first-principles computational scheme for investigating the ballistic transport properties of one-dimensional nanostructures with non-collinear magnetic order. The electronic structure is obtained within density functional theory as implemented in the full-potential linearized augmented plane-wave (FLAPW) method and mapped to a tight-binding like transport Hamiltonian via non-collinear Wannier functions. The conductance is then computed based on the Landauer formula using the Green's function method. As a first application we study the conductance between two ferromagnetic Co monowires terminated by single Mn apex atoms as a function of Mn-Mn separation. We vary the Mn-Mn separation from the contact (about 2.5 to 5 {\AA}) to the far tunneling regime (5 to 10 {\AA}). The magnetization direction of the Co electrodes is chosen either in parallel or antiparallel alignment and we allow for different spin configurations of the two Mn spins. In the tunneling and into the contact regime the conductance is dominated by $s$-$d_{z^2}$-states. In the close contact regime (below 3.5 {\AA}) there is an additional contribution for a parallel magnetization alignment from the $d_{xz}$- and $d_{yz}$-states which give rise to an increase of the magnetoresistance as it is absent for antiparallel magnetization. If we allow the Mn spins to relax a non-collinear spin state is formed close to contact. We demonstrate that the transition from a collinear to such a non-collinear spin structure as the two Mn atoms approach leaves a characteristic fingerprint in the distance-dependent conductance and magnetoresistance of the junction. We explain the effect of the non-collinear spin state on the conductance based on the spin-dependent hybridization between the $d_{xz,yz}$-states of the Mn spins and their coupling to the Co electrodes.
The family of symmetric powers of an $L$-function associated with an elliptic curve with complex multiplication has received much attention from algebraic, automorphic and p-adic points of view. Here we examine one explicit such family from the perspectives of classical analytic number theory and random matrix theory, especially focusing on evidence for the symmetry type of the family. In particular, we investigate the values at the central point and give evidence that this family can be modeled by ensembles of orthogonal matrices. We prove an asymptotic formula with power savings for the average of these L-values, which reproduces, by a completely different method, an asymptotic formula proven by Greenberg and Villegas--Zagier. We give an upper bound for the second moment which is conjecturally too large by just one logarithm. We also give an explicit conjecture for the second moment of this family, with power savings. Finally, we compute the one level density for this family with a test function whose Fourier transform has limited support. It is known by the work of Villegas -- Zagier that the subset of these L-functions from our family which have even functional equations never vanish; we show to what extent this result is reflected by our analytic results.
In this paper, we report our multiwavelength observations of a partial filament eruption event in NOAA active region 11283 on 2011 September 8. A magnetic null point and the corresponding spine and separatrix surface are found in the active region. Beneath the null point, a sheared arcade supports the filament along the highly complex and fragmented polarity inversion line. After being activated, the sigmoidal filament erupted and split into two parts. The major part rose at the speeds of 90$-$150 km s$^{-1}$ before reaching the maximum apparent height of $\sim$115 Mm. Afterwards, it returned to the solar surface in a bumpy way at the speeds of 20$-$80 km s$^{-1}$. The rising and falling motions were clearly observed in the extreme-ultravoilet (EUV), UV, and H$\alpha$ wavelengths. The failed eruption of the main part was associated with an M6.7 flare with a single hard X-ray source. The runaway part of the filament, however, separated from and rotated around the major part for $\sim$1 turn at the eastern leg before escaping from the corona, probably along large-scale open magnetic field lines. The ejection of the runaway part resulted in a very faint coronal mass ejection (CME) that propagated at an apparent speed of 214 km s$^{-1}$ in the outer corona. The filament eruption also triggered transverse kink-mode oscillation of the adjacent coronal loops in the same AR. The amplitude and period of the oscillation were 1.6 Mm and 225 s. Our results are important for understanding the mechanisms of partial filament eruptions and provide new constraints to theoretical models. The multiwavelength observations also shed light on space weather prediction.
Impedance matrices are obtained for radially inhomogeneous structures using the Stroh-like system of six first order differential equations for the time harmonic displacement-traction 6-vector. Particular attention is paid to the newly identified solid-cylinder impedance matrix ${\mathbf Z} (r)$ appropriate to cylinders with material at $r=0$, and its limiting value at that point, the solid-cylinder impedance matrix ${\mathbf Z}_0$. We show that ${\mathbf Z}_0$ is a fundamental material property depending only on the elastic moduli and the azimuthal order $n$, that ${\mathbf Z} (r)$ is Hermitian and ${\mathbf Z}_0$ is negative semi-definite. Explicit solutions for ${\mathbf Z}_0$ are presented for monoclinic and higher material symmetry, and the special cases of $n=0$ and 1 are treated in detail. Two methods are proposed for finding ${\mathbf Z} (r)$, one based on the Frobenius series solution and the other using a differential Riccati equation with ${\mathbf Z}_0$ as initial value. %in a consistent manner as the solution of an algebraic Riccati equation. The radiation impedance matrix is defined and shown to be non-Hermitian. These impedance matrices enable concise and efficient formulations of dispersion equations for wave guides, and solutions of scattering and related wave problems in cylinders.
We show that a cooled region of shocked supernova ejecta forms in a type II supernova-QSO wind interaction, and has a density, an ionization parameter, and a column density compatible with those inferred for the high ionization component of the broad emission line regions in QSOs. The calculations are based on the assumption that the ejecta flow is described initially by a similarity solution investigated by Chevalier (1982) and Nadyozhin (1985) and is spherically symmetric. Heating and cooling appropriate for gas irradiated by a nearby powerful continuum source is included in our model, together with reasonable assumptions for the properties of the QSO wind. The model results are also in agreement with observational correlations and imply reasonable supernova rates.
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient quantum optimization algorithm for the graph coloring problem. Our circuits are deeper than the ones of the standard approach. However, the number of required qubits is exponentially reduced in the number of colors. We present extensive numerical simulations demonstrating the performance of our approach. Furthermore, to explore currently available alternatives, we perform a study of random graph coloring on a quantum annealer to test the limiting factors of that approach, too.