ShantanuT01/DACTYL-Pretraining huggingface dataset:
The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum uncertainty relations construed with relative entropy of coherence, $l_1$ norm of coherence and coherence of formation. In stead of quantum state tomographic technology, we employ the classical shadow algorithm for the detection of lower bounds in quantum uncertainty relations. With an all optical setup, we prepare a family of quantum states whose purity can be fully controlled. We experimentally explore the tightness of various lower bounds in different reference bases on the prepared states. Our results indicate the tightness of quantum coherence lower bounds dependents on the reference bases as well as the purity of quantum state.
The interaction of a kink and a monochromatic plane wave in one dimensional scalar field theories is studied. It is shown that in a large class of models the radiation pressure exerted on the kink is negative, i.e. the kink is {\sl pulled} towards the source of the radiation. This effect has been observed by numerical simulations in the $\phi^4$ model, and it is explained by a perturbative calculation assuming that the amplitude of the incoming wave is small. Quite importantly the effect is shown to be robust against small perturbations of the $\phi^4$ model. In the sine-Gordon (sG) model the time averaged radiation pressure acting on the kink turns out to be zero. The results of the perturbative computations in the sG model are shown to be in full agreement with an analytical solution corresponding to the superposition of a sG kink with a cnoidal wave. It is also demonstrated that the acceleration of the kink satisfies Newton's law.
Using a high quality factor 3 GHz bulk acoustic wave resonator device, we demonstrate the acoustically driven single quantum spin transition ($\left|m_{s}=0\right>\leftrightarrow\left|\pm1\right>$) for diamond NV centers and characterize the corresponding stress susceptibility. A key challenge is to disentangle the unintentional magnetic driving field generated by device current from the intentional stress driving within the device. We quantify these driving fields independently using Rabi spectroscopy before studying the more complicated case in which both are resonant with the single quantum spin transition. By building an equivalent circuit model to describe the device's current and mechanical dynamics, we quantitatively model the experiment to establish their relative contributions and compare with our results. We find that the stress susceptibility of the NV center spin single quantum transition is around $\sqrt{2}(0.5\pm0.2)$ times that for double quantum transition ($\left|+1\right>\leftrightarrow\left|-1\right>$). Although acoustic driving in the double quantum basis is valuable for quantum-enhanced sensing applications, double quantum driving lacks the ability to manipulate NV center spins out of the $\left|m_{s}=0\right>$ initialization state. Our results demonstrate that efficient all-acoustic quantum control over NV centers is possible, and is especially promising for sensing applications that benefit from the compact footprint and location selectivity of acoustic devices.
We study the time dependence of the decoherence factor (DF) of a qubit globally coupled to an environmental spin system (ESS) which is driven across the quantum critical point (QCP) by varying a parameter of its Hamiltonian in time $t$ as $1 -t/\tau$ or $-t/\tau$, to which the qubit is coupled starting at the time $t \to -\infty$; here, $\tau$ denotes the inverse quenching rate. In the limit of weak coupling, we analyze the time evolution of the DF in the vicinity of the QCP (chosen to be at $t=0$) and define three quantities, namely, the generalized fidelity susceptibility $\chi_F(\tau)$ (defined right at the QCP), and the decay constants $\alpha_1 (\tau)$ and $\alpha_2 (\tau)$ which dictate the decay of the DF at a small but finite $t$($>0$). Using a dimensional analysis argument based on the Kibble-Zurek healing length, we show that $\chi_F(\tau)$ as well as $\alpha_1 (\tau)$ and $\alpha_2(\tau)$ indeed satisfy universal power-law scaling relations with $\tau$ and the exponents are solely determined by the spatial dimensionality of the ESS and the exponents associated with its QCP. Remarkably, using the numerical t-DMRG method, these scaling relations are shown to be valid in both the situations when the ESS is integrable and non-integrable and also for both linear and non-linear variation of the parameter. Furthermore, when an integrable ESS is quenched far away from the QCP, there is a predominant Gaussian decay of the DF with a decay constant which also satisfies a universal scaling relation.
We present the results of a reverberation mapping (RM) campaign on the black hole (BH) associated with the active galactic nucleus (AGN) in SDSS J114008.71+030711.4 (hereafter GH08). This object is selected from a sample of 19 candidate intermediate mass BHs (M_{BH} < 10^{6} Msun) found by Greene & Ho 2004 in the Sloan Digital Sky Survey (SDSS). We used the Hobby-Eberly Telescope to obtain 30 spectra over a period of 178 days in an attempt to resolve the reverberation time lag (tau) between the continuum source and the broad line region (BLR) in order to determine the radius of the BLR (R_{BLR}) in GH08. We measure tau to be 2 days with an upper limit of 6 days. We estimate the AGN luminosity at 5100 Angstroms to be approximately 1.1 x 10^{43} erg s^{-1} after deconvolution from the host galaxy. The most well calibrated R_{BLR}-L relation predicts a time lag which is 4 times larger than what we measure. Using the measured H\beta\ full-width-at-half-maximum of 703 (+/-) 110 km s^{-1} and an upper limit for R_{BLR} = 6 light days, we find M_{BH} < 5.8 x 10^{5} Msun as an upper limit to the BH virial mass in GH08, which implies super-Eddington accretion. Based on our measured M_{BH} we propose that GH08 may be another candidate to add to the very short list of AGNs with M_{BH} < 10^{6} Msun determined using RM.
We first develop a descriptor-based representation of atomic environments by devising two local similarity indices defined from an atom-partitioned quantum-chemical descriptor. Then, we employ this representation to explore the size-, shape- and composition-dependent nanocrystal energetics. For this purpose, we utilize an energy difference {\mu} that is related to the atomic chemical potential, which enables one to characterize energetic heterogeneities. Employing first-principles calculations based on the density functional theory for a set of database systems, namely unary atomic clusters in the shape of regular polyhedra and the bulk solids of C, Si, Pd and Pt, we explore the correlations between the energy difference {\mu} and similarity indices. We find that there exists an interconnection between nanocrystal energetics and quantum similarity measures. Accordingly, we develop a means for computing total energy differences from the similarity indices via interpolation, and utilize a test set comprising a variety of unary nanocrystals and binary nanoalloys/nanocompounds for validation. Our findings indicate that the similarity-based energies could be utilized in computer-aided design of nanoparticles.
Let $A=[a_{n,k}]_{n,k\ge 0}$ be an infinite lower triangular matrix defined by the recurrence $$a_{0,0}=1,\quad a_{n+1,k}=r_{k}a_{n,k-1}+s_{k}a_{n,k}+t_{k+1}a_{n,k+1},$$ where $a_{n,k}=0$ unless $n\ge k\ge 0$ and $r_k,s_k,t_k$ are all nonnegative. Many well-known combinatorial triangles are such matrices, including the Pascal triangle, the Stirling triangle (of the second kind), the Bell triangle, the Catalan triangles of Aigner and Shapiro. We present some sufficient conditions such that the recursive matrix $A$ is totally positive. As applications we give the total positivity of the above mentioned combinatorial triangles in a unified approach.
This work deals with a fully parabolic chemotaxis model with nonlinear production and chemoattractant. The problem is formulated on a bounded domain and, depending on a specific interplay between the coefficients associated to such production and chemoattractant, we establish that the related initial-boundary value problem has a unique classical solution which is uniformly bounded in time. To be precise, we study this zero-flux problem \begin{equation}\label{problem_abstract} \tag{$\Diamond$} \begin{cases} u_t= \Delta u - \nabla \cdot (f(u) \nabla v) & \text{ in } \Omega \times (0,T_{max}),\\ v_t=\Delta v-v+g(u) & \text{ in } \Omega \times (0,T_{max}),\\ \end{cases} \end{equation} where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^n$, for $n\geq 2$, and $f(u)$ and $g(u)$ are reasonably regular functions generalizing, respectively, the prototypes $f(u)=u^\alpha$ and $g(u)=u^l$, with proper $\alpha, l>0$. After having shown that any sufficiently smooth $ u(x,0)=u_0(x)\geq 0, \, v(x,0)=v_0(x)\geq 0$ emanate a unique classical and nonnegative solution $(u,v)$ to problem \eqref{problem_abstract}, which is defined on $\Omega \times (0,T_{max})$ with $T_{max}$ denoting the maximum time of existence, we establish that for any $l\in (0,\frac{2}{n})$ and $\frac{2}{n}\leq \alpha<1+\frac{1}{n}-\frac{l}{2}$, $T_{max}=\infty$ and $u$ and $v$ are actually uniformly bounded in time.   This paper is in line with the contribution by Horstmann and Winkler, moreover, extends the result by Liu and Tao. Indeed, in the first work it is proved that for $g(u)=u$ the value $\alpha=\frac{2}{n}$ represents the critical blow-up exponent to the model, whereas in the second, for $f(u)=u$, corresponding to $\alpha=1$, boundedness of solutions is shown under the assumption $0<l<\frac{2}{n}.$
We report the results of our high resolution optical spectroscopic monitoring campaign ($\lambda$ = 3800 -- 8800 A, R = 30000 -- 45000) of the new FU Orionis-type object HBC 722. We observed HBC 722 with the BOES 1.8-m telescope between 2010 November 26 and 2010 December 29 and FU Orionis itself on 2011 January 26. We detect a number of previously unreported high-resolution K I and Ca II lines beyond 7500 A. We resolve the H$\alpha$ and Ca II line profiles into three velocity components, which we attribute to both disk and outflow. The increased accretion during outburst can heat the disk to produce the relatively narrow absorption feature and launch outflows appearing as high velocity blue and redshifted broad features.
Temperature dependent studies of the 1/2(hk0) superlattice reflections \alpha spots by synchrotron x-ray scattering measurements were performed in (PMN) and (PMN-xPT) with Ti doping x<0.32 single crystals. Separation of the \alpha spots from the underlying diffuse scattering background allowed studying them as separate entities for the first time. Structure factor calculations have shown that alpha spots constitute the presence of a new kind of anti-ferrodistortive nanoregions (AFR) in the form of fluctuations produced by anti-parallel short-range correlated <110> Pb^2+ displacements. AFR appear to be different and unrelated to the chemical nanodomains (CND) and ferroelectric polar nanoregions (PNR). Simultaneous presence of AFR and PNR can explain relaxor behavior as a result of competition between randomly occurring ferroelectric and anti-ferroelectric fluctuations. Temperature dependence of the \alpha spots in PMN showed a direct correlation with the freezing phase transition near Tf~220 K.
Double ramification loci, also known as strata of $0$-differentials, are algebraic subvarieties of the moduli space of smooth curves parametrizing Riemann surfaces such that there exists a rational function with prescribed ramification over $0$ and $\infty$. We describe the closure of double ramification loci inside the Deligne-Mumford compactification in geometric terms.   To a rational function we associate its exact differential, which allows us to realize double ramification loci as linear subvarieties of strata of meromorphic differentials. We then obtain a geometric description of the closure using our recent results on the boundary of linear subvarieties. Our approach yields a new way of relating the geometry of loci of rational functions and Teichm\"uller dynamics. We also compare our results to a different approach using admissible covers.
We present a central extension of the $(m,n)$ super-Poincar\'e algebra in two dimensions. Besides the usual Poincar\'e generators and the $(m,n)$ supersymmetry generators we have $(m,n)$ Grassmann generators, a bosonic internal symmetry generator and a central charge. We then build up the topological gauge theory associated to this algebra. We can solve the classical field equations for the fields which do not belong to the supergravity multiplet and to a Lagrange multiplier multiplet. The resulting topological supergravity theory turns out to be non-local in the fermionic sector.
This article presents an analysis of the extent to which local causal models or local realistic models of quantum theory (QT), including quantum field theory (QFT), are theoretically possible and practically feasible in light of the present state of these theories. Quantum physicists consider Bells famous inequality and its violation in experiments to be a strong indication that local realistic or local causal models of QT are not possible and that quantum theory as a whole is therefore not a local realistic or local causal theory. Based on a proposed definition of a "formal causal model" for a theory of physics (such as QT), this paper investigates the possibility of having a local causal model for QT. Areas of QT are identified in which the construction of a causal model is impeded because of deficiencies in the state of the respective theory. It is shown that the removal of the deficiencies can be achieved by the provision of a causal model. Whereas the construction of a causal model of QT, including QFT, appears to be feasible after the removal of certain deficiencies, the construction of a local (causal) model does not appear to be possible. As a consequence of the conclusion that local (causal) models of QT/QFT are not possible, if a strong interpretation of locality is assumed, a locality model is proposed in which the non-localities are confined to "quantum objects".
Nanoelectromechanical systems (NEMS), utilising localised mechanical vibrations, were pioneered for sensors, signal processors and to study macroscopic quantum mechanics. Increasingly the concept of integrating multiple mechanical elements via electrical/optical means has emerged as a challenge towards NEMS circuits. Here we develop phononic crystal waveguides (PnC WGs), using a 1-dimensional array of suspended membranes, that offer purely mechanical means to integrate isolated NEMS resonators. In the first steps to this objective, we demonstrate the PnC WG can support and guide mechanical vibrations where the periodic membrane arrangement also creates a phonon bandgap that enables the phonon propagation velocity to be controlled. Additionally embedding a phonon-cavity into the PnC allows mechanical vibrations in the WG to be dynamically switched or transferred to the cavity, illustrating the availability of WG-resonator coupling. These highly functional traits of the PnC WG architecture exhibit all the ingredients necessary to permit the realisation of all-phononic NEMS circuits.
We present the identification of the companion star to the intermediate mass binary pulsar J1439-5501 obtained by means of ground-based deep images in the B, V and I bands, acquired with FORS2 mounted at the ESO-VLT. The companion is a massive white dwarf (WD) with B=23.57+-0.02, V=23.21+-0.01 and I=22.96+-0.01, located at only ~0.05" from the pulsar radio position. Comparing the WD location in the (B, B-V) and (V, V-I) Color-Magnitude diagrams with theoretical cooling sequences we derived a range of plausible combinations of companion masses (1<~Mcom<~1.3 Msun), distances (d<~1200 pc), radii (<~7.8 10^3 Rsun) and temperatures (T=31350^{+21500}_{-7400}). From the PSR mass function and the estimated mass range we also constrained the inclination angle i >~ 55 degrees and the pulsar mass (Mpsr <~2.2 Msun). The comparison between the WD cooling age and the spin down age suggests that the latter is overestimated by a factor of about ten.
We address the steady-state behavior of a system consisting of several correlated monoatomic layers sandwiched between two metallic leads under the influence of a bias voltage. In particular, we investigate the effect of the local Hubbard and of the long-range Coulomb interactions on the charge redistribution at the interface. We provide a detailed study of the importance of the various system parameters, like Hubbard $U$, lead-correlated region coupling strength, and the applied voltage on the charge distribution in the correlated region and in the adjacent parts of the leads. Our results are obtained within non-equilibrium (steady-state) real-space dynamical mean-field theory (R-DMFT), with a self-consistent treatment of the long-range part of the Coulomb interaction by means of the Poisson equation. The latter is solved by the Newton-Raphson method and we find that this significantly reduces the computational cost compared to existing treatment. As impurity solver for R-DMFT we use the auxiliary master equation approach (AMEA), which addresses the impurity problem within a finite auxiliary system coupled to Markovian environments.
Nonreciprocal systems breaking time-reversal symmetry are essential tools in modern quantum technologies enabling the suppression of unwanted reflected signals or extraneous noise entering through detection ports. Here we propose a scheme enabling nonreciprocal conversion between optical and radio-frequency (rf) photons using exclusively optomechanical and electromechanical interactions. The nonreciprocal transmission is obtained by interference of two dissipative pathways of transmission between the two electromagnetic modes established through two distinct intermediate mechanical modes. In our protocol, we apply a bichromatic drive to the cavity mode and a single-tone drive to the rf resonator, and use the relative phase between the drive tones to obtain nonreciprocity. We show that perfect nonreciprocal transduction can be obtained in the limit of large cooperativity in both directions, from optical to rf and vice versa. We also study the transducer noise and show that mechanical thermal noise is always reflected back onto the isolated port. In the limit of large cooperativity, the input noise is instead transmitted in an unaltered way in the allowed direction; in particular one has only vacuum noise in the output rf port in the case of optical-to-rf conversion.
In this study we investigated by means of density functional theory calculations the adsorption geometry and bonding mechanism of a single thymine (C$_5$H$_6$N$_2$O$_2$) molecule on Cu(110) surface. In the most stable energetic configuration, the molecular plane is oriented perpendicular to substrate along the $[1\bar{1}0]$ direction. For this adsorption geometry, the thymine molecule interacts with the surface via a deprotonated nitrogen atom and two oxygen ones such that the bonding mechanism involves a strong hybridization between the highest occupied molecular orbitals (HOMOs) and the d-states of the substrate. In the case of a parallel adsorption geometry, the long-range van der Waals interactions play an important role on both the molecule-surface geometry and adsorption energy. Their specific role was analyzed by means of a semi-empirical and the seamless methods. In particular, for a planar configuration, the inclusion of the dispersion effects dramatically changes the character of the adsorption process from physisorption to chemisorption. Finally, we predict the real-space topography of the molecule-surface interface by simulating scanning tunneling microscopy (STM) images. From these simulations we anticipate that only certain adsorption geometries can be imaged in STM experiments.
We consider the energy of a randomly charged polymer. We assume that only charges on the same site interact pairwise. We study the lower tails of the energy, when averaged over both randomness, in dimension three or more. As a corollary, we obtain the correct temperature-scale for the Gibbs measure.
We present an eight-band k.p model for the calculation of the electronic structure of wurtzite semiconductor quantum dots (QDs) and its application to indium gallium nitride (InGaN) QDs formed by composition fluctuations in InGaN layers. The eight-band k.p model accounts for strain effects, piezoelectric and pyroelectricity, spin-orbit and crystal field splitting. Exciton binding energies are calculated using the self-consistent Hartree method. Using this model, we studied the electronic properties of InGaN QDs and their dependence on structural properties, i.e., their chemical composition, height, and lateral diameter. We found a dominant influence of the built-in piezoelectric and pyroelectric fields, causing a spatial separation of the bound electron and hole states and a redshift of the exciton transition energies. The single-particle energies as well as the exciton energies depend heavily on the composition and geometry of the QDs.
The purpose of this article is to explain the Pila-Zannier strategy for proving the Andr\'e-Oort conjecture. First, however, we will provide a brief introduction to the theory of Shimura varieties.
The centre of our Galaxy hosts almost two hundreds of very young stars, a subset of which is orbiting the central supermassive black hole (SMBH) in a relatively thin disc-like structure. First analyses indicated a power-law surface density profile of the disc, $\Sigma \propto R^\beta$ with $\beta = -2$. Recently, however, speculations about this profile arose. In particular, it now seems to be better described by a sort of broken power-law. By means of both analytical arguments and numerical N-body modelling, we show that such a broken power-law profile is a natural consequence of the two-body relaxation of the disc which is, due to small relative velocities of stars on nearby co-planar Keplerian orbits around the SMBH, effective enough to affect the evolution of the disc on time-scales comparable to its estimated age. In the inner, densest part of the disc, the profile becomes rather flat ($\beta ~ -1$) while the outer parts keep imprints of the initial state. Our numerical models show that the observed projected surface density profile of the young stellar disc can result from two-body relaxation driven evolution of a disc with initial single power-law profile with $-2 < \beta < -1.5$. In addition, we suggest that two-body relaxation may have caused a significant radial migration of the S-stars towards the central SMBH, thus playing an important role in their formation scenario.
A Keller map is a counterexample to the Jacobian Conjecture. In dimension two every such map, if exists, leads to a complicated set of conditions on the map between the Picard groups of suitable compactifications of the affine plane. This is essentially a combinatorial problem. Some solutions to it, that we call frameworks, are described and discussed. This second version of the paper includes several more frameworks than the first version, including one substantially more complicated framework.