ShantanuT01/DACTYL-Pretraining huggingface dataset:
Grover search algorithm drives a quantum system from an initial state to a desired final state by using selective phase inversions of these two states. In (1), we studied a generalization of Grover algorithm which relaxes the assumption of the efficient implementation of the selective phase inversion of the initial state, also known as diffusion operator. This assumption is known to become a serious handicap in cases of physical interest (2,3,4,5). Our general search algorithm works with almost arbitrary diffusion operator with only restriction of having the initial state as one of its eigenstates. The price that we pay for using arbitrary operator is an increase in the number of oracle queries by a factor of order of B, where B is a characteristic of the eigenspectrum of diffusion operator and it can be large in some situations. Here we show that by using quantum fourier transform, we can regain the optimal query complexity of Grover algorithm without losing the freedom of using arbitrary diffusion operators for quantum searching. However, the total number of operators required by algorithm is still order of B times more than that of Grover algorithm. So our algorithm offers advantage only if oracle operator is computationally more expensive than diffusion operator, which is true in most search problems.
We have studied the Jarzynski equality (JE) in van der Pol and Rayleigh oscillators which are typical deterministic non-Hamiltonian models, but not expected to rigorously satisfy the JE because they are not microscopically reversible. Our simulations that calculate the contribution to the work $W$ of an applied ramp force with a duration $\tau$ show that the JE approximately holds for a fairly wide range of $\tau$ including $\tau \rightarrow 0 $ and $\tau \rightarrow \infty$, except for $\tau \sim T$ where $T$ denotes the period of relaxation oscillations in the limit cycle. The work distribution function (WDF) is shown to be non-Gaussian with the $U$-shaped structure for a strong damping parameter. The $\tau$ dependence of $R$ $(=- k_B T \ln<e^{-\beta W}>)$ obtained by our simulations is semi-quantitatively elucidated with the use of a simple expression for limit-cycle oscillations, where the bracket $<\cdot>$ expresses an average over the WDF. The result obtained in self-excited oscillators is in contrast with the fact that the JE holds in the Nos\'{e}-Hoover oscillator which also belongs to deterministic non-Hamiltonian models.
LaVO$_3$ (LVO) has been proposed as a promising material for photovoltaics because its strongly correlated \textit{d} electrons can facilitate the creation of multiple electron-hole pairs per incoming photon, which would lead to increased device efficiency. In this study, we intentionally grow off-stoichiometric LVO films by changing the growth conditions such as laser fluence. Our aim is to study how deviating La:V stoichiometries affect the electronic properties of LVO thin films. We find that the off-stoichiometry clearly alters the physical properties of the films. Structural characterization shows that both La-rich and V-rich films have different levels of structural distortion, with La-rich (V-rich) films showing a larger (smaller) out-of-plane lattice parameter compared to what one would expect from epitaxial strain effects alone. Both types of films show deviation from the behavior of bulk LVO in optical measurement, i.e., they do not show signatures of the expected long range orbital order, which can be a result of the structural distortions or the presence of structural domains. In transport measurements, La-rich films display clear signatures of electronic phase separation accompanying a temperature induced metal-insulator transition, while V-rich films behave as Mott insulators. The out-of-plane lattice parameter plays a crucial role in determining the transport properties, as the crossover from Mott-insulating to disorder-induced phase-separated behavior occurs around a lattice parameter value of 3.96 $\overset{\circ}{\mathrm{A}}$, quite different from what has been previously reported.
This note is a supplement to our previous papers: Mod. Phys. Lett. A14 (1999) 2427 (math-ph/9911010); Int. J. Mod. Phys. A15 (2000) 2329 (math-ph/9912014). The thermodynamic Bethe ansatz (TBA) equation for an integrable spin chain related to the Lie superalgebra osp(1|2) is analyzed. The central charge determined by low temperature asymptotics of the specific heat can be expressed by the Rogers dilogarithmic function, and identified to be 1. Solving the TBA equation numerically, we evaluate the several thermodynamic quantities. The excited state TBA equation is also discussed.
Understanding spin excitations and their connection to unconventional superconductivity have remained a central issue since the discovery of the cuprates. Direct measurement of the dynamical spin structure factor in the parent compounds can provide key information on important interactions relevant in the doped regime, and variations in the magnon dispersion have been linked closely to differences in crystal structure between families of cuprate compounds. Here, we elucidate the relationship between spin excitations and various controlling factors thought to be significant in high-$T_c$ materials by systematically evaluating the dynamical spin structure factor for the three-orbital Hubbard model, revealing differences in the spin dispersion along the Brillouin zone axis and the diagonal. Generally, we find that the absolute energy scale and momentum dependence of the excitations primarily are sensitive to the effective charge-transfer energy, while changes in the on-site Coulomb interactions have little effect on the details of the dispersion. In particular, our result highlights the splitting between spin excitations along the axial and diagonal directions in the Brillouin zone. This splitting decreases with increasing charge-transfer energy and correlates with changes in the apical oxygen position, and general structural variations, for different cuprate families.
We propose, using the example of the O(4) sigma model, a general method for solving integrable two dimensional relativistic sigma models in a finite size periodic box. Our starting point is the so-called Y-system, which is equivalent to the thermodynamic Bethe ansatz equations of Yang and Yang. It is derived from the Zamolodchikov scattering theory in the cross channel, for virtual particles along the non-compact direction of the space-time cylinder. The method is based on the integrable Hirota dynamics that follows from the Y-system. The outcome is a nonlinear integral equation for a single complex function, valid for an arbitrary quantum state and accompanied by the finite size analogue of Bethe equations. It is close in spirit to the Destri-deVega (DdV) equation. We present the numerical data for the energy of various states as a function of the size, and derive the general Luscher-type formulas for the finite size corrections. We also re-derive by our method the DdV equation for the SU(2) chiral Gross-Neveu model.
We present calculations for the temperature-dependent electronic structure and magnetic properties of thin ferromagnetic EuO films. The treatment is based on a combination of a multiband-Kondo lattice model with first-principles TB-LMTO band structure calculations. The method avoids the problem of double-counting of relevant interactions and takes into account the correct symmetry of the atomic orbitals. We discuss the temperature-dependent electronic structures of EuO(100) films in terms of quasiparticle densities of states and quasiparticle band structures. The Curie temperature T_C of the EuO films turns out to be strongly thickness-dependent, starting from a very low value = 15K for the monolayer and reaching the bulk value at about 25 layers.
Most of our knowledge of the radio morphology and kinematics of X-ray binary partially synchrotron self-absorbed compact jets (hereafter compact jets) is based on the observations of GRS~1915+105 which has the most prominent compact jet. Yet, the compact jet bulk velocity, $v$, is poorly constrained in the literature, $0.07 < v/c < 0.98$. In spite of this uncertainty, compact jets are often unified with relativistic jets in active galactic nuclei. We have estimated $v$ as part of a temporal analysis of GRS~1915+105 jets in "high plateau states" (HPS). We define the HPS as a state showing a hard X-ray spectrum and low level of long-term ($>10$s) X-ray activity associated with 15 GHz flux density $>70$ mJy for $>7$ consecutive days. The radio emission is associated with compact jet emission. Two HPS were monitored at 15 GHz during their termination with e-folding times of 3.8 hrs and 8.6 hrs. We combine this time scale with the scale of spatial variation of the linear source of a VLBA image preceding the fade of one of these HPS in order to estimate the jet speed. Our assumption that the reduction in radio emissivity propagates as an approximate discontinuity down the HPS jet (leaving a weak jet in its wake) indicates $0.17 <v/c< 0.43$. This agrees closely with the only other existing $v$ estimates that are derived directly from radio images, jet asymmetry produced by Doppler enhancement.
Let X be a Fano manifold such that every rational curve in X has anticanonical degree at least the dimension of X. We prove that X is a projective space or a quadric.
The squeezing spectrum of the fluorescence field emitted from a four-level atom in $J=1/2$ to $J=1/2$ configuration driven by two coherent fields is studied. We find that the squeezing properties of the fluorescence radiation are significantly influenced by the presence of vacuum-induced coherence in the atomic system. It is shown that such coherence induces spectral squeezing in phase quadratures of the fluorescence light for both weak and strong driving fields. The dependence of the squeezing spectrum on the relative phase of the driving fields is also investigated. Effects such as enhancement or suppression of the squeezing peaks are shown in the spectrum as the relative phase is varied. An analytical explanation of the numerical findings is presented using dressed-states of the atom-field system.
The Kennicutt-Schmidt (KS) relationship between the surface density of the star formation rate (SFR) and the gas surface density has three distinct power laws that may result from one model in which gas collapses at a fixed fraction of the dynamical rate. The power law slope is 1 when the observed gas has a characteristic density for detection, 1.5 for total gas when the thickness is about constant as in the main disks of galaxies, and 2 for total gas when the thickness is regulated by self-gravity and the velocity dispersion is about constant, as in the outer parts of spirals, dwarf irregulars, and giant molecular clouds. The observed scaling of the star formation efficiency (SFR per unit CO) with the dense gas fraction (HCN/CO) is derived from the KS relationship when one tracer (HCN) is on the linear part and the other (CO) is on the 1.5 part. Observations of a threshold density or column density with a constant SFR per unit gas mass above the threshold are proposed to be selection effects, as are observations of star formation in only the dense parts of clouds. The model allows a derivation of all three KS relations using the probability distribution function of density with no thresholds for star formation. Failed galaxies and systems with sub-KS SFRs are predicted to have gas that is dominated by an equilibrium warm phase where the thermal Jeans length exceeds the Toomre length. A squared relation is predicted for molecular gas-dominated young galaxies.
Using results from Ramanujan's lost notebook, Zudilin recently gave an insightful proof of a radial limit result of Folsom, Ono, and Rhoades for mock theta functions. Here we see that the author's previous work on the dual nature of Appell--Lerch sums and partial theta functions and on constructing bilateral $q$-series with mixed mock modular behaviour is well-suited for such radial limits. We present five more radial limit results which follow from mixed mock modular bilateral $q$-hypergeometric series. We also obtain the mixed mock modular bilateral series for a universal mock theta function of Gordon and McIntosh. The later bilateral series can be used to compute radial limits for many classical second, sixth, eight, and tenth order mock theta functions.
Molecular gas in Arches cloud located near the Arches cluster is one of the emitters of K-$\alpha$ line of neutral iron and X-ray continuum in the Galactic center (GC). Similarly to the cloud Sgr B2, another well-known emitter of the iron line in the GC, the Arches cloud demonstrates temporal decline of the X-ray emission. The most natural origin of this emission is irradiation of primary photons of an X-ray flare from a distant source, most likely Sgr A*. However, recent observations of the Arches cloud discovered variations of equivalent width of the 6.4 keV iron line, which indicated that the X-ray emission from the cloud is a combination of two components with different origin and different equivalent width, one of which is time-variable, while the other is stationary during the period of observations. We considered two different scenarios: a) this emission is formed by reflection from two clouds, which are at some distance from each other, when they are irradiated by two different flares; and b) the other scenario assumes a combination of X-ray fluxes produced in the same cloud by reflection of primary photons and by subrelativistic cosmic rays. We present restrictions for both model and conditions at which these scenarios can be realized. Although none of the models can be completely ruled out, we find that the X-ray reflection model requires less assumption and therefore is the most viable.
In this work the effect of amorphous substrate on crystallization is addressed. By performing Monte-Carlo simulations of solid on solid models we explore the effect of the disorder on crystal growth. The disorder is introduced via local geometry of the lattice, where local connectivity and transition rates are varied from site to site. A comparison to an ordered lattice is accomplished and for both, ordered and disordered substrates, an optimal growth temperature is observed. Moreover, we find that under specific conditions the disordered substrate may have a beneficial effect on crystal growth, i.e., better crystallization as a direct consequence of the presence of disorder.
Inspired by the effectiveness of adversarial training in the area of Generative Adversarial Networks we present a new approach for learning feature representations in person re-identification. We investigate different types of bias that typically occur in re-ID scenarios, i.e., pose, body part and camera view, and propose a general approach to address them. We introduce an adversarial strategy for controlling bias, named Bias-controlled Adversarial framework (BCA), with two complementary branches to reduce or to enhance bias-related features. The results and comparison to the state of the art on different benchmarks show that our framework is an effective strategy for person re-identification. The performance improvements are in both full and partial views of persons.
In this paper we present a detailed analysis of the Faraday depth (FD) spectrum and its clean components obtained through the application of the commonly used technique of Faraday rotation measure synthesis to analyze spectro-polarimetric data. In order to directly compare the Faraday depth spectrum with physical properties of a magneto-ionic medium, we generated synthetic broad-bandwidth spectro-polarimetric observations from magnetohydrodynamic (MHD) simulations of a transonic, isothermal, compressible turbulent medium. We find that correlated magnetic field structures give rise to a combination of spiky, localized peaks at certain FD values, and broad structures in the FD spectrum. Although the majority of these spiky FD structures appear narrow, giving an impression of a Faraday thin medium, we show that they arise from strong synchrotron emissivity at that FD. Strong emissivity at a FD can arise because of both strong spatially-local polarized synchrotron emissivity at a FD or accumulation of weaker emissions along the distance through a medium that have Faraday depths within half the width of the rotation measure spread function. Such a complex Faraday depth spectrum is a natural consequence of MHD turbulence when the lines of sight pass through a few turbulent cells. This therefore complicates the convention of attributing narrow FD peaks to presence of a Faraday rotating medium along the line of sight. Our work shows that it is difficult to extract the FD along a line of sight from the Faraday depth spectrum using standard methods for a turbulent medium in which synchrotron emission and Faraday rotation occur simultaneously.
We apply the theory of semiparametric estimation to a Hong-Ou-Mandel interference experiment with a spectrally entangled two-photon state generated by spontaneous parametric downconversion. Thanks to the semiparametric approach we can evaluate the Cram\'er-Rao bound and find an optimal estimator for a particular parameter of interest without assuming perfect knowledge of the two-photon wave function, formally treated as an infinity of nuisance parameters. In particular, we focus on the estimation of the Hermite-Gauss components of the marginal symmetrised wavefunction, whose Fourier transform governs the shape of the temporal coincidence profile. We show that negativity of these components is an entanglement witness of the two-photon state.
We prove the equivalence of ensembles for Bernoulli measures on $\mathbb{Z}$ conditioned on two conserved quantities under the situation that one of them is spatially inhomogeneous. For the proof, we extend the classical local limit theorem for a sum of Bernoulli independent sequences to those multiplied by linearly growing weights. The motivation comes from the study of random Young diagrams. We discuss the relation between our result and the so-called Vershik curve which appears in a scaling limit for height functions of two-dimensional Young diagrams.
We give an overview about the power product expansion of the exponential series and derive some q-analogs
It is well-known that in dimensions at least three semilinear wave equations with null conditions admit global solutions for small initial data. It is also known that in dimension two such result still holds for a certain class of quasi-linear wave equations with null conditions. The proofs are based on the decay mechanism of linear waves. However, in one dimension, waves do not decay. Nevertheless, we will prove that small data still lead to global solutions if the null condition is satisfied.
The magnitude of $m_u,\,m_d$ and $m_s$ is discussed on the basis of Chiral Perturbation Theory. In particular, the claim that $m_u=0$ leads to a coherent picture for the low energy structure of QCD is examined in detail. It is pointed out that this picture leads to violent flavour asymmetries in the matrix elements of the scalar and pseudoscalar operators, which are in conflict with the hypothesis that the light quark masses may be treated as perturbations. [Talk delivered at the 2nd IFT Workshop, "Yukawa Couplings and the Origins of Mass", Gainesville, Florida, Feb. 1994, to be published by International Press.]
We present a valence transition model for electron- and hole-doped cuprates, within which there occurs a discrete jump in ionicity Cu$^{2+} \to$ Cu$^{1+}$ upon doping, at or near optimal doping in the electron-doped compounds and at the pseudogap phase transition in the hole-doped materials. Doped cuprates have negative charge-transfer gaps, just as rare earth nickelates and BaBiO$_3$. Because of strong correlations and small $d-p$ electron hoppings the systems behave as effective $\frac{1}{2}$-filled Cu-band in the undoped state, and as correlated two-dimensional geometrically frustrated nearly $\frac{1}{4}$-filled O-band in the doped state. The theory gives the simplest yet most comprehensive understanding of experiments in the normal states. The robust antiferromagnetism in the conventional T$^\prime$ crystals, the strong role of oxygen deficiency in driving superconductivity and charge carrier sign corresponding to holes at optimal doping are all manifestations of the same quantum state. In the hole-doped pseudogapped state, a biaxial commensurate period 4 charge density wave state of O$^{1-}$-Cu$^{1+}$-O$^{1-}$ spin-singlets coexists with broken rotational C$_4$ symmetry. Finite domains of this broken symmetry state will exhibit the polar Kerr effect. Superconductivity within the model results from a destabilization of the $\frac{1}{4}$-filled band paired Wigner crystal [Phys. Rev. B {\bf 93}, 165110 and {\bf 93}, 205111]. We posit that a similar valence transition, Ir$^{4+} \to$ Ir$^{3+}$, occurs in electron-doped SrIr$_2$O$_4$. We make testable theoretical predictions on cuprates and iridates. Finally, we note that there exist an unusually large number of unconventional superconductors that exhibit superconductivity proximate to exotic charge ordered states, whose bandfillings are also $\frac{1}{4}$, exactly where the paired Wigner crystal is most stable.
We consider curvature invariants in the context of black hole collision simulations. In particular, we propose a simple and elegant combination of the Weyl invariants I and J, the {\sl speciality index} ${\cal S}$. In the context of black hole perturbations $\cal S$ provides a measure of the size of the distortions from an ideal Kerr black hole spacetime. Explicit calculations in well-known examples of axisymmetric black hole collisions demonstrate that this quantity may serve as a useful tool for predicting in which cases perturbative dynamics provide an accurate estimate of the radiation waveform and energy. This makes ${\cal S}$ particularly suited to studying the transition from nonlinear to linear dynamics and for invariant interpretation of numerical results.
We study a sample of $\sim$50,000 dwarf starburst and late-type galaxies drawn from the COSMOS survey with the aim of investigating the presence of nuclear accreting black holes (BHs) as those seed BHs from which supermassive BHs could grow in the early Universe. We divide the sample into five complete redshift bins up to $z=1.5$ and perform an X-ray stacking analysis using the \textit{Chandra} COSMOS-Legacy survey data. After removing the contribution from X-ray binaries and hot gas to the stacked X-ray emission, we still find an X-ray excess in the five redshift bins that can be explained by nuclear accreting BHs. This X-ray excess is more significant for $z<0.5$. At higher redshifts, these active galactic nuclei could suffer mild obscuration, as indicated by the analysis of their hardness ratios. The average nuclear X-ray luminosities in the soft band are in the range 10$^{39}-10^{40}$ erg s$^{-1}$. Assuming that the sources accrete at $\geq$ 1\% the Eddington rate, their BH masses would be $\leq$ 10$^{5}$ M$_{\odot}$, thus in the intermediate-mass BH regime, but their mass would be smaller than the one predicted by the BH-stellar mass relation. If instead the sources follow the correlation between BH mass and stellar mass, they would have sub-Eddington accreting rates of $\sim$ 10$^{-3}$ and BH masses 1-9 $\times$ 10$^{5}$ M$_{\odot}$. We thus conclude that a population of intermediate-mass BHs exists in dwarf starburst galaxies, at least up to $z$=1.5, though their detection beyond the local Universe is challenging due to their low luminosity and mild obscuration unless deep surveys are employed.
Isospin-breaking effects in the baryonic sector are studied in the framework of a medium-modified Skyrme model. The neutron-proton mass difference in infinite, asymmetric nuclear matter is discussed. In order to describe the influence of the nuclear environment on the skyrmions, we include energy-dependent charged and neutral pion optical potentials in the s- and p-wave channels. The present approach predicts that the neutron-proton mass difference is mainly dictated by its strong part and that it strongly decreases in neutron matter.