ShantanuT01/DACTYL-Pretraining huggingface dataset:
The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. One challenge in realizing simulations on near-term quantum devices is the large number of qubits required by such mappings. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a non-linear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with only a very modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.
We investigate the ground state and the thermal entanglement in the two-qubit Ising model interacting with a site-dependent magnetic field. The degree of entanglement is measured by calculating the concurrence. For zero temperature and for certain direction of the applied magnetic field, the quantum phase transition observed under a uniform external magnetic field disappears once a very small non-uniformity is introduced. Furthermore, we have shown analytically and confirmed numerically that once the direction of one of the magnetic field is along the Ising axis then no entangled states can be produced, independently of the degree of non-uniformity of the magnetic fields on each site.
In this paper we consider a connection between the famous Skorohod embedding problem and the Shiryaev inverse problem for the first hitting time distribution of a Brownian motion: given a probability distribution, $F$, find a boundary such that the first hitting time distribution is $F$. By randomizing the initial state of the process we show that the inverse problem becomes analytically tractable. The randomization of the initial state allows us to significantly extend the class of target distributions in the case of a linear boundary and moreover allows us to establish connection with the Skorohod embedding problem.
We have proposed the phenomenological description of dielectric hysteresis loops in ferroelectric semiconductors with charged defects and prevailing extrinsic conductivity. Exactly we have modified Landau-Ginsburg approach and shown that the macroscopic state of the aforementioned inhomogeneous system can be described by three coupled equations for three order parameters. Both the experimentally observed coercive field values well below the thermodynamic one and the various hysteresis loop deformations (constricted and double loops) have been obtained in the framework of our model. The obtained results quantitatively explain the ferroelectric switching in such ferroelectric materials as thick PZT films.
We study the p-adic behavior of Jacobi Sums for $\mathbb Q(\zeta_p)$ and link this study to the p-Sylow subgroup of the ideal class group of $\mathbb Q(\zeta_p\`a^+$
Knowledge of the structure of galaxy clusters is essential for an understanding of large scale structure in the universe, and may provide important clues to the nature of dark matter. Moreover, the shape of the dark matter distribution in the cluster core may offer insight into the structure formation process. Unfortunately, cluster cores also tend to be the site of complicated astrophysics. X-ray imaging spectroscopy of relaxed clusters, a standard technique for mapping their dark matter distributions, is often complicated by the presence of cool components in cluster cores, and the dark matter profile one derives for a cluster is sensitive to assumptions made about the distribution of this component. In addition, fluctuations in the temperature measurements resulting from normal statistical variance can produce results which are unphysical. We present here a procedure for extracting the dark matter profile of a spherically symmetric, relaxed galaxy cluster which deals with both of these complications. We apply this technique to a sample of galaxy clusters observed with the Chandra X-ray Observatory, and comment on the resulting mass profiles. For some of the clusters we compare their masses with those derived from weak and strong gravitational measurements.
Searching for the high-performance thermoelectric (TE) materials has always been a long-held dream in the thermoelectricity field. Recently, it is found in experiments that the largest figure of merit ZT of $2.6$ can be reached in SnSe crystals at 923 K and Cu2Se sample at 850 K, which arouses the enormous interest of seeking high-ZT materials. Based on first-principle calculations and Boltzman transport equation (BTE), we report in this letter that silver halides (AgCl and AgBr) in rocksalt structure have excellent TE performances. A superhigh ZT of about 7.0 at mid-temperature (~600K) is obtained in the p-type doped AgCl and AgBr crystals, which far exceeds the ZT values of all current bulk TE materials. This record-breaking ZT value is attributed to the ultralow intrinsic lattice thermal conductivity \kappa_L (e.g. \kappa_L ~0.10 and 0.09 Wm^{-1}K^{-1} for AgCl and AgBr at 600 K, respectively). Our results may be a feat that could revolutionize the field of the heat energy conversion.
Using the updated ALEPH V-A spectral function from tau decays, we determine the lowest spectral moments of the left-right correlator and extract dynamical information on order parameters of the QCD chiral symmetry breaking. Uncertainties associated with violations of quark-hadron duality are estimated from the data, imposing all known short-distance constraints on a resonance-based parametrization. Employing proper pinched weight functions, we obtain an accurate determination of the effective chiral couplings L10 and C87 and the dimension-six and -eight contributions in the Operator Product Expansion.
We prove that every biregular automorphism of the affine algebraic variety ${\mathbb P}^M\setminus S$, $M\geqslant 3$, where $S\subset {\mathbb P}^M$ is a hypersurface of degree $m\geqslant M+1$ with a unique singular point of multiplicity $(m-1)$, resolved by one blow up, is a restriction of some automorphism of the projective space ${\mathbb P}^M$, preserving the hypersurface $S$; in particular, for a general hypersurface $S$ the group $\mathop{\rm Aut} ({\mathbb P}^M\setminus S)$ is trivial.
The effects of CP-phases on the three absolute quasi-degenerate Majorana neutrino (QDN) masses are stud-ied with neutrino mass matrices obeying {\mu} - {\tau} symmetry for normal as well as inverted hierarchical mass patterns. We have made further investigations on 1) the prediction of solar mixing angle which lies below tri-bimaximal mixing value in consistent with neutrino oscillation observational data, 2) the prediction on absolute neutrino mass parameter (mee) in 0{\nu}{\beta}{\beta} decay, and 3) cosmological bound on the sum of the three absolute neutrino masses. The numerical analysis is carried out through the parameterization of neu- trino mass matrices using only two unknown parameters ({\epsilon}, {\eta}) within {\mu} - {\tau} symmetry. The results show the validity of QDN mass models in both normal and inverted hierarchical patterns. These models are far from discrimination and hence not yet ruled out. The results presented in this article are new and have subtle ef- fects in the discrimination of neutrino mass models.
Gravitational microlensing has become a mature technique for discovering small gravitational lenses in the Universe which are otherwise beyond our detection limits. Similarly, plasma microlensing can help us explore cosmic plasma lenses. Both pulsar scintillation and extreme scattering events of compact radio sources suggest the existence of $\sim$ AU scale plasma lenses in the ionized interstellar medium (IISM), whose astrophysical correspondence remains a mystery. We demonstrate that plasma microlensing events by these plasma lenses recorded in the form of wide-band dynamic spectra are a powerful probe of their nature. Using the recently developed Picard-Lefschetz integrator for the Kirchhoff-Fresnel integral, we simulate such dynamic spectra for a well-motivated family of single-variable plasma lenses. We demonstrate that the size, strength, and shape of the plasma lens can be measured from the location of the cusp point and the shape of spectral caustics respectively, with a combination of distances and the effective velocity known a priori or measured from the widths of the interference pattern. Future wide-band observations of pulsars, whose plasma microlensing events may be predictable from parabolic arc monitoring, are the most promising ground to apply our results for a deeper insight into the fine structures in the IISM.
We present a systematic study of the sub-sample of Shakhbazyan groups (SHKs) covered by the Sloan Digital Sky Survey Data Release--5 (SDSS-5). SHKs probe an environment with characteristics which are intermediate between those of loose and very compact groups. Surprisingly, we found that several groups identifying algorithms (e.g. Berlind et al. 2006, Tago et al. 2008) miss this type of structures. Using the SDSS-5 spectroscopic data and the photometric redshifts derived in D'Abrusco et al. 2007, we identified possible group members in photometric redshift space and derived, for each group, several individual properties. We also combined pointed and stacked Rosat All Sky Survey data to investigate the X-ray luminosities of these systems. Our study confirms that the majority of groups are physical entities with richness in the range 3--13 galaxies, and properties ranging between those of loose and compact groups. We confirm that SHK groups are richer in early-type galaxies than the surrounding environment and the field, as expected from the morphology-density relation and from the selection of groups of red galaxies. Furthermore, our work supports the existence of two sub-classes of structures, the first one being formed by compact and isolated groups and the second formed by extended structures. We suggest that while the first class of objects dwells in less dense regions like the outer parts of clusters or the field, possibly sharing the properties of Hickson Compact Groups, the more extended structures represent a mixture of [core+halo] configurations and cores of rich clusters. X-ray luminosities for SHKs are generally consistent with these results and with the expectations for the L_X-sigma_v relation, but also suggest the velocity dispersions reported in literature are underestimated for some of the richest systems.
We study a bilayer GaAs hole system that hosts two distinct many-body phases at low temperatures and high perpendicular magnetic fields. The higher-density (top) layer develops a Fermi sea of composite fermions (CFs) in its half-filled lowest Landau level, while the lower-density (bottom) layer forms a Wigner crystal (WC) as its filling becomes very small. Owing to the inter-layer interaction, the CFs in the top-layer feel the periodic Coulomb potential of the WC in the bottom-layer. We measure the magnetoresistance of the top-layer while changing the bottom-layer density. As the WC layer density increases, the resistance peaks separating the adjacent fractional quantum Hall states in the top-layer change nonmonotonically and attain maximum values when the cyclotron orbit of the CFs encloses one WC lattice point. These features disappear at T = 275 mK when the WC melts. The observation of such geometric resonance features is unprecedented and surprising as it implies that the CFs retain a well-defined cyclotron orbit and Fermi wave vector even deep in the fractional quantum Hall regime, far from half-filling.
Recent progress on colour reconnection within the Pythia framework is presented. A new model is introduced, based on the SU(3) structure of QCD and a minimization of the potential string energy. The inclusion of the epsilon structure of SU(3) gives a new baryon production mechanism and makes it possible simultaneously to describe hyperon production at both $e^+e^-$ and pp colliders. Finally, predictions for $e^+e^-$ colliders, both past and potential future ones, are presented.
In this contribution we go through the developments that in the years 1968 to 1974 led from the Veneziano model to the bosonic string.
High frequency (millisecond) quasi-periodic oscillations (HF QPOs) are observed in the X-ray power-density spectra of several microquasars and low mass X-ray binaries. Two distinct QPO peaks, so-called twin peak QPOs, are often detected simultaneously exhibiting their frequency ratio close or equal to 3/2. Following the analytic theory and previous studies of observable spectral signatures, we aim to model the twin peak QPOs as a spectral imprint of specific dual oscillation regime defined by a combination of the lowest radial and vertical oscillation mode of optically thick slender tori with constant specific angular momentum. We examined power spectra and fluorescent K$\alpha$ iron line profiles for two different simulation setups with the mode frequency relations corresponding to the epicyclic resonance HF QPOs model and modified relativistic precession QPOs model. We use relativistic ray-tracing implemented in parallel simulation code LSDplus. In the background of the Kerr spacetime geometry, we analyze the influence of the distant observer inclination and the spin of the central compact object. Relativistic optical projection of the oscillating slender torus is illustrated by images in false colours related to the frequency shift. We show that performed simulations yield power spectra with the pair of dominant peaks corresponding to the frequencies of radial and vertical oscillation modes with the proper ratio equal to 3/2 on a wide range of inclinations and spin values. We also discuss exceptional cases of a very small and very high inclination as well as unstable high spin relativistic precession-like configuration predicting constant frequency ratio equal to 1/2. We demonstrate signifiant dependency of broadened K$\alpha$ iron line profiles on the inclination of the distant observer.
A method has been recently proposed to establish the geometry of the alpha-cluster arrangement in $^{12}$C making use of polarized gamma-rays. The ratio of intensities of scattered radiation at 90 degrees along and perpendicular to the initial direction of the electric field vector, called depolarization ratio, is a key quantity that allows to underpin the nature of totally symmetric modes of vibrations. This allows to connect with the underlying point-group structure and therefore to the geometric shape of the nuclear molecule. This method is reviewed for $^{12}$C and extended to other configurations, such as three unequal clusters and four identical clusters (e.g. $^{16}$O).
We study the profile $X_{n,k}$ of random search trees including binary search trees and $m$-ary search trees. Our main result is a functional limit theorem of the normalized profile $X_{n,k}/\mathbb{E}X_{n,k}$ for $k=\lfloor\alpha\log n\rfloor$ in a certain range of $\alpha$. A central feature of the proof is the use of the contraction method to prove convergence in distribution of certain random analytic functions in a complex domain. This is based on a general theorem concerning the contraction method for random variables in an infinite-dimensional Hilbert space. As part of the proof, we show that the Zolotarev metric is complete for a Hilbert space.
We study theoretically the nature of correlations in space and time of the current in a one-dimensional bilinear array of tunnel junctions in the normal conduction limit, using the kinetic Monte Carlo (KMC) method. The bilinear array consists of two parallel rows of tunnel junctions, capacitively coupled in a ladder configuration. The electrostatic potential landscape and the charge-charge interaction length both depend on the circuit capacitances, which in turn influence transport and charge correlations in the array. We observe the formation of stationary charge states when only one rail is voltage biased. When a symmetric bias is applied to both rails, the site at which the positive and negative charge carriers recombine can drift throughout the array. We also calculate charge densities and auto- and cross-correlation functions.
We investigate the solubility of the congruence xy=1 (mod p), where p is a prime and x,y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums.
Solar dynamo models require some mechanism for magnetic field concentration near the base of the convection zone in order to generate super-kilogauss toroidal fields with sufficiently large (~10^{24} Mx) magnetic flux. We consider the downward diamagnetic pumping near the base of the convection zone as a possible concentration mechanism and derive the pumping velocities with allowance for the effect of rotation. Transport velocities for poloidal and toroidal fields differ in rotating fluid. The toroidal field is transported downward along the radius only but the pumping velocity for the poloidal field has an equatorward meridional component also. Previous results for cases of slow and rapid rotation are reproduced and the diamagnetic pumping expressions adapted for use in dynamo models are presented.
The critical cooling rate $\mathcal{R}_c$, below which liquids crystallize upon cooling, characterizes the glass-forming ability (GFA) of the system. While pure metals are typically poor glass formers with $\mathcal {R}_c>10^{12}\, {\rm K/s}$, specific multi-component alloys can form bulk metallic glasses (BMGs) even at cooling rates below $\mathcal {R}\sim 1\, {\rm K/s}$. Conventional wisdom asserts that metal alloys with three or more components are better glass formers (with smaller ${\cal R}_c$) than binary alloys. However, there is currently no theoretical framework that provides quantitative predictions for $\mathcal{R}_c$ for multi-component alloys. We perform simulations of ternary hard-sphere systems, which have been shown to be accurate models for the glass-forming ability of BMGs, to understand the roles of geometric frustration and demixing in determining $\mathcal {R}_c$. Specifically, we compress ternary hard sphere mixtures into jammed packings and measure the critical compression rate, below which the system crystallizes, as a function of the diameter ratios $\sigma_B/\sigma_A$ and $\sigma_C/\sigma_A$ and number fractions $x_A$, $x_B$, and $x_C$. We find two distinct regimes for the GFA in parameter space for ternary hard spheres. When the diameter ratios are close to $1$, such that the largest ($A$) and smallest ($C$) species are well-mixed, the GFA of ternary systems is no better than that of the optimal binary glass former. However, when $\sigma_C/\sigma_A \lesssim 0.8$ is below the demixing threshold for binary systems, adding a third component $B$ with $\sigma_C < \sigma_B < \sigma_A$ increases the GFA of the system by preventing demixing of $A$ and $C$. Analysis of the available data from experimental studies indicates that most ternary BMGs are below the binary demixing threshold with $\sigma_C/\sigma_A < 0.8$.
We revisit the problem of existence of stable systems of contracts with arbitrary sets of contracts. We show that stable sets of contracts exists if choices of agents satisfy path-independence. We call such choice functions Plott functions. Our proof is based on application of Zorn lemma to a special poset of semi-stable pairs. Moreover, we construct a dynamic process on the poset (generalizing algorithm Gale and Shapley) steady states of which are stable sets.   In Appendix we discuss Lehmann hyper-orders and establish a bijection between the set of Lehmann hyper-orders and the set of Plott functions.
Let X={X_n:n=0,1,2,...} be an irreducible, positive recurrent Markov chain with invariant probability measure \pi. We show that if X satisfies a one-step minorization condition, then \pi can be represented as an infinite mixture. The distributions in the mixture are associated with the hitting times on an accessible atom introduced via the splitting construction of Athreya and Ney [Trans. Amer. Math. Soc. 245 (1978) 493-501] and Nummelin [Z. Wahrsch. Verw. Gebiete 43 (1978) 309-318]. When the small set in the minorization condition is the entire state space, our mixture representation of \pi reduces to a simple formula, first derived by Breyer and Roberts [Methodol. Comput. Appl. Probab. 3 (2001) 161-177] from which samples can be easily drawn. Despite the fact that the derivation of this formula involves no coupling or backward simulation arguments, the formula can be used to reconstruct perfect sampling algorithms based on coupling from the past
Beyond mean-field methods based on restoration of symmetries and configuration mixing by the generator coordinate method (GCM) enable to calculate on the same footing correlations in the ground state and the properties of excited states. Excitation energies are often largely overestimated, especially in nuclei close to magicity, even when transition probabilities are well-described. We analyse here the origin of this failure. The first part of the paper compares realistic projected GCM and QRPA calculations for selected Sn isotopes performed with the same effective Skyrme interaction. Although it is difficult to perform RPA and GCM calculations under exactly the same conditions, this comparison shows that the projected GCM overestimates the RPA results. In the second part of this paper, we compare GCM and RPA in the framework of the exactly solvable Lipkin-Meshkov-Glick model. We show that the discretized GCM works quite well and permits to obtain nearly exact results with a small number of discretization points. This analysis indicates also that to break more symmetries of the nuclear Hamiltonian in the construction of the GCM basis is probably the best way to improve the description of excited states by the GCM.
The development of a dynamical model for investigating the nucleon resonances using the reactions of meson production from \pi N, \gamma N, N(e,e'), and N(\nu,{\it l}) reactions is reviewed. The results for the \Delta (1232) state are summarized and discussed. The progress in investigating higher mass nucleon resonances is reported.
We show in this note how the one-dimensional KZP formula obtained by Benjamini and Schramm can be extended to a multidimensional setting.
Quantum key distribution is widely thought to offer unconditional security in communication between two users. Unfortunately, a widely accepted proof of its security in the presence of source, device and channel noises has been missing. This long-standing problem is solved here by showing that, given fault-tolerant quantum computers, quantum key distribution over an arbitrarily long distance of a realistic noisy channel can be made unconditionally secure. The proof is reduced from a noisy quantum scheme to a noiseless quantum scheme and then from a noiseless quantum scheme to a noiseless classical scheme, which can then be tackled by classical probability theory.
We present calculations for the $c$-coefficients of the isobaric mass multiplet equation for nuclei from $A=42$ to $A=54$ based on input from three realistic nucleon-nucleon interactions. We demonstrate that there is a clear dependence on the short-ranged charge-symmetry breaking (CSB) part of the strong interaction and that there is significant disagreement in the CSB part between the commonly used CD-Bonn, N$^3$LO, and Argonne V18 nucleon-nucleon interactions. In addition, we show that all three interactions give a CSB contribution to the $c$-coefficient that is too large when compared to experiment.