ShantanuT01/DACTYL-Pretraining huggingface dataset:
The quantum interference effect among coupled identical quantum dots is studied in the present paper in the limit of strong intra-dot Coulomb interaction. When the average electron number in each dot is a fraction of an integer, quantum interference effect is greatly enhanced because of the sharing of extra electrons by multiple dots. We show that if the extra electron (hole) number is one, the low energy effective Hamiltonian can be map into the 2-channel SU(M) Coqblin-Schriffer model, where M is the total dot number. In particular, for two-dot system with odd number of total electrons, the model is equivalent to a two channel Kondo problem with anisotropic coupling between local spin and conduction bands. The more general situation with (arbitrary) fractional average electron number in each dot is also discussed. To study the Kondo effect, we apply the self consistent ladder approximation(SCLA) to study the electron spectral function for the two-dot system. Similar method is also used to study the triple-dot system where we show how quantum coherence manifest itself in the Aharonov-Bohm (AB) effect.
We extend the relation between absolutely maximally entangled (AME) states and quantum maximum distance separable (QMDS) codes by constructing whole families of QMDS codes from their parent AME states. We introduce a reduction-friendly form for the generator set of the stabilizer representation of an AME state, from which the stabilizer form for children codes, all QMDS, can be obtained. We then relate this to optimal codes for one-way quantum repeaters, by minimizing the short-term infrastructure cost as well as the long-term running cost of such quantum repeaters. We establish that AME states provide a framework for a class of QMDS codes that can be used in quantum repeaters.
A product difference equation is proved and used for derivation by elementary methods of four combinatorial identities, eight combinatorial identities involving generalized harmonic numbers and eight combinatorial identities involving classical harmonic numbers. For the binomial coefficients the definition with gamma functions is used, thus also allowing non-integer arguments in the identities. The generalized harmonic numbers in this case are harmonic numbers with a complex offset, where the classical harmonic numbers are a special case with offset zero.
Conventionally, long GRBs are thought to be caused by the core collapses of massive stars. During the lifetime of a massive star, a stellar wind bubble environment should be produced. Furthermore, the microphysics shock parameters may vary along with the evolution of the fireball. Here we investigate the variation of the microphysics shock parameters under the condition of wind bubble environment, and allow the microphysics shock parameters to be discontinuous at shocks in the ambient medium. It is found that our model can acceptably reproduce the rebrightenings observed in GRB afterglows, at least in some cases. The effects of various model parameters on rebrightenings are investigated. The rebrightenings observed in both the R-band and X-ray afterglow light curves of GRB 060206, GRB 070311 and GRB 071010A are reproduced in this model.
A quantum processor to import, process, and export optical quantum states is a common core technology enabling various photonic quantum information processing. However, there has been no photonic processor which is simultaneously universal, scalable, and programmable. Here, we report on an original loop-based single-mode versatile photonic quantum processor which is designed to be universal, scalable, and programmable. Our processor can perform arbitrarily many steps of programmable quantum operations on a given single-mode optical quantum state by time-domain processing in a dynamically controlled loop-based optical circuit. We use this processor to demonstrate programmable single-mode Gaussian gates and multi-step squeezing gates. In addition, we prove that the processor can perform universal quantum operations by injecting appropriate ancillary states and also be straightforwardly extended to a multi-mode processor. These results show that our processor is programmable, scalable, and potentially universal, leading to be suitable for general-purpose applications.
A coherent state path integral of anti-commuting fields is considered for a two-band, semiconductor-related solid which is driven by a ultrashort, classical laser field. We describe the generation of exciton quasi-particles from the driving laser field as anomalous pairings of the fundamental, fermionic fields. This gives rise to Hubbard-Stratonovich transformations from the quartic, fermionic interaction to various Gaussian terms of self-energy matrices. We accomplish path integrals of even-valued self-energy matrices with Euclidean integration measure where three cases of increasing complexity are classified (scalar self-energy variable, density-related self-energy matrix and also a self-energy including anomalous-doubled terms). According to the driving, anomalous-doubled Hamiltonian part, we also specify the case of a SSB with 'hinge' fields which factorizes the total self-energy matrix by a coset decomposition into density-related, block diagonal self-energy matrices of a background functional and into coset matrices with off-diagonal block generators for the anomalous pairings of fermions. In particular we investigate the transformation from the coset fields of a curved coset space, as the independent field degrees of freedom, to locally 'flat' fields with Euclidean integration measure. This allows to reduce the final path integral to solely 'Nambu'-doubled fields after a saddle point approximaton for the density-related self-energy matrices and also allows to derive classical field equations for exciton quasi-particles from various kinds of gradient expansions of the determinant.
We construct numerically static vortex solutions in a holographic model of two-band superconductor with an interband Josephson coupling in both the superfluid and superconductor regime. We investigate the effects of the interband coupling on the order parameter of each superconducting band in the vortex solution, and we find that it is different for each of the two bands. We compute also the free energy, critical magnetic field, magnetic penetration length and coherence lengths for the two bands, and we study their dependence on the interband coupling and temperature. Interestingly, we find that the coherence lengths of the two bands are close to identical.
We discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. T-duality along four directions in Poincare parametrization of AdS5 maps the bosonic part of the superstring action into itself. On bosonic level, this duality may be understood as a symmetry of the first-order (phase space) system of equations for the coset components of the current. The associated Lax connection is invariant modulo the action of an so(2,4)-automorphism. We then show that this symmetry extends to the full superstring, provided one supplements the transformation of the bosonic components of the current with a transformation on the fermionic ones. At the level of the action, this symmetry can be seen by combining the bosonic duality transformation with a similar one applied to part of the fermionic superstring coordinates. As a result, the full superstring action is mapped into itself, albeit in a different kappa-symmetry gauge. One implication is that the dual model has the same superconformal symmetry group as the original one, and this may be seen as a consequence of the integrability of the superstring. The invariance of the Lax connection under the duality implies a map on the full set of conserved charges that should interchange some of the Noether (local) charges with hidden (non-local) ones and vice versa.
Near-term quantum computers are limited by the decoherence of qubits to only being able to run low-depth quantum circuits with acceptable fidelity. This severely restricts what quantum algorithms can be compiled and implemented on such devices. One way to overcome these limitations is to expand the available gate set from single- and two-qubit gates to multi-qubit gates, which entangle three or more qubits in a single step. Here, we show that such multi-qubit gates can be realized by the simultaneous application of multiple two-qubit gates to a group of qubits where at least one qubit is involved in two or more of the two-qubit gates. Multi-qubit gates implemented in this way are as fast as, or sometimes even faster than, the constituent two-qubit gates. Furthermore, these multi-qubit gates do not require any modification of the quantum processor, but are ready to be used in current quantum-computing platforms. We demonstrate this idea for two specific cases: simultaneous controlled-Z gates and simultaneous iSWAP gates. We show how the resulting multi-qubit gates relate to other well-known multi-qubit gates and demonstrate through numerical simulations that they would work well in available quantum hardware, reaching gate fidelities well above 99 %. We also present schemes for using these simultaneous two-qubit gates to swiftly create large entangled states like Dicke and Greenberg-Horne-Zeilinger states.
Let $G$ be a simple graph with maximum degree $\Delta(G)$. A subgraph $H$ of $G$ is overfull if $|E(H)|>\Delta(G)\lfloor |V(H)|/2 \rfloor$. Chetwynd and Hilton in 1985 conjectured that a graph $G$ on $n$ vertices with $\Delta(G)>n/3$ has chromatic index $\Delta(G)$ if and only if $G$ contains no overfull subgraph. Glock, K\"{u}hn and Osthus in 2016 showed that the conjecture is true for dense quasirandom graphs with even order, and they conjectured that the same should hold for such graphs with odd order. In this paper, we show that the conjecture of Glock, K\"{u}hn and Osthus is affirmative.
We study the enumerative significance of the s-pointed genus zero Gromov-Witten invariant on a homogeneous space X. For that, we give an interpretation in terms of rational curves on X.
We determine the asymptotic forms of work distributions at arbitrary times $T$, in a class of driven stochastic systems using a theory developed by Engel and Nickelsen (EN theory) (arXiv:1102.4505v1 [cond-mat.stat-mech]), which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in the path integral form, are characterised by having quadratic actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks flucutation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial function. We then extend our analysis to a stochastically driven system, studied in ( arXiv:1212.0704v2 [cond-mat.stat-mech], arXiv:1402.5777v1 [cond-mat.stat-mech]) using a moment-generating-function method, for both equilibrium and non - equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary $T$. For dissipated work in the steady state, we compare the large $T$ asymptotic behaviour of our solution to that already obtained in ( arXiv:1402.5777v1 [cond-mat.stat-mech]). In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with the numerical simulations. Our solutions are exact in the low noise limit.
What forms will have an equations of modern physics if the dimensions of our time and space are fractional? The generalized equations enumerated by title are presented by help the generalized fractional derivatives of Riemann-Liouville.
The dark matter (DM) halos of field elliptical galaxies have not been well studied and their properties appear controversial. While some galaxies appear to be nearly devoid of DM, others show clear evidence of its presence. Furthermore, modified Netonian dynamics (MOND), which has been found to have predictive power in the domain of disk galaxies, has not yet been investigated for isolated elliptical galaxies. We study the kinematics of the isolated elliptical NGC 7507, which has been claimed as a clear example of DM presence in early-type galaxies. We obtained major and minor axis long-slit spectroscopy of NGC 7507 using the Gemini South telescope and deep imaging in Kron-Cousins R and Washington C using the CTIO/MOSAIC camera. Mean velocities, velocity dispersion and higher order moments are measured out to ~90 arcsec. The galaxy, although almost circular, has significant rotation along the minor axis and a rapidly declining velocity dispersion along both axes. Jeans models without DM provide an excellent representation of the data with a mass-to-light ratio (M/L) of 3.1 (R-band). The most massive Navarro-Frenk-White (NFW) halo the data allow has a virial mass of only 3.9+3.1-2.1E11 solar masses, although the data are more consistent with models that have a slight radial anisotropy, which implies the galaxy has an even lower DM halo mass of 2.2+2.0-1.2E11 solar masses. Modeling of the h_4 Gauss-Hermite coefficient is inconclusive but seems to be consistent with mild radial anisotropy. A cored logarithmic DM halo with parameters r0 = 7 kpc and v0 = 100 km/s can also reproduce the observed velocity dispersion profile. In conclusion, we cannot easily reproduce the previous findings of a predominance of DM in NGC 7507 within a simple spherical model. DM may be present, but only in conjunction with a strong radial anisotropy, for which there are some indications. (Abridged).
Pair instability supernovae are thought to restrict the formation of black holes in the mass range ~50 - 135 solar masses. However, black holes with masses within this "high mass gap" are expected to form as the remnants of binary black hole mergers. These remnants can merge again dynamically in densely populated environments such as globular clusters. The hypothesis that the binary black hole merger GW190521 formed dynamically is supported by its high mass. Orbital eccentricity can also be a signature of dynamical formation, since a binary that merges quickly after becoming bound may not circularize before merger. In this work, we measure the orbital eccentricity of GW190521. We find that the data prefer a signal with eccentricity $e \geq 0.1$ at 10 Hz to a non-precessing, quasi-circular signal, with a log Bayes factor $\ln{\cal B}=5.0$. When compared to precessing, quasi-circular analyses, the data prefer a non-precessing, $e \geq 0.1$ signal, with log Bayes factors $\ln{\cal B}\approx2$. Using injection studies, we find that a non-spinning, moderately eccentric ($e = 0.13$) GW190521-like binary can be mistaken for a quasi-circular, precessing binary. Conversely, a quasi-circular binary with spin-induced precession may be mistaken for an eccentric binary. We therefore cannot confidently determine whether GW190521 was precessing or eccentric. Nevertheless, since both of these properties support the dynamical formation hypothesis, our findings support the hypothesis that GW190521 formed dynamically.
We prove the existence of tilting objects on some global quotient stacks. As a consequence we provide further evidence for a conjecture on the Rouquier dimension of derived categories formulated by Orlov.
Let $n$ and $k$ be positive integers. We denote by $v_2(n)$ the 2-adic valuation of $n$. The Stirling numbers of the first kind, denoted by $s(n,k)$, counts the number of permutations of $n$ elements with $k$ disjoint cycles. In recent years, Lengyel, Komatsu and Young, Leonetti and Sanna, and Adelberg made some progress on the $p$-adic valuations of $s(n,k)$. In this paper, by introducing the concept of $m$-th Stirling numbers of the first kind and providing a detailed 2-adic analysis, we show an explicit formula on the 2-adic valuation of $s(2^n, k)$. We also prove that $v_2(s(2^n+1,k+1))=v_2(s(2^n,k))$ holds for all integers $k$ between 1 and $2^n$. As a corollary, we show that $v_2(s(2^n,2^n-k))=2n-2-v_2(k-1)$ if $k$ is odd and $2\le k\le 2^{n-1}+1$. This confirms partially a conjecture of Lengyel raised in 2015. Furthermore, we show that if $k\le 2^n$, then $v_2(s(2^n,k)) \le v_2(s(2^n,1))$ and $v_2(H(2^n,k))\leq -n$, where $H(n,k)$ stands for the $k$-th elementary symmetric functions of $1,1/2,...,1/n$. The latter one supports the conjecture of Leonetti and Sanna suggested in 2017.
The mass of the Higgs boson in the Split Supersymmetric Standard Model is calculated, including all one-loop threshold effects and the renormalization group evolution of the Higgs quartic coupling through two-loops. The two-loop corrections are very small (<<1 GeV), while the one-loop threshold corrections generally push the Higgs mass down several GeV.
The runaway star HD34078, initially selected to investigate small scale structure in a foreground diffuse cloud has been shown to be surrounded by highly excited H2. We first search for an association between the foreground cloud and HD34078. Second, we extend previous investigations of temporal absorption line variations (CH, CH+, H2) in order to better characterize them. We have mapped the CO(2-1) emission at 12 arcsec resolution around HD34078's position, using the 30 m IRAM antenna. The follow-up of CH and CH+ absorption lines has been extended over 5 more years. In parallel, CH absorption towards the reddened star Zeta Per have been monitored to check the homogeneity of our measurements. Three more FUSE spectra have been obtained to search for N(H2) variations. CO observations show a pronounced maximum near HD34078's position, clearly indicating that the star and diffuse cloud are associated. The optical spectra confirm the reality of strong, rapid and correlated CH and CH+ fluctuations. On the other hand, N(H2, J=0) has varied by less than 5 % over 4 years. We also discard N(CH) variations towards Zeta Per at scales less than 20 AU. Observational constraints from this work and from 24 micron dust emission appear to be consistent with H2 excitation but inconsistent with steady-state bow shock models and rather suggest that the shell of compressed gas surrounding HD34078, is seen at an early stage of the interaction. The CH and CH+ time variations as well as their large abundances are likely due to chemical structure in the shocked gas layer located at the stellar wind/ambient cloud interface. Finally, the lack of variations for both N(H2, J=0) towards HD34078 and N(CH) towards Zeta Per suggests that quiescent molecular gas is not subject to pronounced small-scale structure.
We study thermodynamic of strange quark matter (SQM) using the analytic expressions of free and internal energies. We investigate two regimes of the high density and low density separately. As a vital program, in the case of a massless gluon and massless quarks at finite temperature, we also present a geometry of thermodynamics for the gluon and Bosons using a Legendre invariance metric, it is so called as geometrothermodynamic (GTD) to better understanding of the phase transition. The GTD metric and its second order scalar invariant have been obtained, and we clarify the phase transition by study the singularities of the scalar curvature of this Riemannian metric. This method is ensemble dependence and to complete the phase transition. Meanwhile, we also investigate enthalpy and entropy and internal energy representations. Our work exposes new pictures of the nature of phase transitions in SQM.
Background: An electron localization function was originally introduced to visualize bond structures in molecules. It became a useful tool to describe electron configurations in atoms, molecules and solids. In nuclear physics, a nucleon localization function (NLF) has been used to characterize clusters in light nuclei, fragment formation in fission and pasta phases in the inner crust of neutron stars.   Purpose: We use the NLF to study the nuclear response to fast rotation.   Methods: We generalize the NLF to the case of nuclear rotation. The extended expressions involve both time-even and time-odd local densities. Since current density and density gradient contribute to the NLF primarily at the surface, we propose a simpler spatial measure given by the kinetic-energy density. Illustrative calculations for the superdeformed yrast band of $^{152}$Dy were carried out by using the cranked Skyrme-Hartree-Fock method. We also employed the cranked harmonic-oscillator model to gain insights into patterns revealed by the NLF at high angular momentum.   Results: In a deformed rotating nucleus, several NLFs can be introduced, depending on the definition of the spin-quantization axis and self-consistent symmetries of the system. The oscillating pattern of the NLF can be explained by a constructive interference between the kinetic-energy and particle densities. The nodal pattern seen in the NLF along the major axis of a rotating nucleus comes from single-particle orbits with large aligned angular momentum. The variation of the NLF along the minor axis is traced back to deformation-aligned orbits.   Conclusions: The NLF allows a simple interpretation of the shell structure evolution in the rotating nucleus in terms of the angular-momentum alignment of individual nucleons. We expect that the NLF will be useful for the characterization of other collective modes and time-dependent processes.
We report on a microscopic calculation of n-3H and p-3He scattering employing the Argonne v_{18} and v_8' nucleon-nucleon potentials with and without additional three-nucleon force. An R-matrix analysis of the p-3He and n-3H scattering data is presented. Comparisons are made for the phase shifts and a selection of measurements in both scattering systems. Differences between our calculation and the R-matrix results or the experimental data can be attributed to only two partial waves (3P0 and 3P2). We find the effect of the Urbana IX and the Texas-Los Alamos three-nucleon forces on the phase shifts to be negligible.
We introduce K-theoretic Gromov-Witten invariants of algebraic orbifold target spaces. Using the methods developed by Givental-Tonita we characterize Giventals Lagrangian cone of quantum K theory of orbifolds in terms of the cohomological cone.
We present ALMA (0.87~mm and 1.3~mm) and VLA (9~mm) observations toward the candidate intermediate-mass protostar OMC2-FIR3 (HOPS-370; L$_{bol}$~314~L$_{\odot}$) at $\sim$0.1" (40~au) resolution for the continuum emission and ~0.25" (100 au) resolution of nine molecular lines. The dust continuum observed with ALMA at 0.87~mm and 1.3~mm resolve a near edge-on disk toward HOPS-370 with an apparent radius of ~100 au. The VLA observations detect both the disk in dust continuum and free-free emission extended along the jet direction. The ALMA observations of molecular lines (H$_2$CO, SO, CH$_3$OH, $^{13}$CO, C$^{18}$O, NS, and H$^{13}$CN) reveal rotation of the apparent disk surrounding HOPS-370 orthogonal to the jet/outflow direction. We fit radiative transfer models to both the dust continuum structure of the disk and molecular line kinematics of the inner envelope and disk for the H$_2$CO, CH$_3$OH, NS, and SO lines. The central protostar mass is determined to be $\sim$2.5 M_sun with a disk radius of $\sim$94~au, when fit using combinations of the H$_2$CO, CH$_3$OH, NS, and SO lines, consistent with an intermediate-mass protostar. Modeling of the dust continuum and spectral energy distribution (SED) yields a disk mass of 0.035~M$_{\odot}$ (inferred dust+gas) and a dust disk radius of 62~au, thus the dust disk may have a smaller radius than the gas disk, similar to Class II disks. In order to explain the observed luminosity with the measured protostar mass, HOPS-370 must be accreting at a rate between 1.7 and 3.2$\times$10$^{-5}$~M$_{\odot}$~yr$^{-1}$.