Quantum mechanics in an evolving Hilbert space

Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed

First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA.

The NOvA experiment has seen a 4.4σ signal of ν[over ¯]_{e} appearance in a 2 GeV ν[over ¯]_{μ} beam at a distance of 810 km. Using 12.33×10^{20} protons on target delivered to the Fermilab NuMI neutrino beamline, the experiment recorded 27 ν[over ¯]_{μ}→ν[over ¯]_{e} candidates with a background of 10.3 and 102 ν[over ¯]_{μ}→ν[over ¯]_{μ} candidates. This new antineutrino data are combined with neutrino data to measure the parameters |Δm_{32}^{2}|=2.48_{-0.06}^{+0.11}×10^{-3}  eV^{2}/c^{4} and sin^{2}θ_{23} in the ranges from (0.53-0.60) and (0.45-0.48) in the normal neutrino mass hierarchy. The data exclude most values near δ_{CP}=π/2 for the inverted mass hierarchy by more than 3σ and favor the normal neutrino mass hierarchy by 1.9σ and θ_{23} values in the upper octant by 1.6σ

Observation of seasonal variation of atmospheric multiple-muon events in the NOvA Near Detector

Using two years of data from the NOvA Near Detector at Fermilab, we report a seasonal variation of cosmic ray induced multiple-muon (Nμ≥2) event rates which has an opposite phase to the seasonal variation in the atmospheric temperature. The strength of the seasonal multiple-muon variation is shown to increase as a function of the muon multiplicity. However, no significant dependence of the strength of the seasonal variation of the multiple-muon variation is seen as a function of the muon zenith angle, or the spatial or angular separation between the correlated muons

Search for slow magnetic monopoles with the NOvA detector on the surface

We report a search for a magnetic monopole component of the cosmic-ray flux in a 95-day exposure of the NOvA experiment’s Far Detector, a 14 kt segmented liquid scintillator detector designed primarily to observe GeV-scale electron neutrinos. No events consistent with monopoles were observed, setting an upper limit on the flux of 2 × 10−14 cm−2 s−1 sr−1 at 90% C.L. for monopole speed 6 × 10−4 < β < 5 × 10−3 and mass greater than 5 × 108 GeV. Because of NOvA’s small overburden of 3 meters-water equivalent, this constraint covers a previously unexplored low-mass region

Measurement of the double-differential muon-neutrino charged-current inclusive cross section in the NOvA near detector

We report cross-section measurements of the final-state muon kinematics for νμ charged-current interactions in the NOvA near detector using an accumulated 8.09×1020 protons on target in the NuMI beam. We present the results as a double-differential cross section in the observed outgoing muon energy and angle, as well as single-differential cross sections in the derived neutrino energy, Eν, and square of the four-momentum transfer, Q2. We compare the results to inclusive cross-section predictions from various neutrino event generators via χ2 calculations using a covariance matrix that accounts for bin-to-bin correlations of systematic uncertainties. These comparisons show a clear discrepancy between the data and each of the tested predictions at forward muon angle and low Q2, indicating a missing suppression of the cross section in current neutrino-nucleus scattering models

First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA

The NOvA experiment has seen a 4.4σ signal of ν̄e appearance in a 2 GeV ν̄μ beam at a distance of 810 km. Using 12.33×1020 protons on target delivered to the Fermilab NuMI neutrino beamline, the experiment recorded 27 ν̄μ→ν̄e candidates with a background of 10.3 and 102 ν̄μ→ν̄μ candidates. This new antineutrino data are combined with neutrino data to measure the parameters |Δm322|=2.48-0.06+0.11×10-3 eV2/c4 and sin2θ23 in the ranges from (0.53-0.60) and (0.45-0.48) in the normal neutrino mass hierarchy. The data exclude most values near δCP=π/2 for the inverted mass hierarchy by more than 3σ and favor the normal neutrino mass hierarchy by 1.9σ and θ23 values in the upper octant by 1.6σ

New constraints on oscillation parameters from Ve appearance and Vu disappearance in the NOvA experiment

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Search for multimessenger signals in NOvA coincident with LIGO/Virgo detections

Using the NOvA neutrino detectors, a broad search has been performed for any signal coincident with 28 gravitational wave events detected by the LIGO/Virgo Collaboration between September 2015 and July 2019. For all of these events, NOvA is sensitive to possible arrival of neutrinos and cosmic rays of GeV and higher energies. For five (seven) events in the NOvA Far (Near) Detector, timely public alerts from the LIGO/Virgo Collaboration allowed recording of MeV-scale events. No signal candidates were found

First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA

The NOvA experiment has seen a 4.4 σ signal of ¯ ν e appearance in a 2 GeV ¯ ν μ beam at a distance of 810 km. Using 12.33 × 10 20 protons on target delivered to the Fermilab NuMI neutrino beamline, the experiment recorded 27 ¯ ν μ → ¯ ν e candidates with a background of 10.3 and 102 ¯ ν μ → ¯ ν μ candidates. This new antineutrino data are combined with neutrino data to measure the parameters | Δ m 2 32 | = 2.4 8 + 0.11 − 0.06 × 10 − 3     eV 2 / c 4 and sin 2 θ 23 in the ranges from (0.53–0.60) and (0.45–0.48) in the normal neutrino mass hierarchy. The data exclude most values near δ C P = π / 2 for the inverted mass hierarchy by more than 3 σ and favor the normal neutrino mass hierarchy by 1.9 σ and θ 23 values in the upper octant by 1.6 σ