Exact solutions of n-level systems and gauge theories

We find a relationship between unitary transformations of the dynamics of quantum systems with time-dependent Hamiltonians and gauge theories. In particular, we show that the nonrelativistic dynamics of spin-$\frac12$ particles in a magnetic field $B^i (t)$ can be formulated in a natural way as an SU(2) gauge theory, with the magnetic field $B^i(t)$ playing the role of the gauge potential A^i. The present approach can also be applied to systems of n levels with time-dependent potentials, U(n) being the gauge group. This geometric interpretation provides a powerful method to find exact solutions of the Schr\"odinger equation. The root of the present approach rests in the Hermiticity property of the Hamiltonian operators involved. In addition, the relationship with true gauge symmetries of n-level quantum systems is discussed.Comment: LaTeX file, 5 pages, published versio

Real-time remote sensing driven river basin modeling using radar altimetry

Many river basins have a weak in-situ hydrometeorological monitoring infrastructure. However, water resources practitioners depend on reliable hydrological models for management purposes. Remote sensing (RS) data have been recognized as an alternative to in-situ hydrometeorological data in remote and poorly monitored areas and are increasingly used to force, calibrate, and update hydrological models. <br><br> In this study, we evaluate the potential of informing a river basin model with real-time radar altimetry measurements over reservoirs. We present a lumped, conceptual, river basin water balance modeling approach based entirely on RS and reanalysis data: precipitation was obtained from the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA), temperature from the European Centre for Medium-Range Weather Forecast's (ECMWF) Operational Surface Analysis dataset and reference evapotranspiration was derived from temperature data. The Ensemble Kalman Filter was used to assimilate radar altimetry (ERS2 and Envisat) measurements of reservoir water levels. The modeling approach was applied to the Syr Darya River Basin, a snowmelt-dominated basin with large topographical variability, several large reservoirs and scarce hydrometeorological data that is located in Central Asia and shared between 4 countries with conflicting water management interests. <br><br> The modeling approach was tested over a historical period for which in-situ reservoir water levels were available. Assimilation of radar altimetry data significantly improved the performance of the hydrological model. Without assimilation of radar altimetry data, model performance was limited, probably because of the size and complexity of the model domain, simplifications inherent in model design, and the uncertainty of RS and reanalysis data. Altimetry data assimilation reduced the mean absolute error of the simulated reservoir water levels from 4.7 to 1.9 m, and overall model RMSE from 10.3 m to 6.7 m. Model performance was variable for the different reservoirs in the system. The RMSE ranged from 10% to 76% of the mean seasonal reservoir level variation. <br><br> Because of its easy accessibility and immediate availability, radar altimetry lends itself to being used in real-time hydrological applications. As an impartial source of information about the hydrological system that can be updated in real time, the modeling approach described here can provide useful medium-term hydrological forecasts to be used in water resources management

Vortex lines of the electromagnetic field

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schroedinger wave mechanics to Maxwell theory. It is shown that time evolution of vortex lines has universal features; in Maxwell theory it is very similar to that in Schroedinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of Maxwell equations with embedded vortex lines are given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.Comment: 11 pages, 6 figures, to be published in Phys. Rev.

Abelian Magnetic Monopole Dominance in Quark Confinement

We prove Abelian magnetic monopole dominance in the string tension of QCD. Abelian and monopole dominance in low energy physics of QCD has been confirmed for various quantities by recent Monte Carlo simulations of lattice gauge theory. In order to prove this dominance, we use the reformulation of continuum Yang-Mills theory in the maximal Abelian gauge as a deformation of a topological field theory of magnetic monopoles, which was proposed in the previous article by the author. This reformulation provides an efficient way for incorporating the magnetic monopole configuration as a topological non-trivial configuration in the functional integral. We derive a version of the non-Abelian Stokes theorem and use it to estimate the expectation value of the Wilson loop. This clearly exhibits the role played by the magnetic monopole as an origin of the Berry phase in the calculation of the Wilson loop in the manifestly gauge invariant manner. We show that the string tension derived from the diagonal (abelian) Wilson loop in the topological field theory (studied in the previous article) converges to that of the full non-Abelian Wilson loop in the limit of large Wilson loop. Therefore, within the above reformulation of QCD, this result (together with the previous result) completes the proof of quark confinement in QCD based on the criterion of the area law of the full non-Abelian Wilson loop.Comment: 33 pages, Latex, no figures, version accepted for publication in Phys. Rev. D (additions of sec. 4.5 and references, and minor changes

Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics

To build genuine generators of the rotations group in noncommutative quantum mechanics, we show that it is necessary to extend the noncommutative parameter $\theta$ to a field operator, which one proves to be only momentum dependent. We find consequently that this field must be obligatorily a dual Dirac monopole in momentum space. Recent experiments in the context of the anomalous Hall effect provide for a monopole in the crystal momentum space. We suggest a connection between the noncommutative field and the Berry curvature in momentum space which is at the origine of the anomalous Hall effect.Comment: 4 page

Solar variability and planetary alignments

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