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Register a new userOn the Geodesic Nature of Wegners Flow
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Wegners method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding flow of a quantum state becomes geodesic in a submanifold of the projective Hilbert space, independently of specific initial conditions. This implies the geometric optimality of the present method as an algorithm of generating stationary states. The result is illustrated by analyzing some physical examples.
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We completely integrate the magnetic geodesic flow on a flat two-torus with the magnetic field $F = cos (x) dx wedge dy$ and describe all contractible periodic magnetic geodesics. It is shown that there are no such geodesics for energy $E geq 1/2$, for $E< 1/2$ simple periodic magnetic geodesics form two $S^1$-families for which the (fixed energy) action functional is positive and therefore there are no periodic magnetic geodesics for which the action functional is negative.
Microfludic channels are now a well established platform for many purposes, including bio-medical research and Lab on a Chip applications. However, the nature of flow within these channels is still unclear. There is evidence that the mean drift velocity in these channels deviates from the regular Navier-Stokes solution with `no slip boundary conditions. Understanding these effects, is not only of value for fundamental fluid mechanics interest, but it also has practical importance for the future development of microfluidic and nanofludic infrastructures. We propose a nano-NMR based setup for measuring the drift velocity near the surface of a microfludic channel in a non-intrusive fashion. We discuss different possible protocols, and provide a detailed analysis of the measurements sensitivity in each case. We show that the nano-NMR scheme outperforms current fluorescence based techniques.
This note describes the behavior of null-geodesics near nondegenerate Killing horizons in language amenable to the application of a general framework, due to Vasy and Hintz, for the analysis of both linear and nonlinear wave equations. Throughout, the viewpoint of Melroses b-geometry on a suitable compactification of spacetime at future infinity is adopted.
We relate the existence of many infinite geodesics on Alexandrov spaces to a statement about the average growth of volumes of balls. We deduce that the geodesic flow exists and preserves the Liouville measure in several important cases. The developed analytic tool has close ties to integral geometry.
In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real-analytic Riemannian manifold. Motivated by the complexifier approach of T. Thiemann as well as certain formulas of V. Guillemin and M. Stenzel, we obtain the polarization associated to the adapted complex structure by applying the imaginary-time geodesic flow to the vertical polarization. Meanwhile, at the level of functions, we show that every holomorphic function is obtained from a function that is constant along the fibers by composition with the imaginary-time geodesic flow. We give several equivalent interpretations of this composition, including a convergent power series in the vector field generating the geodesic flow.
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