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321.
We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification. 相似文献
322.
323.
324.
Imre Bárány Krystyna Kuperberg Tudor Zamfirescu 《Discrete and Computational Geometry》2003,30(2):167-176
This paper gives a partial confirmation of a conjecture of
Agarwal, Har-Peled, Sharir, and Varadarajan that the total
curvature of a
shortest path on the boundary of a convex polyhedron in R
3
cannot be
arbitrarily large. It is shown here that the conjecture holds for a class of
polytopes
for which the ratio of the radii of the circumscribed and inscribed ball is
bounded. On
the other hand, an example is constructed to show that the total curvature
of a
shortest path on the boundary of a convex polyhedron in R
3 can
exceed 2. Another example shows that the spiralling number of a
shortest path on the boundary of a convex polyhedron can be arbitrarily
large. 相似文献
325.
326.
Tudor Zamfirescu 《Geometriae Dedicata》1996,62(1):99-105
This paper discusses conjugate points on the geodesics of convex surfaces. It establishes their relationship with the cut locus. It shows the possibility of having many geodesics with conjugate points at very large distances from each other. It also shows that on many surfaces there are arbitrarily many closed geodesic arcs originating and ending at a common point. To achieve these goals, Baire category methods are employed. 相似文献
327.
Tudor Zamfirescu 《Geometriae Dedicata》1981,10(1-4):205-217
328.
Tudor Zamfirescu 《Monatshefte für Mathematik》1987,103(3):241-247
In the sense of Baire categories, most convex curves on a smooth twodimensional closed convex surface are smooth. Moreover, if the set of all closed geodesics has empty interior in the space of all convex curves, then most convex curves are strictly convex.This paper was written during the author's visit at Western Washington University, whose substantial support is acknowledged. 相似文献
329.
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element. 相似文献
330.
Marco Castrilló n Ló pez Tudor S. Ratiu Steve Shkoller 《Proceedings of the American Mathematical Society》2000,128(7):2155-2164
Let be a principal -bundle, and let be a -invariant Lagrangian density. We obtain the Euler-Poincaré equations for the reduced Lagrangian defined on , the bundle of connections on .