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961.
Gyula Bene 《Central European Journal of Physics》2003,1(2):332-343
An “almost diagonal” reduced density matrix (in coordinate representation) is usually a result of environment induced decherence
and is considered the sign of classical behavior. We show that the proton of a ground state hydrogen atom can indeed possess
such a density matrix. This example demonstrates that the “almost diagonal” structure may be derived from an interaction with
a low number of degrees of freedom which play the role of the environment. We also show that decoherence effects in our example
can only be observed if the interaction with the measuring device is significantly faster than the interaction with the environment
(the electron). In the opposite case, when the interaction with the environment is significant during the measurement process,
coherence is maintained. Finally, we propose a neutron scattering experiment on cold He atoms to observe decoherence which
shows up as an additional positive contribution to the differential scattering cross section. This contribution is inversely
proportional to the bombarding energy. 相似文献
962.
We show that if a closed manifold M admits an ℱ-structure (not necessarily polarized, possibly of rank zero) then its minimal entropy vanishes. In particular,
this is the case if M admits a non-trivial S
1-action. As a corollary we obtain that the simplicial volume of a manifold admitting an ℱ-structure is zero.?We also show
that if M admits an ℱ-structure then it collapses with curvature bounded from below. This in turn implies that M collapses with bounded scalar curvature or, equivalently, its Yamabe invariant is non-negative.?We show that ℱ-structures
of rank zero appear rather frequently: every compact complex elliptic surface admits one as well as any simply connected closed
5-manifold.?We use these results to study the minimal entropy problem. We show the following two theorems: suppose that M is a closed manifold obtained by taking connected sums of copies of S
4, ℂP
2,
2,S
2×S
2and the K3 surface. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
4,ℂP
2,S
2×S
2,ℂP
2#
2 or ℂP
2# ℂP
2. Finally, suppose that M is a closed simply connected 5-manifold. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
5,S
3×S
2, then on trivial S
3-bundle over S
2 or the Wu-manifold SU(3)/SO(3).
Oblatum 13-III-2002 & 12-VIII-2002?Published online: 8 November 2002
G.P. Paternain was partially supported by CIMAT, Guanajuato, México.?J. Petean is supported by grant 37558-E of CONACYT. 相似文献
963.
964.
The Spectrum of a Linearized 2D Euler Operator 总被引:1,自引:0,他引:1
We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two-dimensional fluid at a steady state with the vorticity that contains only two nonzero complex conjugate Fourier modes. We prove that the essential spectrum coincides with the imaginary axis, and give an estimate from above for the number of isolated nonimaginary eigenvalues. In addition, we prove that the spectral mapping theorem holds for the group generated by the linearized 2D Euler operator. 相似文献
965.
966.
Marco Andreatta 《manuscripta mathematica》2003,110(4):505-512
We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector
bundle adjunction. We use methods and techniques of the so called Mori theory, in particular the study of rational curves
on projective manifolds.
Received: 16 May 2002 / Revised version: 18 November 2002 Published online: 3 March 2003
Mathematics Subject Classification (2000): 14E30, 14J40, 14J45 相似文献
967.
968.
969.
970.