Warianty tytułu
Języki publikacji
Abstrakty
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the complex polynomial (i.e. Borel-Weil) realization of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schrödinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly determine the critical points of the pressure of this “Schrödinger fluid”, together with its vorticity, which turns out to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.
Czasopismo
Rocznik
Tom
Numer
Strony
42-48
Opis fizyczny
Daty
wydano
2010-02-01
online
2009-11-15
Twórcy
autor
- Dipartimento di Informatica, Università degli Studi di Verona, Ca’ Vignal 2, Strada le Grazie 15, I-37134, Verona, Italia, mauro.spera@univr.it
Bibliografia
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- [2] V. I. Arnol’d, B. Khesin, Topological Methods in Hydrodynamics (Springer, Berlin, 1998)
- [3] A. Ashtekar, T. A. Schilling, In: On Einstein’s path (Springer, New York, 1999) 23
- [4] A. Benvegnu, N. Sansonetto, M. Spera, J. Geom. Phys. 51, 229 (2004) http://dx.doi.org/10.1016/j.geomphys.2003.10.008[Crossref]
- [5] A. Benvegnu, M. Spera, Rev. Math. Phys. 18, 1075 (2006) http://dx.doi.org/10.1142/S0129055X06002863[Crossref]
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- [16] P. Griffiths, J. Harris, Principles of Algebraic Geometry (J. Wiley & Sons, New York, 1978)
- [17] T. Guenault, Basic Superfluids (Taylor & Francis, London, 2003)
- [18] R. C. Gunning, Lectures on Riemann Surfaces (Princeton University Press, Princeton, New Jersey, 1966)
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- [20] E. Joos et al., Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin, 2003)
- [21] S. Kobayashi, K. Nomizu, Foundations of Differential Geometry I (Wiley - Interscience Publishers, New York, 1963)
- [22] L. D. Landau, M. E. Lifšits, Quantum Mechanics (Pergamon, London, 1960)
- [23] J. E. Marsden, A. Weinstein, Physica 7 D, 305 (1983)
- [24] D. McDuff, D. Salamon, Introduction to Symplectic Topology (Clarendon Press, Oxford, 1998)
- [25] R. Narasimhan, Lectures on Riemann surfaces (Birkhauser, Basel, 1994)
- [26] V. Penna, M. Spera, J. Geom. Phys. 27, 99 (1998) http://dx.doi.org/10.1016/S0393-0440(97)00070-3[Crossref]
- [27] A. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin, 1986)
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-009-0070-4