“Maurice A. de Gosson”的意思、由来-开放百科全书

After completing his PhD in microlocal analysis at the University of Nice in 1978 under the supervision of Jacques Chazarain, de Gosson soon became fascinated by Jean Leray's Lagrangian analysis. Under Leray's tutorship de Gosson completed a Habilitation à Diriger des Recherches en Mathématiques at the University of Paris 6 (1992). During this period he specialized in the study of the Leray–Maslov index and in the theory of the metaplectic group, and their applications to mathematical physics. In 1998 de Gosson met Basil Hiley, who triggered his interest in conceptual question in quantum mechanics. Basil Hiley wrote a foreword to de Gosson's book The Principles of Newtonian and Quantum Mechanics (Imperial College Press, London).

After having spent several years in Sweden as Associate Professor and Professor in Sweden, de Gosson was appointed in 2006 at the Numerical Harmonic Analysis Group of the University of Vienna, created by Hans Georg Feichtinger (see www.nuhag.eu). He currently works in symplectic methods in harmonic analysis, and on conceptual questions in quantum mechanics, often in collaboration with Basil Hiley.^[4]^[5]

Visiting positions

,^[8] University of Potsdam, Albert-Einstein-Institut (Golm), Max-Planck-Institut für Mathematik (Bonn), Université Paul Sabatier (Toulouse), Jacobs Universität (Bremen)

The symplectic camel

Maurice de Gosson was the first to prove that Mikhail Gromov's symplectic non-squeezing theorem (also called „the Principle of the Symplectic Camel“) allowed the derivation of a classical uncertainty principle formally totally similar to the Robertson–Schrödinger uncertainty relations (i.e. the Heisenberg inequalities in a stronger form where the covariances are taken into account).^[9] This rather unexpected result was discussed in the media.^[10]

Quantum blobs

In 2003, Gosson introduced the notion of quantum blobs, which are defined in terms of symplectic capacities and are invariant under canonical transformations.^[11] Shortly after,^[12] he showed that Gromov's non-squeezing theorem allows a coarse graining of phase space by such quantum blobs (or symplectic quantum cells), each described by a mean momentum and a mean position:

Their invariance property distinguishes de Gosson's quantum blobs from the "quantum cells" known in thermodynamics, which are units of phase space with a volume of the size of Planck's constant h to the power of 3.^[15]^[16]

Together with G. Dennis and Basil Hiley, de Gosson laid out examples of how the quantum blob can be seen as a "blow-up" of a particle in phase space. To demonstrate this, they picking up on “Fermi's trick”^[17] which allows to identify an arbitrary wavefunction as a stationary state for some Hamiltonian operator. They showed that this blow-up requires internal energy that comes from the particle itself, involving the kinetic energy and David Bohm's quantum potential.^[18]^[19]

Influence

De Gosson's notion of quantum blobs has given rise to a proposal for a new formulation of quantum mechanics, which is derived from postulates on quantum-blob-related limits to the extent and localization of quantum particles in phase space;^[14]^[21] this proposal is strengthened by the development of a phase space approach that applies to both quantum and classical physics, where a quantum-like evolution law for observables can be recovered from the classical Hamiltonian in a non-commutative phase space, where x and p are (non-commutative) c-numbers, not operators.^[22]

Publications

Books

Selected recent papers

References

1. ^Biography at the NuHAG website – University of Vienna, ( )
2. ^Numerical Harmonic Analysis Group website, University of Vienna ( )
3. ^Homepage at the NuHAG website – University of Vienna, ( )
4. ^University website, short biography – 2011 ( )
5. ^University website, Research section( )
6. ^AMS.org - Mathematics Calendar( )
7. ^IOPscience, ip.org ( )
8. ^AMS.org - Mathematics Calendar( )
9. ^Reich, New Scientist – ([https://www.newscientist.com/article/mg20126973.900-how-camels-could-explain-quantum-uncertainty.html]), 2009
10. ^{{Cite web | last = Samuel Reich| first = Eugenie | title = How camels could explain quantum uncertainty | url = https://www.newscientist.com/article/mg20126973.900-how-camels-could-explain-quantum-uncertainty.html | publisher = New Scientist | date = 26 February 2009 | accessdate = 18 December 2013 }}
11. ^{{cite journal|last1=de Gosson|first1=Maurice A|title=Phase space quantization and the uncertainty principle|journal=Physics Letters A|volume=317|issue=5-6|year=2003|pages=365–369|issn=0375-9601|doi=10.1016/j.physleta.2003.09.008|bibcode=2003PhLA..317..365D}}
12. ^M. de Gosson (2004), Phys. Lett. A, vol. 330, pp. 161 ff., and M. de Gosson (2005), Bull. Sci. Math., vol. 129, pp. 211, both cited according to M. de Gosson (2005), Symplectically covariant Schrödinger equation in phase space, Journal of Physics A, Mathematics and General, vol. 38, pp. 9263-9287 (2005)
13. ^Maurice A. de Gosson: On the goodness of "quantum blobs" in phase space quantization, [https://arxiv.org/abs/quant-ph/0407129v1 arXiv:quant-ph/0407129v1], submitted 16 July 2004 (however, dated February 1, 2008)
14. ^¹Maurice A. de Gosson: Quantum blobs, [https://arxiv.org/abs/1106.5468v1 https://arxiv.org/abs/1106.5468v1], submitted 27 June 2011
15. ^The symplectic camel: the tip of an iceberg?, website of Maurice A. de Gosson, downloaded October 5, 2012
16. ^M. A. de Gosson: The Principles of Newtonian & Quantum Mechanics: The Need for Planck's Constant, h, Imperial College Press, 2001, {{ISBN|978-1860942747}}, p. 120
17. ^Maurice A. de Gosson: A Geometric Picture of the Wave Function: Fermi's Trick, [https://arxiv.org/abs/1208.0908 arXiv:1208.0908], 4 August 2012
18. ^{{cite journal|last1=Dennis|first1=Glen|last2=de Gosson|first2=Maurice A.|last3=Hiley|first3=Basil J.|title=Fermi's ansatz and Bohm's quantum potential|journal=Physics Letters A|volume=378|issue=32-33|year=2014|pages=2363–2366|issn=0375-9601|doi=10.1016/j.physleta.2014.05.020|bibcode=2014PhLA..378.2363D}}
19. ^Glen Dennis, Maurice de Gosson, Basil Hiley: Bohm's Quantum Potential as an Internal Energy. [https://arxiv.org/abs/1412.5133 arXiv:1412.5133], 15 December 2014
20. ^See for example: B. J. Hiley: Foundations of Quantum Theory in the Light of Bohmian Non-commutative Dynamics, The Finnish Society for Natural Philosophy 25 Years K.V. Laurikainen Honorary Symposium 2013 / 2 April 2014
21. ^D. Dragoman: Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem, 2005 Physica Scripta, vol. 72, no. 2, pp. 290–295, {{DOI|10.1238/Physica.Regular.072a00290}}, [https://arxiv.org/abs/quant-ph/0402100 arXiv:quant-ph/0402100] submitted 16 February 2004
22. ^D. Dragoman: Quantum-like classical mechanics in non-commutative phase space, Proceedings of the Romanian Academy, Series A, vol. 12, no. 2/2011, pp. 95–99 (full text)
23. ^¹Springer, ([https://www.springer.com/?SGWID=0-102-24-0-0&searchType=EASY_CDA&queryText=de+Gosson])
24. ^Journal de Mathématiques Pures et Appliquées Volume 96, Issue 5, ( )
25. ^J. Pseudo-Differ. Oper. Appl. 2 (2011), no. 1, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/publications.html?pg1=ISSI&s1=291105])
26. ^Phys. Rep. 484 (2009), no. 5, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/publications.html?pg1=ISSI&s1=278137])
27. ^Found. Phys. 39 (2009), no. 2, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/journaldoc.html?cn=Found_Phys])
28. ^J. Math. Pures Appl. (9) 91(2009), no. 6, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/publications.html?pg1=ISSI&s1=274281])

Work