Article

Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text
Advertising


Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    6 0 0 0


Comptes Rendus Mathématique
Volume 349, n° 19-20
pages 1117-1122 (novembre 2011)
Doi : 10.1016/j.crma.2011.09.007
Received : 24 November 2010 ;  accepted : 12 September 2011
Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics
Étude dʼun opérateur auto-adjoint qui indique la direction du temps en mécanique quantique
 

Yossef Strauss a , Jonathan Silman b, 1 , Shai Machnes b, 2 , Lawrence P. Horwitz b, c, d
a Einstein Institute of Mathematics, Edmond J. Safra campus, The Hebrew University of Jerusalem, Jerusalem 91904, Israel 
b School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel 
c Physics Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel 
d Department of Physics, The Ariel University Center of Samaria, Ariel 40700, Israel 

Abstract

In [Y. Strauss, Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schrödinger evolution, J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its expectation value decreases monotonically for any initial state. In this paper we study some of this operatorʼs properties. In particular, we derive its spectrum and generalized eigenstates, and treat the example of the free particle.

The full text of this article is available in PDF format.
Résumé

Dans [Y. Strauss, Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schrödinger evolution, J. Math. Phys. 51 (2010) 022104], un opérateur auto-adjoint a été introduit ayant la propriété dʼindiquer la direction du temps dans le formalisme standard de la mécanique quantique, au sens où sa valeur moyenne décroit de façon monotone avec le temps pour tout état initial. Dans cet article, nous étudions les propriétés de cet opérateur. En particulier, nous dérivons son spectre et ses vecteurs propres généralisés et traitons en détail lʼexample de la particule libre

The full text of this article is available in PDF format.
1  Present address: Laboratoire dʼinformation quantique, université libre de Bruxelles, B-1050 Bruxelles, Belgium.
2  Present address: Institut für Theoretische Physik, Universität Ulm, 89069 Ulm, Germany.


© 2011  Académie des sciences@@#104156@@
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Close
Article Outline
You can move this window by clicking on the headline
@@#110903@@