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 operator's properties. In particular, we derive its spectrum and generalized eigenstates, and treat the example of the free particle.
|Number of pages||6|
|Journal||Comptes Rendus Mathematique|
|State||Published - Nov 2011|
Bibliographical noteFunding Information:
Y.S. acknowledges the support of the Israeli Science Foundation Grants no. 1169/06 and 1105/10, and the Center for Advanced Studies in Mathematics at Ben-Gurion University, where part of this research was conducted. J.S. and S.M. acknowledge the support of the Israeli Science Foundation Grant no. 784/06.