Typicality of the response by quantum pure states

Typicality of the response by quantum pure states Barbara Fresch, Giorgio J. Moro Dipartimento di Science Chimiche, Università di Padova, via Marzolo 1, 35131 Padova, Italy Mainly because of the objective of realizing quantum computers, in recent years an intense research activity has been developed about the statistical and dynamical properties of quantum pure states, that is of quantum systems without entanglement with the environment. In such a framework several fundamental issues have been risen, concerning for instance the description of equilibrium properties [1-4]. Indeed, in opposition to standard microcanonical quantum description, one has to take into account that different quantum pure states, with well defined sets of populations for the Hamiltonian eigenstates [5], are compatible with a given macrostate. We have proposed the Random Pure State Ensemble (RPSE) as the self-consistent statistical ensemble of quantum pure states, which is able to generate a macroscopic description in agreement with thermodynamics [6,7]. More recently we have analyzed the predictions of RPSE statistics in presence of an external time dependent field, in order to test its capability of supplying the correct framework for the study of dynamical properties [8]. Several important features emerge from the simulations of spin systems, like the relaxation after a quench. It is shown that typicality of equilibrium states is generalized to the response, so that the dynamical properties become independent of the particular realization of the quantum pure state. [1] J. Gemmer, M. Michel, G. Mahler, Quantum Thermodynamics (Springer, New York, 2004). [2] S. Goldestein, J.L. Lebowitz, R. Tumulka, N. Zanghi, Phys. Rev. Lett. 96 (2006), 050403; S. Goldstein, J.L. Lebowitz, C. Mastrodonato, R. Tumulka, N. Zanghi, Phys. Rev. E 81 (2010), 0111098. [3] S. Popescu, A.J. Short, A. Winter, Nature Phys. 2 (2006); N. Linden, S. Popescu, A.J. Short, A. Winter, Phys. Rev. E 79 (2009), 055021. [4] P. Reiman, Phys. Rev. Lett. 99 (2007) 160404, Phys. Rev. Lett. 101 (2008) 190403. [5] B. Fresch and G. J. Moro, J. Phys. Chem. A 113 (2009), 14502. [6] B. Fresch and G. J. Moro J. Chem. Phys. 133 (2010), 034509, 034510. [7] B. Fresch and G. J. Moro, J. Chem. Phys. 134 (2011), 054510. [8] B. Fresch and G. J. Moro, (2011) arXiv:1104.4625.