TY - JOUR

T1 - Revisiting the Mazur bound and the Suzuki equality

AU - Dhar, Abhishek

AU - Kundu, Aritra

AU - Saito, Keiji

N1 - Funding Information:
We thank Sriram Shastry and Peter Young for very useful comments and suggestions. A.D. acknowledges support of the Department of Atomic Energy, Government of India, under project no.12-R& D-TFR-5.10-1100. K.S. was supported by Grants-in-Aid for Scientific Research (JP16H02211, JP19H05603, JP19H05791).
Publisher Copyright:
© 2020

PY - 2021/3

Y1 - 2021/3

N2 - Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality. The Mazur inequality gives a lower bound, on the long-time average of the time-dependent auto-correlation function of observables, in terms of equilibrium correlation functions involving conserved quantities. On the other hand, Suzuki proposes an exact equality for quantum systems. In this paper, we discuss the relation between the two results and in particular, look for the analogue of the Suzuki result for classical systems. This requires us to examine as to what constitutes a complete set of conserved quantities required to saturate the Mazur bound. We present analytic arguments as well as illustrative numerical results from a number of different systems. Our examples include systems with few degrees of freedom as well as many-particle integrable models, both free and interacting.

AB - Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality. The Mazur inequality gives a lower bound, on the long-time average of the time-dependent auto-correlation function of observables, in terms of equilibrium correlation functions involving conserved quantities. On the other hand, Suzuki proposes an exact equality for quantum systems. In this paper, we discuss the relation between the two results and in particular, look for the analogue of the Suzuki result for classical systems. This requires us to examine as to what constitutes a complete set of conserved quantities required to saturate the Mazur bound. We present analytic arguments as well as illustrative numerical results from a number of different systems. Our examples include systems with few degrees of freedom as well as many-particle integrable models, both free and interacting.

KW - Auto-correlation functions and ergodicity

KW - Integrable systems

KW - Mazur bound

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U2 - 10.1016/j.chaos.2020.110618

DO - 10.1016/j.chaos.2020.110618

M3 - Article

AN - SCOPUS:85099514064

VL - 144

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

M1 - 110618

ER -