Time reversal and symmetries of time correlation functions |
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Authors: | Alessandro Coretti Lamberto Rondoni Giovanni Ciccotti |
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Affiliation: | 1. Department of Mathematical Sciences, Politecnico di Torino , Torino, Italy;2. Department of Mathematical Sciences, Politecnico di Torino , Torino, Italy;3. Department of Mathematical Sciences and Graphene@PoliTO Lab, Politecnico di Torino , Torino, Italy;4. Istituto Nazionale di Fisica Nucleare, Sezione di Torino , Torino, Italy;5. Institute for Applied Computing “Mauro Picone” (IAC), CNR , Rome, Italy;6. School of Physics, University College of Dublin UCD-Belfield , Dublin, Ireland;7. Department of Physics, Università di Roma La Sapienza , Rome, Italy |
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Abstract: | ABSTRACTThe time reversal invariance of classical dynamics is reconsidered in this paper with specific focus on its consequences for time correlation functions and associated properties such as transport coefficients. We show that, under fairly common assumptions on the interparticle potential, an isolated Hamiltonian system obeys more than one time reversal symmetry and that this entails non trivial consequences. Under an isotropic and homogeneous potential, in particular, eight valid time reversal operations exist. The presence of external fields that reduce the symmetry of space decreases this number, but does not necessarily impair all time reversal symmetries. Thus, analytic predictions of symmetry properties of time correlation functions and, in some cases, even of their null value are still possible. The noteworthy case of a constant external magnetic field, usually assumed to destroy time reversal symmetry, is considered in some detail. We show that, in this case too, some of the new time reversal operations hold, and that this makes it possible to derive relevant properties of correlation functions without the uninteresting inversion of the direction of the magnetic field commonly enforced in the literature. |
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Keywords: | Time reversal symmetry Hamiltonian system correlation functions linear response theory magnetic field electric field |
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