Time reversal for systems with internal symmetry

E. C. G. Sudarshan

Roland Cristopher F. Caballar, Leonard R. Ocampo, Eric A. Galapon

Internal symmetries can be used to classify multiple solutions to the time-energy canonical commutation relation (TE-CCR). The dynamical behavior of solutions to the TE-CCR possessing particular internal symmetries involving time reversal differ significantly from solutions to the TE-CCR without those particular symmetries, implying a connection between the internal symmetries of a quantum system, its internal unitary dynamics, and the TE-CCR.

Jose A. Magpantay

Time-reversal had always been assumed to be a symmetry of physics at the fundamental level. In this paper we will explore the violations of time-reversal symmetry at the fundamental level and the consequence on thermodynamic systems. First, we will argue from current physics that the universe dynamics is not time-reversal invariant. Second, we will argue that any thermodynamic system cannot be isolated completely from the universe. We then discuss how these two make the dynamics of thermodynamics systems very weakly irreversible at the classical and quantum level. Since time-reversal is no longer a symmetry of realistic systems, the problem of how macroscopic irreversibility arises from microscopic reversibility becomes irrelevant because there is no longer microscopic reversibility. At the classical level of a thermodynamic system, we show that the H theorem of Boltzmann is still valid even without microscopic reversibility. We do this by deriving a modified H theorem, which still shows entropy monotonically increasing. At the quantum level, we explicitly show the effect of CP violation, small irreversible changes on the internal states of the nuclear and atomic energy levels of thermodynamic systems. Thus, we remove Loschmidt's objection to Boltzmann's ideas.

Woon Siong Gan

Lea E. Bottini, Nick G. Jones

Symmetry under time-reversal appears in the microscopic description of many physical systems. In a quantum mechanical setting it acts as an anti-unitary operator, so does not fall under general analyses based on unitary symmetries. In classifying zero temperature phases of matter in (1+1)d lattice models, the role of anti-unitary symmetries is, however, well-understood. In recent years, the Symmetry Topological Field Theory (SymTFT) approach to this classification has given a general framework to understand symmetries as topological defects, but does not naturally include anti-unitary symmetries. Following recent proposals in the literature, we adopt a symmetry-enriched SymTFT for a theory with both internal and time-reversal symmetry. In particular, we take a standard SymTFT associated with an internal unitary symmetry that is then enriched by a background time-reversal symmetry. A detailed analysis of the topological boundary conditions of this enriched SymTFT allows us to characterize the corresponding (1+1)d gapped phases that preserve the enriching symmetry (i.e. those that do not spontaneously break this symmetry in the ground state). Line operators in the SymTFT approach are related to non-local string-order parameters (with charged end-point operators) for SPT phases. These are subtle in the anti-unitary case and we explore them both on the lattice and in the continuum. We include an analysis of unitary string order parameters that reveal the Klein bottle SPT invariant. On the lattice, we show that the correct end-point charge coincides with the time-reversal-charge only when the end-point operator is hermitian.

P. Sisterna