In this paper, the symmetry property of time reversal, which is a consequence of the fundamental quantum-mechanical microreversibility principle, is analyzed in the context of relativistic open-shell and multireference coupled cluster theory. The fact is discussed that in projective theories, in contrast to variational theories such as configuration interaction models, the implementation of time-reversal symmetry is far less straightforward and even depends on the projective model theory in question. An operator basis of time reversal even $n$ -body operators is introduced which allows for the formulation of a fully time-reversal-adapted and practical general coupled cluster theory, i.e., covering open-shell models and various types of multireference approaches. The resulting model theory is noncommuting but truncating, albeit at a higher order of commutator nesting.In this paper, the symmetry property of time reversal, which is a consequence of the fundamental quantum-mechanical microreversibility principle, is analyzed in the context of relativistic open-shell and multireference coupled cluster theory. The fact is discussed that in projective theories, in contrast to variational theories such as configuration interaction models, the implementation of time-reversal symmetry is far less straightforward and even depends on the projective model theory in question. An operator basis of time reversal even $n$-body operators is introduced which allows for the formulation of a fully time-reversal-adapted and practical general coupled cluster theory, i.e., covering open-shell models and various types of multireference approaches. The resulting model theory is noncommuting but truncating, albeit at a higher order of commutator nesting.

Physical Review AJun 4, 200810 citations

NON-HERMITIAN QUANTUM MECHANICS

Katherine Jones-Smith

The basic structure of quantum mechanics was delineated in the early days of the theory and has not been modified since.One of the fundamental assumptions used in formulating the theory is that operators are represented by Hermitian matrices.In recent years it has been shown that quantum mechanics can be formulated consistently without making this assumption, using instead a combination of the parity (P) and time-reversal (T) operators and a number of other requirements related to P and T .Only the case of even T has been analyzed in the literature; here we generalize the principles to include odd time-reversal.We use this generalization to construct a non-Hermitian version of the Dirac equation, and in doing so discover a new type of particle not allowed within the (Hermitian) Standard Model.Finally we present a potential application of the ideas of non-Hermitian quantum mechanics to the unsolved problems of quantum magnetism and high temperature superconductivity.The basic structure of quantum mechanics was delineated in the early days of the theory and has not been modified since.One of the fundamental assumptions used in formulating the theory is that operators are represented by Hermitian matrices.In recent years it has been shown that quantum mechanics can be formulated consistently without making this assumption, using instead a combination of the parity (P) and time-reversal (T) operators and a number of other requirements related to P and T .Only the case of even T has been analyzed in the literature; here we generalize the principles to include odd time-reversal.We use this generalization to construct a non-Hermitian version of the Dirac equation, and in doing so discover a new type of particle not allowed within the (Hermitian) Standard Model.Finally we present a potential application of the ideas of non-Hermitian quantum mechanics to the unsolved problems of quantum magnetism and high temperature superconductivity.

Jan 1, 20107 citations

Operational approach to time and clocks in quantum theory

Sandra Stupar

Jan 1, 20180 citations

Dynamical resource theory of time-reversal symmetry breaking

Jisho Miyazaki, Kohdai Kuroiwa, Mio Murao

Time-reversal symmetry and its violation (T-violation) are fundamental across diverse physics domains, from particle physics to fluctuation theorems and reciprocity. While time-reversal symmetry for isolated systems is simply determined by the Hamiltonian, quantifying the magnitude of T-violation, especially in noisy quantum processes, has been a subject of ongoing debate. Here, we propose an operationally meaningful framework to quantify the intrinsic T-violation of quantum channels. We integrate operationally defined time-reversal transformations into dynamical resource theory to formulate T-violation as a resource. T-violation decomposes into two distinct components: kinematic T-violation originating from antiunitary motion-reversal, and nonunitality driven purely by thermodynamics. This decomposition resolves the longstanding confusion between broken time-reversal symmetry and non-invertibility. Finally, we analyze the resulting resource theory of kinematic T-violation, showing that it is neither quality-like nor quantity-like, and proving the existence of a universal golden unit even within classical channels.Time-reversal symmetry and its violation (T-violation) are fundamental across diverse physics domains, from particle physics to fluctuation theorems and reciprocity. While time-reversal symmetry for isolated systems is simply determined by the Hamiltonian, quantifying the magnitude of T-violation, especially in noisy quantum processes, has been a subject of ongoing debate. Here, we propose an operationally meaningful framework to quantify the intrinsic T-violation of quantum channels. We integrate operationally defined time-reversal transformations into dynamical resource theory to formulate T-violation as a resource. T-violation decomposes into two distinct components: kinematic T-violation originating from antiunitary motion-reversal, and nonunitality driven purely by thermodynamics. This decomposition resolves the longstanding confusion between broken time-reversal symmetry and non-invertibility. Finally, we analyze the resulting resource theory of kinematic T-violation, showing that it is neither quality-like nor quantity-like, and proving the existence of a universal golden unit even within classical channels.

quant-pharXiv:2609.36408Sep 30, 20260 citations

Understanding Time Reversal in Quantum Mechanics: A New Derivation

Shan Gao

Foundations of PhysicsOct 1, 20221 citation

n

-body operators is introduced which allows for the formulation of a fully time-reversal-adapted and practical general coupled cluster theory, i.e., covering open-shell models and various types of multireference approaches. The resulting model theory is noncommuting but truncating, albeit at a higher order of commutator nesting.