Rotational-permutational dual-pairing and long-lived spin order

Abstract

Quantum systems in contact with a thermal environment experience coherent and incoherent dynamics. These drive the system back towards thermal equilibrium after an initial perturbation. The relaxation process involves the reorganisation of spin state populations and the decay of spin state coherences. In general individual populations and coherences may exhibit different relaxation time constants. Particular spin configurations may exhibit exceptionally long relaxation time constants. Such spin configurations are known as long-lived spin order. The existence of long-lived spin order is a direct consequence of the symmetries of the system. For nuclear spin systems rotational and permutational symmetries are of fundamental importance. Based on the Schur-Weyl duality theorem we describe a theoretical framework for the study of rotational and permutational dual-symmetries in the context of long-lived spin order. Making use of the proposed formalism we derive exact bounds on the number on long-lived spin populations and coherences for systems exhibiting rotational-permutational dual-symmetries.

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