A geometric framework for spin relaxation
Abstract
Spin relaxation is conventionally described by two independent phenomenological rates - longitudinal (R1) and transverse (R2) - whose separation obscures a deeper structural unity. Here we develop a geometric framework in which dissipation is represented by a single covariant relaxation tensor acting in Liouville space, from which R1 and R2 emerge as complementary projections. This tensor structure is not merely formal but is experimentally accessible through pulse sequences that probe noncommuting directions in spin space. Using hyperpolarized 13C spins in diamond with nitrogen-vacancy centers, we show that commuting pulse trains yield effective relaxation matrices that are approximately diagonal, while noncommuting sequences produce off-diagonal components that vary with transmitter frequency offset and pulse ordering, providing evidence that relaxation is a directional process governed by a tensor rather than a pair of scalar rates. Complementary measurements of geometric phase demonstrate that noncommuting dynamics introduce ordering-dependent effects that are separable from dissipation, consistent with the interpretation of relaxation as geometric transport on the state manifold. This framework unifies Bloch, Redfield, and Lindblad descriptions within a coordinate-independent formulation and provides a natural language for relaxation in driven, anisotropic, and non-equilibrium spin systems.
Versions
Related
- Spin-Hall devices: spin relaxation spatially separates current injection from Joule dissipation
- Quantum Relaxation Dynamics of Vacuum Energy from Pre-Geometric Gravity
- Resonant spin mode from retarded relaxation
- Information-geometric bounds on nonequilibrium relaxation in quantum Markov dynamics
- Spin Relaxation and Electrical Control of Spin Transport in Few-Layer Td-MoTe2
BibTeX
@misc{fricke2026geometric,
title = {{A geometric framework for spin relaxation}},
author = {Sophia N. Fricke and Kieren A. Harkins and Ashok Ajoy and Jeffrey A. Reimer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.21569},
eprint = {2607.21569},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21569},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A geometric framework for spin relaxation
AU - Sophia N. Fricke
AU - Kieren A. Harkins
AU - Ashok Ajoy
AU - Jeffrey A. Reimer
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2607.21569
UR - https://arxiv.org/abs/2607.21569
AB - Spin relaxation is conventionally described by two independent phenomenological rates - longitudinal (R_1) and transverse (R_2) - whose separation obscures a deeper structural unity. Here we develop a geometric framework in which dissipation is represented by a single covariant relaxation tensor acting in Liouville space, from which R_1 and R_2 emerge as complementary projections. This tensor structure is not merely formal but is experimentally accessible through pulse sequences that probe noncommuting directions in spin space. Using hyperpolarized ^13C spins in diamond with nitrogen-vacancy centers, we show that commuting pulse trains yield effective relaxation matrices that are approximately diagonal, while noncommuting sequences produce off-diagonal components that vary with transmitter frequency offset and pulse ordering, providing evidence that relaxation is a directional process governed by a tensor rather than a pair of scalar rates. Complementary measurements of geometric phase demonstrate that noncommuting dynamics introduce ordering-dependent effects that are separable from dissipation, consistent with the interpretation of relaxation as geometric transport on the state manifold. This framework unifies Bloch, Redfield, and Lindblad descriptions within a coordinate-independent formulation and provides a natural language for relaxation in driven, anisotropic, and non-equilibrium spin systems.
ER -