(A)Symmetric Complexity and the Quantum Mpemba Effect
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915487418417152 |
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| author | Beetar, Cameron Murugan, Jeff van Zyl, Hendrik J. R. |
| author_facet | Beetar, Cameron Murugan, Jeff van Zyl, Hendrik J. R. |
| contents | The Quantum Mpemba Effect (QME) -- the counter-intuitive phenomenon where states further from equilibrium can relax faster than those closer to it -- challenges standard expectations of quantum thermalization. In this work, we introduce Krylov complexity as a sensitive diagnostic for the QME. We show that Krylov spread complexity encodes the asymmetry essential to the effect, and we define a new class of projective (a)symmetric complexities that sharpen this connection. Strikingly, the structure of these projective complexities at the initial moment ($t=0$) already carries predictive power for the onset of Mpemba-like inversions, obviating the need for explicit time evolution. Our results suggest that the geometry of states in Krylov space captures deep information about non-monotonic relaxation and provides a powerful framework for diagnosing and anticipating anomalous thermalization phenomena in quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | (A)Symmetric Complexity and the Quantum Mpemba Effect Beetar, Cameron Murugan, Jeff van Zyl, Hendrik J. R. High Energy Physics - Theory The Quantum Mpemba Effect (QME) -- the counter-intuitive phenomenon where states further from equilibrium can relax faster than those closer to it -- challenges standard expectations of quantum thermalization. In this work, we introduce Krylov complexity as a sensitive diagnostic for the QME. We show that Krylov spread complexity encodes the asymmetry essential to the effect, and we define a new class of projective (a)symmetric complexities that sharpen this connection. Strikingly, the structure of these projective complexities at the initial moment ($t=0$) already carries predictive power for the onset of Mpemba-like inversions, obviating the need for explicit time evolution. Our results suggest that the geometry of states in Krylov space captures deep information about non-monotonic relaxation and provides a powerful framework for diagnosing and anticipating anomalous thermalization phenomena in quantum systems. |
| title | (A)Symmetric Complexity and the Quantum Mpemba Effect |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.08078 |