Quantum tunneling Mpemba effect
Abstract
We investigate a quantum tunneling Mpemba effect for a particle in a continuous one-dimensional symmetric double-well potential subject to irreversible boundary loss. The dissipation is described by a complex absorbing potential (CAP) and the corresponding conditional no-jump evolution. Using a biorthogonal spectral representation, we derive the exact non-Hermitian decomposition of the subnormalized density matrix and analyze the corresponding relaxation dynamics. We show that the off-diagonal coefficients exhibit a parity selection rule, leaving same-parity interference terms in general. To isolate the interplay between thermal spectral preparation and mode-dependent decay rates, we introduce a diagonal spectral relaxation measure S(t,Ti). For a quartic double well, numerical calculations reveal finite-time crossings of S(t,Ti) prepared at different initial temperatures, as well as a non-monotonic temperature dependence of selected diagonal spectral weights. These features are explained by the enhanced thermal population of spatially extended, rapidly leaking excited states. In contrast, the trace distance of the normalized conditional state to the asymptotic quasi-stationary state exhibits no crossing, demonstrating that the anomalous ordering is specifically a spectral Mpemba effect rather than a universal acceleration of the complete conditional state. Our continuous-space formulation provides a real-space perspective on anomalous quantum relaxation without invoking universal nodal or topological theorems.
Related
- Mpemba effects in quantum complexity
- Observation and Modulation of the Quantum Mpemba Effect on a Superconducting Quantum Processor
- Initial-Slip Dynamics Enables the Quantum Mpemba Effect
- Quantum Computing for Entanglement Asymmetry and the Quantum Mpemba Effect in Field Theory
- Permanent Thermodynamic Mpemba Inversion from Quantum-Jump Feedback
BibTeX
@misc{hayakawa2026quantum,
title = {{Quantum tunneling Mpemba effect}},
author = {Hisao Hayakawa and Satoshi Takada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.03845},
eprint = {2607.03845},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.03845},
note = {CC0},
}
RIS
TY - UNPB
TI - Quantum tunneling Mpemba effect
AU - Hisao Hayakawa
AU - Satoshi Takada
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2607.03845
UR - https://arxiv.org/abs/2607.03845
AB - We investigate a quantum tunneling Mpemba effect for a particle in a continuous one-dimensional symmetric double-well potential subject to irreversible boundary loss. The dissipation is described by a complex absorbing potential (CAP) and the corresponding conditional no-jump evolution. Using a biorthogonal spectral representation, we derive the exact non-Hermitian decomposition of the subnormalized density matrix and analyze the corresponding relaxation dynamics. We show that the off-diagonal coefficients exhibit a parity selection rule, leaving same-parity interference terms in general. To isolate the interplay between thermal spectral preparation and mode-dependent decay rates, we introduce a diagonal spectral relaxation measure S(t,T_i). For a quartic double well, numerical calculations reveal finite-time crossings of S(t,T_i) prepared at different initial temperatures, as well as a non-monotonic temperature dependence of selected diagonal spectral weights. These features are explained by the enhanced thermal population of spatially extended, rapidly leaking excited states. In contrast, the trace distance of the normalized conditional state to the asymptotic quasi-stationary state exhibits no crossing, demonstrating that the anomalous ordering is specifically a spectral Mpemba effect rather than a universal acceleration of the complete conditional state. Our continuous-space formulation provides a real-space perspective on anomalous quantum relaxation without invoking universal nodal or topological theorems.
ER -