Bose-hubbard Model Study Reveals Mpemba Effect Emerges in Clean Regimes, Driving Nonlinear Relaxation

The surprising phenomenon where hot water freezes faster than cold water, known as the Mpemba effect, continues to challenge our understanding of thermal dynamics, and scientists are now exploring its quantum counterpart. Asad Ali, Saif Al-Kuwari, both from Qatar Center for Quantum Computing, and Hamid Arian Zad from P. J. ˇSaf ́arik University, alongside their colleagues, investigate this quantum Mpemba effect within a simplified model of interacting quantum particles. Their work demonstrates that strong interactions between these particles can lead to counterintuitive behaviour, allowing a system to relax to its lowest energy state via unexpected pathways, and potentially ‘overtake’ other systems starting closer to that state. This research sheds light on the fundamental role of interactions in controlling thermalisation, offering insights that could be relevant to emerging quantum technologies and the manipulation of ultra-cold atomic systems.

This research explores whether this counterintuitive effect, known classically, can occur in quantum systems and what mechanisms might drive it. The team focused on how the initial conditions and the system’s dynamics influence the speed of relaxation. The study centers on open quantum systems, which interact with their environment, leading to loss of coherence and energy dissipation, crucial factors in understanding how systems settle into equilibrium.

Researchers utilized the Bose-Hubbard model, a standard framework in condensed matter physics, to describe interacting particles on a lattice, allowing them to explore many-body quantum phenomena. A key aspect of the research involved carefully choosing different initial states to see how they affected the relaxation rate. The team compared the effects of disorder, created by random potential, and a Stark potential, a uniform electric field, on the system’s behaviour. They employed numerical simulations to solve the Schrödinger equation for the open quantum system and track its evolution over time.

To quantify changes in quantum coherence, they used metrics like the l1-norm of the density matrix and Rényi entropy to measure entanglement. The results demonstrate that, under specific conditions, the quantum system exhibits accelerated relaxation, mirroring the classical Mpemba effect. The choice of initial state is critical; certain states lead to significantly faster relaxation rates. Disorder can enhance relaxation by providing additional pathways for energy dissipation, while a Stark potential creates more complex dynamics. The team observed that the QME is associated with specific changes in quantum coherence and entanglement, highlighting the importance of these quantum properties.

Furthermore, the restoration of symmetry within the system plays a crucial role in the observed dynamics. This research provides a comprehensive investigation of the QME within a well-established quantum model, employing rigorous numerical simulations and detailed analysis. The availability of data further enhances the study’s value. The authors suggest future research could explore larger system sizes, different dissipation mechanisms, and ultimately, experimental verification of their predictions. In summary, this work makes a significant contribution to the field of quantum thermodynamics and provides valuable insights into the dynamics of open quantum systems.

Quantum Mpemba Effect Driven by Many-Body Correlations

Scientists investigated the quantum Mpemba effect (QME), a counterintuitive phenomenon where a quantum system initially farther from equilibrium can relax faster than one closer to equilibrium, within the one-dimensional Bose-Hubbard model. The team explored how interactions between particles, spatial disorder, and external electric fields influence this effect, focusing on systems experiencing dephasing, a loss of quantum coherence. Results demonstrate that QME emerges prominently in clean, interacting systems, driven by many-body correlations that create nonlinear relaxation pathways allowing initially distant states to overtake closer ones. This challenges the conventional expectation that colder objects typically reach equilibrium faster.

Non-interacting systems exhibit standard thermalization, while the application of electric fields or the introduction of random disorder suppresses QME by creating barriers to relaxation. Disorder causes milder delays compared to the pronounced effects of electric fields, indicating a sensitivity to the system’s potential landscape. The team quantified QME using multiple metrics, including trace distance, quantum relative entropy, entanglement asymmetry, and measures of quantum coherence, providing a comprehensive characterization of anomalous relaxation dynamics. Findings show that entanglement asymmetry is particularly sensitive to the symmetry restoration dynamics underlying QME, offering a valuable tool for monitoring this process. The research elucidates the critical role of interactions in enabling QME and provides insights into controlling quantum thermalization in experimental platforms such as ultra-cold atomic systems. This work builds upon recent experimental demonstrations of QME in trapped-ion systems and offers a theoretical framework for understanding and potentially harnessing this intriguing phenomenon.