Nonreciprocal Quantum Mpemba Effect

The Nonreciprocal Quantum Mpemba Effect

The Mpemba effect is a counterintuitive phenomenon where a system prepared further from equilibrium relaxes to the steady state faster than one prepared closer. While previously observed in various classical and quantum systems, this paper introduces the Nonreciprocal Quantum Mpemba Effect (NQME). In this framework, the presence or absence of the Mpemba effect is determined by the direction of a bias between two reservoirs, which can be toggled by a discrete swap operation.

Mechanism: Spectral Pinning and Eigenvector Rotation

The authors analyze open quantum systems coupled to two isomorphic reservoirs through symmetric ports. When the reservoir parameters are swapped, the system's Liouvillian operator undergoes a transformation. Crucially, the authors show that this transformation possesses a structural symmetry that keeps the Liouvillian eigenvalues constant (spectral pinning) while rotating the eigenvectors.

Because the relaxation rate of an initial state is determined by its projection onto the slowest-decaying eigenmode, the rotation of these eigenvectors under a swap can cause a state that was previously orthogonal to the slowest mode (and thus experienced a speedup) to suddenly gain a non-zero overlap. This effectively turns the Mpemba effect on or off without changing the initial state or the system's fundamental decay rates.

Exceptional Points and Critical Slowing

The study further explores the NQME at a Liouvillian exceptional point (EP), where eigenvalues coalesce and the Liouvillian becomes non-diagonalizable. In this regime, the system typically exhibits critical slowing down, characterized by non-exponential decay. The authors demonstrate that the NQME persists here as a nonreciprocal critical slowing: the swap determines whether the initial state is protected from this slowing or caught by it, providing a clear, spectrum-independent demonstration of the effect.

This research provides a new perspective on non-equilibrium thermodynamics and quantum control. By decoupling the Mpemba effect from the system's spectrum and linking it to the geometric properties of the eigenvectors, the authors offer a robust mechanism for controlling relaxation speeds. This has potential applications in quantum state preparation and the design of thermodynamic cycles where rapid, tunable relaxation is required.