Quantum Tunneling Mpemba Effect: Paradoxical Cooling in Open Double-Well Potentials ✛ ✦
Context
The Mpemba paradox, where hot water freezes faster than cold, has long sparked debate, but in the past decade it found rigorous explanation within non-equilibrium statistical mechanics. In classical systems, boundaries play a key role: the effect 'likes to hit the wall'. In parallel, the quantum Mpemba effect is being actively studied, but until now there has been no clear link between coherent tunneling and spatial boundary losses. The new study fills this gap by formulating the problem in continuous coordinate space using Schrödinger quantum mechanics and a non-Hermitian Hamiltonian.
Methods
The authors considered a single particle in a symmetric double-well potential with a complex absorbing potential (CAP) near the boundaries. Within the framework of von Neumann open quantum systems, instead of the standard Lindblad equation, they used a non-Hermitian effective Hamiltonian $H_{eff}$ = H0 − iW, where W(x) is a smooth spatial absorption profile. Then the evolution of the surviving part of the ensemble is described by the non-Hermitian Schrödinger equation iℏ ∂ψ/∂t = $H_{eff}$ ψ. Thanks to superposition of states and wave-particle duality, the wave function is expanded in a biorthogonal basis of right and left eigenstates of $H_{eff}$. The model relies on quantum field ideas of open systems, and the superposition principle guarantees the linearity of the expansion. Numerically, the problem was solved on a uniform grid using the finite difference method followed by diagonalization.
Results
The central result is the proof that the coefficient a2(Ti), responsible for the first excited even decay mode, has a non-monotonic peak at an intermediate initial temperature Ti. This peak is universal: at low Ti, the contribution vanishes due to weak overlap of deeply localized ground states with the delocalized mode φ2; at high Ti, the coefficient vanishes due to equal population of all states. The existence of the maximum is guaranteed by the Sturm–Liouville theorem and does not depend on system size L, which starkly contrasts with the classical counterpart. For observing anomalous crossings in the survival probability S(t,Ti) and trace distance, it is necessary that the over-barrier escape rate Γ2 significantly exceeds the tunneling decay rates of the deep doublets Γ0 and Γ1. Numerical simulations confirmed these predictions, demonstrating clear crossings of S(t,Ti) curves for different Ti, as well as the temperature invariance of the a2(Ti) peak when varying L. Thus, the anomalous acceleration of relaxation for heated quantum states is a consequence of optimal population of delocalized channels that effectively absorb the particle at the boundaries. This mechanism resembles quantum decoherence, causing effective wave function collapse upon measuring survival.
Implications
The results merge the physical picture of the classical Mpemba effect, governed by boundaries, with quantum-mechanical coherence and tunneling. This opens up a new class of problems in quantum information science and quantum measurements, where boundary losses can be designed for accelerated preparation of strongly non-equilibrium states. The universality of the a2(Ti) peak also points to a deep connection between wave function topology and thermodynamic properties of open systems.
Future development
Further research will aim at generalizing to asymmetric potentials, where the parity selection rule is lifted, but the peak persists due to the ordering of the number of nodes in the wave functions. Experimental realization is possible in platforms with ultracold atoms, for instance in Bose-Einstein condensates with optical traps, where the potential shape can be precisely controlled and controllable losses introduced. Also promising is the study of the role of non-Hermitian exceptional points and multiple crossings in the trace distance, which could lead to a multiple quantum Mpemba effect.
Impact
This work will impact the development of quantum thermodynamics, open quantum system theory, and quantum computing, providing a new tool for controlling the relaxation of qubits and quantum simulators.
Next steps
Key steps include experimental verification of the predictions in trapped ions or ultracold atom systems, as well as studying multimode coherent effects, including verifying the existence of multiple crossings in nonlinear state metrics.
Key open problems
The research touches on fundamental problems of the quantum-classical transition and the foundations of statistical mechanics: how the discreteness of the energy spectrum and the topology of wave functions give rise to macroscopic anomalous behavior that is independent of system size. It also sheds light on the nature of irreversibility in quantum systems interacting with an environment.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors examined a single particle in an open double-well potential with a complex absorbing potential and a non-Hermitian effective Hamiltonian. They showed that the occupation coefficient of the first excited even mode exhibits a non-monotonic peak at an intermediate initial temperature, leading to anomalous crossings of survival curves. This peak is universal and independent of system size.
Where its strength is
The work establishes a direct link between coherent tunneling and spatial boundary losses, demonstrating that the quantum Mpemba effect can arise from optimal occupation of delocalized decay channels rather than from system size.
Where it could go next
- It might be interesting to see how the proposed mechanism of optimal occupation of delocalized modes relates to the role of walls in the classical Mpemba effect, where boundaries also play a key role.based on: Hotter Faster? It's All in the Wall arXiv:2604.01543
- A nearby work on the quantum Mpemba effect at ultra-low temperatures shows behavior that may differ due to the dominance of tunneling processes; comparing with your regime of above-barrier escape could reveal a transition between the two mechanisms.based on: Quantum Mpemba effect: hot cools faster, but only near absolute zero arXiv:2607.06071
- It would be interesting to test whether your result holds in the presence of entanglement, as there are works in the archive linking the Mpemba effect to entanglement dynamics, where it can either accelerate or slow down relaxation.based on: Quantum Mpemba: Strong Entanglement Melts Faster arXiv:2605.23197
Worth trying
- Test your model on potentials with asymmetric wells to see how the mode occupation peak and survival curve crossings change.
- Consider the case of multiple particles to check whether the universality of the peak persists under interactions and possible entanglement formation.
- Use your approach to analyze quantum temperature sensors, where anomalous relaxation could enhance measurement precision, as suggested in a related work.
Why this may matter
This work could be important for controlling cooling processes in nanodevices, as it shows that the Mpemba effect can be controlled by altering the shape of boundaries rather than system size, paving the way for more flexible design of quantum systems.
Nearby works in our archive
- Hotter Faster? It's All in the Wallsimilarity 0.74
- Quantum Mpemba effect: hot cools faster, but only near absolute zerosimilarity 0.69
- Hot Cools Down Faster: The Quantum Paradoxsimilarity 0.69
- Hot Cools Faster: The Quantum Mpemba Effectsimilarity 0.69
- The Mpemba Paradox: Hot Quantum Sensors Measure Temperature More Accuratelysimilarity 0.69
- Hotter Cools Faster: The Mpemba Effect for Thermal Radiationsimilarity 0.68
- Quantum Mpemba: Strong Entanglement Melts Fastersimilarity 0.65
The archive is crowded around this work: 8 reviews nearby, closest at 0.74. This ground is well walked — and there is plenty to compare against.
Original abstract
as written by the authors arXiv:2607.03845
The quantum tunneling Mpemba effect is investigated within a continuous one-dimensional symmetric double-well potential open to external environmental sinks at the boundaries ($$x=\pm L$$). Using a non-Hermitian spectral decomposition of the effective Hamiltonian, we characterize the open-system relaxation dynamics without relying on abstract state-space quenches. We mathematically prove that the non-monotonic behavior of the first non-trivial even-parity spectral coefficient, $$a_{2}(T_{i})$$, with respect to the initial preparation temperature $$T_{i}$$ is a universal topological property born from quantum statistical mechanics. Crucially, we demonstrate that this intermediate thermal peak is governed by the Sturm-Liouville oscillation theorem and remains completely invariant with respect to the global system size $$L$$, contrasting sharply with the boundary-driven classical Mpemba effect. This universal peak arises from the geometric and nodal alignment between highly localized unperturbed states and extended non-Hermitian decay channels. Furthermore, we clarify that while this mechanism is robust, the actual observation of anomalous crossings in the total survival probability trace $$S(t,T_{i})$$ and the trace distance $$\mathcal{D}(t,T_i)$$ demand a strict separation of timescales, requiring the over-barrier escape rate to vastly exceed the decay rate of the deep-well tunneling doublet ($$\Gamma_{2}\gg \Gamma_{0}$$ and $$\Gamma_2\gg \Gamma_1$$). Our continuous formulation successfully bridges real-space classical boundary-driven dissipation with open quantum dynamics, providing novel insights for engineering non-equilibrium states via tailored boundary loss.
Unlike its classical counterpart, which, according to recent work, 'likes to hit the wall', the quantum Mpemba effect turns out to be remarkably robust to system size: increasing the distance to the absorbing boundaries does not change the optimal 'hot' start temperature. This counterintuitive result is a direct consequence of the discrete structure of quantized states and the precise tuning of the number of nodes in the wave function.
Key numbers
- a2(Ti) peak temperature: ≈ 3.26 (in units of the potential barrier)
- decay rate ratio Γ2/Γ0,1: >> 1
- system width L: 5 (in length units)
- absorption strength η: 5
- absorption region length x_abs: 4