Paper: The Kubo-Thermalization Correspondence Authors: Songtao Huang, Xingyu Li, Jianyi Chen, Alan Tsidilkovski, Gabriel G. T. Assumpção, Pengfei Zhang, Hui Zhai, Nir Navon Institutions: Yale University, Tsinghua University, Fudan University arXiv: 2605.06666v1 [cond-mat.quant-gas]
Key points
- Unifying two parallel fields: Linear response theory (Kubo) and quantum thermalization have long been treated as independent frameworks — one describing short-time system reactions to weak perturbations, the other describing long-time equilibration and 'forgetting' of initial conditions. This paper shows they are quantitatively linked by an exact identity.
- The central equation: For a driven spin coupled to a thermal bath at inverse temperature β = 1/(k_B T), the zero-crossing of the steady-state magnetization Δ₀ is determined by the transition spectrum R(ℰ) measured at short times:
- Why it must hold: The key insight is that the bath is the same bath in both regimes — it always obeys the Boltzmann distribution e^(−βE). The transition spectrum already encodes all the bath's statistical information (temperature, density of states, correlations), so knowing how the system 'questions' the bath (short-time spectroscopy) reveals its long-time 'answer' (steady state).
- Generalization: The correspondence extends beyond two-level spins to arbitrary N-level systems: the steady-state null point is determined by the thermally weighted sum of transition spectra from any initial state. It does not require any specific bath Hamiltonian, interaction form, weak coupling, or Markovianity.
- Experimental verification: The authors used an ultracold lithium-6 Fermi gas in a cylindrical optical box trap at nanokelvin temperatures, with atoms in two internal spin states as the system and a third state as the bath. By tuning the magnetic field, they spanned the full BCS regime (weak attraction), the unitary limit (strong interactions), and the BEC regime (tightly bound molecules).
- Beyond equilibrium: The correspondence was even verified for a metastable repulsive branch — a state that should decay and lies far from equilibrium, where conventional thermalization theory fails. This shows the correspondence captures something deeper than equilibration: the universal structure of information exchange between a driven system and its bath.
- Why it matters:
- Thermalization is slow and hard to observe directly; this result means the equilibration endpoint can be predicted from short-time linear response alone — relevant to quantum many-body physics, quantum chaos, and even black-hole information questions.
- The relation is universal and free of microscopic details — a rarity in physics.
- It continues the tradition of unification (electricity and magnetism, spacetime and gravity), showing spectroscopy and thermodynamics share a single mathematical backbone.
Δ₀ = −(1/β) · ln[ ∫ R(ℰ) · e^(−βℰ) dℰ ]
In plain terms: the long-time steady-state null point equals a thermally weighted average of the short-time spectrum. The identity is exact, not an approximation or numerical coincidence.
1. Short time: driven by a very weak RF field (ℏΩ₀ ≈ 0.003 E_F) for 12 ms to measure the transition spectrum R(Δ). 2. Long time: driven by a stronger RF field (ℏΩ₀ ≈ 0.27 E_F) for 200 ms to measure the steady-state magnetization ℳ∞(Δ).
The spectral peak Δₚ and the magnetization null Δ₀ coincide perfectly across the entire BCS-BEC crossover.
Paper details
| Item | Content | |------|---------| | Title | The Kubo-Thermalization Correspondence | | Authors | Songtao Huang, Xingyu Li, Jianyi Chen, Alan Tsidilkovski, Gabriel G. T. Assumpção, Pengfei Zhang, Hui Zhai, Nir Navon | | Institutions | Yale University, Tsinghua University, Fudan University | | arXiv | 2605.06666v1 | | Date | 2026-05-07 | | Categories | cond-mat.quant-gas, cond-mat.stat-mech, quant-ph | | Core equation | Δ₀ = −(1/β)·ln[∫R(ℰ)·e^(−βℰ)dℰ] | | Experimental platform | Ultracold ⁶Li Fermi gas, optical box trap | | Validated range | BCS regime → unitary limit → BEC regime, including a metastable repulsive branch |