Universal Non-Equilibrium Cascade in QGP Light-Nuclei Formation and Cosmological Bose-Einstein Condensation

Recent ALICE results demonstrate that over 90% of light nuclei and anti-nuclei ($d$, $\bar d$) observed in heavy-ion collisions originate from a non-equilibrium, multi-stage process: $Δ$-resonance production, decay into correlated nucleons, and their subsequent coalescence in a cooler hadronic environment. Although the final particle yields appear thermal, the underlying dynamics is strongly time-ordered and highly non-equilibrium. We show that this mechanism exhibits a striking universality with the formation of Bose-Einstein condensates (BEC) and associated density spikes in cosmological scalar-field dark-matter scenarios. In both systems – the quark-gluon plasma near hadronization and the early universe approaching the BEC critical temperature – the relevant degrees of freedom reorganize through a hierarchical cascade: high-energy modes first convert into intermediate excitations, which then seed low-energy coherent structures once the temperature crosses a threshold. This work highlights an unexpected theoretical bridge between heavy-ion physics and cosmology, suggesting a common class of emergent non-equilibrium phenomena behind structure formation in both extremes.

💡 Research Summary

The paper presents a unified description of two seemingly unrelated phenomena – the production of light nuclei (especially deuterons) in relativistic heavy‑ion collisions and the cosmological Bose‑Einstein condensation (BEC) of scalar‑field dark matter – as manifestations of a universal non‑equilibrium cascade. Recent ALICE measurements have shown that more than 90 % of observed deuterons and anti‑deuterons are not emitted directly from the hot quark‑gluon plasma (QGP) but are created through a multi‑stage process: abundant Δ‑resonance production at hadronization, subsequent decay Δ → N + π that injects correlated nucleon pairs, and finally nucleon coalescence into deuterons once the hadronic medium has cooled enough that the temperature‑dependent breakup rate becomes negligible.

The authors formalize this picture with a set of rate equations for the densities of Δ resonances (n_Δ), nucleons (n_N) and deuterons (n_d). The equations capture three essential ingredients: (i) a source term S_Δ that populates Δ’s at early times, (ii) the decay width Γ_Δ that continuously feeds nucleons, and (iii) a temperature‑dependent deuteron destruction rate Γ_br_d(T) that suppresses deuteron formation at high temperature. As the system expands, the temperature drops, Γ_br_d(T) falls sharply, and the nucleon reservoir supplied by Δ‑decays enables the coalescence reaction N + N → d + X. The resulting deuteron yield follows the familiar coalescence scaling N_d ∝ B_2 N_p N_n, but the coalescence parameter B_2 now encodes the delayed, correlated nucleon supply rather than a simple phase‑space overlap. This time‑ordered cascade explains why the final deuteron yields appear thermal (well described by statistical hadronization models) even though the underlying dynamics is far from equilibrium; the thermal pattern emerges as a dynamical attractor of the coupled rate equations.

Turning to cosmology, the paper examines a scalar‑field dark‑matter model (the Fukuyama‑Morikawa‑Tatekawa scenario) in which the field behaves as a gas of incoherent excitations at temperatures far above a critical temperature T_c. As the universe expands and cools below T_c, a macroscopic occupation of the ground mode (the BEC) becomes possible. However, the transition is not a quasi‑static equilibrium process. Non‑linear self‑gravity and self‑interaction generate transient, high‑density “lumps” or collapse‑induced spikes. These lumps act as intermediate, unstable excitations that temporarily store energy and particle number, then re‑disperse, feeding the coherent condensate fraction. The authors again write a pair of rate equations for the condensate density n_0 and the excited fraction n_ex, with an in‑rate Γ_in(T) describing re‑condensation of excitations and an out‑rate Γ_out(T) accounting for disruption by further collapses, plus a dilution term S_ex(t) from cosmic expansion. When T ≫ T_c, Γ_in≈0 and n_0≈0; as T approaches T_c, Γ_in grows, leading to rapid growth of n_0 at the expense of n_ex. Repeated collapse episodes produce a series of density spikes that gradually build up a stable condensate core.

The central claim is that the heavy‑ion cascade (Δ → N → d) and the cosmological BEC cascade (collapse lump → excited fraction → condensate) share the same structural pattern: high‑energy modes first populate unstable intermediate excitations, which later release correlations into low‑energy coherent structures once the environment has cooled or expanded sufficiently. The mapping is explicit: free nucleons ↔ excited fraction, Δ resonances ↔ collapse‑induced lumps, deuterons ↔ condensate core. The corresponding rate equations have identical schematic form, highlighting a universal competition between formation rates, destruction rates, and the cooling/expansion timescale.

In the discussion, the authors argue that the apparent thermal spectra of deuterons and of the dark‑matter condensate do not imply genuine early‑time equilibration; instead, they are fixed points of non‑equilibrium dynamics. This insight has broad implications: fragile bound states or coherent structures can survive in extreme environments not because their binding energy exceeds the ambient temperature, but because a delayed, intermediate reservoir shields them from rapid destruction. The paper suggests cross‑fertilization between heavy‑ion physics and cosmology: techniques developed for real‑time QCD (Keldysh‑Schwinger formalism, effective kinetic theory) could be adapted to study scalar‑field dark matter, while concepts from BEC physics (macroscopic wavefunction, Gross‑Pitaevskii dynamics) may inspire new effective models for light‑nucleus formation.

Overall, the work identifies a universal non‑equilibrium cascade mechanism that bridges the micro‑scale world of quark‑gluon plasma and the macro‑scale evolution of the early universe, offering a fresh perspective on how weakly bound or coherent structures emerge and persist across vastly different energy and length scales.