Quantum Thermalization beyond Non-Integrability and Quantum Scars in a Multispecies Bose-Josephson Junction

Abstract

This work investigates the relationship between quantum chaos and thermalization in a three-species Bose-Josephson Junction (BJJ) with mutual interactions, without coupling to any external environment. The analysis is grounded in the Eigenstate Thermalization Hypothesis (ETH), the modern framework for quantum thermalization, in which non-integrability and chaos are historically assumed as prerequisites. After a thorough characterization of quantum chaos in this system, we examine the occurrence of thermal behavior expected when ETH holds. We identify three distinct regimes: chaotic, integrable, and separable. Remarkably, quantum thermalization occurs in both the chaotic and integrable regimes, while it breaks down in the separable limit - supporting that non-integrability is not a necessary condition for thermalization. Furthermore, since the system exhibits collective phenomena in the semiclassical limit, we identify athermal states in the chaotic regime classifiable as quantum scars, which show no signs of thermalization, consistently with a weak form of ETH. These findings contribute to the understanding of ergodicity breaking, emerging statistical behavior, and non-equilibrium dynamics in ultracold many-body quantum systems.

Figures (7)

• Figure 1: Unfolded level spacing distribution with parameters $U = 1$, $V=2$ and $S_\alpha = 8$. The dashed and the continuous lines give respectively the Poisson and Wigner-Dyson distribution.
• Figure 2: Averaged level spacing ratio in the $(U,V)$-parameter space with $S_\alpha = 5$. The black triangle and square in the colorbar indicate the theoretical values of $\langle r \rangle$ for the Poisson and Wigner-Dyson distributions, respectively.
• Figure 3: Region of stability (sky blue) and the unstability (yellow) for (a) '$\pi00$-mode' and (b) '$\pi\pi0$-mode'. The scar analysis in the text is performed using the parameters corresponding to the red points.
• Figure 4: Survival probability for both the scar states $-$ in panel a) the '$\pi 0 0$-mode' and in b) the '$\pi\pi 0$-mode' $-$ and the corresponding random states. The simulation was carried out with every $S_i$ = 6 and the parameters $U = 1, V = 2$.
• Figure 5: Panels (a) and (c) show the '$\pi00$' and '$\pi\pi0$' scar modes, respectively. For comparison, panels (b) and (d) display random coherent states at the same semiclassical energy of the corresponding scar. The snapshots are taken at times $t = 45.50$ for the '$\pi00$-mode' and $t = 49.30$ for the $\pi\pi0$-mode. The simulation was performed with each $S_i$ = 6 and parameters $U = 1, V = 2$.