Anomalous thermalization, particularly the crossings of temperature trajectories from different initial states termed Mpemba crossings (MPCs), have intrigued scientists for decades. While recent studies in quantum systems suggest that initial conditions play a decisive role in its emergence, they offer limited insight into MPCs in complex, highly nonequilibrium systems. In this study, we investigate temperature dynamics in the strongly coupled, quantum chaotic Sachdev-Ye-Kitaev (SYK) model, which is dual to the low-energy dynamics of 2D dilaton gravity. Our findings reveal a dynamically driven nonequilibrium mechanism underlying MPCs during rapid thermalization, with implications for gravitational systems. We explore quench dynamics in SYK systems under three conditions: coupling to a single SYK thermal bath, coupling to two thermal baths at different temperatures, and dissipative SYKs modeled by the Lindblad equation. We find that strong system-bath coupling induces oscillating effective temperatures and trajectory crossings in transient states due to nonequilibrium statistics, phenomena absent in quasi-static thermodynamics and Lindbladian SYKs. These MPCs highlight a unique feature of anomalous thermalization of strongly coupled quantum chaotic systems driven far from equilibrium. Besides, the results also provide qualitative insights into the nonequilibrium thermodynamics of black holes strongly interacting with their environment, such as primordial black holes in the early universe.
Anomalous thermalization, particularly the crossings of temperature trajectories from different initial states termed Mpemba crossings (MPCs), have intrigued scientists for decades. While recent studies in quantum systems suggest that initial conditions play a decisive role in its emergence, they offer limited insight into MPCs in complex, highly nonequilibrium systems. In this study, we investigate temperature dynamics in the strongly coupled, quantum chaotic Sachdev-Ye-Kitaev (SYK) model, which is dual to the low-energy dynamics of 2D dilaton gravity. Our findings reveal a dynamically driven nonequilibrium mechanism underlying MPCs during rapid thermalization, with implications for gravitational systems. We explore quench dynamics in SYK systems under three conditions: coupling to a single SYK thermal bath, coupling to two thermal baths at different temperatures, and dissipative SYKs modeled by the Lindblad equation. We find that strong system-bath coupling induces oscillating effective temperatures and trajectory crossings in transient states due to nonequilibrium statistics, phenomena absent in quasi-static thermodynamics and Lindbladian SYKs. These MPCs highlight a unique feature of anomalous thermalization of strongly coupled quantum chaotic systems driven far from equilibrium. Besides, the results also provide qualitative insights into the nonequilibrium thermodynamics of black holes strongly interacting with their environment, such as primordial black holes in the early universe.
This dissertation presents a comprehensive investigation of fermionic quantum matter into the intricate relationship between quantum chaos, thermalization, and their connection to gravitational duals, with particular emphasis on the Sachdev-Ye-Kitaev (SYK) model and its extensions. Through an integrated approach combining analytical solutions in the large-N limit with advanced numerical techniques, we explore fundamental questions in quantum many-body physics, including the interplay of chaos and ergodicity, universal transport in non-Fermi liquids, and the role of gravitational analogs in strongly correlated systems. We first demonstrate that coupled SYK lattices evade instantaneous thermalization despite weak charge fluctuations, governed by a discrete wave equation dependent solely on hopping strength, independent of on-site interactions. Thermodynamically, coupled SYK models exhibit critical exponents universal to van der Waals fluids and AdS black holes, yet diverge from the Hawking-Page transition at ultralow temperatures, revealing a continuum of first-order phase transitions. They simultaneously retain the quantum chaotic properties of both a single-dot SYK model and black holes. In extended SYK chains, we identify a universal DC conductivity bound across interaction regimes, identifying crossovers between insulating, Fermi liquid, strange metal, and bad metal phases with signatures of holographic insulator behavior. Quench dynamics in mixed SYK systems reveal rapid thermalization without prethermal plateaus, enabling direct observation of thermalization in closed quantum systems in the thermodynamic limit. To diagnose ergodicity-breaking, we introduce the Krylov variance, a probe of operator localization in Krylov space, validated through mass-deformed SYK and quantum East models. Finally, we uncover Page curve entanglement dynamics and temporal quantum phase transitions in entanglement Hamiltonians of interacting fermionic chains, where symmetry-sector crossings highlight limitations of perturbative calculations performed around initial times, such as in Hawking’s analysis of black hole evaporation. We provide a condensed matter analog of the holographic “island formula” — a mechanism invoking quantum extremal surfaces to resolve the black hole information paradox. Methodologically, this work integrates large-N-type expansions, Keldysh contour techniques, and numerical methods to bridge condensed matter physics, quantum information, and gravitational duality. The results establish SYK-type systems as a universal framework for studying non-Fermi liquids, quantum criticality, and black hole analogs, while paving the way for exploring bosonic extensions and generalizations to open quantum systems.
In interacting quantum many-body systems, relaxation toward equilibrium reflects a competition between internal chaotic dynamics and environmental dissipation. While conventional Markovian baths typically produce exponential decay, non-Markovian dissipation can give rise to more intricate behavior, including algebraic relaxation. We study an open Sachdev-Ye-Kitaev (SYK) model coupled to a pseudogapped fermionic bath, using the Keldysh formalism to compute steady-state correlations in the large-N limit. Our results uncover a rich dynamical phase diagram, with regimes of bath-driven power-law relaxation, chaos-driven exponential decay, and an intermediate pre-relaxation phase where exponential decay crosses over to algebraic decay. These findings demonstrate that non-Markovian environments can qualitatively reshape relaxation mechanisms in strongly correlated quantum many-body systems.
Energy transport in quantum many-body systems with well defined quasiparticles has recently attracted interest across different fields, including out of equilibrium conformal field theories, one dimensional quantum lattice models and holographic matter. Here we study energy transport between \emph{strange quantum baths} without quasiparticles, made by two Sachdev-Ye-Kitaev (SYK) models at temperatures TL=TR and connected by a Fermi-Liquid system. We obtain an exact expression for the nonequilibrium energy current, valid in the limit of large bath and system size and for any system-bath coupling V. We show that the peculiar criticality of the SYK baths has direct consequences on the thermal conductance, which above a temperature T∗(V)∼V4 is parametrically enhanced with respect to the linear-T behavior expected in systems with quasiparticles. Interestingly, below T∗(V) the linear thermal conductance behavior is restored, yet transport is not due to quasiparticles. Rather the system gets strongly renormalized by the strange bath and becomes Non-Fermi-Liquid and maximally chaotic. Finally, we discuss the full nonequilibrium energy current and show that its form is compatible with the structure J=Φ(TL)−Φ(TR), with Φ(T)∼Tγ and power law crossing over from γ=3/2 to γ=2 below T∗.
The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random interaction, which displays many interesting properties such as non-Fermi liquid behavior, quantum chaos, emergent conformal symmetry and holographic duality. Here we consider a SYK model or a chain of SYK models with N Majorana fermion modes coupled to another SYK model with N 2 Majorana fermion modes, in which the latter has many more degrees of freedom and plays the role as a thermal bath. For a single SYK model coupled to the thermal bath, we show that although the Lyapunov exponent is still proportional to temperature, it monotonically decreases from 2π/β (β = 1/(k B T), T is temperature) to zero as the coupling strength to the thermal bath increases. For a chain of SYK models, when they are uniformly coupled to the thermal bath, we show that the butterfly velocity displays a crossover from a T -dependence at relatively high temperature to a linear T-dependence at low temperature, with the crossover temperature also controlled by the coupling strength to the thermal bath. If only the end of the SYK chain is coupled to the thermal bath, the model can introduce a spatial dependence of both the Lyapunov exponent and the butterfly velocity. Our models provide canonical examples for the study of thermalization within chaotic models.
The Mpemba effect was originally referred to as the faster icing of a higher-temperature system than a lower-temperature system, and was later generalized to anomalous decays of both classical and quantum observables to equilibrium states. Mpemba effect is mostly considered in classical systems and during cooling processes toward equilibrium states. We investigate the emergence of the effect in nonequilibrium quantum systems where the system has no asymptotic equilibrium state to approach. Instead, the system is put in contact with two different baths, and only a nonequilibrium state exists, sustained by constant energy injection from the surrounding thermal baths. First, we show that the nonequilibrium conditions can dramatically enlarge the parameter regimes where the MPE emerges. Second, we demonstrate that the anomalous MPEs and inverse MPEs emerge in the evolution of quantum correlations in the two-site fermionic system and that nonequilibrium conditions can expedite or delay the MPEs. Third, we show that the nonequilibrium-induced quantum coherence can have considerable contributions to the emergence of the MPE which the conventional Lindbladian dynamics fails to capture. Published by the American Physical Society 2024
The question of thermalization of a closed quantum system is of central interest in nonequilibrium quantum many-body physics. Here we present one such study analyzing the dynamics of a closed coupled Majorana SYK system. We have a large- q SYK model prepared initially at equilibrium quenched by introducing a random hopping term, thus leading to nonequilibrium dynamics. We find that the final stationary state reaches thermal equilibrium with respect to the Green's functions and energy. Accordingly, the final state is characterized by calculating its final temperature and the thermalization rate. We provide a detailed review of analytical methods and derive the required Kadanoff-Baym equations, which are then solved using the algorithm developed in this work. Our results display rich thermalization dynamics in a closed quantum system in the thermodynamic limit.