In this Letter, we study the mean-field dynamics of a general class of many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter m(t)∼t^{-χ} with an exponent χ=1/3 that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states, and even the driving protocols. It is shown that such a dynamical universality class can be understood as a consequence of a diffusive process with a time-dependent diffusion coefficient which is determined self-consistently during the evolution. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.
Understanding the collective dynamics in many-particle systems is of important significance in nonequilibrium physics. In this paper, we systematically study the long-time behavior in stochastically driven interacting quantum systems. We find that even though the stochastic forces will inevitably drive a system into a featureless steady state, the asymptotic behavior to approach the steady state can be highly nontrivial and exhibits rich universal dynamics due to the interplay between the stochastic driving and quantum many-body effects. Special attention is devoted to the effect of the mode-coupling perturbations, which may have important consequence for the long-time dynamics of the stochastically driven quantum many-body systems.
We demonstrate that fluctuation-induced bistability is a robust and generic phenomenon in strongly interacting many-body systems with strong light-matter coupling. We identify a common microscopic mechanism based on resonances between photonic transitions and many-body energy scales, unifying the emergence of fluctuation-induced bistability across a broad class of models, including interacting spins, fermions, and bosons coupled to cavity modes. We develop complementary methods to study both the steady-state properties of fluctuation-induced bistability and its dynamical formation at finite times. In particular, we introduce the dressed-state rate equation approach, which reveals rich metastable dynamics and enables the investigation of its system-size dependence. By comparing its predictions with numerically-exact tensor-network simulations, we identify signatures of fluctuation-induced bistability already in small systems on finite timescales. Our results establish fluctuation-induced bistability as a universal feature of dissipative cavity-coupled many-body systems and provide a general framework for the investigation of its non-equilibrium dynamics across a wide range of hybrid quantum platforms.
While imaginary-time evolution has long served as a standard paradigm for ground-state preparation in numerical simulations and quantum devices, its intrinsic dynamical properties has been largely overlooked. Here, we investigate the short-imaginary-time critical dynamics in quantum systems with boundaries. A universal scaling theory is developed and verified in the two-dimensional quantum Ising model, uncovering rich dynamic critical behaviors dictated by boundary universality classes. For ordered initial states, the boundary order parameter
Ms decays with imaginary time
τ as
Ms∝τ−β1/νz, where
β1 denotes the boundary order parameter exponent, and
ν and
z correspond to the correlation length exponent and the dynamic exponent, respectively. For disordered initial states, the autocorrelation of the boundary order parameter is governed by a novel critical exponent
θ1, which is closely related to the critical initial slip behavior of
Ms characterized by the corresponding exponent
θ1′. In contrast to its positive bulk counterpart, the boundary initial-slip exponent
θ1′ is negative for the ordinary transition while remaining positive for the special transition. Although the static universality classes of
d-dimensional quantum phase transitions generally coincide with those of
(d+1)-dimensional classical phase transitions, we show that
θ1 does not follow this conventional quantum-classical mapping. We further discuss the implications of our results for more exotic forms of boundary criticality. Our findings provide new physical insights into boundary critical dynamics and offer a novel route for probing exotic boundary critical behaviors in quantum many-body systems.
The question of whether interactions can break dynamical localization in quantum kicked rotor systems has been the subject of a long-standing debate. Here, we introduce an extended mapping from the kicked Lieb-Liniger model to a high-dimensional lattice model and reveal universal features: on-site pseudorandomness and hybrid exponential-algebraic decay couplings with increasing momenta. We find that the exponent and the amplitude of the algebraic decay undergo a crossover as the interaction strength increases. This mapping uncovers the origin of dynamical localization and the interaction effect on the integrability of the system. An analysis of the generalized fractal dimension and level-spacing ratio supports these findings, highlighting the presence of near integrability and multifractality in different regions of parameter space. Our results offer an explanation for the occurrence of many-body dynamical localization, particularly in strongly correlated quantum gases, and are anticipated to generalize to systems of many particles.
Numerically, we study the time fluctuations of few-body observables after relaxation in isolated dynamical quantum systems of interacting particles. Our results suggest that they decay exponentially with system size in both regimes, integrable and chaotic. The integrable systems considered are solvable with the Bethe ansatz and have a highly nondegenerate spectrum. This is in contrast with integrable Hamiltonians mappable to noninteracting ones. We show that the coefficient of the exponential decay depends on the level of delocalization of the initial state with respect to the energy shell.