Universality in the Dynamics of Second-Order Phase Transitions

Universal Anti-Kibble-Zurek Scaling in Fully Connected Systems

We investigate the quench dynamics of an open quantum system involving a quantum phase transition. In the isolated case, the quench dynamics involving the phase transition exhibits a number of scaling relations with the quench rate as predicted by the celebrated Kibble-Zurek mechanism. In contact with an environment however, these scaling laws break down and one may observe an anti-Kibble-Zurek behavior: slower ramps lead to less adiabatic dynamics, increasing thus nonadiabatic effects with the quench time. In contrast to previous works, we show here that such anti-Kibble-Zurek scaling can acquire a universal form in the sense that it is determined by the equilibrium critical exponents of the phase transition, provided the excited states of the system exhibit singular behavior, as observed in fully connected models. This demonstrates novel universal scaling laws granted by a system-environment interaction in a critical system. We illustrate these findings in two fully connected models, namely, the quantum Rabi and the Lipkin-Meshkov-Glick models. In addition, we discuss the impact of nonlinear ramps and finite-size systems.

Absence of Criticality in the Phase Transitions of Open Floquet Systems

We address the nature of phase transitions in periodically driven systems coupled to a bath. The latter enables a synchronized nonequilibrium Floquet steady state at finite entropy, which we analyze for rapid drives within a nonequilibrium renormalization group (RG) approach. While the infinitely rapidly driven limit exhibits a second-order phase transition, here we reveal that fluctuations turn the transition first order when the driving frequency is finite. This can be traced back to a universal mechanism, which crucially hinges on the competition of degenerate, near critical modes associated with higher Floquet Brillouin zones. The critical exponents of the infinitely rapidly driven system-including a new, independent one-can yet be probed experimentally upon smoothly tuning towards that limit.

On critical dynamics and thermodynamic efficiency of urban transformations

Urban transformations within large and growing metropolitan areas often generate critical dynamics affecting social interactions, transport connectivity and income flow distribution. We develop a statistical-mechanical model of urban transformations, exemplified for Greater Sydney, and derive a thermodynamic description highlighting critical regimes. We consider urban dynamics at two time scales: fast dynamics for the distribution of population and income, modelled via the maximum entropy principle, and slower dynamics evolving the urban structure under spatially distributed competition. We identify phase transitions between dispersed and polycentric phases, induced by varying the social disposition-a factor balancing the suburbs' attractiveness-in contrast with the travel impedance. Using the Fisher information, we identify critical thresholds and quantify the thermodynamic cost of urban transformation, as the minimal work required to vary the underlying parameter. Finally, we introduce the notion of thermodynamic efficiency of urban transformation, as the ratio of the order gained during a change to the amount of required work, showing that this measure is maximized at criticality.

Probing the Dynamics of a Superradiant Quantum Phase Transition with a Single Trapped Ion

We demonstrate that the quantum phase transition (QPT) of the Rabi model and critical dynamics near the QPT can be probed in the setup of a single trapped ion. We first demonstrate that there exists equilibrium and nonequilibrium scaling functions of the Rabi model by finding a proper rescaling of the system parameters and observables, and show that those scaling functions are representative of the universality class to which the Rabi model belongs. We then propose a scheme that can faithfully realize the Rabi model in the limit of a large ratio of the effective atomic transition frequency to the oscillator frequency using a single trapped ion and, therefore, the QPT. It is demonstrated that the predicted universal functions can indeed be observed based on our scheme. Finally, the effects of realistic noise sources on probing the universal functions in experiments are examined.

Universal Off-Equilibrium Scaling of Critical Cumulants in the QCD Phase Diagram

Exploiting the universality between the QCD critical point and the three-dimensional Ising model, closed form expressions derived for nonequilibrium critical cumulants on the crossover side of the critical point reveal that they can differ in both magnitude and sign from equilibrium expectations. We demonstrate here that key elements of the Kibble-Zurek framework of nonequilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expressible as universal scaling functions, thereby providing powerful model-independent guidance in searches for the QCD critical point.