Exact pretransition effects in kinetically constrained circuits: Dynamical fluctuations in the Floquet-East model.

We study the dynamics of a classical circuit corresponding to a discrete-time version of the kinetically constrained East model. We show that this classical "Floquet-East" model displays pre-transition behavior which is a dynamical equivalent of the hydrophobic effect in water. For the deterministic version of the model, we prove exactly (i) a change in scaling with size in the probability of inactive space-time regions (akin to the "energy-entropy" crossover of the solvation free energy in water), (ii) a first-order phase transition in the dynamical large deviations, (iii) the existence of the optimal geometry for local phase separation to accommodate space-time solutes, and (iv) a dynamical analog of "hydrophobic collapse.

Combining Reinforcement Learning and Tensor Networks, with an Application to Dynamical Large Deviations.

We present a framework to integrate tensor network (TN) methods with reinforcement learning (RL) for solving dynamical optimization tasks. We consider the RL actor-critic method, a model-free approach for solving RL problems, and introduce TNs as the approximators for its policy and value functions. Our "actor-critic with tensor networks" (ACTeN) method is especially well suited to problems with large and factorizable state and action spaces.

Universal and nonuniversal probability laws in Markovian open quantum dynamics subject to generalized reset processes.

We consider quantum-jump trajectories of Markovian open quantum systems subject to stochastic in time resets of their state to an initial configuration. The reset events provide a partitioning of quantum trajectories into consecutive time intervals, defining sequences of random variables from the values of a trajectory observable within each of the intervals. For observables related to functions of the quantum state, we show that the probability of certain orderings in the sequences obeys a universal law.

Topological phases in the dynamics of the simple exclusion process.

We study the dynamical large deviations of the classical stochastic symmetric simple exclusion process (SSEP) by means of numerical matrix product states. We show that for half filling, long-time trajectories with a large enough imbalance between the number hops in even and odd bonds of the lattice belong to distinct symmetry-protected topological (SPT) phases. Using tensor network techniques, we obtain the large deviation (LD) phase diagram in terms of counting fields conjugate to the dynamical activity and the total hop imbalance.

Exact Quench Dynamics of the Floquet Quantum East Model at the Deterministic Point.

We study the nonequilibrium dynamics of the Floquet quantum East model (a Trotterized version of the kinetically constrained quantum East spin chain) at its "deterministic point," where evolution is defined in terms of CNOT permutation gates. We solve exactly the thermalization dynamics for a broad class of initial product states by means of "space evolution." We prove: (i) the entanglement of a block of spins grows at most at one-half the maximal speed allowed by locality (i.