Control of spatiotemporal chaos by stochastic resetting.

We study how spatiotemporal chaos in dynamical systems can be controlled by stochastically returning them to their initial conditions. Focusing on discrete nonlinear maps, we analyze how key measures of chaos-the Lyapunov exponent and butterfly velocity, which quantify sensitivity to initial perturbations and the ballistic spread of information, respectively-are reduced by stochastic resetting. We identify a critical resetting rate that induces a dynamical phase transition, characterized by the simultaneous vanishing of the Lyapunov exponent and butterfly velocity, effectively arresting the spread of information.

Diffraction and pseudospectra in non-Hermitian quasiperiodic lattices.

Wave dynamics in disordered open media is an intriguing topic and has lately attracted a lot of attention in non-Hermitian physics, especially in photonics. In fact, spatial distributions of gain and loss elements are physically possible in the context of integrated photonic waveguide arrays. In these type of lattices, counterintuitive quantized jumps along the propagation direction appear in the strong disorder limit (where all eigenstates are localized), and they have also been recently experimentally observed.

Generalized Hydrodynamic Description of the Page Curve-like Dynamics of a Freely Expanding Fermionic Gas.

We consider an analytically tractable model that exhibits the main features of the Page curve characterizing the evolution of entanglement entropy during evaporation of a black hole. Our model is a gas of noninteracting fermions on a lattice that is released from a box into the vacuum. More precisely, our Hamiltonian is a tight-binding model with a defect at the junction between the filled box and the vacuum.

Nonequilibrium spin transport in integrable and nonintegrable classical spin chains.

Anomalous transport in low dimensional spin chains is an intriguing topic that can offer key insights into the interplay of integrability and symmetry in many-body dynamics. Recent studies have shown that spin-spin correlations in spin chains, where integrability is either perfectly preserved or broken by symmetry-preserving interactions, fall in the Kardar-Parisi-Zhang (KPZ) universality class. Similarly, energy transport can show ballistic or diffusive-like behavior.

Unusual ergodic and chaotic properties of trapped hard rods.

We investigate ergodicity, chaos, and thermalization for a one-dimensional classical gas of hard rods confined to an external quadratic or quartic trap, which breaks microscopic integrability. To quantify the strength of chaos in this system, we compute its maximal Lyapunov exponent numerically. The approach to thermal equilibrium is studied by considering the time evolution of particle position and velocity distributions and comparing the late-time profiles with the Gibbs state.

Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations.

The out-of-time-ordered correlator (OTOC) has emerged as an interesting object in both classical and quantum systems for probing the spatial spread and temporal growth of initially local perturbations in spatially extended chaotic systems. Here, we study the (classical) OTOC and its "light cone" in the nonlinear Kuramoto-Sivashinsky (KS) equation, using extensive numerical simulations. We also show that the linearized KS equation exhibits a qualitatively similar OTOC and light cone, which can be understood via a saddle-point analysis of the linearly unstable modes.

Universal Subdiffusive Behavior at Band Edges from Transfer Matrix Exceptional Points.

We discover a deep connection between parity-time symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of 2×2 transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the parity-time symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points.

Finite-temperature equilibrium density profiles of integrable systems in confining potentials.

We study the equilibrium density profile of particles in two one-dimensional classical integrable models, namely hard rods and the hyperbolic Calogero model, placed in confining potentials. For both of these models the interparticle repulsion is strong enough to prevent particle trajectories from intersecting. We use field theoretic techniques to compute the density profile and their scaling with system size and temperature, and we compare them with results from Monte Carlo simulations.

Dynamical regimes of finite-temperature discrete nonlinear Schrödinger chain.

We show that the one-dimensional discrete nonlinear Schrödinger chain (DNLS) at finite temperature has three different dynamical regimes (ultralow-, low-, and high-temperature regimes). This has been established via (i) one-point macroscopic thermodynamic observables (temperature T, energy density ε, and the relationship between them), (ii) emergence and disappearance of an additional almost conserved quantity (total phase difference), and (iii) classical out-of-time-ordered correlators and related quantities (butterfly speed and Lyapunov exponents). The crossover temperatures T_{l-ul} (between low- and ultra-low-temperature regimes) and T_{h-l} (between the high- and low-temperature regimes) extracted from these three different approaches are consistent with each other.

Spatiotemporal spread of perturbations in power-law models at low temperatures: Exact results for classical out-of-time-order correlators.

We present exact results for the classical version of the out-of-time-order commutator (OTOC) for a family of power-law models consisting of N particles in one dimension and confined by an external harmonic potential. These particles are interacting via power-law interaction of the form ∝∑_{i,j=1(i≠j)}^{N}|x_{i}-x_{j}|^{-k}∀k>1 where x_{i} is the position of the ith particle. We present numerical results for the OTOC for finite N at low temperatures and short enough times so that the system is well approximated by the linearized dynamics around the many-body ground state.

Spatiotemporal spread of perturbations in a driven dissipative Duffing chain: An out-of-time-ordered correlator approach.

Out-of-time-ordered correlators (OTOCs) have been extensively used as a major tool for exploring quantum chaos, and recently there has been a classical analog. Studies have been limited to closed systems. In this work, we probe an open classical many-body system, more specifically, a spatially extended driven dissipative chain of coupled Duffing oscillators using the classical OTOC to investigate the spread and growth (decay) of an initially localized perturbation in the chain.

Particles confined in arbitrary potentials with a class of finite-range repulsive interactions.

In this paper, we develop a large N field theory for a system of N classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, V_{ex}(x), and repel each other via a class of pairwise interaction potentials V_{int}(r) (where r is distance between a pair of particles) such that V_{int}∼|r|^{-k} when r→0. We consider the case where every particle is interacting with d (finite-range parameter) number of particles to its left and right.

Transport, correlations, and chaos in a classical disordered anharmonic chain.

We explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size N, disorder strength Δ, and temperature T. The conductivity κ_{N}, obtained for finite length (N), saturates to a value κ_{∞}>0 in the large N limit, for all values of disorder strength Δ and temperature T>0.

Kardar-Parisi-Zhang scaling for an integrable lattice Landau-Lifshitz spin chain.

Recent studies report on anomalous spin transport for the integrable Heisenberg spin chain at its isotropic point. Anomalous scaling is also observed in the time evolution of nonequilibrium initial conditions, the decay of current-current correlations, and nonequilibrium steady state averages. These studies indicate a space-time scaling with x∼t^{2/3} behavior at the isotropic point, in sharp contrast to the ballistic form x∼t generically expected for integrable systems.

Cavity-mediated near-critical dissipative dynamics of a driven condensate.

We investigate the near-critical dynamics of atomic density fluctuations in the nonequilibrium self-organization transition of an optically driven quantum gas coupled to a single mode of a cavity. In this system cavity-mediated long-range interactions between atoms, tunable by the drive strength, lead to softening of an excitation mode recently observed in experiments. This phenomenon has previously been studied within a two-mode approximation for the collective motional degrees of freedom of the atomic condensate, which results in an effective open-system Dicke model.