Universal spectra of random Lindblad operators

To understand typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate Markovian completely positive evolution in the space of density matrices. Spectral properties of these operators, including the shape of the spectrum in the complex plane, are evaluated by using methods of free probabilities and explained with non-Hermitian random matrix models. We also demonstrate universality of the spectral features. The notion of ensemble of random generators of Markovian qauntum evolution constitutes a step towards categorization of dissipative quantum chaos.Comment: 6 pages, 4 figures + supplemental materia

Explosive synchronization in multiplex neuron-glial networks

Explosive synchronization refers to an abrupt (first order) transition to non-zero phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this phenomenon might be no less general then the celebrated Kuramoto scenario that belongs to the second order universality class. Importantly, the recent examples demonstrate that explosive synchronization can occur for certain network topologies and coupling types, like the global higher-order coupling, without specific requirements on the individial oscillator dynamics or dynamics-network correlations. Here we demonstrate a rich picture of explosive synchronization and desynchronization transitions in multiplex networks, where it is sufficient to have a single random sparsly connected layer with higher-order coupling terms (and not necessarily in the synchronization regime on its own), the other layer being a regular lattice without own phase transitions at all. Moreover, explosive synchronization emerges even when the random layer has only low-order pairwise coupling, althoug the hysteresis interval becomes narrow and explosive desynchronization is no longer observed. The relevance to the normal and pathological dynamics of neural-glial networks is pointed out.Comment: 8 pages, 6 figure

Nonlinear waves in random lattices: localization and spreading

Heterogeneity in lattice potentials (like random or quasiperiodic) can localize linear, non-interacting waves and halt their propagation. Nonlinearity induces wave interactions, enabling energy exchange and leading to chaotic dynamics. Understanding the interplay between the two is one of the topical problems of modern wave physics. In particular, one questions whether nonlinearity destroys localization and revives wave propagation, whether thresholds in wave energy/norm exist, and what the resulting wave transport mechanisms and characteristics are. Despite remarkable progress in the field, the answers to these questions remain controversial and no general agreement is currently achieved. This thesis aims at resolving some of the controversies in the framework of nonlinear dynamics and computational physics. Following common practice, basic lattice models (discrete Klein-Gordon and nonlinear Schroedinger equations) were chosen to study the problem analytically and numerically. In the disordered linear case all eigenstates of such lattices are spatially localized manifesting Anderson localization, while nonlinearity couples them, enabling energy exchange and chaotic dynamics. For the first time we present a comprehensive picture of different subdiffusive spreading regimes and self-trapping phenomena, explain the underlying mechanisms and derive precise asymptotics of spreading. Moreover, we have successfully generalized the theory to models with spatially inhomogeneous nonlinearity, quasiperiodic potentials, higher lattice dimensions and arbitrary nonlinearity index. Furthermore, we have revealed a remarkable similarity to the evolution of wave packets in the nonlinear diffusion equation. Finally, we have studied the limits of strong disorder and small nonlinearities to discover the probabilistic nature of Anderson localization in nonlinear disordered systems, demonstrating the finite probability of its destruction for arbitrarily small nonlinearity and exponentially small probability of its survival above a certain threshold in energy. Our findings give a new dimension to the theory of wave packet spreading in localizing environments, explain existing experimental results on matter and light waves dynamics in disordered and quasiperiodic lattice potentials, and offer experimentally testable predictions

Nonlinear waves in random lattices: localization and spreading

Heterogeneity in lattice potentials (like random or quasiperiodic) can localize linear, non-interacting waves and halt their propagation. Nonlinearity induces wave interactions, enabling energy exchange and leading to chaotic dynamics. Understanding the interplay between the two is one of the topical problems of modern wave physics. In particular, one questions whether nonlinearity destroys localization and revives wave propagation, whether thresholds in wave energy/norm exist, and what the resulting wave transport mechanisms and characteristics are. Despite remarkable progress in the field, the answers to these questions remain controversial and no general agreement is currently achieved. This thesis aims at resolving some of the controversies in the framework of nonlinear dynamics and computational physics. Following common practice, basic lattice models (discrete Klein-Gordon and nonlinear Schroedinger equations) were chosen to study the problem analytically and numerically. In the disordered linear case all eigenstates of such lattices are spatially localized manifesting Anderson localization, while nonlinearity couples them, enabling energy exchange and chaotic dynamics. For the first time we present a comprehensive picture of different subdiffusive spreading regimes and self-trapping phenomena, explain the underlying mechanisms and derive precise asymptotics of spreading. Moreover, we have successfully generalized the theory to models with spatially inhomogeneous nonlinearity, quasiperiodic potentials, higher lattice dimensions and arbitrary nonlinearity index. Furthermore, we have revealed a remarkable similarity to the evolution of wave packets in the nonlinear diffusion equation. Finally, we have studied the limits of strong disorder and small nonlinearities to discover the probabilistic nature of Anderson localization in nonlinear disordered systems, demonstrating the finite probability of its destruction for arbitrarily small nonlinearity and exponentially small probability of its survival above a certain threshold in energy. Our findings give a new dimension to the theory of wave packet spreading in localizing environments, explain existing experimental results on matter and light waves dynamics in disordered and quasiperiodic lattice potentials, and offer experimentally testable predictions

Nonlinear waves in random lattices: localization and spreading

Heterogeneity in lattice potentials (like random or quasiperiodic) can localize linear, non-interacting waves and halt their propagation. Nonlinearity induces wave interactions, enabling energy exchange and leading to chaotic dynamics. Understanding the interplay between the two is one of the topical problems of modern wave physics. In particular, one questions whether nonlinearity destroys localization and revives wave propagation, whether thresholds in wave energy/norm exist, and what the resulting wave transport mechanisms and characteristics are. Despite remarkable progress in the field, the answers to these questions remain controversial and no general agreement is currently achieved. This thesis aims at resolving some of the controversies in the framework of nonlinear dynamics and computational physics. Following common practice, basic lattice models (discrete Klein-Gordon and nonlinear Schroedinger equations) were chosen to study the problem analytically and numerically. In the disordered linear case all eigenstates of such lattices are spatially localized manifesting Anderson localization, while nonlinearity couples them, enabling energy exchange and chaotic dynamics. For the first time we present a comprehensive picture of different subdiffusive spreading regimes and self-trapping phenomena, explain the underlying mechanisms and derive precise asymptotics of spreading. Moreover, we have successfully generalized the theory to models with spatially inhomogeneous nonlinearity, quasiperiodic potentials, higher lattice dimensions and arbitrary nonlinearity index. Furthermore, we have revealed a remarkable similarity to the evolution of wave packets in the nonlinear diffusion equation. Finally, we have studied the limits of strong disorder and small nonlinearities to discover the probabilistic nature of Anderson localization in nonlinear disordered systems, demonstrating the finite probability of its destruction for arbitrarily small nonlinearity and exponentially small probability of its survival above a certain threshold in energy. Our findings give a new dimension to the theory of wave packet spreading in localizing environments, explain existing experimental results on matter and light waves dynamics in disordered and quasiperiodic lattice potentials, and offer experimentally testable predictions

Quantum subdiffusion with two- and three-body interactions

We study the dynamics of a few-quantum-particle cloud in the presence of two- and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ1 of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m2 ∼ tα, α < 1, on length scales beyond ξ1. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices. c EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 20171221sciescopu

Quantum subdiffusion with two- and three-body interactions

We study the dynamics of a few-quantum-particle cloud in the presence of two- and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ1 of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m2 ∼ tα, α < 1, on length scales beyond ξ1. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices. c EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 20171221sciescopu