Showing papers on "Dissipative system published in 2015"

Dissipative Kerr solitons in optical microresonators

Abstract: This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb generation where they are of particular importance. Here, one example is spectral broadening and self-referencing enabled by the ultra-short pulsed nature of the solitons. Another example is dissipative Kerr soliton formation in integrated on-chip microresonators where the emission of a dispersive wave allows for the direct generation of unprecedentedly broadband and coherent soliton spectra with smooth spectral envelope.

Two-Dimensional Dissipative Control and Filtering for Roesser Model

Abstract: This paper investigates the problems of two-dimensional (2-D) dissipative control and filtering for a linear discrete-time Roesser model. First, a novel sufficient condition is proposed such that the discrete-time Roesser system is asymptotically stable and 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative. Special cases, such as 2-D passivity performance and 2-D $H_{\infty} $ performance, and feedback interconnected systems are also discussed. Based on this condition, new 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative state-feedback and output-feedback control problems are defined and solved for a discrete-time Roesser model. The design problems of 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative filters of observer form and general form are also considered using a linear matrix inequality (LMI) approach. Two examples are given to illustrate the effectiveness and potential of the proposed design techniques.

Dissipative adaptation in driven self-assembly.

Abstract: In a collection of assembling particles that is allowed to reach thermal equilibrium, the energy of a given microscopic arrangement and the probability of observing the system in that arrangement obey a simple exponential relationship known as the Boltzmann distribution. Once the same thermally fluctuating particles are driven away from equilibrium by forces that do work on the system over time, however, it becomes significantly more challenging to relate the likelihood of a given outcome to familiar thermodynamic quantities. Nonetheless, it has long been appreciated that developing a sound and general understanding of the thermodynamics of such non-equilibrium scenarios could ultimately enable us to control and imitate the marvellous successes that living things achieve in driven self-assembly. Here, I suggest that such a theoretical understanding may at last be emerging, and trace its development from historic first steps to more recent discoveries. Focusing on these newer results, I propose that they imply a general thermodynamic mechanism for self-organization via dissipation of absorbed work that may be applicable in a broad class of driven many-body systems.

Spatial Localization in Dissipative Systems

Abstract: Spatial localization is a common feature of physical systems, occurring in both conservative and dissipative systems. This article reviews the theoretical foundations of our understanding of spatial localization in forced dissipative systems, from both a mathematical point of view and a physics perspective. It explains the origin of the large multiplicity of simultaneously stable spatially localized states present in a parameter region called the pinning region and its relation to the notion of homoclinic snaking. The localized states are described as bound states of fronts, and the notions of front pinning, self-pinning, and depinning are emphasized. Both one-dimensional and two-dimensional systems are discussed, and the reasons behind the differences in behavior between dissipative systems with conserved and nonconserved dynamics are explained. The insights gained are specific to forced dissipative systems and are illustrated here using examples drawn from fluid mechanics (convection and shear flows) an...

Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems

Abstract: We present a new variational method based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate representation of the system evolution until the stationary state is attained, the algorithm directly targets the final state, thus, allowing for a faster convergence when the steady state is a MPO with small bond dimension. Our numerical simulations for several dissipative spin models over a wide range of parameters illustrate the performance of the method and show that, indeed, the stationary state is often well described by a MPO of very moderate dimensions.

Viscosity and dissipative hydrodynamics from effective field theory

Abstract: With the goal of deriving dissipative hydrodynamics from an action, we study classical actions for open systems, which follow from the generic structure of effective actions in the Schwinger-Keldysh closed-time-path (CTP) formalism with two time axes and a doubling of degrees of freedom. The central structural feature of such effective actions is the coupling between degrees of freedom on the two time axes. This reflects the fact that from an effective field theory point of view, dissipation is the loss of energy of the low-energy hydrodynamical degrees of freedom to the integrated-out, UV degrees of freedom of the environment. The dynamics of only the hydrodynamical modes may therefore not possess a conserved stress-energy tensor. After a general discussion of the CTP effective actions, we use the variational principle to derive the energy-momentum balance equation for a dissipative fluid from an effective Goldstone action of the long-range hydrodynamical modes. Despite the absence of conserved energy and momentum, we show that we can construct the first-order dissipative stress-energy tensor and derive the Navier-Stokes equations near hydrodynamical equilibrium. The shear viscosity is shown to vanish in the classical theory under consideration, while the bulk viscosity is determined by the form of the effective action. We also discuss the thermodynamics of the system and analyze the entropy production.

Variational principle for steady states of dissipative quantum many-body systems.

Abstract: We present a novel generic framework to approximate the nonequilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the dynamics. We show how to apply this approach to different classes of variational quantum states and demonstrate its successful application to a dissipative extension of the Ising model, which is of importance to ongoing experiments on ultracold Rydberg atoms, as well as to a driven-dissipative variant of the Bose-Hubbard model. Finally, we identify several advantages of the variational approach over previously employed mean-field-like methods.

Dynamics of Quasi-Stable Dissipative Systems

Abstract: Preface.- Introduction.- Basic Concepts.- General Facts on Dissipative Systems.- Finite-Dimensional Behavior and Quasi-Stability.- Abstract Parabolic Problems.- Second Order Evolution Equations.- Delay equations in infinite-dimensional spaces.- Auxiliary Facts.- References.- Index.

Adiabatic hydrodynamics: The eightfold way to dissipation

Abstract: Hydrodynamics is the low-energy effective field theory of any interacting quantum theory, capturing the long-wavelength fluctuations of an equilibrium Gibbs densitymatrix. Conventionally, one views the effective dynamics in terms of the conserved currents, which should be expressed via the constitutive relations in terms of the fluid velocity and the intensive parameters such as the temperature, chemical potential, etc. . . However, not all constitutive relations are acceptable; one has to ensure that the second law of thermodynamics is satisfied on all physical configurations. In this paper, we provide a complete solution to hydrodynamic transport at all orders in the gradient expansion compatible with the second law constraint. The key new ingredient we introduce is the notion of adiabaticity, which allows us to take hydrodynamics off-shell. Adiabatic fluids are such that off-shell dynamics of the fluid compensates for entropy production. The space of adiabatic fluids is quite rich, and admits a decomposition into seven distinct classes. Together with the dissipative class this establishes the eightfold way of hydrodynamic transport. Furthermore, recent results guarantee that dissipative terms beyond leading order in the gradient expansion are agnostic of the second law. While this completes a transport taxonomy, we go on to argue for a new symmetry principle, an Abelian gauge invariance that guarantees adiabaticity in hydrodynamics. We suggest that this symmetry is the macroscopic manifestation of the microscopic KMS invariance. We demonstrate its utility by explicitly constructing effective actions for adiabatic transport. The theory of adiabatic fluids, we speculate, provides a useful starting point for a new framework to describe non-equilibrium dynamics, wherein dissipative effects arise by Higgsing the Abelian symmetry.

Relaxation times of dissipative many-body quantum systems.

Abstract: We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap cannot be larger than ∼1/L. In integrable systems with boundary dissipation one typically observes scaling of ∼1/L(3), while in chaotic ones one can have faster relaxation with the gap scaling as ∼1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays

Abstract: We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization-group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method brings considerable advantage when compared to the integration of the time-dependent problem via Trotter decomposition, as it can address arbitrarily long-ranged couplings. Additionally, it ensures numerical stability in the case of weakly dissipative systems thanks to a slow tuning of the dissipation rates along the sweeps. We have tested the method on a driven-dissipative spin chain, under various assumptions for the Hamiltonian, drive, and dissipation parameters, and compared the results to those obtained both by Trotter dynamics and Monte Carlo wave function methods. Accurate and numerically stable convergence was always achieved when applying the method to systems with a gapped Liouvillian and a nondegenerate steady state.

Adaptive Optimal Control of Highly Dissipative Nonlinear Spatially Distributed Processes With Neuro-Dynamic Programming

Abstract: Highly dissipative nonlinear partial differential equations (PDEs) are widely employed to describe the system dynamics of industrial spatially distributed processes (SDPs). In this paper, we consider the optimal control problem of the general highly dissipative SDPs, and propose an adaptive optimal control approach based on neuro-dynamic programming (NDP). Initially, Karhunen-Loeve decomposition is employed to compute empirical eigenfunctions (EEFs) of the SDP based on the method of snapshots. These EEFs together with singular perturbation technique are then used to obtain a finite-dimensional slow subsystem of ordinary differential equations that accurately describes the dominant dynamics of the PDE system. Subsequently, the optimal control problem is reformulated on the basis of the slow subsystem, which is further converted to solve a Hamilton-Jacobi–Bellman (HJB) equation. HJB equation is a nonlinear PDE that has proven to be impossible to solve analytically. Thus, an adaptive optimal control method is developed via NDP that solves the HJB equation online using neural network (NN) for approximating the value function; and an online NN weight tuning law is proposed without requiring an initial stabilizing control policy. Moreover, by involving the NN estimation error, we prove that the original closed-loop PDE system with the adaptive optimal control policy is semiglobally uniformly ultimately bounded. Finally, the developed method is tested on a nonlinear diffusion-convection-reaction process and applied to a temperature cooling fin of high-speed aerospace vehicle, and the achieved results show its effectiveness.

Wave kinetics of random fibre lasers

Abstract: Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrodinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics.

Effective field theory of dissipative fluids

Abstract: We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional $Z_2$ symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.

Corner-Space Renormalization Method for Driven-Dissipative Two-Dimensional Correlated Systems.

Abstract: We present a theoretical method to study driven-dissipative correlated quantum systems on lattices with two spatial dimensions (2D). The steady-state density matrix of the lattice is obtained by solving the master equation in a corner of the Hilbert space. The states spanning the corner space are determined through an iterative procedure, using eigenvectors of the density matrix of smaller lattice systems, merging in real space two lattices at each iteration and selecting M pairs of states by maximizing their joint probability. The accuracy of the results is then improved by increasing the dimension M of the corner space until convergence is reached. We demonstrate the efficiency of such an approach by applying it to the driven-dissipative 2D Bose-Hubbard model, describing lattices of coupled cavities with quantum optical nonlinearities.

Observation of generalized optomechanical coupling and cooling on cavity resonance.

Abstract: Optomechanical coupling between a light field and the motion of a cavity mirror via radiation pressure plays an important role for the exploration of macroscopic quantum physics and for the detection of gravitational waves (GWs). It has been used to cool mechanical oscillators into their quantum ground states and has been considered to boost the sensitivity of GW detectors, e.g., via the optical spring effect. Here, we present the experimental characterization of generalized, that is, dispersive and dissipative, optomechanical coupling, with a macroscopic ð1.5 mmÞ 2 -size silicon nitride membrane in a cavityenhanced Michelson-type interferometer. We report for the first time strong optomechanical cooling based on dissipative coupling, even on cavity resonance, in excellent agreement with theory. Our result will allow for new experimental regimes in macroscopic quantum physics and GW detection.

Continuum thermodynamics of chemically reacting fluid mixtures

Abstract: We consider viscous, heat-conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of partial mass and partial momentum balances plus a mixture balance of internal energy. This is achieved by careful exploitation of the entropy principle and requires appropriate definitions of absolute temperature and chemical potentials, based on an adequate definition of thermal energy excluding diffusive contributions. The resulting interaction forces split into a thermo-mechanical and a chemical part, where the former turns out to be symmetric in case of binary interactions. For chemically reacting systems and as a new result, the chemical interaction force is a contribution being non-symmetric outside of chemical equilibrium. The theory also provides a rigorous derivation of the so-called generalized thermodynamic driving forces, avoiding the use of approximate solutions to the Boltzmann equations. Moreover, using an appropriately extended version of the entropy principle and introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations become a strict consequence. With a classification of the factors in the binary products of the entropy production according to their parity—instead of the classical partition into so-called fluxes and driving forces—the apparent antisymmetry of certain couplings is thereby also revealed. If the diffusion velocities are small compared with the speed of sound, the Maxwell–Stefan equations follow in the case without chemistry, thereby neglecting wave phenomena in the diffusive motion. This results in a reduced model with only mass being balanced individually. In the reactive case, this approximation via a scale separation argument is no longer possible. We introduce the new concept of entropy invariant model reduction, leaving the entropy production unchanged under the reduction from partial momentum balances to a single mixture momentum balance. This results in an extension of the Maxwell–Stefan equations to chemically active mixtures with an additional contribution to the transport coefficients due to the chemical interactions.

Eightfold Classification of Hydrodynamic Dissipation.

Abstract: We provide a complete characterization of hydrodynamic transport consistent with the second law of thermodynamics at arbitrary orders in the gradient expansion. A key ingredient in facilitating this analysis is the notion of adiabatic hydrodynamics, which enables isolation of the genuinely dissipative parts of transport. We demonstrate that most transport is adiabatic. Furthermore, in the dissipative part, only terms at the leading order in gradient expansion are constrained to be sign definite by the second law (as has been derived before).

Intermittent chaotic chimeras for coupled rotators.

Abstract: Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other jumps erratically between laminar and turbulent phases. These states have finite lifetimes diverging as a power law with N and m. Lyapunov analyses reveal chaotic properties in quantitative agreement with theoretical predictions for globally coupled dissipative systems.

Synchronization and circuit design of a chaotic system with coexisting hidden attractors

Abstract: This paper investigates an unusual example of a three- dimensional dissipative chaotic flow with quadratic nonlinearites in which there is no equilibrium. This system belongs to a newly introduced category of chaotic systems: systems with hidden attractors which have important and potentially problematic engineering consequences. It is more interesting when we show there are coexisting hidden attractors for some range of parameters. We investigate this system through some analysis, circuit design and finally we use it as a benchmark for synchronization using a Robust Adaptive Sliding Mode Control (RASMC). This synchronization is performed through a nonlinear controller based on Lyapunov Stability Theory to stabilize the error dynamics.

Dissipative preparation of Chern insulators

Abstract: Engineered dissipation can be employed to prepare interesting quantum many-body states in a nonequilibrium fashion. The basic idea is to obtain the state of interest as the unique steady state of a quantum master equation, irrespective of the initial state. Due to a fundamental competition of topology and locality, the dissipative preparation of gapped topological phases with a nonvanishing Chern number has so far remained elusive. Here, we study the open quantum system dynamics of fermions on a two-dimensional lattice in the framework of a Lindblad master equation. In particular, we discover a mechanism to dissipatively prepare a topological steady state with nonzero Chern number by means of short-range system bath interaction. Quite remarkably, this gives rise to a stable topological phase in a nonequilibrium phase diagram. We demonstrate how our theoretical construction can be implemented in a microscopic model that is experimentally feasible with cold atoms in optical lattices.

Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition.

Abstract: The dynamic structure factor is a central quantity describing the physics of quantum many-body systems, capturing structure and collective excitations of a material. In condensed matter, it can be measured via inelastic neutron scattering, which is an energy-resolving probe for the density fluctuations. In ultracold atoms, a similar approach could so far not be applied because of the diluteness of the system. Here we report on a direct, real-time and nondestructive measurement of the dynamic structure factor of a quantum gas exhibiting cavity-mediated long-range interactions. The technique relies on inelastic scattering of photons, stimulated by the enhanced vacuum field inside a high finesse optical cavity. We extract the density fluctuations, their energy and lifetime while the system undergoes a structural phase transition. We observe an occupation of the relevant quasi-particle mode on the level of a few excitations, and provide a theoretical description of this dissipative quantum many-body system.

Strange attractors with various equilibrium types

Abstract: Of the eight types of hyperbolic equilibrium points in three-dimensional flows, one is overwhelmingly dominant in dissipative chaotic systems This paper shows examples of chaotic systems for each of the eight types as well as one without any equilibrium and two that are nonhyperbolic The systems are a generalized form of the Nose-Hoover oscillator with a single equilibrium point Six of the eleven cases have hidden attractors, and six of them exhibit multistability for the chosen parameters

Precisely cyclic sand: Self-organization of periodically sheared frictional grains

Abstract: The disordered static structure and chaotic dynamics of frictional granular matter has occupied scientists for centuries, yet there are few organizational principles or guiding rules for this highly hysteretic, dissipative material. We show that cyclic shear of a granular material leads to dynamic self-organization into several phases with different spatial and temporal order. Using numerical simulations, we present a phase diagram in strain–friction space that shows chaotic dispersion, crystal formation, vortex patterns, and most unusually a disordered phase in which each particle precisely retraces its unique path. However, the system is not reversible. Rather, the trajectory of each particle, and the entire frictional, many–degrees-of-freedom system, organizes itself into a limit cycle absorbing state. Of particular note is that fact that the cyclic states are spatially disordered, whereas the ordered states are chaotic.

Cavity-funneled generation of indistinguishable single photons from strongly dissipative quantum emitters.

Abstract: We investigate theoretically the generation of indistinguishable single photons from a strongly dissipative quantum system placed inside an optical cavity. The degree of indistinguishability of photons emitted by the cavity is calculated as a function of the emitter-cavity coupling strength and the cavity linewidth. For a quantum emitter subject to strong pure dephasing, our calculations reveal that an unconventional regime of high indistinguishability can be reached for moderate emitter-cavity coupling strengths and high-quality factor cavities. In this regime, the broad spectrum of the dissipative quantum system is funneled into the narrow line shape of the cavity. The associated efficiency is found to greatly surpass spectral filtering effects. Our findings open the path towards on-chip scalable indistinguishable-photon-emitting devices operating at room temperature.

Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method

Abstract: We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without a choice of frame such as the Landau-Lifshitz or Eckart frame.

Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems

Abstract: We consider a general Euler-Korteweg-Poisson system in R 3, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics equations with capillarity are recovered as particular examples. We show that the system admits infinitely many global-in-time weak solutions for any sufficiently smooth initial data including the case of a vanishing initial density - the vacuum zones. Moreover, there is a vast family of initial data, for which the Cauchy problem possesses infinitely many dissipative weak solutions, i.e. the weak solutions satisfying the energy inequality. Finally, we establish the weak-strong uniqueness property in a class of solutions without vacuum. In this paper we show that, even in presence of a dispersive tensor, we have the same phenomena found by De Lellis and Szekelyhidi.

Dissipative properties of hot and dense hadronic matter in an excluded-volume hadron resonance gas model

Abstract: In this work we estimate dissipative properties viz: shear and bulk viscosities of hadronic matter using relativistic Boltzmann equation in relaxation time approximation within ambit of excluded volume hadron resonance gas (EHRG) model. We find that at zero chemical potential the shear viscosity to entropy ratio (�/s) decreases with temperature and reaches very close to Kovtun-SonStarinets (KSS) bound as compared to the results based on molecular kinetic theory approach. At finite chemical potential this ratio shows same behavior as a function of temperature but goes below KSS bound. We further find that along chemical freezout line �/s increases monotonically while the bulk viscosity to entropy ratio (�/s) decreases monotonically.