Showing papers on "Dissipative system published in 2012"

Dissipative solitons for mode-locked lasers

Abstract: This Review explains the concept of dissipative solitons and their application to high-energy mode-locked fibre laser cavities. Dynamics and effects such as dissipative soliton ‘explosions’ and ‘rain’ are summarized, and an outlook of the field is also provided.

Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser

Abstract: Rare events of extremely high optical intensity are experimentally recorded at the output of a mode-locked fiber laser that operates in a strongly dissipative regime of chaotic multiple-pulse generation. The probability distribution of these intensity fluctuations, which highly depend on the cavity parameters, features a long-tailed distribution. Recorded intensity fluctuations result from the ceaseless relative motion and nonlinear interaction of pulses within a temporally localized multisoliton phase.

Nonlinear maximum principles for dissipative linear nonlocal operators and applications

Abstract: We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative anti-symmetric perturbation of 2D incompressible Euler equations and generalized fractional dissipative 2D Boussinesq equations.

Dissipative phase transition in a central spin system

Abstract: We investigate dissipative phase transitions in an open central spin system. In our model the central spin interacts coherently with the surrounding many-particle spin environment and is subject to coherent driving and dissipation. We develop analytical tools based on a self-consistent Holstein-Primakoff approximation that enable us to determine the complete phase diagram associated with the steady states of this system. It includes first- and second-order phase transitions, as well as regions of bistability, spin squeezing, and altered spin-pumping dynamics. Prospects of observing these phenomena in systems such as electron spins in quantum dots or nitrogen-vacancy centers coupled to lattice nuclear spins are briefly discussed.

Effective operator formalism for open quantum systems

Abstract: We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method with the hitherto existing concepts for effective interactions and present physical examples for the application of our formalism, including dissipative state preparation by engineered decay processes.

Decay of Dissipative Equations and Negative Sobolev Spaces

Abstract: We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible Navier-Stokes equations and the Boltzmann equation. In particular, the optimal decay rates of the higher-order spatial derivatives of solutions are obtained. The negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis.

Engineered Open Systems and Quantum Simulations with Atoms and Ions

Abstract: The enormous experimental progress in atomic, molecular, and optical (AMO) physics during the last decades allows us nowadays to isolate single, a few or even many-body ensembles of microscopic particles, and to manipulate their quantum properties at a level of precision, which still seemed unthinkable some years ago. This versatile set of tools has enabled the development of the well-established concept of engineering of many-body Hamiltonians in various physical platforms. These available tools, however, can also be harnessed to extend the scenario of Hamiltonian engineering to a more general Liouvillian setting, which in addition to coherent dynamics also includes controlled dissipation in many-body quantum systems. Here, we review recent theoretical and experimental progress in different directions along these lines, with a particular focus on physical realizations with systems of atoms and ions. This comprises digital quantum simulations in a general open system setting, as well as engineering and understanding new classes of systems far away from thermodynamic equilibrium. In the context of digital quantum simulation, we first outline the basic concepts and illustrate them on the basis of a recent experiment with trapped ions. We also discuss theoretical work proposing an intrinsically scalable simulation architecture for spin models with high-order interactions such as Kitaev’s toric code, based on Rydberg atoms stored in optical lattices. We then turn to the digital simulation of dissipative many-body dynamics, pointing out a route for the general quantum state preparation in complex spin models, and discuss a recent experiment demonstrating the basic building blocks of a full-fledged open-system quantum simulator. In view of creating novel classes of out-of-equilibrium systems, we focus on ultracold atoms. We point out how quantum mechanical long-range order can be established via engineered dissipation, and present genuine many-body aspects of this setting: in the context of bosons, we discuss dynamical phase transitions resulting from competing Hamiltonian and dissipative dynamics. In the context of fermions, we present a purely dissipative pairing mechanism, and show how this could pave the way for the quantum simulation of the Fermi–Hubbard model. We also propose and analyze the key properties of dissipatively targeted topological phases of matter.

Dissipative continuous Euler flows

Abstract: We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy.

Model of dissipative dielectric elastomers

Abstract: The dynamic performance of dielectric elastomer transducers and their capability of electromechanical energy conversion are affected by dissipative processes, such as viscoelasticity, dielectric relaxation, and current leakage. This paper describes a method to construct a model of dissipative dielectric elastomers on the basis of nonequilibrium thermodynamics. We characterize the state of the dielectric elastomer with kinematic variables through which external loads do work, and internal variables that measure the progress of the dissipative processes. The method is illustrated with examples motivated by existing experiments of polyacrylate very-high-bond dielectric elastomers. This model predicts the dynamic response of the dielectric elastomer and the leakage current behavior. We show that current leakage can be significant under large deformation and for long durations. Furthermore, current leakage can result in significant hysteresis for dielectric elastomers under cyclic voltage.

Long-Lived Electronic Coherence in Dissipative Exciton-Dynamics of Light-Harvesting Complexes

Abstract: The observed prevalence of oscillatory signals in the spectroscopy of biological light-harvesting complexes at ambient temperatures has led to a search for mechanisms supporting coherent transport through larger molecules in noisy environments. We demonstrate a generic mechanism supporting long-lasting electronic coherence up to 0.3 ps at a temperature of 277 K. The mechanism relies on two properties of the spectral density: (i) a large dissipative coupling to a continuum of higher-frequency vibrations required for efficient transport and (ii) a small slope of the spectral density at zero frequency.

Nonlinear damping in a micromechanical oscillator

Abstract: Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). A Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator, which exhibits nonlinearity in both elastic and dissipative properties. The dynamics of the oscillator is measured in both frequency and time domains and compared to theoretical predictions based on a Duffing-like model with nonlinear dissipation. We especially focus on the behavior of the system near bifurcation points. The results show that nonlinear dissipation can have a significant impact on the dynamics of micromechanical systems. To account for the results, we have developed a continuous model of a geometrically nonlinear beam-string with a linear Voigt–Kelvin viscoelastic constitutive law, which shows a relation between linear and nonlinear damping. However, the experimental results suggest that this model alone cannot fully account for all the experimentally observed nonlinear dissipation, and that additional nonlinear dissipative processes exist in our devices.

The Thermodynamics of Simple Materials with Fading Memory

Abstract: 1 Preliminaries.- 1.1 Vector and Tensor Analysis.- 1.2 Paths and Line Integrals.- 1.3 Kinematics and the Balance Laws.- 1.4 Simple Materials with Memory.- 2 A Theory of Thermodynamics.- 2.1 Processes.- 2.2 The Thermodynamic Inequality.- 2.3 Heat Conduction Inequalities.- 2.4 The Conversion of Heat into Mechanical Work.- 3 The Construction of the Entropy.- 3.1 The Clausius Inequality.- 3.2 Fading Memory.- 3.3 The Entropy in Equilibrium. Thermostatics.- 3.4 The Entropy away from Equilibrium. The Clausius-Planck Inequality.- 4 Applications.- 4.1 Thermoelasticity and Materials of Differential Type.- 4.2 A Class of Viscoelastic Materials.- 5 Thermodynamics based on the Clausius-Duhem Inequality.- 5.1 The Clausius-Duhem Inequality.- 5.2 Materials of the Differential Type.- 5.3 Materials with Fading Memory and Instantaneous Elastic Response.- 5.4 Behaviour near Equilibrium.- 5.5 The Internal Energy as an Independent Variable.- 6 Thermodynamic Restrictions on Isothermal Linear Viscoelasticity.- 6.1 Compatibility with Thermodynamics. Dissipative Relaxation Functions.- 6.2 The Symmetry of the Relaxation Function.- 6.3 A Remark on the Monotonicity of Relaxation Functions.- References.

Generalized surface quasi-geostrophic equations with singular velocities

Abstract: This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The first family is a generalized surface quasigeostrophic (SQG) equation with the velocity field u related to the scalar θ by , where and is the Zygmund operator. The borderline case β = 1 corresponds to the SQG equation and the situation is more singular for β > 1. We obtain the local existence and uniqueness of classical solutions, the global existence of weak solutions, and the local existence of patch-type solutions. The second family is a dissipative active scalar equation with , which is at least logarithmically more singular than the velocity in the first family. We prove that this family with any fractional dissipation possesses a unique local smooth solution for any given smooth data. This result for the second family constitutes a first step towards resolving the global regularity issue recently proposed by K. Ohkitani. © 2012 Wiley Periodicals, Inc.

Driven-dissipative preparation of entangled states in cascaded quantum-optical networks

Abstract: We study the dissipative dynamics and the formation of entangled states in driven cascaded quantum networks, where multiple systems are coupled to a common unidirectional bath. Specifically, we identify the conditions under which emission and coherent reabsorption of radiation drives the whole network into a pure stationary state with non-trivial quantum correlations between the individual nodes. We illustrate this effect in more detail for the example of cascaded two-level systems, where we present an explicit preparation scheme that allows one to tune the whole network through 'bright' and 'dark' states associated with different multi-partite entanglement patterns. In a complementary setting consisting of cascaded nonlinear cavities, we find that two cavity modes can be driven into a non-Gaussian entangled dark state. Potential realizations of such cascaded networks with optical and microwave photons are discussed.

Collective behavior of thermally active colloids.

Abstract: Colloids with patchy metal coating under laser irradiation could act as local heat sources and generate temperature gradients that could induce self-propulsion and interactions between them. The collective behavior of a dilute solution of such thermally active particles is studied using a stochastic formulation. It is found that when the Soret coefficient is positive, the system could be described in a stationary state by the nonlinear Poisson-Boltzmann equation and could adopt density profiles with significant depletion in the middle region when confined. For colloids with a negative Soret coefficient, the system can be described as a dissipative equivalent of a gravitational system. It is shown that in this case the thermally active colloidal solution could undergo an instability at a critical laser intensity, which has similarities to a supernova explosion.

Time series irreversibility: a visibility graph approach

Abstract: We propose a method to measure real-valued time series irreversibility which combines two different tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the inand outdegree distributions of the associated graph. The method is computationally efficient and does not require any ad hoc symbolization process. We find that the method correctly distinguishes between reversible and irreversible stationary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic processes (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identify the irreversible nature of the series.

Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two- dimensionalcorrelation spectroscopy

Abstract: We theoretically investigate an electron transfer (ET) process in a dissipative environment by means of two-dimensional (2D) correlation spectroscopy. We extend the reduced hierarchy equations of motion approach to include both overdamped Drude and underdamped Brownian modes. While the overdamped mode describes the inhomogeneity of a system in the slow modulation limit, the underdamped mode expresses the primary vibrational mode coupled with the electronic states. We outline a procedure for calculating 2D correlation spectrum that incorporates the ET processes. The present approach has the capability of dealing with system-bath coherence under an external perturbation, which is important to calculate nonlinear response functions for non-Markovian noise. The calculated 2D spectrum exhibits the effects of the ET processes through the presence of ET transition peaks along the $\Omega_1$ axis, as well as the decay of echo signals.

Dynamical phases and intermittency of the dissipative quantum Ising model

Abstract: We employ the concept of a dynamical, activity order parameter to study the Ising model in a transverse magnetic field coupled to a Markovian bath. For a certain range of values of the spin-spin coupling, magnetic field, and dissipation rate, we identify a first-order dynamical phase transition between active and inactive dynamical phases. We demonstrate that dynamical phase coexistence becomes manifest in an intermittent behavior of the bath quanta emission. Moreover, we establish the connection between the dynamical order parameter that quantifies the activity and the longitudinal magnetization that serves as static order parameter. The system that we consider can be implemented in current experiments with Rydberg atoms and trapped ions.

Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy

Abstract: We theoretically investigate an electron transfer (ET) process in a dissipative environment by means of two-dimensional (2D) correlation spectroscopy. We extend the reduced hierarchy equations of motion approach to include both overdamped Drude and underdamped Brownian modes. While the overdamped mode describes the inhomogeneity of a system in the slow modulation limit, the underdamped mode expresses the primary vibrational mode coupled with the electronic states. We outline a procedure for calculating 2D correlation spectrum that incorporates the ET processes. The present approach has the capability of dealing with system-bath coherence under an external perturbation, which is important to calculate nonlinear response functions for non-Markovian noise. The calculated 2D spectrum exhibits the effects of the ET processes through the presence of ET transition peaks along the Ω1 axis, as well as the decay of echo signals.

Cylindrically symmetric relativistic fluids: a study based on structure scalars

Abstract: Applying the 1 + 3 formalism we write down the full set of equations governing the structure and the evolution of self-gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, in terms of scalar quantities obtained from the orthogonal splitting of the Riemann tensor (structure scalars), in the context of general relativity. These scalars which have been shown previously (in the spherically symmetric case) to be related to fundamental properties of the fluid distribution, such as: energy density, energy density inhomogeneity, local anisotropy of pressure, dissipative flux, active gravitational mass etc, are shown here to play also a very important role in the dynamics of cylindrically symmetric fluids. It is also shown that in the static case, all possible solutions to Einstein equations may be expressed explicitly through three of these scalars.

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation

Abstract: Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.

Current-induced atomic dynamics, instabilities, and Raman signals: Quasiclassical Langevin equation approach

Abstract: We derive and employ a semiclassical Langevin equation obtained from path integrals to describe the ionic dynamics of a molecular junction in the presence of electrical current. The electronic environment serves as an effective nonequilibrium bath. The bath results in random forces describing Joule heating, current-induced forces including the nonconservative wind force, dissipative frictional forces, and an effective Lorentz-type force due to the Berry phase of the nonequilibrium electrons. Using a generic two-level molecular model, we highlight the importance of both current-induced forces and Joule heating for the stability of the system. We compare the impact of the different forces, and the wide-band approximation for the electronic structure on our result. We examine the current-induced instabilities (excitation of runaway ``waterwheel'' modes) and investigate the signature of these in the Raman signals.

The equilibrium tide in stars and giant planets: I - the coplanar case

Abstract: Context. Since 1995, more than 500 extrasolar planets have been discovered orbiting very close to their parent star, where they experience strong tidal interactions. Their orbital evolution depends on the physical mechanisms that cause tidal dissipation, which remain poorly understood. Aims. We refine the theory of the equilibrium tide in fluid bodies that are partly or entirely convective, to predict the dynamical evolution of the systems. In particular, we examine the validity of modeling the tidal dissipation using the quality factor Q , which is commonly done. We consider here the simplest case where the considered star or planet rotates uniformly, all spins are aligned, and the companion is reduced to a point mass. Methods. We expand the tidal potential as a Fourier series, and express the hydrodynamical equations in the reference frame, which rotates with the corresponding Fourier component. The results are cast in the form of a complex disturbing function, which may be implemented directly in the equations governing the dynamical evolution of the system.Results. The first manifestation of the tide is to distort the shape of the star or planet adiabatically along the line of centers. This generates the divergence-free velocity field of the adiabatic equilibrium tide, which is stationary in the frame rotating with the considered Fourier component of the tidal potential; this large-scale velocity field is decoupled from the dynamical tide. The tidal kinetic energy is dissipated into heat by means of turbulent friction, which is modeled here as an eddy-viscosity acting on the adiabatic tidal flow. This dissipation induces a second velocity field, the dissipative equilibrium tide, which is in quadrature with the exciting potential; this field is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which one derives the characteristic evolutionary times.Conclusions. The rate at which the system evolves depends on the physical properties of the tidal dissipation, and specifically on both how the eddy viscosity varies with tidal frequency and the thickness of the convective envelope for the fluid equilibrium tide. At low frequency, this tide is retarded by a constant time delay, whereas it lags behind by a constant angle when the tidal frequency exceeds the convective turnover rate.

Performance of dissipative dielectric elastomer generators

Abstract: Dielectric elastomer generators are high-energy-density electromechanical transducers. Their performance is affected by dissipative losses. This paper presents a theoretical analysis of a dielectric elastomer generator with two dissipative processes: viscoelasticity and current leakage. Conversion cycles are shown to attain steady-state after several cycles. Performance parameters such as electrical energy generated per cycle, average power, and mechanical to electrical energy conversion efficiency are introduced. Trade-offs between large electrical energy and power output and poor conversion efficiency are discussed. Excessive current leakage results in negative efficiency—the dielectric elastomer generator wastes energy instead of generating it. The general framework developed in this paper helps in the design and assessment of conversion cycles for dissipative dielectric elastomer generators.

Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities

Abstract: We prove the existence of regular dissipative solutions and global attractors for the 3D Brinkmann-Forchheimer equations with a nonlinearity of arbitrary polynomial growth rate. In order to obtain this result, we prove the maximal regularity estimate for the corresponding semi-linear stationary Stokes problem using some modification of the nonlinear localization technique. The applications of our results to the Brinkmann-Forchheimer equation with the Navier-Stokes inertial term are also considered.