Showing papers on "Dissipative system published in 2011"
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28 Sep 2011
TL;DR: A detailed review of state-of-the-art theoretical, analytical and numerical methodologies for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate is given in this article.
Abstract: Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence. Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. Whenever possible the link between theory and experiment is illustrated, and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of basic, underlying physics.
311 citations
TL;DR: This analysis indicates that dissipative state preparation is more than just a new conceptual approach, but can allow for significant improvement as compared to preparation protocols based on coherent unitary dynamics.
Abstract: We propose a novel scheme for the preparation of a maximally entangled state of two atoms in an optical cavity. Starting from an arbitrary initial state, a singlet state is prepared as the unique fixed point of a dissipative quantum dynamical process. In our scheme, cavity decay is no longer undesirable, but plays an integral part in the dynamics. As a result, we get a qualitative improvement in the scaling of the fidelity with the cavity parameters. Our analysis indicates that dissipative state preparation is more than just a new conceptual approach, but can allow for significant improvement as compared to preparation protocols based on coherent unitary dynamics.
299 citations
TL;DR: The existence of localized modes supported by the PT-symmetric nonlinear lattices is reported in this article, and the system considered reveals unusual properties: unlike other typical dissipative systems, it possesses families (branch) of solutions, which can be parametrized by the propagation constant.
Abstract: The existence of localized modes supported by the $\mathcal{PT}$-symmetric nonlinear lattices is reported. The system considered reveals unusual properties: unlike other typical dissipative systems, it possesses families (branches) of solutions, which can be parametrized by the propagation constant; relatively narrow localized modes appear to be stable, even when the conservative nonlinear lattice potential is absent; and finally, the system supports stable multipole solutions.
294 citations
TL;DR: In this paper, a review of the linear theory of MHD resonant waves in inhomogeneous plasmas is presented, where the authors discuss the properties of driven resonant MHD waves.
Abstract: The linear theory of MHD resonant waves in inhomogeneous plasmas is reviewed. The review starts from discussing the properties of driven resonant MHD waves. The dissipative solutions in Alfven and slow dissipative layers are presented. The important concept of connection formulae is introduced. Next, we proceed on to non-stationary resonant MHD waves. The relation between quasi-modes of ideal MHD and eigenmodes of dissipative MHD are discussed. The solution describing the wave motion in non-stationary dissipative layers is given. It is shown that the connection formulae remain valid for non-stationary resonant MHD waves. The initial-value problem for resonant MHD waves is considered. The application of theory of resonant MHD waves to solar physics is discussed.
241 citations
TL;DR: In this article, the authors introduce a new framework of highly anisotropic hydrodynamics that includes dissipation effects, defined by the form of the entropy source that depends on the pressure anisotropy and vanishes for the isotropic fluid.
Abstract: We introduce a new framework of highly anisotropic hydrodynamics that includes dissipation effects Dissipation is defined by the form of the entropy source that depends on the pressure anisotropy and vanishes for the isotropic fluid With a simple ansatz for the entropy source obeying general physical requirements, we are led to a nonlinear equation describing the time evolution of the anisotropy in purely longitudinal boost-invariant systems Matter that is initially highly anisotropic approaches naturally the regime of the perfect fluid Thus, the resulting evolution agrees with the expectations about the behavior of matter produced at the early stages of relativistic heavy-ion collisions The equilibration is identified with the processes of entropy production
235 citations
Posted Content•
TL;DR: In this article, the authors developed a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space, which is applied to classical examples such as the heat equation, the compressible Navier-Stokes equations and the Boltzmann equation.
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.
217 citations
Posted Content•
TL;DR: In this paper, a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile, were obtained and used to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations.
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.
193 citations
TL;DR: In this paper, the authors present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding, where the fluid is indeed imperfect because the energy flows neither along the field gradient nor along the shift current.
Abstract: We present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding. In particular, this picture applies to the simplest galileons and k-essence. The fluid variables not only have a clear physical meaning but also drastically simplify the analysis of the system. The fluid carries charges corresponding to shifts in field space. This shift-charge current contains a spatial part responsible for diffusion of the charges. Moreover, in the incompressible limit, the equation of motion becomes the standard diffusion equation. The fluid is indeed imperfect because the energy flows neither along the field gradient nor along the shift current. The fluid has zero vorticity and is not dissipative: there is no entropy production, the energy-momentum is exactly conserved, the temperature vanishes and there is no shear viscosity. Still, in an expansion around a perfect fluid one can identify terms which correct the pressure in the manner of bulk viscosity. We close by formulating the non-trivial conditions for the thermodynamic equilibrium of this imperfect fluid.
177 citations
TL;DR: Results are presented which indicate that, even though the method is based on a "mean trajectory" like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.
Abstract: An approach for treating dissipative, non-adiabatic quantum dynamics in general model systems at finite temperature based on linearizing the density matrix evolution in the forward-backward path difference for the environment degrees of freedom is presented. We demonstrate that the approach can capture both short time coherent quantum dynamics and long time thermal equilibration in an application to excitation energy transfer in a model photosynthetic light harvesting complex. Results are also presented for some nonadiabatic scattering models which indicate that, even though the method is based on a "mean trajectory" like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.
162 citations
TL;DR: This work studies numerically rogue waves in dissipative systems, taking as an example a unidirectional fiber laser in a nonstationary regime of operation and finding that the probability of producing extreme pulses in this setup is higher than in any other system considered so far.
Abstract: We study numerically rogue waves in dissipative systems, taking as an example a unidirectional fiber laser in a nonstationary regime of operation. The choice of specific set of parameters allows the laser to generate a chaotic sequence of pulses with a random distribution of peak amplitudes. The probability density function for the intensity maxima has an elevated tail at higher intensities. We have found that the probability of producing extreme pulses in this setup is higher than in any other system considered so far.
158 citations
TL;DR: In this paper, a hybrid transport approach for the bulk evolution of viscous QCD matter produced in ultra-relativistic heavy-ion collisions is presented, where the expansion of the dense deconfined phase of the reaction is modeled with viscous hydrodynamics, while the dilute late hadron gas stage is described microscopically by the Boltzmann equation.
Abstract: A hybrid transport approach for the bulk evolution of viscous QCD matter produced in ultra-relativistic heavy-ion collisions is presented. The expansion of the dense deconfined phase of the reaction is modeled with viscous hydrodynamics, while the dilute late hadron gas stage is described microscopically by the Boltzmann equation. The advantages of such a hybrid approach lie in the improved capability of handling large dissipative corrections in the late dilute phase of the reaction, including a realistic treatment of the nonequilibrium hadronic chemistry and kinetic freeze-out. By varying the switching temperature at which the hydrodynamic output is converted to particles for further propagation with the Boltzmann cascade we test the ability of the macroscopic hydrodynamic approach to emulate the microscopic evolution during the hadronic stage and extract the temperature dependence of the effective shear viscosity of the hadron resonance gas produced in the collision. We find that the extracted values depend on the prior hydrodynamic history and hence do not represent fundamental transport properties of the hadron resonance gas. We conclude that viscous fluid dynamics does not provide a faithful description of hadron resonance gas dynamics with predictive power, and that both components of the hybrid approach are needed for a quantitative description of the fireball expansion and its freeze-out.
TL;DR: In this paper, the authors present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding, where the fluid is indeed imperfect because the energy flows neither along the field gradient nor along the shift current.
Abstract: We present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding. In particular, this picture applies to the simplest galileons and k-essence. The fluid variables not only have a clear physical meaning but also drastically simplify the analysis of the system. The fluid carries charges corresponding to shifts in field space. This shift-charge current contains a spatial part responsible for diffusion of the charges. Moreover, in the incompressible limit, the equation of motion becomes the standard diffusion equation. The fluid is indeed imperfect because the energy flows neither along the field gradient nor along the shift current. The fluid has zero vorticity and is not dissipative: there is no entropy production, the energy-momentum is exactly conserved, the temperature vanishes and there is no shear viscosity. Still, in an expansion around a perfect fluid one can identify terms which correct the pressure in the manner of bulk viscosity. We close by formulating the non-trivial conditions for the thermodynamic equilibrium of this imperfect fluid.
TL;DR: In this paper, a constitutive framework for solids with dissipative micro-structures based on compact variational statements is presented, where incremental minimization and saddle point principles for a class of gradient-type dissipative materials are developed.
Abstract: The paper presents a constitutive framework for solids with dissipative micro-structures based on compact variational statements. It develops incremental minimization and saddle point principles for a class of gradient-type dissipative materials which incorporate micro-structural fields (micro-displacements, order parameters, or generalized internal variables), whose gradients enter the energy storage and dissipation functions. In contrast to classical local continuum approaches to inelastic solids based on locally evolving internal variables, these global micro-structural fields are governed by additional balance equations including micro-structural boundary conditions. They describe changes of the substructure of the material which evolve relatively to the material as a whole. Typical examples are theories of phase field evolution, gradient damage, or strain gradient plasticity. Such models incorporate non-local effects based on length scales, which reflect properties of the material micro-structure. We outline a unified framework for the broad class of first-order gradient-type standard dissipative solids. Particular emphasis is put on alternative multi-field representations, where both the microstructural variable itself as well as its dual driving force are present. These three-field settings are suitable for models with threshold- or yield-functions formulated in the space of the driving forces. It is shown that the coupled macro- and micro-balances follow in a natural way as the Euler equations of minimization and saddle point principles, which are based on properly defined incremental potentials. These multi-field potential functionals are outlined in both a continuous rate formulation and a time–space-discrete incremental setting. The inherent symmetry of the proposed multi-field formulations is an attractive feature with regard to their numerical implementation. The unified character of the framework is demonstrated by a spectrum of model problems, which covers phase field models and formulations of gradient damage and plasticity.
TL;DR: A phenomenological theory of current-induced staggered magnetization dynamics in antiferromagnets is derived, which captures the reactive and dissipative current- induced torques and the conventional effects of magnetic fields and damping.
Abstract: We derive a phenomenological theory of current-induced staggered magnetization dynamics in antiferromagnets. The theory captures the reactive and dissipative current-induced torques and the conventional effects of magnetic fields and damping. A Walker ansatz describes the dc current-induced domain-wall motion when there is no dissipation. If magnetic damping and dissipative torques are included, the Walker ansatz remains robust when the domain wall moves slowly. As in ferromagnets, the domain-wall velocity is proportional to the ratio between the dissipative torque and the magnetization damping. In addition, a current-driven antiferromagnetic domain wall acquires a net magnetic moment.
TL;DR: A method to measure real-valued time series irreversibility which combines two different tools: the horizontal visibility algorithm and the Kullback-Leibler divergence, which correctly distinguishes between reversible and irreversible stationary time series.
Abstract: We propose a method to measure real-valued time series irreversibility which combines two differ- ent 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 in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (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 identifiy the irreversible nature of the series.
TL;DR: In this paper, the authors describe an approach to construct models of dielectric elastomers undergoing dissipative processes, such as viscoelastic, dielectrics and conductive relaxation, guided by nonequilibrium thermodynamics.
Abstract: This paper describes an approach to construct models of dielectric elastomers undergoing dissipative processes, such as viscoelastic, dielectric and conductive relaxation. This approach is guided by nonequilibrium thermodynamics, characterizing the state of a dielectric elastomer with kinematic variables through which external loads do work, as well as internal variables that describe the dissipative processes. Within this approach, a method is developed to calculate the critical condition for electromechanical instability. This approach is illustrated with a specific model of a viscoelastic dielectric elastomer, which is fitted to stress-strain curves of a dielectric elastomer (VHB tape), measured at various strain rates. The model shows that a higher critical voltage can be achieved by applying a constant voltage for a shorter time, or by applying ramping voltage with a higher rate. A viscoelastic dielectric elastomer can attain a larger strain of actuation than an elastic dielectric elastomer.
TL;DR: In this article, the authors compute the primordial curvature spectrum generated during warm inflation, including shear viscous effects, and show that when the shear viscosity is larger than 3ρ{sub s}/H at horizon crossing, ρ{sub r} being the radiation energy density, the damping effect wins and there is no growing mode in the spectrum.
Abstract: We compute the primordial curvature spectrum generated during warm inflation, including shear viscous effects. The primordial spectrum is dominated by the thermal fluctuations of the radiation bath, sourced by the dissipative term of the inflaton field. The dissipative coefficient Υ, computed from first principles in the close-to-equilibrium approximation, depends in general on the temperature T, and this dependence renders the system of the linear fluctuations coupled. Whenever the dissipative coefficient is larger than the Hubble expansion rate H, there is a growing mode in the fluctuations before horizon crossing. However, dissipation intrinsically means departures from equilibrium, and therefore the presence of a shear viscous pressure in the radiation fluid. This in turn acts as an extra friction term for the radiation fluctuations that tends to damp the growth of the perturbations. Independently of the T functional dependence of the dissipation and the shear viscosity, we find that when the shear viscous coefficient ζ{sub s} is larger than 3ρ{sub r}/H at horizon crossing, ρ{sub r} being the radiation energy density, the shear damping effect wins and there is no growing mode in the spectrum.
TL;DR: In this paper, a phenomenological picture of very large-scale motions coexisting and interacting with structures from the hairpin paradigm is provided for the high-Reynolds-number case.
Abstract: Simultaneous streamwise velocity measurements across the vertical direction obtained in the atmospheric surface layer (Re_τ ≃ 5 × 10^5) under near thermally neutral conditions are used to outline and quantify interactions between the scales of turbulence, from the very-large-scale motions to the dissipative scales. Results from conditioned spectra, joint probability density functions and conditional averages show that the signature of very-large-scale oscillations can be found across the whole wall region and that these scales interact with the near-wall turbulence from the energy-containing eddies to the dissipative scales, most strongly in a layer close to the wall, z^+ ≲ 10^3. The scale separation achievable in the atmospheric surface layer appears to be a key difference from the low-Reynolds-number picture, in which structures attached to the wall are known to extend through the full wall-normal extent of the boundary layer. A phenomenological picture of very-large-scale motions coexisting and interacting with structures from the hairpin paradigm is provided here for the high-Reynolds-number case. In particular, it is inferred that the hairpin-packet conceptual model may not be exhaustively representative of the whole wall region, but only of a near-wall layer of z^+ = O(10^3), where scale interactions are mostly confined.
TL;DR: This work proposes and theoretically explore a realization of this system in the optical domain, using a combined Michelson-Sagnac interferometer, which enables a strong and tunable dissipative coupling.
Abstract: Dissipative optomechanics studies the coupling of the motion of an optical element to the decay rate of a cavity We propose and theoretically explore a realization of this system in the optical domain, using a combined Michelson-Sagnac interferometer, which enables a strong and tunable dissipative coupling Quantum interference in such a setup results in the suppression of the lower motional sideband, leading to strongly enhanced cooling in the non-sideband-resolved regime With state-of-the-art parameters, ground-state cooling and low-power quantum-limited position transduction are both possible The possibility of a strong, tunable dissipative coupling opens up a new route towards observation of such fundamental optomechanical effects as nonlinear dynamics Beyond optomechanics, the suggested method can be readily transferred to other setups involving nonlinear media, atomic ensembles, or single atoms
TL;DR: In this paper, the coupled balance equations for a large class of dissipative materials can be cast in the form of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling).
Abstract: We show that the coupled balance equations for a large class of dissipative materials can be cast in the form of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). In dissipative solids (generalized standard materials), the state of a material point is described by dissipative internal variables in addition to the elastic deformation and the temperature. The framework GENERIC allows for an efficient derivation of thermodynamically consistent coupled field equations, while revealing additional underlying physical structures, like the role of the free energy as the driving potential for reversible effects and the role of the free entropy (Massieu potential) as the driving potential for dissipative effects. Applications to large and small-strain thermoplasticity are given. Moreover, for the quasistatic case, where the deformation can be statically eliminated, we derive a generalized gradient structure for the internal variable and the temperature with a reduced entropy as driving functional.
TL;DR: In this paper, a relaxation-based optimal control is proposed to govern quantum systems within subspaces of weak relaxation whenever the drift Hamiltonian would otherwise drive the system through fast decaying modes.
Abstract: Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations to unitary gates under relaxation. The potential gain by optimal control fully exploiting known relaxation parameters against time-optimal control (the alternative for unknown relaxation parameters) is explored and exemplified in numerical and in algebraic terms: for instance, relaxation-based optimal control is the method of choice to govern quantum systems within subspaces of weak relaxation whenever the drift Hamiltonian would otherwise drive the system through fast decaying modes. In a standard model system generalizing ideal decoherence-free subspaces to more realistic scenarios, opengrape-derived controls realize a CNOT with fidelities beyond 95% instead of at most 15% for a standard Trotter expansion. As additional benefit their control fields are orders of magnitude lower in power than bang-bang decouplings.
TL;DR: In this paper, a gate-based simulation approach for open-system dynamics with trapped ions is presented, which can be adapted to scalable and two-dimensional ion-trap architectures, which are currently under development.
Abstract: In a recent experiment, Barreiro et al. demonstrated the fundamental building blocks of an open-system quantum simulator with trapped ions (Nature 470, 486 (2011)). Using up to ve ions, single- and multi-qubit entangling gate operations were combined with optical pumping in stroboscopic sequences. This enabled the implementation of both coherent many-body dynamics as well as dissipative processes by controlling the coupling of the system to an articial, suitably tailored environment. This engineering was illustrated by the dissipative preparation of entangled two- and four-qubit states, the simulation of coherent four-body spin interactions and the quantum non-demolition measurement of a multi-qubit stabilizer operator. In the present paper, we present the theoretical framework of this gate-based (\digital") simulation approach for open-system dynamics with trapped ions. In addition, we discuss how within this simulation approach minimal instances of spin models of interest in the context of topological quantum computing and condensed matter physics can be realized in state-of-the-art linear ion-trap quantum computing architectures. We outline concrete simulation schemes for Kitaev's toric code Hamiltonian and a recently suggested color code model. The presented simulation protocols can be adapted to scalable and two-dimensional ion-trap architectures, which are currently under development.
TL;DR: The extensive Monte Carlo simulations show that the threshold density ρ(th)(h(0)) of the FES converges rapidly to ρ (s) for h(0) < 1 and the conservative fixed energy sandpile (FES).
Abstract: We consider the Abelian sandpile model (ASM) on the square lattice with a single dissipative site (sink). Particles are added one by one per unit time at random sites and the resulting density of particles is calculated as a function of time. We observe different scenarios of evolution depending on the value of initial uniform density (height) h0. During the first stage of the evolution, the density of particles increases linearly. Reaching a critical density ρc(h0), the system changes its behavior and relaxes exponentially to the stationary state of the ASM with density ρs. Considering initial heights −1≤h0≤4, we observe a dramatic decrease of the difference ρc(h0)−ρs when h0 is zero or negative. In parallel with the ASM, we consider the conservative fixed energy sandpile (FES). The extensive Monte Carlo simulations show that the threshold density ρth(h0) of the FES converges rapidly to ρs for h0<1.
TL;DR: In this article, a novel type of partially polarized dissipative soliton was reported in a mode-locked erbium-doped all-fiber laser with strong net normal dispersion.
Abstract: We have reported a novel type of partially polarized dissipative soliton in a mode-locked erbium-doped all-fiber laser with strong net normal dispersion. The output pulses exhibit as quasi-trapezoid spectral profiles with 3-dB width as large as 83 nm. The maximum pulse energy and peak power approach 75 nJ and 6 kW at the available pump power of 1 W, respectively. Experimental observations show that the polarization state of the broadband dissipative soliton changes along the cavity position from totally to partially polarized, which is distinct from the typical dissipative soliton that is completely polarized throughout the cavity. It is found that the polarization state of mode-locked dissipative solitons strongly depends on the peak power of pulses, and the partially polarized state results from nonlinear phase shift accumulated in laser cavity.
TL;DR: It is shown for models of the B850 bacteriochlorophylls of LH2 that correlated bath fluctuations have a significant effect on the LH2→LH2 excitation transfer rate and it is demonstrated that inclusion of static disorder is crucial for an accurate description of transfer dynamics.
Abstract: Excitation dynamics of various light harvesting systems have been investigated with many theoretical methods including various non-Markovian descriptions of dissipative quantum dynamics. It is typically assumed that each excited state is coupled to an independent thermal environment, i.e., that fluctuations in different environments are uncorrelated. Here the assumption is dropped and the effect of correlated bath fluctuations on excitation transfer is investigated. Using the hierarchy equations of motion for dissipative quantum dynamics it is shown for models of the B850 bacteriochlorophylls of LH2 that correlated bath fluctuations have a significant effect on the LH2 → LH2 excitation transfer rate. It is also demonstrated that inclusion of static disorder is crucial for an accurate description of transfer dynamics.
TL;DR: In this paper, the real-time quantum dynamics of a biomolecular donor-acceptor system were determined in order to describe excitonic energy transfer in the presence of slow environmental Gaussian fluctuations.
Abstract: We determine the real-time quantum dynamics of a biomolecular donor–acceptor system in order to describe excitonic energy transfer in the presence of slow environmental Gaussian fluctuations. For this, we compare two different approaches. On the one hand, we use the numerically exact iterative quasi-adiabatic propagator path-integral scheme that incorporates all non-Markovian contributions. On the other, we apply the second-order cumulant time-nonlocal quantum master equation that includes non-Markovian effects. We show that both approaches yield coinciding results in the relevant crossover regime from weak to strong electronic couplings, displaying coherent as well as incoherent transitions.
TL;DR: In this paper, a generalization of Clark and Putterman's equations to a set of superfluid equations parameterized by 14 dissipative parameters is presented. But this generalization does not fit into the 13 parameter Clark-Putterman framework.
Abstract: Charged asymptotically AdS
5 black branes are sometimes unstable to the condensation of charged scalar fields. For fields of infinite charge and squared mass −4 Herzog was able to analytically determine the phase transition temperature and compute the endpoint of this instability in the neighborhood of the phase transition. We generalize Herzog’s construction by perturbing away from infinite charge in an expansion in inverse charge and use the solutions so obtained as input for the fluid gravity map. Our tube wise construction of patched up locally hairy black brane solutions yields a one to one map from the space of solutions of superfluid dynamics to the long wavelength solutions of the Einstein Maxwell system. We obtain explicit expressions for the metric, gauge field and scalar field dual to an arbitrary superfluid flow at first order in the derivative expansion. Our construction allows us to read off the the leading dissipative corrections to the perfect superfluid stress tensor, current and Josephson equations. A general framework for dissipative superfluid dynamics was worked out by Landau and Lifshitz for zero superfluid velocity and generalized to nonzero fluid velocity by Clark and Putterman. Our gravitational results do not fit into the 13 parameter Clark-Putterman framework. Purely within fluid dynamics we present a consistent new generalization of Clark and Putterman’s equations to a set of superfluid equations parameterized by 14 dissipative parameters. The results of our gravitational calculation fit perfectly into this enlarged framework. In particular we compute all the dissipative constants for the gravitational superfluid.
Abstract: We show how the linearized equations of motion of any dissipative current are determined by the analytical structure of the associated retarded Green's function. If the singularity of Green's function, which is nearest to the origin in the complex-frequency plane, is a simple pole on the imaginary frequency axis, the linearized equations of motion can be reduced to relaxation type equations for the dissipative currents. The value of the relaxation time is given by the inverse of this pole. We prove that, if the relaxation time is sent to zero, or equivalently, the pole to infinity, the dissipative currents approach the values given by the standard gradient expansion.
TL;DR: It is shown that the Gilbert equation of motion, which is often used to describe the fast dissipative magnetization dynamics, must be extended in several aspects and a relation between the quantity α characterizing the damping of the fast dynamics in simple situations and the time T(1) is derived.
Abstract: For metallic magnets we review the experimental and electron-theoretical investigations of fast magnetization dynamics (on a timescale of ns to 100 ps) and of laser-pulse-induced ultrafast dynamics (few hundred fs). It is argued that for both situations the dominant contributions to the dissipative part of the dynamics arise from the excitation of electron-hole pairs and from the subsequent relaxation of these pairs by spin-dependent scattering processes, which transfer angular momentum to the lattice. By effective field theories (generalized breathing and bubbling Fermi-surface models) it is shown that the Gilbert equation of motion, which is often used to describe the fast dissipative magnetization dynamics, must be extended in several aspects. The basic assumptions of the Elliott-Yafet theory, which is often used to describe the ultrafast spin relaxation after laser-pulse irradiation, are discussed very critically. However, it is shown that for Ni this theory probably yields a value for the spin-relaxation time T(1) in good agreement with the experimental value. A relation between the quantity α characterizing the damping of the fast dynamics in simple situations and the time T(1) is derived.
TL;DR: This paper considers several interconnected ISS systems supplied with ISS Lyapunov functions defined in the dissipative form and provides a condition of a small gain type under which this construction is possible and describes a method of an explicit construction of such an ISS LyAPunov function.