Showing papers on "Dissipative system published in 2006"
TL;DR: In this paper, the authors give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of their works, and cast the equation into the hierarchy of equations which can be solved analytically or computationally in a nonperturbative manner including the effect of a colored noise.
Abstract: Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9 (1954) 316 and 935, respectively. In this review, we give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of their works. With the aid of path integral formalism, we derive the stochastic Liouville equation for density matrices of a system. We then cast the equation into the hierarchy of equations which can be solved analytically or computationally in a nonperturbative manner including the effect of a colored noise. We elucidate the applications of the stochastic theory from the unified theoretical basis to analyze the dynamics of a system as probed by experiments. We illustrate this as a review of several experimental examples including NMR, dielectric relaxation, Mossbauer spectroscopy, neutron scattering, and linear and nonlinear laser spectroscop...
806 citations
Posted Content•
TL;DR: In this paper, it was shown that the critical dissipative quasi-geostrophic equation with L 2 initial data and minimal assumptions on the drift is locally smooth for any space dimension.
Abstract: Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with L^2 initial data and minimal assumptions on the drift are locally Holder continuous. As an application we show that solutions of the quasi-geostrophic equation with initial L^2 data and critical diffusion (-\Delta)^{1/2}, are locally smooth for any space dimension.
568 citations
TL;DR: In this paper, a hybrid approach which combines early ideal fluid dynamical evolution with late hadronic rescattering was used to demonstrate strong dissipative effects from the late rescattering stage on the elliptic flow coefficient v 2 ( η, b ) in Au + Au collisions at s = 200 A GeV as a function of pseudorapidity η and impact parameter b.
368 citations
TL;DR: In this article, the Navier-Stokes equations in globally unstable configurations are computed by damping the unstable (temporal) frequencies, which is achieved by adding a dissipative relaxation term proportional to the high-frequency content of the velocity fluctuations.
Abstract: A new method, enabling the computation of steady solutions of the Navier-Stokes equations in globally unstable configurations, is presented. We show that it is possible to reach a steady state by damping the unstable (temporal) frequencies. This is achieved by adding a dissipative relaxation term proportional to the high-frequency content of the velocity fluctuations. Results are presented for cavity-driven boundary-layer separation and a separation bubble induced by an external pressure gradient.
333 citations
TL;DR: It is demonstrated experimentally that the momentum distribution of cold atoms in dissipative optical lattices is a Tsallis distribution, which can be continuously varied by changing the parameters of the optical potential.
Abstract: We demonstrated experimentally that the momentum distribution of cold atoms in dissipative optical lattices is a Tsallis distribution. The parameters of the distribution can be continuously varied by changing the parameters of the optical potential. In particular, by changing the depth of the optical lattice, it is possible to change the momentum distribution from Gaussian, at deep potentials, to a power-law tail distribution at shallow optical potentials.
286 citations
TL;DR: The results of studies of proton transfer in condensed phase and reactive dynamics in a dissipative environment are presented to illustrate applications of the quantum-classical Liouville formalism.
Abstract: Quantum-classical Liouville dynamics can be used to study the properties of open quantum systems that are coupled to bath or environmental degrees of freedom whose dynamics can be approximated by classical equations of motion. In contrast to many open quantum system approaches, quantum-classical dynamics provides a detailed description of the bath molecules. Such a description is especially appropriate for the study of quantum rate processes, such as proton and electron transport, where the detailed dynamics of the bath has a strong influence on the quantum rate. The quantum-classical Liouville equation can also serve as a starting point for the derivation of reduced descriptions where all or some of the bath degrees of freedom are projected out. Quantum-classical Liouville dynamics can be simulated in terms of an ensemble of surface-hopping trajectories whose character differs from that in other surface-hopping schemes. The results of studies of proton transfer in condensed phase and reactive dynamics in a dissipative environment are presented to illustrate applications of the formalism.
277 citations
TL;DR: In this article, the existence of a compact global random attractor within the set of tempered random bounded sets was shown to converge under the forward flow to a random compact invariant set.
Abstract: We consider a one-dimensional lattice with diffusive nearest neighbor interaction, a dissipative nonlinear reaction term and additive independent white noise at each node. We prove the existence of a compact global random attractor within the set of tempered random bounded sets. An interesting feature of this is that, even though the spatial domain is unbounded and the solution operator is not smoothing or compact, pulled back bounded sets of initial data converge under the forward flow to a random compact invariant set.
275 citations
TL;DR: It is argued that a union of ideas from thermodynamics and dynamic systems' theory can provide a general description of DySA and heuristic design rules can be used to construct DySA systems of increasing complexities based on a variety of suitable interactions/potentials on length scales from nanoscopic to macroscopic.
Abstract: Dynamic self-assembly (DySA) processes occurring outside of thermodynamic equilibrium underlie many forms of adaptive and intellligent behaviors in natural systems Relatively little, however, is known about the principles that govern DySA and the ways in which it can be extended to artificial ensembles This article discusses recent advances in both the theory and the practice of nonequilibrium self-assembly It is argued that a union of ideas from thermodynamics and dynamic systems' theory can provide a general description of DySA In parallel, heuristic design rules can be used to construct DySA systems of increasing complexities based on a variety of suitable interactions/potentials on length scales from nanoscopic to macroscopic Applications of these rules to magnetohydrodynamic DySA are also discussed
273 citations
TL;DR: In this article, the authors considered wave dynamics with small dispersion and showed that this provides a mechanism for the generation of a dispersive shock wave (DSW) in a Bose-Einstein condensate.
Abstract: A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.
267 citations
TL;DR: Spontaneous quantum coherence in an out of an equilibrium system, coupled to multiple baths describing pumping and decay is studied, leading to correlation functions that differ both from an isolated condensate and from a laser.
Abstract: We study spontaneous quantum coherence in an out of an equilibrium system, coupled to multiple baths describing pumping and decay. For a range of parameters describing coupling to, and occupation of the baths, a stable steady-state condensed solution exists. The presence of pumping and decay significantly modifies the spectra of phase fluctuations, leading to correlation functions that differ both from an isolated condensate and from a laser.
240 citations
TL;DR: It is shown how the analysis of the multi-dimensional case may be reduced to consideration of one-dimensional problems and the dispersion error for various schemes is derived and conjecture on the generalisation to higher order approximation in space is conjecture.
Abstract: Discontinuous Galerkin finite element methods (DGFEM) offer certain advantages over standard continuous finite element methods when applied to the spatial discretisation of the acoustic wave equation. For instance, the mass matrix has a block diagonal structure which, used in conjunction with an explicit time stepping scheme, gives an extremely economical scheme for time domain simulation. This feature is ubiquitous and extends to other time-dependent wave problems such as Maxwell's equations. An important consideration in computational wave propagation is the dispersive and dissipative properties of the discretisation scheme in comparison with those of the original system. We investigate these properties for two popular DGFEM schemes: the interior penalty discontinuous Galerkin finite element method applied to the second-order wave equation and a more general family of schemes applied to the corresponding first order system. We show how the analysis of the multi-dimensional case may be reduced to consideration of one-dimensional problems. We derive the dispersion error for various schemes and conjecture on the generalisation to higher order approximation in space
TL;DR: A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented in this paper, where a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler-Lagrange equations.
Abstract: A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipative solids, including finite elastic and plastic deformations, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rules, as well as heat conduction. We show that a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler–Lagrange equations. The identification of the joint potential requires a careful distinction between equilibrium and external temperatures, which are equal at equilibrium. The variational framework predicts the fraction of dissipated energy that is converted to heat. A comparison of this prediction and experimental data suggests that α-titanium and Al2024-T conform to the variational framework.
TL;DR: In this article, the applicability of fluid dynamics to quantify the size of corresponding dissipative effects was discussed, and it was shown that for too early initialization of the hydrodynamic evolution, or for too high transverse momentum in the final state, the expected dissipative corrections are too large for a fluid description to be reliable.
Abstract: Recent discussions of RHIC data emphasized the exciting possibility that the matter produced in nucleus-nucleus collisions shows properties of a near-perfect fluid. Here, we aim at delineating the applicability of fluid dynamics, which is needed to quantify the size of corresponding dissipative effects. We start from the equations for dissipative fluid dynamics, which we derive from kinetic theory up to second order (Israel-Stewart theory) in a systematic gradient expansion. In model studies, we then establish that for too early initialization of the hydrodynamic evolution (${\ensuremath{\tau}}_{0}\ensuremath{\lesssim}1\phantom{\rule{0.3em}{0ex}}\mathrm{fm}/c$) or for too high transverse momentum (${p}_{T}\ensuremath{\lesssim}1$ GeV) in the final state, the expected dissipative corrections are too large for a fluid description to be reliable. Moreover, viscosity-induced modifications of hadronic transverse momentum spectra can be accommodated to a significant degree in an ideal fluid description by modifications of the decoupling stage. We argue that these conclusions, drawn from model studies, can also be expected to arise in significantly more complex, realistic fluid dynamics simulations of heavy ion collisions.
TL;DR: In this article, the authors show how the entropy method enables to get in an elementary way (and without linearization) estimates of exponential decay towards equilibrium for solutions of reaction-diffusion equations corresponding to a reversible reaction.
TL;DR: In this article, a large class of generalized variable-coefficient Korteweg-de Vries (KdV) models with external-force and perturbed/dissipative terms is studied.
TL;DR: In this paper, the authors considered a gravity dual description of time dependent, strongly interacting large-Nc = 4 SYM and obtained the dual geometry at the late time that is consistent with dissipative hydrodynamics.
Abstract: We consider a gravity dual description of time dependent, strongly interacting large-Nc = 4 SYM. We regard the gauge theory system as a fluid with shear viscosity. Our fluid is expanding in one direction following the Bjorken's picture that is relevant to RHIC experiments. We obtain the dual geometry at the late time that is consistent with dissipative hydrodynamics. We show that the integration constants that cannot be determined by hydrodynamics are given by looking at the horizon of the dual geometry. Relationship between time dependence of the energy density and bulk singularity is also discussed.
TL;DR: In this article, the authors investigate the crystallization of a uniformly heated quasi-2D granular fluid as a function of the filling fraction and show that the results for the Lindemann melting criterion, the radial distribution function, the bond order parameter, and the statistics of topological changes at the particle level are the same as those found in simulations of equilibrium hard disks.
Abstract: We experimentally investigate the crystallization of a uniformly heated quasi-2D granular fluid as a function of the filling fraction. Our experimental results for the Lindemann melting criterion, the radial distribution function, the bond order parameter, and the statistics of topological changes at the particle level are the same as those found in simulations of equilibrium hard disks. This direct mapping suggests that the study of equilibrium systems can be effectively applied to study nonequilibrium steady states such as those found in our driven and dissipative granular system.
TL;DR: In this article, the second-order Israel-Stewart approach is used to describe the space-time evolution of relativistic fluids undergoing boost-invariant longitudinal and arbitrary transverse expansion.
Abstract: Explicit equations are given for describing the space-time evolution of nonideal (viscous) relativistic fluids undergoing boost-invariant longitudinal and arbitrary transverse expansion. The equations are derived from the second-order Israel-Stewart approach which ensures causal evolution. Both azimuthally symmetric (1+1)-dimensional and nonsymmetric (2+1)-dimensional transverse expansion are discussed. The latter provides the formal basis for the hydrodynamic computation of elliptic flow in relativistic heavy ion collisions including dissipative effects.
TL;DR: In this paper, the authors considered the evolution of a system composed of two predator-prey deterministic systems described by Lotka-Volterra equations in random environment and proved that under the influence of telegraph noise, all positive trajectories of such a system always go out from any compact set of int R + 2 with probability one if two rest points of the two systems do not coincide.
TL;DR: The results provide the first example of stable vortex tori in a 3D dissipative medium, as well as the first examples of higher-order tori (with S=2) in any nonlinear medium.
Abstract: We demonstrate the existence of stable toroidal dissipative solitons with the inner phase field in the form of rotating spirals, corresponding to vorticity S=0, 1, and 2, in the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. The stable solitons easily self-trap from pulses with embedded vorticity. The stability is corroborated by accurate computation of growth rates for perturbation eigenmodes. The results provide the first example of stable vortex tori in a 3D dissipative medium, as well as the first example of higher-order tori (with S=2) in any nonlinear medium. It is found that all stable vortical solitons coexist in a large domain of the parameter space; in smaller regions, there coexist stable solitons with either S=0 and S=1, or S=1 and S=2.
TL;DR: These schemes have already been developed for N-body mechanical problems and are known as symplectic schemes and are transformed and applied to DGTD methods on wave propagation problems in order to obtain stable and accurate local time-stepping algorithms.
Abstract: The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle
easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh, calls for the construction of local-time stepping algorithms. These schemes have already been developed for N-body mechanical problems and are known as symplectic schemes. They are applied here to DGTD methods on wave propagation problems.
TL;DR: The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the (D + 1)-dimensional complex cubic-quintic Ginzburg-Landau equation.
Abstract: The generation and nonlinear dynamics of multidimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the (D + 1)-dimensional complex cubic-quintic Ginzburg-Landau equation (D = 1, 2, 3). A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of any input pulse from this domain leads to stable dissipative solitons.
TL;DR: It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath, and possible applications include circuit QED and molecular nanomagnets.
Abstract: We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.
TL;DR: It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.
Abstract: Using the nonperturbative approach to the calculation of nonlinear optical spectra developed in a foregoing paper [Mancal et al., J. Chem. Phys. 124, 234504 (2006), preceding paper], calculations of two-dimensional electronic spectra of an excitonically coupled dimer model system are presented. The dissipative exciton transfer dynamics is treated within the Redfield theory and energetic disorder within the molecular ensemble is taken into account. The manner in which the two-dimensional spectra reveal electronic couplings in the aggregate system and the evolution of the spectra in time is studied in detail. Changes in the intensity and shape of the peaks in the two-dimensional relaxation spectra are related to the coherent and dissipative dynamics of the system. It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.
TL;DR: In this paper, the authors derived Gilbert damping and spin transfer torques entering the Landau-Lifshitz equation to linear order in frequency and wave vector, with the result that a steady current-driven domain-wall motion is insensitive to spin dephasing in the limit of weak ferromagnetic metal.
Abstract: Current-driven magnetization dynamics in ferromagnetic metals is studied in a self-consistent adiabatic local-density approximation in the presence of spin-conserving and spin-dephasing impurity scattering. Based on a quantum kinetic equation, we derive Gilbert damping and spin-transfer torques entering the Landau-Lifshitz equation to linear order in frequency and wave vector. Gilbert damping and a current-driven dissipative torque scale identically and compete, with the result that a steady current-driven domain-wall motion is insensitive to spin dephasing in the limit of weak ferromagnetism. A uniform magnetization is found to be much more stable against spin torques in the itinerant than in the s-d model for ferromagnetism. A dynamic spin-transfer torque reminiscent of the spin pumping in multilayers is identified and shown to govern the current-induced domain-wall distortion.
TL;DR: In this paper, the authors discuss the global solvability and asymptotic behavior of solutions to the Cauchy problem for some nonlinear hyperbolic-elliptic system with a fourth-order elliptic part.
Abstract: We discuss the global solvability and asymptotic behavior of solutions to the Cauchy problem for some nonlinear hyperbolic–elliptic system with a fourth-order elliptic part. This system is a modified version of the simplest radiating gas model and verifies a decay property of regularity-loss type. Such a dissipative structure also appears in the dissipative Timoshenko system studied by Rivera and Racke. This dissipative property is very weak in high frequency region and causes the difficulty in deriving the desired a priori estimates for global solutions to the nonlinear problem. In fact, it turns out that the usual energy method does not work well. We overcome this difficulty by employing a time-weighted energy method which is combined with the optimal decay for lower order derivatives of solutions, and we establish a global existence and asymptotic decay result. Furthermore, we show that the solution has an asymptotic self-similar profile described by the Burgers equation as time tends to infinity.
TL;DR: In this article, a flux-conservative formalism for a Newtonian multi-fluid system, including dissipation and entrainment, was developed, which allows the momentum of one fluid to be a linear combination of the velocities of all fluids.
Abstract: We develop a flux-conservative formalism for a Newtonian multi-fluid system, including dissipation and entrainment (i.e. allowing the momentum of one fluid to be a linear combination of the velocities of all fluids). Maximum use is made of mass, energy and linear and angular momentum conservation to specify the equations of motion. Also used extensively are insights gleaned from a convective variational action principle, the key being the distinction between each velocity and its canonically conjugate momentum (which is modified because of entrainment). Dissipation is incorporated to second order in the 'thermodynamic forces' via the approach pioneered by Onsager, which makes it transparent how to guarantee the law of increase of entropy. An immediate goal of the investigation is to understand better the number, and form, of independent dissipation terms required for a consistent set of equations of motion in the multi-fluid context. A significant, but seemingly innocuous detail is that one must be careful to isolate 'forces' that can be written as total gradients, otherwise errors can be made in relating the net internal force to the net externally applied force. Our long-range aim is to provide a formalism that can be used to model dynamical multi-fluid systems both perturbatively and via fully nonlinear 3D numerical evolutions. To elucidate the formalism we consider the standard model for a heat-conducting, superfluid neutron star, which is believed to be dominated by superfluid neutrons, superconducting protons and a highly degenerate, ultra-relativistic gas of normal fluid electrons. We determine that in this case there are, in principle, 19 dissipation coefficients in the final set of equations. A final reduction of the system is made by neglecting heat conduction. This leads to an extension of the standard two-fluid model for neutron star cores, which has been used in a number of previous applications, and illustrates how mutual friction is represented in our formalism.
TL;DR: An experiment for generating and detecting vacuum-induced dissipative motion via photon emission with high frequency mechanical resonator driven in resonance results in a detectable radio-frequency signal temporally distinguishable from the expected background.
Abstract: We propose an experiment for generating and detecting vacuum-induced dissipative motion. A high frequency mechanical resonator driven in resonance is expected to dissipate mechanical energy in quantum vacuum via photon emission. The photons are stored in a high quality electromagnetic cavity and detected through their interaction with ultracold alkali-metal atoms prepared in an inverted population of hyperfine states. Superradiant amplification of the generated photons results in a detectable radio-frequency signal temporally distinguishable from the expected background.
TL;DR: In this article, the critical and super-critical dissipative quasi-geostrophic equations are investigated in the H2-2α space, and the authors prove local existence of a unique regular solution for arbitrary initial data.
Abstract: The critical and super-critical dissipative quasi-geostrophic equations are investigated in \(\mathbb{R}^2\). We prove local existence of a unique regular solution for arbitrary initial data in H2-2α which corresponds to the scaling invariant space of the equation. We also consider the behavior of the solution near t = 0 in the Sobolev space.
TL;DR: This paper studies the dynamics of two interacting electrons on a two-dimensional quantum strip of finite size and shows explicitly how dissipation arises through multiple particle-hole excitations, and how the nonadiabatic extension of the ALDA fails for finite systems but becomes correct in the thermodynamic limit.
Abstract: Most applications of time-dependent density-functional theory (TDDFT) use the adiabatic local-density approximation (ALDA) for the dynamical exchange-correlation potential V(xc)(r,t). An exact (i.e., nonadiabatic) extension of the ground-state LDA into the dynamical regime leads to a V(xc)(r,t) with a memory, which causes the electron dynamics to become dissipative. To illustrate and explain this nonadiabatic behavior, this paper studies the dynamics of two interacting electrons on a two-dimensional quantum strip of finite size, comparing TDDFT within and beyond the ALDA with numerical solutions of the two-electron time-dependent Schrodinger equation. It is shown explicitly how dissipation arises through multiple particle-hole excitations, and how the nonadiabatic extension of the ALDA fails for finite systems but becomes correct in the thermodynamic limit.