Dissipative Time Research Articles

Experiments and characterization of low-frequency oscillations in a granular column.

The behavior of a vertically vibrated granular bed is reminiscent of a liquid in that it exhibits many phenomena such as convection and Faraday-like surface waves. However, when the lateral dimensions of the bed are confined such that a quasi-one-dimensional geometry is formed, the only phenomena that remain are bouncing bed and the granular Leidenfrost effect. This permits the observation of the granular Leidenfrost state for a wide range of energy injection parameters and more specifically allows for a thorough characterization of the low-frequency oscillation (LFO) that is present in this state. In both experiments and particle simulations we determine the LFO frequency from the power spectral density of the center-of-mass signal of the grains, varying the amplitude and frequency of the driving, the particle diameter, and the number of layers in the system. We thus find that the LFO frequency (i) is inversely proportional to the fast inertial timescale and (ii) decorrelates with a typical decay time proportional to the slow dissipative timescale in the system. The latter is consistent with the view that the LFO is driven by the inherent noise that is present in the granular Leidenfrost state with a low number of particles.

Stabilization of strictly dissipative discrete time systems with discounted optimal control

We consider stabilization of an equilibrium point via infinite horizon discounted optimal control in discrete-time. In addition to applications in economics and social sciences, discounted optimal control is a commonly used numerical technique guaranteeing solvability of certain classes of optimal control problems. In this paper, we present conditions based on strict dissipativity that ensure that the optimally controlled system is asymptotically stable or practically asymptotically stable. These conditions are shown to be complementary to recently proposed conditions based on a detectability property. Illustrative examples are provided.

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems.

Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic dynamics of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.

Noise suppression via generalized-Markovian processes

It is by now well established that noise itself can be useful for performing quantum information processing tasks. We present results which show how one can effectively reduce the error rate associated with a noisy quantum channel by counteracting its detrimental effects with another form of noise. In particular, we consider the effect of adding on top of a purely Markovian (Lindblad) dynamics, a more general form of dissipation, which we refer to as generalized-Markovian noise. This noise has an associated memory kernel and the resulting dynamics are described by an integrodifferential equation. The overall dynamics are characterized by decay rates which depend not only on the original dissipative time scales but also on the new integral kernel. We find that one can engineer this kernel such that the overall rate of decay is lowered by the addition of this noise term. We illustrate this technique for the case where the bare noise is described by a dephasing Pauli channel. We analytically solve this model and show that one can effectively double (or even triple) the length of the channel, while achieving the same fidelity, entanglement, and error threshold. We numerically verify this scheme can also be used to protect against thermal Markovian noise (at nonzero temperature), which models spontaneous emission and excitation processes. A physical interpretation of this scheme is discussed, whereby the added generalized-Markovian noise causes the system to become periodically decoupled from the background Markovian noise.

Lyapunov exponents and poles in a non Hermitian dynamics

By means of expressing volumes in phase space in terms of traces of quantum operators, a relationship between the poles of the scattering matrix and the Lyapunov exponents in a non Hermitian quantum dynamics, is presented. We illustrate the formalism by characterizing the behavior of the Gamow model whose dissipative decay time, measured by its decoherence time, is found to be inversely proportional to the Lyapunov exponents of the unstable periodic orbits. The results are in agreement with those obtained by means of the semiclassical periodic–orbit approach in quantum resonances theory but using a simpler mathematics.

Dissipative time evolution of a chiral state after a quantum quench

We investigate the dynamics of fermionic atoms in a high-finesse optical resonator after a sudden switch on of the coupling between the atoms and the cavity. The atoms are additionally confined by optical lattices to a ladder geometry. The tunneling mechanism on a rung of a ladder is induced by a cavity assisted Raman process. At long times after the quantum quench the arising steady state can carry a chiral current. In this work we employ exact diagonalization techniques on small system sizes to study the dissipative attractor dynamics after the quench towards the steady state and deviations of the properties of the steady state from predictions obtained by adiabatically eliminating the cavity mode.

A finite element model for seismic response analysis of deformable rocking frames

SummaryA new finite element model to analyze the seismic response of deformable rocking bodies and rocking structures is presented. The model comprises a set of beam elements to represent the rocking body and zero‐length fiber cross‐section elements at the ends of the rocking body to represent the rocking surfaces. The energy dissipation during rocking motion is modeled using a Hilber–Hughes–Taylor numerically dissipative time step integration scheme. The model is verified through correct prediction of the horizontal and vertical displacements of a rigid rocking block and validated against the analytical Housner model solution for the rocking response of rigid bodies subjected to ground motion excitation. The proposed model is augmented by a dissipative model of the ground under the rocking surface to facilitate modeling of the rocking response of deformable bodies and structures. The augmented model is used to compute the overturning and uplift rocking response spectra for a deformable rocking frame structure to symmetric and anti‐symmetric Ricker pulse ground motion excitation. It is found that the deformability of the columns of a rocking frame does not jeopardize its stability under Ricker pulse ground motion excitation. In fact, there are cases where a deformable rocking frame is more stable than its rigid counterpart. Copyright © 2016 John Wiley & Sons, Ltd.

Precision Limits in Quantum Metrology with Open Quantum Systems

Abstract The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcomewhen using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining general precision bounds in the presence of an environment.We adopt a complementary approach,wherewe first analyze the problem within the general framework of describing the quantum systems in terms of quantum dynamical maps and then relate this abstract formalism to a microscopic description of the system’s dissipative time evolution.We will show that although some forms of noise do render quantum systems standard quantum limited, precision beyond classical bounds is still possible in the presence of different forms of local environmental fluctuations.

Real-time evolution of strongly coupled fermions driven by dissipation

We consider the real-time evolution of a strongly coupled system of lattice fermions whose dynamics is driven entirely by dissipative Lindblad processes, with linear or quadratic quantum jump operators. The fermion 2-point functions obey a closed set of differential equations, which can be solved with linear algebra methods. The staggered occupation order parameter of the t-V model decreases exponentially during the dissipative time evolution. The structure factor associated with the various Fourier modes shows the slowing down of low-momentum modes, which is due to particle number conservation. The processes with nearest-neighbor-dependent Lindblad operators have a decay rate that is proportional to the coordination number of the spatial lattice.

Long-lived pressure-driven coherent structures in KSTAR plasmas

Highly coherent structures associated with an extremely long-lived saturated magnetohydrodynamic instability have been observed in KSTAR tokamak under a long-pulse and steady-state operation. They persist essentially unchanged for the full duration of a discharge up to 40 s, much longer than any dynamical or dissipative time scales in the system. Analysis of the data, supported by numerical simulations, indicates that they may be associated with a pressure-driven mode causing some degradation in the toroidal rotation, electron, and ion energy confinement.

Infragravity waves on fringing reefs in the tropical Pacific: Dynamic setup

AbstractCross‐shore pressure and current observations from four fringing reefs of lengths ranging from 135 to 420 m reveal energetic low‐frequency (∼0.001–0.05 Hz) motions. The spatial structure and temporal amplitudes of an empirical orthogonal function analysis of the pressure measurements suggest the dominant low‐frequency variability is modal. Incoming and outgoing linear flux estimates also support partially standing modes on the reef flat during energetic events. A cross‐covariance analysis suggests that breakpoint forcing excites these partially standing modes, similar to previous findings at other steep reefs. The dynamics of Symonds et al. (1982) with damping are applied to a step reef, with forcing obtained by extending a point break model of Vetter et al. (2010) for breaking wave setup to the low‐frequency band using the shoaled envelope of the incident free surface elevation. A one parameter, linear analytical model for the reef flat free surface elevation is presented, which describes between 75% and 97% of the variance of the observed low‐frequency shoreline significant wave height for all reefs considered over a range of conditions. The linear model contains a single dimensionless parameter that is the ratio of the inertial to dissipative time scales, and the observations from this study exhibit more low‐frequency variability when the dissipative time scale is greater than the inertial time scale for the steep reefs considered.

The mechanism by which CH2O and H2O2 additives affect the autoignition of CH4/air mixtures

When the fast dissipative time scales become exhausted, the evolution of reacting processes is characterized by slower time scales. Here the case where these slower time scales are of explosive character is considered. This feature allows for the acquisition of significant physical understanding; among others, the identification of intermediates in the reacting process that can be used as additives for the control of the ignition delay. The case of the homogeneous autoignition of CH4/air mixtures is analyzed here and the effects of adding the stable intermediates CH2O and H2O2 to the fuel. These two species are identified as those relating the most to the explosive mode that causes autoignition, throughout the largest part of the ignition delay. Small quantities of these species in the initial mixture decrease considerably the ignition delay, by expediting the development of the thermal runaway.

Role of the basin boundary conditions in gravity wave turbulence

Gravity wave turbulence is investigated experimentally in a large wave basin in which irregular waves are generated unidirectionally. The roles of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. A quasi-one-dimensional field of nonlinear waves propagates towards the beach, where they are damped whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency power law with an exponent that increases continuously with the forcing amplitude up to a value close to $-4$. The physical mechanisms involved most likely differ with the boundary condition used, but cannot be easily discriminated with only temporal measurements. We also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation that highlights the important role of a large-scale Fourier mode. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov–Zakharov constant of the weak turbulence theory is evaluated and found to be compatible with a recently obtained theoretical value.

Enhanced Dissipation and Inviscid Damping in the Inviscid Limit of the Navier–Stokes Equations Near the Two Dimensional Couette Flow

In this work we study the long time, inviscid limit of the 2D Navier-Stokes equations near the periodic Couette flow, and in particular, we confirm at the nonlinear level the qualitative behavior predicted by Kelvin's 1887 linear analysis. At high Reynolds number Re, we prove that the solution behaves qualitatively like 2D Euler for times t \lesssim Re^(1/3), and in particular exhibits inviscid damping (e.g. the vorticity weakly approaches a shear flow). For times t \gtrsim Re^(1/3), which is sooner than the natural dissipative time scale O(Re), the viscosity becomes dominant and the streamwise dependence of the vorticity is rapidly eliminated by an enhanced dissipation effect. Afterward, the remaining shear flow decays on very long time scales t \gtrsim Re back to the Couette flow. When properly defined, the dissipative length-scale in this setting is L_D \sim Re^(-1/3), larger than the scale L_D \sim Re^(-1/2) predicted in classical Batchelor-Kraichnan 2D turbulence theory. The class of initial data we study is the sum of a sufficiently smooth function and a small (with respect to Re^(-1)) $L^2$ function.

The “hidden” dynamics of the Rössler attractor

The fast/slow dynamics of the Rössler model in the chaotic regime are compared to the dynamics of the reduced (slow) model governing the flow along the slow invariant manifold, on which the trajectory is restrained to evolve during the slow part of the attractor. It is shown that the dynamics of the reduced model incorporate the slow time scales of the full model. However, instead of the fast dissipative time scale of the full model that restrains the trajectory on the slow invariant manifold, the reduced model generates a new time scale that (i) relates to the curvature of the manifold and (ii) becomes faster as higher order corrections are incorporated in the approximation of the manifold and the reduced model. It is shown that this new time scale does not characterize the motion of the solution on the manifold but it can be employed as a signal for the strengthening or weakening of the manifold, depending on whether it relates to components of the reduced model that tend to lead its solution towards equilibrium or away from it. Finally, it is demonstrated that the new time scale introduced by the reduced model has a significant role in determining the maximum accuracy that can be delivered by the singular perturbation methodology.

Proton-induced fission cross sections onPb208at high kinetic energies

Total fission cross sections of Pb-208 induced by protons have been determined at 370A, 500A, and 650A MeV. The experiment was performed at GSI Darmstadt where the combined use of the inverse kinematics technique with an efficient detection setup allowed us to determine these cross sections with an uncertainty below 6%. This result was achieved by an accurate beam selection and registration of both fission fragments in coincidence which were also clearly distinguished from other reaction channels. These data solve existing discrepancies between previous measurements, providing new values for the Prokofiev systematics. The data also allow us to investigate the fission process at high excitation energies and small deformations. In particular, some fundamental questions about fission dynamics have been addressed, which are related to dissipative and transient time effects.

The Double Absorbing Boundary method

A new approach is devised for solving wave problems in unbounded domains. It has common features to each of two types of existing techniques: local high-order Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML). However, it is different from both and enjoys relative advantages with respect to both. The new method, called the Double Absorbing Boundary (DAB) method, is based on truncating the unbounded domain to produce a finite computational domain Ω, and on applying a local high-order ABC on two parallel artificial boundaries, which are a small distance apart, and thus form a thin non-reflecting layer. Auxiliary variables are defined on the two boundaries and inside the layer bounded by them, and participate in the numerical scheme. The DAB method is first introduced in general terms, using the 2D scalar time-dependent wave equation as a model. Then it is applied to the 1D Klein–Gordon equation, using finite difference discretization in space and time, and to the 2D wave equation in a wave guide, using finite element discretization in space and dissipative time stepping. The computational aspects of the method are discussed, and numerical experiments demonstrate its performance.

The role of slow system dynamics in predicting the degeneracy of slow invariant manifolds: The case of vdP relaxation–oscillations

The development of dissipative time scales, which are much faster than the rest, force the solution of a system of 1st order ODEs to land and then evolve on a slow invariant manifold. The slow evolution on this manifold can be approximated by a reduced system, which is constructed with asymptotic analysis and is free of the fast scales. In this work, the dynamics of the reduced system are compared to the fast and slow dynamics of the original system. The comparison is based on the van der Pol system, which is typical of those exhibiting relaxation–oscillation behavior and is characterized by successive dissipative and explosive phases. Special attention is given to the dissipative phase, during which the solution evolves on a slow invariant manifold and the fast/slow time scale gap tends to contract. It is shown that one cannot predict from the dynamics of the van der Pol system the approaching explosive phase and the associated degeneracy of the manifold. Such a prediction is possible only through the dynamics of the reduced system, which involves an explosive component that is absent in the original system. This explosive component accelerates as higher order effects are incorporated in the reduced system, resulting in a smaller gap between the fast time scale of the original system and the fast time scale of the reduced one. This feature sets a limit on the accuracy singular perturbation techniques can deliver, even in the presence of a reasonably large fast/slow time scale gap in the dynamics of the original system. Given a fast/slow system, predicting forthcoming changes in the dimensions of the manifold is very important when it is desired to identify the underlying major physical mechanisms or to control the process.

Time scales of turbulent relative dispersion

Tracers in a turbulent flow separate according to the celebrated t3/2 Richardson-Obukhov law, which is usually explained by a scale-dependent effective diffusivity. Here, supported by state-of-the-art numerics, we revisit this argument. The Lagrangian correlation time of velocity differences increases too quickly for validating this approach, but acceleration differences decorrelate on dissipative time scales. Phenomenological arguments are used to relate the behavior of separations to that of a "local energy dissipation," defined as the average ratio between the cube of the longitudinal velocity difference and the distance between the two tracers. This quantity is shown to stabilize on short time scales and this results in an asymptotic diffusion ∝t1/2 of velocity differences. The time of convergence to this regime is shown to be that of deviations from Batchelor's initial ballistic regime, given by a scale-dependent energy dissipation time rather than the usual turnover time. It is finally demonstrated that the fluid flow intermittency should not affect this long-time behavior of the relative motion.

Dual-phase-lag transfer equations and entropy behavior in relaxational hydrodynamics

Extended thermodynamics of irreversible processes is developed; based on two postulates by which additional variables of the entropy density are dissipative fluxes and material time derivatives of the ordinary thermodynamic variables. Within these theories a more general approximation of entropy production is obtained. As a consequence of the proposed formalism, the constitutive dual-phase-lag equations, as well as equations of the conventional version of extended irreversible thermodynamics are obtained. The behavior of the entropy during oscillatory approach to equilibrium is considered. The proposed theory leads to a strictly monotonic dependency of the entropy on time.