Showing papers on "Dissipative system published in 2019"
TL;DR: In this paper, it was shown that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy, and that they can be obtained as a strong vanishing viscosity limit of a sequence of finite energy weak solutions.
Abstract: For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy. Moreover, we prove that Holder continuous dissipative weak solutions of the 3D Euler equations may be obtained as a strong vanishing viscosity limit of a sequence of finite energy weak solutions of the 3D Navier-Stokes equations.
304 citations
TL;DR: In this article, the effects of a system's proximity to an exceptional point on its quantum evolution were investigated, where the eigenvalues and corresponding eigenmodes coalesce.
Abstract: Open physical systems can be described by effective non-Hermitian Hamiltonians that characterize the gain or loss of energy or particle numbers from the system. Experimental realization of optical1–7 and mechanical8–13 non-Hermitian systems has been reported, demonstrating functionalities such as lasing14–16, topological features7,17–19, optimal energy transfer20,21 and enhanced sensing22,23. Such realizations have been limited to classical (wave) systems in which only the amplitude information, not the phase, is measured. Thus, the effects of a systems’s proximity to an exceptional point—a degeneracy of such non-Hermitian Hamiltonians where the eigenvalues and corresponding eigenmodes coalesce24–29—on its quantum evolution remain unexplored. Here, we use post-selection on a three-level superconducting transmon circuit to carry out quantum state tomography of a single dissipative qubit in the vicinity of its exceptional point. We observe the spacetime reflection symmetry-breaking transition30,31 at zero detuning, decoherence enhancement at finite detuning and a quantum signature of the exceptional point in the qubit relaxation state. Our experiments show phenomena associated with non-Hermitian physics such as non-orthogonality of eigenstates in a fully quantum regime, which could provide a route to the exploration and harnessing of exceptional point degeneracies for quantum information processing. The dynamics of a single dissipative qubit undergoing non-Hermitian quantum dynamics in the vicinity of an exceptional point is experimentally studied in a superconducting transmon circuit.
285 citations
TL;DR: In this article, the authors used superconducting circuits to explore strongly correlated quantum matter by building a Bose-Hubbard lattice for photons in the strongly interacting regime, and developed a versatile method for dissipative preparation of incompressible many-body phases through reservoir engineering and applied it to their system to stabilize a Mott insulator of photons against losses.
Abstract: Superconducting circuits are a competitive platform for quantum computation because they offer controllability, long coherence times and strong interactions—properties that are essential for the study of quantum materials comprising microwave photons. However, intrinsic photon losses in these circuits hinder the realization of quantum many-body phases. Here we use superconducting circuits to explore strongly correlated quantum matter by building a Bose–Hubbard lattice for photons in the strongly interacting regime. We develop a versatile method for dissipative preparation of incompressible many-body phases through reservoir engineering and apply it to our system to stabilize a Mott insulator of photons against losses. Site- and time-resolved readout of the lattice allows us to investigate the microscopic details of the thermalization process through the dynamics of defect propagation and removal in the Mott phase. Our experiments demonstrate the power of superconducting circuits for studying strongly correlated matter in both coherent and engineered dissipative settings. In conjunction with recently demonstrated superconducting microwave Chern insulators, we expect that our approach will enable the exploration of topologically ordered phases of matter. Engineered dissipation is used to stabilize a Mott-insulator phase of photons trapped in a superconducting circuit, providing insights into thermalization processes in strongly correlated quantum matter.
236 citations
TL;DR: The cooperative effect of coherent and dissipative magnon-photon couplings in an open cavity magnonic system is revealed, which leads to nonreciprocity with a considerably large isolation ratio and flexible controllability.
Abstract: We reveal the cooperative effect of coherent and dissipative magnon-photon couplings in an open cavity magnonic system, which leads to nonreciprocity with a considerably large isolation ratio and flexible controllability. Furthermore, we discover unidirectional invisibility for microwave propagation, which appears at the zero-damping condition for hybrid magnon-photon modes. A simple model is developed to capture the generic physics of the interference between coherent and dissipative couplings, which accurately reproduces the observations over a broad range of parameters. This general scheme could inspire methods to achieve nonreciprocity in other systems.
226 citations
TL;DR: The dynamical exchange of excitations between a single artificial atom and an entangled collective state of an atomic array is observed through the precise positioning of artificial atoms realized as superconducting qubits along a one-dimensional waveguide, reaching the regime of strong coupling.
Abstract: It has long been recognized that atomic emission of radiation is not an immutable property of an atom, but is instead dependent on the electromagnetic environment1 and, in the case of ensembles, also on the collective interactions between the atoms2–6. In an open radiative environment, the hallmark of collective interactions is enhanced spontaneous emission—super-radiance2—with non-dissipative dynamics largely obscured by rapid atomic decay7. Here we observe the dynamical exchange of excitations between a single artificial atom and an entangled collective state of an atomic array9 through the precise positioning of artificial atoms realized as superconducting qubits8 along a one-dimensional waveguide. This collective state is dark, trapping radiation and creating a cavity-like system with artificial atoms acting as resonant mirrors in the otherwise open waveguide. The emergent atom–cavity system is shown to have a large interaction-to-dissipation ratio (cooperativity exceeding 100), reaching the regime of strong coupling, in which coherent interactions dominate dissipative and decoherence effects. Achieving strong coupling with interacting qubits in an open waveguide provides a means of synthesizing multi-photon dark states with high efficiency and paves the way for exploiting correlated dissipation and decoherence-free subspaces of quantum emitter arrays at the many-body level10–13. An array of superconducting qubits in an open one-dimensional waveguide is precisely controlled to create an artificial quantum cavity–atom system that reaches the strong-coupling regime without substantial decoherence.
209 citations
TL;DR: Breathers introduce a new regime of mode locking into ultrafast lasers and may contribute to the design of advanced laser sources and open up new possibilities of generating breathers in various dissipative systems.
Abstract: Dissipative solitons are self-localized coherent structures arising from the balance between energy supply and dissipation. Besides stationary dissipative solitons, there are dynamical ones exhibiting oscillatory behavior, known as breathing dissipative solitons. Substantial interest in breathing dissipative solitons is driven by both their fundamental importance in nonlinear science and their practical applications, such as in spectroscopy. Yet, the observation of breathers has been mainly restricted to microresonator platforms. Here, we generate breathers in a mode-locked fiber laser. They exist in the laser cavity under the pump threshold of stationary mode locking. Using fast detection, we are able to observe the temporal and spectral evolutions of the breathers in real time. Breathing soliton molecules are also observed. Breathers introduce a new regime of mode locking into ultrafast lasers. Our findings may contribute to the design of advanced laser sources and open up new possibilities of generating breathers in various dissipative systems.
173 citations
TL;DR: A new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems, which is dubbed as the neural stationary state ansatz, and shown to simulate various spin systems efficiently.
Abstract: A theoretical exploration of exotic properties in open quantum many-body systems requires an efficient search of the nonequillibrum stationary states. Aiming to accelerate the process, the authors develop here a variational method, in which the ansatz for the mixed states is based on the restricted Boltzmann machine, motivated by its high expressive power shown in various recent works. It is demonstrated that the ansatz successfully simulates dissipative spin systems both in one and two dimensions.
173 citations
TL;DR: In this paper, the authors presented an approach to the effective simulation of the dynamics of open quantum many-body systems based on machine-learning techniques and derived a variational Monte-Carlo algorithm for their time evolution and stationary states.
Abstract: In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master equation. However, solving this master equation for quantum many-body systems becomes exceedingly hard due to the high dimension of the Hilbert space. Here we present an approach to the effective simulation of the dynamics of open quantum many-body systems based on machine-learning techniques. We represent the mixed many-body quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte Carlo algorithm for their time evolution and stationary states. We document the accuracy of the approach with numerical examples for a dissipative spin lattice system.
171 citations
TL;DR: Stable Kerr soliton singlet formation and soliton bursts are demonstrated and an application of automatic soliton comb recovery and long-term stabilization against strong external perturbations is demonstrated, holding potential to expand the parameter space for ultrafast nonlinear dynamics and precision optical frequency comb stabilization.
Abstract: Dissipative Kerr solitons in resonant frequency combs offer a promising route for ultrafast mode-locking, precision spectroscopy and time-frequency standards. The dynamics for the dissipative soliton generation, however, are intrinsically intertwined with thermal nonlinearities, limiting the soliton generation parameter map and statistical success probabilities of the solitary state. Here, via use of an auxiliary laser heating approach to suppress thermal dragging dynamics in dissipative soliton comb formation, we demonstrate stable Kerr soliton singlet formation and soliton bursts. First, we access a new soliton existence range with an inverse-sloped Kerr soliton evolution—diminishing soliton energy with increasing pump detuning. Second, we achieve deterministic transitions from Turing-like comb patterns directly into the dissipative Kerr soliton singlet pulse bypassing the chaotic states. This is achieved by avoiding subcomb overlaps at lower pump power, with near-identical singlet soliton comb generation over twenty instances. Third, with the red-detuned pump entrance route enabled, we uncover unique spontaneous soliton bursts in the direct formation of low-noise optical frequency combs from continuum background noise. The burst dynamics are due to the rapid entry and mutual attraction of the pump laser into the cavity mode, aided by the auxiliary laser and matching well with our numerical simulations. Enabled by the auxiliary-assisted frequency comb dynamics, we demonstrate an application of automatic soliton comb recovery and long-term stabilization against strong external perturbations. Our findings hold potential to expand the parameter space for ultrafast nonlinear dynamics and precision optical frequency comb stabilization. Ultrafast optical states called solitons can be prevented from thermally breaking down by carefully heating them with a laser, researchers in the US and China show. Solitons are optical fields that exist in isolation, like smoke rings in air or bubbles in water, and they could greatly improve precision laser measurements and spectroscopy. However, it is difficult to maintain robust soliton states due to nonlinear thermal effects that cause them to break down. Heng Zhou at UESTC, Chee Wei Wong at UCLA, and co-workers generated solitons by directing a ‘frequency comb’ source (comprising discrete, equally-spaced laser lines) onto a silicon nitride optical microcavity. Crucially, they employed a second laser to provide heating to the system and suppress the thermal nonlinearities. This enabled smooth transitions between useful soliton states, while avoiding chaotic intermediate states.
170 citations
TL;DR: A second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies, is introduced and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models.
Abstract: We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multiplasmon or multiphoton Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off-diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission. To illustrate the practical application of the theory, we show examples using a gold nanorod dimer and a hybrid dielectric-metal cavity structure.
167 citations
TL;DR: In this paper, transfer matrices are used to explain the properties of non-Hermitian Hamiltonians and predict their topological properties, including their sensitivity to boundary conditions and a piling up of all states at the boundary, signalling a breakdown of the conventional bulk boundary correspondence.
Abstract: Non-Hermitian Hamiltonians---proposed to describe dissipative systems where the particles have a finite lifetime---exhibit many puzzling properties, strongly contrasting their Hermitian counterparts. In particular, their spectra exhibit extreme sensitivity to boundary conditions and a piling up of all states at the boundary, signalling a breakdown of the conventional bulk-boundary correspondence. The authors study these systems using transfer matrices, whereby they can explain as well as predict the aforementioned features without resorting to numerical computations. This analytical approach allows for a deeper understanding of the topological properties of non-Hermitian systems.
TL;DR: A general variational approach to determine the steady state of open quantum lattice systems via a neural-network approach is presented and applied to the dissipative quantum transverse Ising model.
Abstract: We present a general variational approach to determine the steady state of open quantum lattice systems via a neural-network approach. The steady-state density matrix of the lattice system is constructed via a purified neural-network Ansatz in an extended Hilbert space with ancillary degrees of freedom. The variational minimization of cost functions associated to the master equation can be performed using a Markov chain Monte Carlo sampling. As a first application and proof of principle, we apply the method to the dissipative quantum transverse Ising model.
TL;DR: In this article, a two-dimensional chiral liquid consisting of millions of spinning colloidal magnets was created and its flows were studied, and it was shown that dissipative viscous "edge-pumping" is a key and general mechanism of chiral hydrodynamics, driving unidirectional surface waves and instabilities.
Abstract: In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent ‘atoms’ is determined by the flow and that viscous stresses damp motion. Activation of the rotational degrees of freedom of a fluid by spinning its atomic building blocks breaks these constraints and has thus been the subject of fundamental theoretical interest across classical and quantum fluids. However, the creation of a model liquid that isolates chiral hydrodynamic phenomena has remained experimentally elusive. Here, we report the creation of a cohesive two-dimensional chiral liquid consisting of millions of spinning colloidal magnets and study its flows. We find that dissipative viscous ‘edge-pumping’ is a key and general mechanism of chiral hydrodynamics, driving unidirectional surface waves and instabilities, with no counterpart in conventional fluids. Spectral measurements of the chiral surface dynamics suggest the presence of Hall viscosity, an experimentally elusive property of chiral fluids. Precise measurements and comparison with theory demonstrate excellent agreement with a minimal chiral hydrodynamic model, paving the way for the exploration of chiral hydrodynamics in experiment. A chiral fluid comprising spinning colloidal magnets exhibits macroscopic dynamics reminiscent of the free surface flows of Newtonian fluids, together with unique features suggestive of Hall—or odd—viscosity.
TL;DR: Dissipativity analysis and synthesis are both investigated for the closed-loop system, and consequently sufficient conditions are derived, which pave the way for solving the event-triggering observer-based dissipative sliding mode control problem.
TL;DR: In this paper, the authors formulate the theory of nonlinear viscoelastic hydrodynamics of anisotropic crystals in terms of dynamical Goldstone scalars of spontaneously broken translational symmetries, under the assumption of homogeneous lattices and absence of plastic deformations.
Abstract: We formulate the theory of nonlinear viscoelastic hydrodynamics of anisotropic crystals in terms of dynamical Goldstone scalars of spontaneously broken translational symmetries, under the assumption of homogeneous lattices and absence of plastic deformations. We reformulate classical elasticity effective field theory using surface calculus in which the Goldstone scalars naturally define the position of higher-dimensional crystal cores, covering both elastic and smectic crystal phases. We systematically incorporate all dissipative effects in viscoelastic hydrodynamics at first order in a long-wavelength expansion and study the resulting rheology equations. In the process, we find the necessary conditions for equilibrium states of viscoelastic materials. In the linear regime and for isotropic crystals, the theory includes the description of Kelvin-Voigt materials. Furthermore, we provide an entirely equivalent description of viscoelastic hydrodynamics as a novel theory of higher-form superfluids in arbitrary dimensions where the Goldstone scalars of partially broken generalised global symmetries play an essential role. An exact map between the two formulations of viscoelastic hydrodynamics is given. Finally, we study holographic models dual to both these formulations and map them one-to-one via a careful analysis of boundary conditions. We propose a new simple holographic model of viscoelastic hydrodynamics by adopting an alternative quantisation for the scalar fields.
TL;DR: In this article, the authors show that the chaotic operating regimes of driven optical micro-resonators significantly impact the dynamics of soliton crystals and realize deterministic generation of perfect soliton crystal states, which correspond to a stable, defect free lattice of intracavity optical pulses.
Abstract: Dissipative Kerr solitons in optical microresonators combine nonlinear optical physics with photonic-integrated technologies. They are promising for a number of applications ranging from optical coherent communications to astrophysical spectrometer calibration, and are also of fundamental interest to the physical sciences. Dissipative Kerr solitons can form a variety of stable states, including breathers and multiple-soliton formations. Among these states, soliton crystals stand out: temporally ordered ensembles of soliton pulses, which are regularly arranged by a modulation of the continuous-wave intracavity driving field. To date, however, the dynamics of soliton crystals and their defect-free generation remain unexplored. Here, we show that the chaotic operating regimes of driven optical microresonators significantly impact the dynamics of soliton crystals. We realize deterministic generation of perfect soliton crystal states, which correspond to a stable, defect-free lattice of intracavity optical pulses. We reveal a critical pump power, below which the stochastic process of soliton excitation abruptly becomes deterministic, which enables faultless, device-independent access to perfect soliton crystals. We also demonstrate the switching of these states and its relation to the regime of transient chaos. Finally, we report on other dynamical phenomena observed in soliton crystals including the formation of breathers, transitions between perfect soliton crystals, their melting and recrystallization. A dissipative Kerr soliton crystal state is a temporally ordered regular ensemble of soliton pulses within a cavity. Chaotic driving of optical resonators enables the defect-free creation and dynamical characterization of these states.
TL;DR: In this article, the authors show that explicit splitting schemes generically exploit symmetries in the applied external forces which often strongly suppress integration errors, and demonstrate that weak splitting correctors apply equally well to weakly dissipative systems and can thus be more generally thought of as ''symplectic correctors''.
Abstract: Symplectic methods, in particular the Wisdom-Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophysically important effects are dissipative. The consequences of incorporating such forces into otherwise symplectic schemes is not always clear. We show that moving to a general framework of non-commutative operators (dissipative or not) clarifies many of these questions, and that several important properties of symplectic schemes carry over to the general case. In particular, we show that explicit splitting schemes generically exploit symmetries in the applied external forces which often strongly suppress integration errors. Furthermore, we demonstrate that so-called `symplectic correctors' (which reduce energy errors by orders of magnitude at fixed computational cost) apply equally well to weakly dissipative systems and can thus be more generally thought of as `weak splitting correctors.' Finally, we show that previously advocated approaches of incorporating additional forces into symplectic methods work well for dissipative forces, but give qualitatively wrong answers for conservative but velocity-dependent forces like post-Newtonian corrections. We release REBOUNDx, an open-source C library for incorporating additional effects into REBOUND N-body integrations, together with a convenient Python wrapper. All effects are machine-independent and we provide a binary format that interfaces with the SimulationArchive class in REBOUND to enable the sharing and reproducibility of results. Users can add effects from a list of pre-implemented astrophysical forces, or contribute new ones.
TL;DR: A semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role.
Abstract: We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of disorder, but relies instead on the emergence of a metastable regime. We investigate this in detail in an open quantum spin system, which is a canonical model for the exploration of collective phenomena in strongly interacting dissipative Rydberg gases. Here, a semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role. We perform numerical simulations in order to investigate the dependence on the range of interactions, from all to all to short ranged, and the scaling with system size of the lifetime of the time crystal.
TL;DR: In this article, two paradigmatic concepts of topology in physics, namely, knots and topological properties of energy bands, are brought together to introduce a form of topological matter, best labeled as knotted non-Hermitian metals.
Abstract: Topology, the theory of global properties invariant under continuous deformation, has proven essential for understanding the variety of forms of matter occurring in nature. Here, two paradigmatic concepts of topology in physics, namely, knots and topological properties of energy bands, are brought together to introduce a form of topological matter, best labeled as knotted non-Hermitian metals. Remarkably, non-Hermitian terms accounting for the dissipative coupling of the system to its environment are crucial for the generic stability of these exotic systems.
TL;DR: In this article, it was shown that weak solutions of the inviscid SQG equations are not unique, thereby answering Open Problem 11 in the survey arXiv:1111.2700 by De Lellis and Szekelyhidi Jr.
Abstract: We prove that weak solutions of the inviscid SQG equations are not unique, thereby answering Open Problem 11 in the survey arXiv:1111.2700 by De Lellis and Szekelyhidi Jr. Moreover, we also show that weak solutions of the dissipative SQG equation are not unique, even if the fractional dissipation is stronger than the square root of the Laplacian.
TL;DR: It is shown that a cyclic unitary process can extract work from the thermodynamic equilibrium state of an engineered quantum dissipative process, and situations in which the extractable work is maximal, and circumstances inWhich the efficiency of the process is maximal.
Abstract: We show that a cyclic unitary process can extract work from the thermodynamic equilibrium state of an engineered quantum dissipative process. Systems in the equilibrium states of these processes serve as batteries, storing energy. The dissipative process that brings the battery to the active equilibrium state is driven by an agent that couples the battery to thermal systems. The second law of thermodynamics imposes a work cost for the process; however, no work is needed to keep the battery in that charged state. We consider simple examples of these batteries and discuss situations in which the charged state has full population inversion, in which case the extractable work is maximal, and circumstances in which the efficiency of the process is maximal.
TL;DR: In this paper, the dissipative dynamics of contact Hamiltonian systems are interpreted as a Legendrian submanifold and a coisotropic reduction theorem similar to the one in symplectic mechanics is proved.
Abstract: In this paper, we study Hamiltonian systems on contact manifolds, which is an appropriate scenario to discuss dissipative systems. We show how the dissipative dynamics can be interpreted as a Legendrian submanifold, and also prove a coisotropic reduction theorem similar to the one in symplectic mechanics; as a consequence, we get a method to reduce the dynamics of contact Hamiltonian systems.In this paper, we study Hamiltonian systems on contact manifolds, which is an appropriate scenario to discuss dissipative systems. We show how the dissipative dynamics can be interpreted as a Legendrian submanifold, and also prove a coisotropic reduction theorem similar to the one in symplectic mechanics; as a consequence, we get a method to reduce the dynamics of contact Hamiltonian systems.
TL;DR: The impurity dynamics can be described by an effective potential that deforms from a harmonic to a double-well one when crossing the miscibility-immiscibility threshold and an orthogonality catastrophe occurs and the polaron picture breaks down.
Abstract: We monitor the correlated quench induced dynamical dressing of a spinor impurity repulsively interacting with a Bose-Einstein condensate. Inspecting the temporal evolution of the structure factor, three distinct dynamical regions arise upon increasing the interspecies interaction. These regions are found to be related to the segregated nature of the impurity and to the Ohmic character of the bath. It is shown that the impurity dynamics can be described by an effective potential that deforms from a harmonic to a double-well one when crossing the miscibility-immiscibility threshold. In particular, for miscible components the polaron formation is imprinted on the spectral response of the system. We further illustrate that for increasing interaction an orthogonality catastrophe occurs and the polaron picture breaks down. Then a dissipative motion of the impurity takes place leading to a transfer of energy to its environment. This process signals the presence of entanglement in the many-body system.
TL;DR: In this article, the authors investigated the transport equations for the variances of the velocity components using data from direct numerical simulations of incompressible channel flows at friction Reynolds number up to.
Abstract: The transport equations for the variances of the velocity components are investigated using data from direct numerical simulations of incompressible channel flows at friction Reynolds number ( ) up to . Each term in the transport equation has been spectrally decomposed to expose the contribution of turbulence at different length scales to the processes governing the flow of energy in the wall-normal direction, in scale and among components. The outer-layer turbulence is dominated by very large-scale streamwise elongated modes, which are consistent with the very large-scale motions (VLSM) that have been observed by many others. The presence of these VLSMs drives many of the characteristics of the turbulent energy flows. Away from the wall, production occurs primarily in these large-scale streamwise-elongated modes in the streamwise velocity, but dissipation occurs nearly isotropically in both velocity components and scale. For this to happen, the energy is transferred from the streamwise-elongated modes to modes with a range of orientations through nonlinear interactions, and then transferred to other velocity components. This allows energy to be transferred more-or-less isotropically from these large scales to the small scales at which dissipation occurs. The VLSMs also transfer energy to the wall region, resulting in a modulation of the autonomous near-wall dynamics and the observed Reynolds number dependence of the near-wall velocity variances. The near-wall energy flows are more complex, but are consistent with the well-known autonomous near-wall dynamics that gives rise to streaks and streamwise vortices. Through the overlap region between outer- and inner-layer turbulence, there is a self-similar structure to the energy flows. The VLSM production occurs at spanwise scales that grow with . There is transport of energy away from the wall over a range of scales that grows with . Moreover, there is transfer of energy to small dissipative scales which grows like , as expected from Kolmogorov scaling. Finally, the small-scale near-wall processes characterised by wavelengths less than 1000 wall units are largely Reynolds number independent, while the larger-scale outer-layer processes are strongly Reynolds number dependent. The interaction between them appears to be relatively simple.
TL;DR: In this paper, the authors identify conditions under which dissipation prevents quantum many-body systems from reaching a steady state and they instead exhibit coherent oscillations, which constitutes a dissipative version of a quantum time crystal.
Abstract: The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices. Typically, a quantum system that dissipates into the environment relaxes to a stationary state. Here the authors identify conditions under which dissipation prevents quantum many-body systems from reaching a steady state and they instead exhibit coherent oscillations.
TL;DR: Gong et al. as discussed by the authors investigated whether such a Dicke time crystal (TC) is stable to perturbations that explicitly break the mean-field solvability of the conventional DICke model, and they considered the addition of short-range interactions between the atoms which breaks the collective coupling and leads to complex many-body dynamics.
Abstract: The Dicke model—a paradigmatic example of superradiance in quantum optics—describes an ensemble of atoms which are collectively coupled to a leaky cavity mode. As a result of the cooperative nature of these interactions, the system's dynamics is captured by the behavior of a single mean-field, collective spin. In this mean-field limit, it has recently been shown that the interplay between photon losses and periodic driving of light–matter coupling can lead to time-crystalline-like behavior of the collective spin (Gong et al 2018 Phys. Rev. Lett. 120 040404). In this work, we investigate whether such a Dicke time crystal (TC) is stable to perturbations that explicitly break the mean-field solvability of the conventional Dicke model. In particular, we consider the addition of short-range interactions between the atoms which breaks the collective coupling and leads to complex many-body dynamics. In this context, the interplay between periodic driving, dissipation and interactions yields a rich set of dynamical responses, including long-lived and metastable Dicke-TCs, where losses can cool down the many-body heating resulting from the continuous pump of energy from the periodic drive. Specifically, when the additional short-range interactions are ferromagnetic, we observe time crystalline behavior at non-perturbative values of the coupling strength, suggesting the possible existence of stable dynamical order in a driven-dissipative quantum many-body system. These findings illustrate the rich nature of novel dynamical responses with many-body character in quantum optics platforms.
TL;DR: A linear, decoupled, and unconditionally energy stable numerical scheme is developed by combining the modified projection scheme for the Navier-Stokes equations, the Invariant Energy Quadratization approach for the nonlinear anisotropic potential, and some subtle explicit-implicit treatments for nonlinear coupling terms.
TL;DR: In this article, the authors observed a nonstationary state of chiral nature in a synthetic many-body system with independently controllable unitary and dissipative couplings.
Abstract: Dissipative and unitary processes define the evolution of a many-body system. Their interplay gives rise to dynamical phase transitions and can lead to instabilities. In this study, we observe a nonstationary state of chiral nature in a synthetic many-body system with independently controllable unitary and dissipative couplings. Our experiment is based on a spinor Bose gas interacting with an optical resonator. Orthogonal quadratures of the resonator field coherently couple the Bose-Einstein condensate to two different atomic spatial modes, whereas the dispersive effect of the resonator losses mediates a dissipative coupling between these modes. In a regime of dominant dissipative coupling, we observe the chiral evolution and relate it to a positional instability.
TL;DR: This work identifies this dissipative third party as the invisible cavity mode with large leakage in cavity-magnon experiments and enables one to design dissipative coupling in all sorts of coupled systems.
Abstract: The new field of spin cavitronics focuses on the interaction between the magnon excitation of a magnetic element and the electromagnetic wave in a microwave cavity. In the strong interaction regime, such an interaction usually gives rise to the level anticrossing for the magnonic and the electromagnetic mode. Recently, the attractive level crossing has been observed, and it is explained by a non-Hermitian model Hamiltonian. However, the mechanism of such attractive coupling is still unclear. We reveal the secret by using a simple model with two harmonic oscillators coupled to a third oscillator with large dissipation. We further identify this dissipative third party as the invisible cavity mode with large leakage in cavity-magnon experiments. This understanding enables one to design dissipative coupling in all sorts of coupled systems.
TL;DR: This paper addresses the dissipative asynchronous filtering problem for a class of Takagi–Sugeno fuzzy Markov jump systems in the continuous-time domain and establishes two different methods for the existence of desired filter.
Abstract: This paper addresses the dissipative asynchronous filtering problem for a class of Takagi–Sugeno fuzzy Markov jump systems in the continuous-time domain. The hidden Markov model is applied to describe the asynchronous situation between the designed filter and the original system. Based on the stochastic Lyapunov function, a sufficient condition is developed to guarantee the stochastic stability of the filtering error systems with a given dissipative performance. Two different methods for the existence of desired filter are established. Due to the Finsler’s lemma, the second approach has fewer variables to decide and brings less conservatism than the first one. Finally, an example is provided to demonstrate the correctness and advantage of the proposed approaches.