Showing papers on "Dissipative system published in 2018"

Dissipative Kerr Solitons in Optical Microresonators

Abstract: The development of compact, chip-scale optical frequency comb sources (microcombs) based on parametric frequency conversion in microresonators has seen applications in terabit optical coherent communications, atomic clocks, ultrafast distance measurements, dual-comb spectroscopy, and the calibration of astophysical spectrometers and have enabled the creation of photonic-chip integrated frequency synthesizers. Underlying these recent advances has been the observation of temporal dissipative Kerr solitons in microresonators, which represent self-enforcing, stationary, and localized solutions of a damped, driven, and detuned nonlinear Schrodinger equation, which was first introduced to describe spatial self-organization phenomena. The generation of dissipative Kerr solitons provide a mechanism by which coherent optical combs with bandwidth exceeding one octave can be synthesized and have given rise to a host of phenomena, such as the Stokes soliton, soliton crystals, soliton switching, or dispersive waves. Soliton microcombs are compact, are compatible with wafer-scale processing, operate at low power, can operate with gigahertz to terahertz line spacing, and can enable the implementation of frequency combs in remote and mobile environments outside the laboratory environment, on Earth, airborne, or in outer space.

Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws

Abstract: A new quantum model explores the emergence of irreversible macroscopic behavior from reversible microscopic dynamics.

Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser

Abstract: Dissipative solitons are remarkably localized states of a physical system that arise from the dynamical balance between nonlinearity, dispersion and environmental energy exchange. They are the most universal form of soliton that can exist, and are seen in far-from-equilibrium systems in many fields, including chemistry, biology and physics. There has been particular interest in studying their properties in mode-locked lasers, but experiments have been limited by the inability to track the dynamical soliton evolution in real time. Here, we use simultaneous dispersive Fourier transform and time-lens measurements to completely characterize the spectral and temporal evolution of ultrashort dissipative solitons as their dynamics pass through a transient unstable regime with complex break-up and collisions before stabilization. Further insight is obtained from reconstruction of the soliton amplitude and phase and calculation of the corresponding complex-valued eigenvalue spectrum. These findings show how real-time measurements provide new insights into ultrafast transient dynamics in optics. The simultaneous use of dispersive Fourier transform and time-lens measurements allows complete characterization of the unstable spectral and temporal evolution of ultrashort dissipative solitons, providing further insight into ultrafast transient dynamics in optics.

Level Attraction Due to Dissipative Magnon-Photon Coupling.

Abstract: We report dissipative magnon-photon coupling caused by the cavity Lenz effect, where the magnons in a magnet induce a rf current in the cavity, leading to a cavity backaction that impedes the magnetization dynamics. This effect is revealed in our experiment as level attraction with a coalescence of hybridized magnon-photon modes, which is distinctly different from level repulsion with mode anticrossing caused by coherent magnon-photon coupling. We develop a method to control the interpolation of coherent and dissipative magnon-photon coupling, and observe a matching condition where the two effects cancel. Our work sheds light on the so-far hidden side of magnon-photon coupling, opening a new avenue for controlling and utilizing light-matter interactions.

Spectral theory of Liouvillians for dissipative phase transitions

Abstract: A state of an open quantum system is described by a density matrix, whose dynamics is governed by a Liouvillian superoperator. Within a general framework, we explore fundamental properties of both first-order dissipative phase transitions and second-order dissipative phase transitions associated with a symmetry breaking. In the critical region, we determine the general form of the steady-state density matrix and of the Liouvillian eigenmatrix whose eigenvalue defines the Liouvillian spectral gap. We illustrate our exact results by studying some paradigmatic quantum optical models exhibiting critical behavior.

Energy consumption in chemical fuel-driven self-assembly

Abstract: Nature extensively exploits high-energy transient self-assembly structures that are able to perform work through a dissipative process. Often, self-assembly relies on the use of molecules as fuel that is consumed to drive thermodynamically unfavourable reactions away from equilibrium. Implementing this kind of non-equilibrium self-assembly process in synthetic systems is bound to profoundly impact the fields of chemistry, materials science and synthetic biology, leading to innovative dissipative structures able to convert and store chemical energy. Yet, despite increasing efforts, the basic principles underlying chemical fuel-driven dissipative self-assembly are often overlooked, generating confusion around the meaning and definition of scientific terms, which does not favour progress in the field. The scope of this Perspective is to bring closer together current experimental approaches and conceptual frameworks. From our analysis it also emerges that chemically fuelled dissipative processes may have played a crucial role in evolutionary processes.

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

Abstract: 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.

Few-layer bismuthene for ultrashort pulse generation in a dissipative system based on an evanescent field.

Abstract: Bismuthene has attracted a great deal of attention because of its unique electronic and optical properties. However, there are few reported applications of bismuthene in nonlinear optical applications. In this research, a dissipative soliton ytterbium-doped mode-locked fiber laser at 1 μm regime with a bismuthene saturable absorber (SA) by using evanescent field interaction for the first time is demonstrated. The nonlinear optical absorption of microfiber-based bismuthene SA is shown experimentally by using a homemade ultrafast fiber laser, whose saturation intensity and modulation depth are about 13 MW cm-2 and 2.2%, respectively. Relying on the excellent nonlinear optical property of the bismuthene SA, the typical dissipative solitons with a repetition rate of 21.74 MHz are generated at a center wavelength of 1034.4 nm. The time-bandwidth product of the pulse is about 23.07 with a pulse width of 30.25 ps. The results demonstrate that bismuthene is a good candidate for application in a 1 μm wave-breaking-free mode-locked fiber laser and nonlinear photonic components.

Asynchronous Dissipative Control for Fuzzy Markov Jump Systems

Abstract: The problem of asynchronous dissipative control is investigated for Takagi–Sugeno fuzzy systems with Markov jump in this paper. Hidden Markov model is introduced to represent the nonsynchronization between the designed controller and the original system. By the fuzzy-basis-dependent and mode-dependent Lyapunov function, a sufficient condition is achieved such that the resulting closed-loop system is stochastically stable with a strictly ( $ {\mathcal {Q}}$ , $ {\mathcal {S}}$ , $ {\mathcal {R}}$ )- $ {\alpha }$ -dissipative performance. The controller parameter is derived by applying MATLAB to solve a set of linear matrix inequalities. Finally, we present two examples to confirm the validity and correctness of our developed approach.

Thermal and Nonlinear Dissipative-Soliton Dynamics in Kerr-Microresonator Frequency Combs.

Abstract: We explore the dynamical response of dissipative Kerr solitons to changes in pump power and detuning and show how thermal and nonlinear processes couple these parameters to the frequency-comb degrees of freedom. Our experiments are enabled by a Pound-Drever-Hall (PDH) stabilization approach that provides on-demand, radio-frequency control of the frequency comb. PDH locking not only guides Kerr-soliton formation from a cold microresonator but opens a path to decouple the repetition and carrier-envelope-offset frequencies. In particular, we demonstrate phase stabilization of both Kerr-comb degrees of freedom to a fractional frequency precision below 10^{-16}, compatible with optical-time-keeping technology. Moreover, we investigate the fundamental role that residual laser-resonator detuning noise plays in the spectral purity of microwave generation with Kerr combs.

Dissipative Self-Assembly Driven by the Consumption of Chemical Fuels

Abstract: Dissipative self-assembly leads to structures and materials that exist away from equilibrium by continuously exchanging energy and materials with the external environment. Although this mode of self-assembly is ubiquitous in nature, where it gives rise to functions such as signal processing, motility, self-healing, self-replication, and ultimately life, examples of dissipative self-assembly processes in man-made systems are few and far between. Herein, recent progress in developing diverse synthetic dissipative self-assembly systems is discussed. The systems reported thus far can be categorized into three classes, in which: i) the fuel chemically modifies the building blocks, thus triggering their self-assembly, ii) the fuel acts as a template interacting with the building blocks noncovalently, and iii) transient states are induced by the addition of two mutually exclusive stimuli. These early studies give rise to materials that would be difficult to obtain otherwise, including hydrogels with programmable lifetimes, vesicular nanoreactors, and membranes exhibiting transient conductivity.

A Dissipatively Stabilized Mott Insulator of Photons

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.

Build-Up of Dissipative Optical Soliton Molecules via Diverse Soliton Interactions

Abstract: Solitons can form bound states that are frequently referred to as soliton molecules as they exhibit molecule-like dynamics. The build-up phase of the optical soliton molecule remains elusive. Here, by means of a time-stretch technique that enables real-time access to the spectral and temporal dynamics, rich nonlinear processes involved in the build-up of soliton molecules are revealed in an ultrafast fibre laser. Specifically, the formation of closelyand well-separated bound solitons are resolved. In both cases, the build-up phases consist of three nonlinear stages including mode locking, soliton splitting, and soliton interactions. For closely-separated bound solitons, soliton interactions display wide diversities in repeated measurements, including soliton attraction, repelling, collision, vibration, and annihilation. For well-separated bound solitons, repulsive interactions dominate the soliton interactions. Numerical simulations corroborate these experimental observations. Furthermore, a conceptually different soliton molecule, the intermittent-vibration soliton molecule, is discovered and characterized. It is the intermediate state between the vibrational and stationary soliton molecules. The author’s findings could assist in the understanding of the build-up phase of localized structures in different dissipative systems.

Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems

Abstract: In this paper, the issues of finite-time extended dissipative analysis and non-fragile control are investigated for a class of uncertain discrete time switched linear systems. Based on average dwell-time approach, sufficient conditions for the finite-time boundedness and finite-time extended dissipative performance of the considered systems are proposed by solving some linear matrix inequalities, where using the concept of extended dissipative, we can solve the H∞, L 2 − L ∞ , Passivity and (Q, S, R)-dissipativity performance in a unified framework. Furthermore, two form of non-fragile state feedback controllers are designed to guarantee that the closed-loop systems satisfy the finite-time extended dissipative performance. Finally, simulation example is given to show the efficiency of the proposed methods.

Self-selection of dissipative assemblies driven by primitive chemical reaction networks

Abstract: Life is a dissipative nonequilibrium structure that requires constant consumption of energy to sustain itself. How such an unstable state could have selected from an abiotic pool of molecules remains a mystery. Here we show that liquid phase-separation offers a mechanism for the selection of dissipative products from a library of reacting molecules. We bring a set of primitive carboxylic acids out-of-equilibrium by addition of high-energy condensing agents. The resulting anhydrides are transiently present before deactivation via hydrolysis. We find the anhydrides that phase-separate into droplets to protect themselves from hydrolysis and to be more persistent than non-assembling ones. Thus, after several starvation-refueling cycles, the library self-selects the phase-separating anhydrides. We observe that the self-selection mechanism is more effective when the library is brought out-of-equilibrium by periodic addition of batches as opposed to feeding it continuously. Our results suggest that phase-separation offers a selection mechanism for energy dissipating assemblies.

Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves

Abstract: The goal of this review article is to assess how relevant is the concept of dissipative structure for understanding the dynamical bases of non-equilibrium self-organization in biological systems, and to see where it has been applied in the five decades since it was initially proposed by Ilya Prigogine. Dissipative structures can be classified into four types, which will be considered, in turn, and illustrated by biological examples: (i) multistability, in the form of bistability and tristability, which involve the coexistence of two or three stable steady states, or in the form of birhythmicity, which involves the coexistence between two stable rhythms; (ii) temporal dissipative structures in the form of sustained oscillations, illustrated by biological rhythms; (iii) spatial dissipative structures, known as Turing patterns; and (iv) spatio-temporal structures in the form of propagating waves. Rhythms occur with widely different periods at all levels of biological organization, from neural, cardiac and metabolic oscillations to circadian clocks and the cell cycle; they play key roles in physiology and in many disorders. New rhythms are being uncovered while artificial ones are produced by synthetic biology. Rhythms provide the richest source of examples of dissipative structures in biological systems. Bistability has been observed experimentally, but has primarily been investigated in theoretical models in an increasingly wide range of biological contexts, from the genetic to the cell and animal population levels, both in physiological conditions and in disease. Bistable transitions have been implicated in the progression between the different phases of the cell cycle and, more generally, in the process of cell fate specification in the developing embryo. Turing patterns are exemplified by the formation of some periodic structures in the course of development and by skin stripe patterns in animals. Spatio-temporal patterns in the form of propagating waves are observed within cells as well as in intercellular communication. This review illustrates how dissipative structures of all sorts abound in biological systems.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Definition of complexity for dynamical spherically symmetric dissipative self-gravitating fluid distributions

Abstract: The recently proposed definition of complexity for static and spherically symmetric self-gravitating systems [Herrera, Phys. Rev. D 97, 044010 (2017)] is extended to the fully dynamic situation. In this latter case we have to consider not only the complexity factor of the structure of the fluid distribution but also the condition of minimal complexity of the pattern of evolution. As we shall see, these two issues are deeply intertwined. For the complexity factor of the structure we choose the same as for the static case, whereas for the simplest pattern of evolution we assume the homologous condition. The dissipative and nondissipative cases are considered separately. In the latter case the fluid distribution, satisfying the vanishing complexity factor condition and evolving homologously, corresponds to a homogeneous (in the energy density), geodesic and shear-free, isotropic (in the pressure) fluid. In the dissipative case the fluid is still geodesic, but shearing, and there exists (in principle) a large class of solutions. Finally, we discuss the stability of the vanishing complexity condition.

Dissipative hydrodynamics in superspace

Abstract: We construct a Schwinger-Keldysh effective field theory for relativistic hydrodynamics for charged matter in a thermal background using a superspace formalism. Superspace allows us to efficiently impose the symmetries of the problem and to obtain a simple expression for the effective action. We show that the theory we obtain is compatible with the Kubo-Martin-Schwinger condition, which in turn implies that Green’s functions obey the fluctuation-dissipation theorem. Our approach complements and extends existing formulations found in the literature.

Spectral analysis of the budget equation in turbulent channel flows at high Re

Abstract: The transport equations for velocity variances are investigated using data from DNS of incompressible channel flows at $Re_\tau$ up to 5200. 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. 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 non-linear 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. The near-wall energy flows are consistent with the well-known autonomous near-wall dynamics. 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 $y$. There is transport of energy away from the wall over a range of scales that grows with $y$. And, there is transfer of energy to small dissipative scales which grow like $y^{1/4}$. 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 process are strongly Reynolds number dependent. The interaction between them appears to be relatively simple.

Spontaneous emission of matter waves from a tunable open quantum system

Abstract: The decay of an excited atom undergoing spontaneous photon emission into the fluctuating quantum-electrodynamic vacuum is an emblematic example of the dynamics of an open quantum system. Recent experiments have demonstrated that the gapped photon dispersion in periodic structures, which prevents photons in certain frequency ranges from propagating, can give rise to unusual spontaneous-decay behaviour, including the formation of dissipative bound states1–3. So far, these effects have been restricted to the optical domain. Here we demonstrate similar behaviour in a system of artificial emitters, realized using ultracold atoms in an optical lattice, which decay by emitting matter-wave, rather than optical, radiation into free space. By controlling vacuum coupling and the excitation energy, we directly observe exponential and partly reversible non-Markovian dynamics and detect a tunable bound state that contains evanescent matter waves. Our system provides a flexible platform for simulating open-system quantum electrodynamics and for studying dissipative many-body physics with ultracold atoms4–6. An open quantum system containing ultracold rubidium atoms trapped in an optical lattice undergoes spontaneous emission of matter waves into free space.

Dissipative phase transition in the open quantum Rabi model

Abstract: We demonstrate that the open quantum Rabi model (QRM) exhibits a second-order dissipative phase transition (DPT) and propose a method to observe this transition with trapped ions. The interplay between the ultrastrong qubit-oscillator coupling and the oscillator damping brings the system into a steady state with a diverging number of excitations, in which a DPT is allowed to occur even with a finite number of system components. The universality class of the open QRM, modified from the closed QRM by a Markovian bath, is identified by finding critical exponents and scaling functions using the Keldysh functional integral approach. We propose to realize the open QRM with two trapped ions where the coherent coupling and the rate of dissipation can be individually controlled and adjusted over a wide range. Thanks to this controllability, our work opens a possibility to investigate potentially rich dynamics associated with a dissipative phase transition.

Critical slowing down in driven-dissipative Bose-Hubbard lattices

Abstract: We explore theoretically the dynamical properties of a first-order dissipative phase transition in coherently driven Bose-Hubbard systems, describing, e.g., lattices of coupled nonlinear optical cavities. Via stochastic trajectory calculations based on the truncated Wigner approximation, we investigate the dynamical behavior as a function of system size for one-dimensional (1D) and 2D square lattices in the regime where mean-field theory predicts nonlinear bistability. We show that a critical slowing down emerges for increasing number of sites in 2D square lattices, while it is absent in 1D arrays. We characterize the peculiar properties of the collective phases in the critical region.

Broken Symmetry, Emergent Properties, Dissipative Structures, Life: are they Related?

Abstract: : We conclude that there is no analogy visible between the stability, rigidity and other emergent properties of equilibrium broken symmetry systems, and the properties of dissipative systems driven far from equilibrium. The latter types of systems have never been observed to, nor can any mathematical reason be found why they should, exhibit the rigidity, stability, and permanence which characterizes the thermodynamically stable broken symmetry systems. (A case point of a driven system that might have exhibited broken symmetry but failed to do so is described.) The reason this is unfortunate is that many authors have chosen to use such systems as the laser and the Benard instability as models for the nature and origin of life itself, as an emergent property of inanimate matter. It is indeed an obvious fact, noted since Schrodinger's 1940 book, that life succeeds in maintaining its stability and integrity, and the identity of its genetic material, at the cost of increasing the rate of entropy production of the world as a whole. It is at least in that sense a stable 'dissipative structure'-i.e., an existence proof by example. Let us then conclude by reiterating our main point: we still believe, since in fact we understand the process in all details, in the reality of emergent properties: the ability of complex physical systems to exhibit properties unrelated to those of their constituents. But we do not believe that stable 'dissipative structures' maintained by dynamic driving forces can be shown to exist in any inanimate system, and thus we do not see how speculations about such structures and their broken symmetry can yet be relevant to the still open question of the origin and nature of life.

Design and Fabrication of Bioinspired Hierarchical Dissipative Elastic Metamaterials

Abstract: The authors propose a strategy to integrate $h\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}y$ into the design of elastic metamaterials and produce lightweight solutions for multiscale frequency attenuation, with applications ranging from nondestructive testing to seismic protection. This study shows the benefits of hierarchical structure in porous, viscoelastic single-phase materials, demonstrating efficient multifrequency attenuation---including low frequencies---while reducing structural weight. The results can be applied over a wide range of length scales, providing engineering solutions to vibration-damping problems.

Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model

Abstract: We investigate dissipative extensions of the Su-Schrieffer-Heeger model with regard to different approaches of modeling dissipation. In doing so, we use two distinct frameworks to describe the gain and loss of particles: One uses Lindblad operators within the scope of Lindblad master equations, and the other uses complex potentials as an effective description of dissipation. The reservoirs are chosen in such a way that the non-Hermitian complex potentials are $\mathcal{PT}$-symmetric. From the effective theory we extract a state which has similar properties as the nonequilibrium steady state following from Lindblad master equations with respect to lattice site occupation. We find considerable similarities in the spectra of the effective Hamiltonian and the corresponding Liouvillian. Further, we generalize the concept of the Zak phase to the dissipative scenario in terms of the Lindblad description and relate it to the topological phases of the underlying Hermitian Hamiltonian.

From the Lugiato-Lefever equation to microresonator-based soliton Kerr frequency combs.

Abstract: The model, that is usually called the Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a perfect and exact description of Kerr frequency combs-first observed in 2007, i.e. 20 years after the original formulation of the LLE-and in particular describe soliton states. Observed to spontaneously form in Kerr frequency combs in crystalline microresonators in 2013, such DKS are preferred state of operation, offering coherent and broadband optical frequency combs, whose bandwidth can be extended exploiting soliton-induced broadening phenomena. Combined with the ability to miniaturize and integrate on-chip, microresonator-based soliton Kerr frequency combs have already found applications in self-referenced frequency combs, dual-comb spectroscopy, frequency synthesis, low noise microwave generation, laser frequency ranging, and astrophysical spectrometer calibration, and have the potential to make comb technology ubiquitous. As such, pattern formation in driven, dissipative nonlinear optical systems is becoming the central Physics of soliton micro-comb technology.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Shattered time: can a dissipative time crystal survive many-body correlations?

Abstract: We investigate the emergence of a time crystal (TC) in a driven dissipative many-body spin array. In this system the interplay between incoherent spin pumping and collective emission stabilizes a synchronized non-equilibrium steady state which in the thermodynamic limit features a self-generated time-periodic pattern imposed by collective elastic interactions. In contrast to prior realizations where the time symmetry is already broken by an external drive, here it is only spontaneously broken by the elastic exchange interactions and manifest in the two-time correlation spectrum. Employing a combination of exact numerical calculations and a second-order cumulant expansion, we investigate the impact of many-body correlations on the TC formation and establish a connection between the regime where it is stable and where the system features a slow growth rate of the mutual information. This observation allows us to conclude that the TC studied here is an emergent semi-classical out-of-equilibrium state of matter. We also confirm the rigidity of the TC to single-particle dephasing. Finally, we discuss an experimental implementation using long lived dipoles in an optical cavity.

Nonresistive dissipative magnetohydrodynamics from the Boltzmann equation in the 14-moment approximation

Abstract: We derive the equations of motion of relativistic, nonresistive, second-order dissipative magnetohydrodynamics from the Boltzmann equation using the method of moments. We assume the fluid to be composed of a single type of point-like particles with vanishing dipole moment or spin, so that the fluid has vanishing magnetization and polarization. In a first approximation, we assume the fluid to be nonresistive, which allows to express the electric field in terms of the magnetic field. We derive equations of motion for the irreducible moments of the deviation of the single-particle distribution function from local thermodynamical equilibrium. We analyze the Navier-Stokes limit of these equations, reproducing previous results for the structure of the first-order transport coefficients. Finally, we truncate the system of equations for the irreducible moments using the 14-moment approximation, deriving the equations of motion of relativistic, nonresistive, second-order dissipative magnetohydrodynamics. We also give expressions for the new transport coefficients appearing due to the coupling of the magnetic field to the dissipative quantities.