Showing papers on "Dissipative system published in 2013"
TL;DR: In this paper, a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity is used for frequency comb generation in whispering-gallery-mode resonators.
Abstract: We demonstrate that frequency (Kerr) comb generation in whispering-gallery-mode resonators can be modeled by a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatiotemporal model allows us to explore pulse formation in which a large number of modes interact cooperatively. Pulse formation is shown to play a critical role in comb generation, and we find conditions under which single pulses (dissipative solitons) and multiple pulses (rolls) form. We show that a broadband comb is the spectral signature of a dissipative soliton, and we also show that these solitons can be obtained by using a weak anomalous dispersion and subcritical pumping.
431 citations
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06 Jun 2013
TL;DR: In this paper, the Evans function for boundary value problems for Sturm-Liouville operators on the real line and the Evans functions for nth-order operators on real line are presented.
Abstract: Introduction.- Background material and notation.- Essential and absolute spectra.- Dynamical implications of spectra: dissipative systems.- Dynamical implications of spectra: Hamiltonian systems.- Dynamical implications of spectra: Hamiltonian systems.- Point spectrum: reduction to finite-rank eigenvalue problems.- Point spectrum: linear Hamiltonian systems.- The Evans function for boundary value problems.- The Evans function for Sturm-Liouville operators on the real line.- The Evans function for nth-order operators on the real line.- Index.- References.
345 citations
TL;DR: This work employs a Gutzwiller ansatz as well as semiclassical Langevin equations on finite lattices, and proposes a realistic experimental implementation in optomechanical crystals for weak intercellular coupling.
Abstract: We study the nonlinear driven dissipative quantum dynamics of an array of optomechanical systems. At each site of such an array, a localized mechanical mode interacts with a laser-driven cavity mode via radiation pressure, and both photons and phonons can hop between neighboring sites. The competition between coherent interaction and dissipation gives rise to a rich phase diagram characterizing the optical and mechanical many-body states. For weak intercellular coupling, the mechanical motion at different sites is incoherent due to the influence of quantum noise. When increasing the coupling strength, however, we observe a transition towards a regime of phase-coherent mechanical oscillations. We employ a Gutzwiller ansatz as well as semiclassical Langevin equations on finite lattices, and we propose a realistic experimental implementation in optomechanical crystals.
275 citations
TL;DR: The nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates, is explored and a critical exponent special to the driven system is identified, showing that it defines a new dynamical universality class.
Abstract: We explore the nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates. Using a functional renormalization group approach formulated in the Keldysh framework, we characterize the dynamical critical behavior that governs decoherence and an effective thermalization of the low frequency dynamics. We identify a critical exponent special to the driven system, showing that it defines a new dynamical universality class. Hence critical points in driven systems lie beyond the standard classification of equilibrium dynamical phase transitions. We show how the new critical exponent can be probed in experiments with driven cold atomic systems and exciton-polariton condensates.
263 citations
TL;DR: The link between the dissipative dynamics and the measurement of the density distribution of the BEC allowing for a generalized definition of the Zeno effect is demonstrated.
Abstract: We experimentally investigate the action of a localized dissipative potential on a macroscopic matter wave, which we implement by shining an electron beam on an atomic Bose-Einstein condensate (BEC). We measure the losses induced by the dissipative potential as a function of the dissipation strength observing a paradoxical behavior when the strength of the dissipation exceeds a critical limit: for an increase of the dissipation rate the number of atoms lost from the BEC becomes lower. We repeat the experiment for different parameters of the electron beam and we compare our results with a simple theoretical model, finding excellent agreement. By monitoring the dynamics induced by the dissipative defect we identify the mechanisms which are responsible for the observed paradoxical behavior. We finally demonstrate the link between our dissipative dynamics and the measurement of the density distribution of the BEC allowing for a generalized definition of the Zeno effect. Because of the high degree of control on every parameter, our system is a promising candidate for the engineering of fully governable open quantum systems.
239 citations
TL;DR: The leading singularity in the Borel transform of the hydrodynamic energy density with the lowest nonhydrod dynamic excitation corresponding to a 'nonhydrodynamic' quasinormal mode on the gravity side is identified.
Abstract: We utilize the fluid-gravity duality to investigate the large order behavior of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma system. This corresponds to the inclusion of dissipative terms and transport coefficients of very high order. Using the dual gravity description, we calculate numerically the form of the stress tensor for a boost-invariant flow in a hydrodynamic expansion up to terms with 240 derivatives. We observe a factorial growth of gradient contributions at large orders, which indicates a zero radius of convergence of the hydrodynamic series. Furthermore, we identify the leading singularity in the Borel transform of the hydrodynamic energy density with the lowest nonhydrodynamic excitation corresponding to a ‘nonhydrodynamic’ quasinormal mode on the gravity side.
235 citations
TL;DR: In this article, the authors show that a slow divergence away from exact commensurability is a natural outcome of dissipative evolution and demonstrate that libration of critical angles can be maintained tens of percent away from nominal resonance.
Abstract: A considerable fraction of multi-planet systems discovered by the observational surveys of extrasolar planets reside in mild proximity to first-order mean-motion resonances However, the relative remoteness of such systems from nominal resonant period ratios (eg, 2:1, 3:2, and 4:3) has been interpreted as evidence for lack of resonant interactions Here, we show that a slow divergence away from exact commensurability is a natural outcome of dissipative evolution and demonstrate that libration of critical angles can be maintained tens of percent away from nominal resonance We construct an analytical theory for the long-term dynamical evolution of dissipated resonant planetary pairs and confirm our calculations numerically Collectively, our results suggest that a significant fraction of the near-commensurate extrasolar planets are in fact resonant and have undergone significant dissipative evolution
225 citations
TL;DR: In this article, the authors show how large amounts of steady-state quantum squeezing (beyond 3 dB) of a mechanical resonator can be obtained by driving an optomechanical cavity with two control lasers with differing amplitudes.
Abstract: We discuss how large amounts of steady-state quantum squeezing (beyond 3 dB) of a mechanical resonator can be obtained by driving an optomechanical cavity with two control lasers with differing amplitudes. The scheme does not rely on any explicit measurement or feedback, nor does it simply involve a modulation of an optical spring constant. Instead, it uses a dissipative mechanism with the driven cavity acting as an engineered reservoir. It can equivalently be viewed as a coherent feedback process, obtained by minimally perturbing the quantum nondemolition measurement of a single mechanical quadrature. This shows that in general the concepts of coherent feedback schemes and reservoir engineering are closely related. We analyze how to optimize the scheme, how the squeezing scales with system parameters, and how it may be directly detected from the cavity output. Our scheme is extremely general, and could also be implemented with, e.g., superconducting circuits.
213 citations
TL;DR: In this article, the concept of topological order has been explored in the context of dissipative dynamics for fermionic systems, where the spectrum and the state of the system are not as tightly related as in the Hamiltonian context.
Abstract: Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted cooling into topological phases starting from arbitrary initial states. We explore the concept of topological order in this setting, developing and applying a general theoretical framework based on the system density matrix that replaces the wave function appropriate for the discussion of Hamiltonian ground-state physics. We identify key analogies and differences to the more conventional Hamiltonian scenario. Differences essentially arise from the fact that the properties of the spectrum and of the state of the system are not as tightly related as in the Hamiltonian context. We provide a symmetry-based topological classification of bulk steady states and identify the classes that are achievable by means of quasi-local dissipative processes driving into superfluid paired states. We also explore the fate of the bulk-edge correspondence in the dissipative setting and demonstrate the emergence of Majorana edge modes. We illustrate ourfindings in one- and two-dimensional models that are experimentally realistic in the context of cold atoms.
211 citations
TL;DR: A formulation of Hamilton's principle that is compatible with initial value problems is presented, which leads to a natural formulation for the Lagrangian and Hamiltonian dynamics of generic nonconservative systems, thereby filling a long-standing gap in classical mechanics.
Abstract: Hamilton’s principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton’s principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. This subtlety can have undesirable effects. I present a formulation of Hamilton’s principle that is compatible with initial value problems. Remarkably, this leads to a natural formulation for the Lagrangian and Hamiltonian dynamics of generic nonconservative systems, thereby filling a long-standing gap in classical mechanics. Thus, dissipative effects, for example, can be studied with new tools that may have applications in a variety of disciplines. The new formalism is demonstrated by two examples of nonconservative systems: an object moving in a fluid with viscous drag forces and a harmonic oscillator coupled to a dissipative environment.
194 citations
TL;DR: Investigation of spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group finds that the decoherence time diverges in the thermodynamic limit, and the coherence decay is then algebraic instead of exponential.
Abstract: The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-$1/2$ chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group. For the open $XXZ$ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative treatment. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence.
TL;DR: In this article, the authors investigate nonequilibrium phase transitions for driven atomic ensembles interacting with a cavity mode and coupled to a Markovian dissipative bath, and show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength.
Abstract: We investigate nonequilibrium phase transitions for driven atomic ensembles interacting with a cavity mode and coupled to a Markovian dissipative bath. In the thermodynamic limit and at low frequencies, we show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path-integral approach that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number $N$ of atoms. For finite $N$, the photon mode behaves as a damped classical nonlinear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any $N$ and correctly captures the atoms' depolarization due to dissipative dephasing.
TL;DR: The steady-state phases of a driven-dissipative Bose-Hubbard model are determined, describing, e.g., an array of coherently pumped nonlinear cavities with a finite photon lifetime, and a tunneling-induced transition between monostable and bistable phases is shown.
Abstract: We determine the steady-state phases of a driven-dissipative Bose-Hubbard model, describing, e.g., an array of coherently pumped nonlinear cavities with a finite photon lifetime. Within a mean-field master equation approach using exact quantum solutions for the one-site problem, we show that the system exhibits a tunneling-induced transition between monostable and bistable phases. We characterize the corresponding quantum correlations, highlighting the essential differences with respect to the equilibrium case. We also find collective excitations with a flat energy-momentum dispersion over the entire Brillouin zone that trigger modulational instabilities at specific wave vectors.
TL;DR: Using a dissipation channel to nondestructively gain information about a quantum many-body system provides a unique path to study the physics of driven-dissipative systems.
Abstract: We experimentally study the influence of dissipation on the driven Dicke quantum phase transition, realized by coupling external degrees of freedom of a Bose–Einstein condensate to the light field of a high-finesse optical cavity. The cavity provides a natural dissipation channel, which gives rise to vacuum-induced fluctuations and allows us to observe density fluctuations of the gas in real-time. We monitor the divergence of these fluctuations over two orders of magnitude while approaching the phase transition, and observe a behavior that deviates significantly from that expected for a closed system. A correlation analysis of the fluctuations reveals the diverging time scale of the atomic dynamics and allows us to extract a damping rate for the external degree of freedom of the atoms. We find good agreement with our theoretical model including dissipation via both the cavity field and the atomic field. Using a dissipation channel to nondestructively gain information about a quantum many-body system provides a unique path to study the physics of driven-dissipative systems.
TL;DR: In this article, the concept of topological order was explored in the context of dissipative dynamics of fermionic systems, where the spectrum and the state of the system are not as tightly related as in a Hamiltonian context.
Abstract: Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted cooling into a topological phase starting from an arbitrary initial state. We explore the concept of topological order in this setting, developing and applying a general theoretical framework based on the system density matrix which replaces the wave function appropriate for the discussion of Hamiltonian ground-state physics. We identify key analogies and differences to the more conventional Hamiltonian scenario. Differences mainly arise from the fact that the properties of the spectrum and of the state of the system are not as tightly related as in a Hamiltonian context. We provide a symmetry-based topological classification of bulk steady states and identify the classes that are achievable by means of quasi-local dissipative processes driving into superfluid paired states. We also explore the fate of the bulk-edge correspondence in the dissipative setting, and demonstrate the emergence of Majorana edge modes. We illustrate our findings in one- and two-dimensional models that are experimentally realistic in the context of cold atoms.
TL;DR: It is concluded that, at low frequencies and amplitudes, currents induce collective motion by means of dissipative rather than reactive torques.
Abstract: Antiferromagnets can be used to store and manipulate spin information, but the coupled dynamics of the staggered field and the magnetization are very complex. We present a theory which is conceptually much simpler and which uses collective coordinates to describe staggered field dynamics in antiferromagnetic textures. The theory includes effects from dissipation, external magnetic fields, as well as reactive and dissipative current-induced torques. We conclude that, at low frequencies and amplitudes, currents induce collective motion by means of dissipative rather than reactive torques. The dynamics of a one-dimensional domain wall, pinned at 90\ifmmode^\circ\else\textdegree\fi{} at its ends, are described as a driven harmonic oscillator with a natural frequency inversely proportional to the length of the texture.
TL;DR: In this article, the authors review recent progress achieved in the study of dissipative optical lattices and emphasize the generality of the findings for a broad class of physical, chemical and biological systems.
Abstract: Cold atoms in dissipative optical lattices exhibit an unusual transport behaviour that cannot be described within Boltzmann–Gibbs statistical mechanics. New theoretical tools and concepts need thus be developed to account for their observable macroscopic properties. Here we review recent progress achieved in the study of these processes. We emphasize the generality of the findings for a broad class of physical, chemical and biological systems, and discuss open questions and perspectives for future work. Cold atoms trapped in dissipative optical lattices can behave in ways that cannot be described within the framework of Boltzmann–Gibbs statistical mechanics. Recent theoretical and experimental developments may lead to a better understanding of these processes.
TL;DR: In this paper, the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy has been shown, which is the case of the continuous periodic solution of this paper.
Abstract: We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy.
TL;DR: In this article, the authors present a theoretical framework to tackle quantum non-Markovian dynamics based on a microscopic collision model (CM), where the bath consists of a large collection of initially uncorrelated ancillas.
Abstract: We present a theoretical framework to tackle quantum non-Markovian dynamics based on a microscopic collision model (CM), where the bath consists of a large collection of initially uncorrelated ancillas. Unlike standard memoryless CMs, we endow the bath with memory by introducing interancillary collisions between next system-ancilla interactions. Our model interpolates between a fully Markovian dynamics and the continuous interaction of the system with a single ancilla, i.e., a strongly non-Markovian process. We show that in the continuous limit one can derive a general master equation, which, while keeping such features, is guaranteed to describe an unconditionally completely positive and trace-preserving dynamics. We apply our theory to an atom in a dissipative cavity for a Lorentzian spectral density of bath modes, a dynamics which can be exactly solved. The predicted evolution shows a significant improvement in approaching the exact solution with respect to two well-known memory-kernel master equations.
TL;DR: It is predicted that the existence of novel magnetic phases in the steady state of this system, subject to dissipative spin-flip processes associated with optical pumping, will emerge due to the competition between coherent and dissipative processes.
Abstract: We consider strongly interacting systems of effective spins, subject to dissipative spin-flip processes associated with optical pumping. We predict the existence of novel magnetic phases in the steady state of this system, which emerge due to the competition between coherent and dissipative processes. Specifically, for strongly anisotropic spin-spin interactions, we find ferromagnetic, antiferromagnetic, spin-density-wave, and staggered-$XY$ steady states, which are separated by nonequilibrium phase transitions meeting at a Lifshitz point. These transitions are accompanied by quantum correlations, resulting in spin squeezing. Experimental implementations in ultracold atoms and trapped ions are discussed.
TL;DR: The existence of a collective atomic dark state, decoupled from the radiation field, is demonstrated and it is shown that such dark states can be deterministically prepared via dissipative means, thus turning dissipation into a resource for entanglement.
Abstract: We present and analyze a new approach for the generation of atomic spin-squeezed states. Our method involves the collective coupling of an atomic ensemble to a decaying mode of an open optical cavity. We demonstrate the existence of a collective atomic dark state, decoupled from the radiation field. By explicitly constructing this state we find that it can feature spin squeezing bounded only by the Heisenberg limit. We show that such dark states can be deterministically prepared via dissipative means, thus turning dissipation into a resource for entanglement. The scaling of the phase sensitivity taking realistic imperfections into account is discussed.
TL;DR: In this paper, the authors derived a third-order hydrodynamic evolution equation for the shear stress tensor from kinetic theory and showed that the results obtained using the thirdorder viscous equations derived here provide a very good approximation to the exact solution of the Boltzmann equation in a relaxation time approximation.
Abstract: We present the derivation of a novel third-order hydrodynamic evolution equation for the shear stress tensor from kinetic theory. The Boltzmann equation with a relaxation time approximation for the collision term is solved iteratively using a Chapman-Enskog-like expansion to obtain the nonequilibrium phase-space distribution function. Subsequently, the evolution equation for the shear stress tensor is derived from its kinetic definition up to third order in gradients. We quantify the significance of the new derivation within a one-dimensional scaling expansion and demonstrate that the results obtained using the third-order viscous equations derived here provides a very good approximation to the exact solution of the Boltzmann equation in a relaxation time approximation. We also show that the time evolution of pressure anisotropy obtained using our equations is in better agreement with transport results than that obtained with an existing third-order calculation based on the second law of thermodynamics.
TL;DR: In this article, the authors studied the Cauchy problem for abstract dissipative equations in Hilbert spaces generalizing wave equations with strong damping terms in R N or exterior domains.
TL;DR: In this paper, the authors generalize the theory of strong convergence rates for the backward Euler-Maruyama scheme for highly non-linear stochastic differential equations, which appear in both mathematical finance and bio-mathematics.
Abstract: In this work, we generalize the current theory of strong convergence rates for the backward Euler–Maruyama scheme for highly non-linear stochastic differential equations, which appear in both mathematical finance and bio-mathematics. More precisely, we show that under a dissipative condition on the drift coefficient and super-linear growth condition on the diffusion coefficient the BEM scheme converges with strong order of a half. This type of convergence gives theoretical foundations for efficient variance reduction techniques for Monte Carlo simulations. We support our theoretical results with relevant examples, such as stochastic population models and stochastic volatility models.
TL;DR: A new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible two-dimensional Navier–Stokes equations is presented.
Abstract: We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible two-dimensional Navier--Stokes equations. These ideas are motivated by the fact that dissipative dynamical systems possess finite numbers of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages which govern their long-term behavior. Therefore, our algorithm allows the use of any type of measurement data for which a general type of approximation interpolation operator exists. Our main result provides conditions, on the finite-dimensional spatial resolution of the collected data, sufficient to guarantee that the approximating solution, obtained by our algorithm from the measurement data, converges to the unknown reference solution over time. Our algorithm is also applicable in the context of signal synchronization in which one can recover, asymptotically in time, the solution (signal) of the underlying dissipative system that is corresponding to a continuously transmitted partial data.
TL;DR: In this article, a particle approach is proposed to describe the formation of spatially extended patterns in all kinds of physical, chemical, biological and other systems, where the underlying field equations are reduced to order-parameter equations with a finite and possibly small number of degrees of freedom, without losing the important information.
Abstract: A major goal of natural science is to understand the formation of spatiallyextended patterns in all kinds of physical, chemical, biological and other systems. In many cases, it is advantageous to interpret the overall pattern under consideration in terms of a superposition of certain spatially well-localized elementary patterns that we may refer to as “particles”. In the simplest case, all these particles are of the same kind and the complex behavior of the extended pattern can be described in terms of simple individual properties of the particles and their interaction. A clear illustrative example for this approach is the concept of atoms. In this case, the elementary pattern or particle is the atom and the complex spatially-extended pattern is, e.g., the crystal. From a theoretical point of view, pattern forming systems are described by field equations with infinitely many degrees of freedom. However, a powerful technique for describing their temporal evolution is to use a “particle approach”. In this approach, well-localized solutions of the field equation are viewed as particles. The dynamic behavior and the interaction of these particles are described by ordinary differential equations, using center-of-mass co-ordinates and possibly some other variables. The decisive advantage of such an approach is that the underlying field equations, with infinitely many degrees of freedom, can be reduced to order-parameter equations with a finite and possibly small number of degrees of freedom, without losing the important information. An extremely powerful and far-reaching application is the notion of atoms. We recall that macroscopic physical systems can be separated into two classes, according to their long-time behavior. One class approaches thermodynamic equilibrium, resulting in a vanishing exchange of energy with the surroundings. The second class is characterized by external driving “forces” which lead to a finite energy transfer to the system, and, correspondingly, to a finite dissipation in the long run. For the first class of systems, general techniques to find physical solutions have been developed. Systems in thermodynamic equilibrium can be described by a thermodynamic potential, of which one has to find the absolute
TL;DR: In this paper, the dynamics of systems describing the rolling without slipping and spinning (rubber rolling) of various rigid bodies on a plane and a sphere are investigated, and a hierarchy of possible types of dynamical behavior arises depending on the body's surface geometry and mass distribution.
Abstract: In this paper, we investigate the dynamics of systems describing the rolling without slipping and spinning (rubber rolling) of various rigid bodies on a plane and a sphere. It is shown that a hierarchy of possible types of dynamical behavior arises depending on the body’s surface geometry and mass distribution. New integrable cases and cases of existence of an invariant measure are found. In addition, these systems are used to illustrate that the existence of several nontrivial involutions in reversible dissipative systems leads to quasi-Hamiltonian behavior.
TL;DR: In this article, the authors derived hydrodynamic evolution equations for dissipative quantities directly from their definition and showed that these results are in better agreement with a numerical solution of the Boltzmann equation as compared to the traditional Israel-Stewart results.
Abstract: Starting from the Boltzmann equation with the relaxation time approximation for the collision term and using a Chapman-Enskog-like expansion for the distribution function close to equilibrium, we derive hydrodynamic evolution equations for the dissipative quantities directly from their definition. Although the form of the equations is identical to those obtained in traditional Israel-Stewart approaches employing Grad's 14-moment approximation and the second moment of the Boltzmann equation, the coefficients obtained are different. In the case of a one-dimensional scaling expansion, we demonstrate that our results are in better agreement with a numerical solution of the Boltzmann equation as compared to Israel-Stewart results. We also show that including approximate higher-order corrections in viscous evolution significantly improves this agreement, thus justifying the relaxation time approximation for the collision term.
TL;DR: The collective behavior of cold atomic and molecular ensembles can be similar to that found in soft condensed-matter systems, and the evolution towards equilibrium in one and two dimensions is studied.
Abstract: We show that the dynamics of a laser driven Rydberg gas in the limit of strong dephasing is described by a master equation with manifest kinetic constraints. The equilibrium state of the system is uncorrelated but the constraints in the dynamics lead to spatially correlated collective relaxation reminiscent of glasses. We study and quantify the evolution towards equilibrium in one and two dimensions, and analyze how the degree of glassiness and the relaxation time are controlled by the interaction strength between Rydberg atoms. We also find that spontaneous decay of Rydberg excitations leads to an interruption of glassy relaxation that takes the system to a highly correlated nonequilibrium stationary state. The results presented here, which are in principle also applicable to other systems such as polar molecules and atoms with large magnetic dipole moments, show that the collective behavior of cold atomic and molecular ensembles can be similar to that found in soft condensed-matter systems.
TL;DR: In this article, the authors introduce dissipative effects in the effective field theory of hydrodynamics and derive the Kubo relations for these transport coefficients using a generic sector that lives in the fluid.
Abstract: We introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory to a generic sector that ``lives in the fluid,'' which corresponds physically to the microscopic constituents of the fluid. At linear order in perturbations, the symmetries, the derivative expansion, and the assumption that this microscopic sector is thermalized allow us to characterize the leading dissipative effects at low frequencies via three parameters only, which correspond to bulk viscosity, shear viscosity, and---in the presence of a conserved charge---heat conduction. Using our methods we rederive the Kubo relations for these transport coefficients.