Exponential Decay of Wavelength in a Dissipative System

Applying a technique developed in a recent work[1] to calculate wavefunction evolution in a dissipative system with Ohmic friction, we show that the wavelength of the wavefunction decays exponentially, while the Brownian motion width gradually increases. In an interference experiment, when these two parameters become equal, the Brownian motion erases the fringes, the system thus approaches classical limit. We show that the wavelength decay is an observable phenomenon.Comment: 12 pages, 3 Postscript figures, uses standard late

Nonlinear dynamics of flexural wave turbulence

The Kolmogorov-Zakharov spectrum predicted by the Weak Turbulence Theory remains elusive for wave turbulence of flexural waves at the surface of an thin elastic plate. We report a direct measurement of the nonlinear timescale $T_{NL}$ related to energy transfer between waves. This time scale is extracted from the space-time measurement of the deformation of the plate by studying the temporal dynamics of wavelet coefficients of the turbulent field. The central hypothesis of the theory is the time scale separation between dissipative time scale, nonlinear time scale and the period of the wave ($T_d>>T_{NL}>>T$). We observe that this scale separation is valid in our system. The discrete modes due to the finite size effects are responsible for the disagreement between observations and theory. A crossover from continuous weak turbulence and discrete turbulence is observed when the nonlinear time scale is of the same order of magnitude as the frequency separation of the discrete modes. The Kolmogorov-Zakharov energy cascade is then strongly altered and is frozen before reaching the dissipative regime expected in the theory.Comment: accepted for publication in Physical Review

Extension of Haff's cooling law in granular flows

The total energy E(t) in a fluid of inelastic particles is dissipated through inelastic collisions. When such systems are prepared in a homogeneous initial state and evolve undriven, E(t) decays initially as t^{-2} \aprox exp[ - 2\epsilon \tau] (known as Haff's law), where \tau is the average number of collisions suffered by a particle within time t, and \epsilon=1-\alpha^2 measures the degree of inelasticity, with \alpha the coefficient of normal restitution. This decay law is extended for large times to E(t) \aprox \tau^{-d/2} in d-dimensions, far into the nonlinear clustering regime. The theoretical predictions are quantitatively confirmed by computer simulations, and holds for small to moderate inelasticities with 0.6< \alpha< 1.Comment: 7 pages, 4 PostScript figures. To be published in Europhysics Letter

Instability of a uniformly collapsing cloud of classical and quantum self-gravitating Brownian particles

We study the growth of perturbations in a uniformly collapsing cloud of self-gravitating Brownian particles. This problem shares analogies with the formation of large-scale structures in a universe experiencing a "big-crunch" or with the formation of stars in a molecular cloud experiencing gravitational collapse. Starting from the barotropic Smoluchowski-Poisson system, we derive a new equation describing the evolution of the density contrast in the comoving (collapsing) frame. This equation can serve as a prototype to study the process of self-organization in complex media with structureless initial conditions. We solve this equation analytically in the linear regime and compare the results with those obtained by using the "Jeans swindle" in a static medium. The stability criteria, as well as the laws for the time evolution of the perturbations, are different. The Jeans criterion is expressed in terms of a critical wavelength $\lambda_J$ while our criterion is expressed in terms of a critical polytropic index $\gamma_{4/3}$. We also study the fragmentation process in the nonlinear regime. We determine the growth of the skewness, the long-wavelength tail of the power spectrum and find a self-similar solution to the nonlinear equations valid for large times. Finally, we consider dissipative self-gravitating Bose-Einstein condensates with short-range interactions and show that, in a strong friction limit, the dissipative Gross-Pitaevskii-Poisson system is equivalent to the quantum barotropic Smoluchowski-Poisson system. This yields a new type of nonlinear mean field Fokker-Planck equations including quantum effects

Keldysh Field Theory for Driven Open Quantum Systems

Recent experimental developments in diverse areas - ranging from cold atomic gases over light-driven semiconductors to microcavity arrays - move systems into the focus, which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in condensed matter. This concerns both their non-thermal flux equilibrium states, as well as their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.Comment: 73 pages, 13 figure

A Holographic Path to the Turbulent Side of Gravity

We study the dynamics of a 2+1 dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the "gravity/fluid correspondence", to 3+1 dimensional asymptotically anti-de Sitter (AAdS) black brane solutions to the Einstein equation. We examine stability properties of shear flows, which correspond to hydrodynamic quasinormal modes of the black brane. We find that, for sufficiently high Reynolds number, the solution undergoes an inverse turbulent cascade to long wavelength modes. We then map this fluid solution, via the gravity/fluid duality, into a bulk metric. This suggests a new and interesting feature of the behavior of perturbed AAdS black holes and black branes, which is not readily captured by a standard quasinormal mode analysis. Namely, for sufficiently large perturbed black objects (with long-lived quasinormal modes), nonlinear effects transfer energy from short to long wavelength modes via a turbulent cascade within the metric perturbation. As long wavelength modes have slower decay, this lengthens the overall lifetime of the perturbation. We also discuss various implications of this behavior, including expectations for higher dimensions, and the possibility of predicting turbulence in more general gravitational scenarios.Comment: 24 pages, 10 figures; v2: references added, and several minor change

Dissipative Dicke Model with Collective Atomic Decay: Bistability, Noise-Driven Activation and Non-Thermal First Order Superradiance Transition

The Dicke model describes the coherent interaction of a laser-driven ensemble of two level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature dissipation due to e.g. atomic spontaneous emission and cavity photon loss. Spontaneous emission supports the uncorrelated decay of individual atomic excitations as well as the enhanced, collective decay of an excitation that is shared by $N$ atoms and whose strength is determined by the cavity geometry. We derive a many-body master equation for the dissipative Dicke model including both spontaneous emission channels and analyze its dynamics on the basis of Heisenberg-Langevin and stochastic Bloch equations. We find that the collective loss channel leads to a region of bistability between the empty and the superradiant state. Transitions between these states are driven by non-thermal, markovian noise. The interplay between dissipative and coherent elements leads to a genuine non-equilibrium dynamics in the bistable regime, which is expressed via a non-conservative force and a multiplicative noise kernel appearing in the stochastic Bloch equations. We present a semiclassical approach, based on stochastic nonlinear optical Bloch equations, which for the infinite-range Dicke Model become exact in the large-$N$-limit. The absence of an effective free energy functional, however, necessitates to include fluctuation corrections with $\mathcal{O}(1/N)$ for finite $N<\infty$ to locate the non-thermal first-order phase transition between the superradiant and the empty cavity.Comment: as published in Physical Review

Optical emission near a high-impedance mirror

Solid state light emitters rely on metallic contacts with high sheet-conductivity for effective charge injection. Unfortunately, such contacts also support surface plasmon polariton (SPP) excitations that dissipate optical energy into the metal and limit the external quantum efficiency. Here, inspired by the concept of radio-frequency (RF) high-impedance surfaces and their use in conformal antennas we illustrate how electrodes can be nanopatterned to simultaneously provide a high DC electrical conductivity and high-impedance at optical frequencies. Such electrodes do not support SPPs across the visible spectrum and greatly suppress dissipative losses while facilitating a desirable Lambertian emission profile. We verify this concept by studying the emission enhancement and photoluminescence lifetime for a dye emitter layer deposited on the electrodes