The Glassy Wormlike Chain

We introduce a new model for the dynamics of a wormlike chain in an environment that gives rise to a rough free energy landscape, which we baptise the glassy wormlike chain. It is obtained from the common wormlike chain by an exponential stretching of the relaxation spectrum of its long-wavelength eigenmodes, controlled by a single stretching parameter. Predictions for pertinent observables such as the dynamic structure factor and the microrheological susceptibility exhibit the characteristics of soft glassy rheology and compare favourably with experimental data for reconstituted cytoskeletal networks and live cells. We speculate about the possible microscopic origin of the stretching, implications for the nonlinear rheology, and the potential physiological significance of our results.Comment: 12 pages, 8 figures. Minor correction

Chaos and Complexity of quantum motion

The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external perturbations and decoherence, (ii) efficiency of quantum simulation in terms of classical computation and entanglement production in operator spaces, (iii) quantum transport, relaxation to equilibrium and quantum mixing, and (iv) computation of quantum dynamical entropies. Discussions of all these criteria will be confronted with the established criteria of integrability or quantum chaos, and sometimes quite surprising conclusions are found. Some conjectures and interesting open problems in ergodic theory of the quantum many problem are suggested.Comment: 45 pages, 22 figures, final version, at press in J. Phys. A, special issue on Quantum Informatio

Spectral signatures of many-body localization with interacting photons

Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate regardless of parameter values\,? The energy spectrum of a system can answer this question and reveal the nature of the underlying phases. However, most experimental techniques only indirectly probe the many-body energy spectrum. Using a chain of nine superconducting qubits, we implement a novel technique for directly resolving the energy levels of interacting photons. We benchmark this method by capturing the intricate energy spectrum predicted for 2D electrons in a magnetic field, the Hofstadter butterfly. By increasing disorder, the spatial extent of energy eigenstates at the edge of the energy band shrink, suggesting the formation of a mobility edge. At strong disorder, the energy levels cease to repel one another and their statistics approaches a Poisson distribution - the hallmark of transition from the thermalized to the many-body localized phase. Our work introduces a new many-body spectroscopy technique to study quantum phases of matter

Theoretical study of stimulated and spontaneous Hawking effects from an acoustic black hole in a hydrodynamically flowing fluid of light

We propose an experiment to detect and characterize the analog Hawking radiation in an analog model of gravity consisting of a flowing exciton-polariton condensate. Under a suitably designed coherent pump configuration, the condensate features an acoustic event horizon for sound waves that at the semiclassical level is equivalent to an astrophysical black hole horizon. We show that a continuous-wave pump-and-probe spectroscopy experiment allows to measure the analog Hawking temperature from the dependence of the stimulated Hawking effect on the pump-probe detuning. We anticipate the appearance of an emergent resonant cavity for sound waves between the pump beam and the horizon, which results in marked oscillations on top of an overall exponential frequency dependence. We finally analyze the spatial correlation function of density fluctuations and identify the hallmark features of the correlated pairs of Bogoliubov excitations created by the spontaneous Hawking process, as well as novel signatures characterizing the emergent cavity

Photon Statistics; Nonlinear Spectroscopy of Single Quantum Systems

A unified description of multitime correlation functions, nonlinear response functions, and quantum measurements is developed using a common generating function which allows a direct comparison of their information content. A general formal expression for photon counting statistics from single quantum objects is derived in terms of Liouville space correlation functions of the material system by making a single assumption that spontaneous emission is described by a master equation