Mesoscopic fluctuations in entanglement dynamics.

Understanding fluctuation phenomena plays a dominant role in the development of many-body physics. The time evolution of entanglement is essential to a broad range of subjects in many-body physics, ranging from exotic quantum matter to quantum thermalization. Stemming from various dynamical processes of information, fluctuations in entanglement evolution differ conceptually from out-of-equilibrium fluctuations of traditional physical quantities. Their studies remain elusive. Here we uncover an emergent random structure in the evolution of the many-body wavefunction in two classes of integrable-either interacting or noninteracting-lattice models. It gives rise to out-of-equilibrium entanglement fluctuations which fall into the paradigm of mesoscopic fluctuations of wave interference origin. Specifically, the entanglement entropy variance obeys a universal scaling law in each class, and the full distribution displays a sub-Gaussian upper and a sub-Gamma lower tail. These statistics are independent of both the system's microscopic details and the choice of entanglement probes, and broaden the class of mesoscopic universalities. They have practical implications for controlling entanglement in mesoscopic devices.

Invariance Principle for Wave Propagation inside Inhomogeneously Disordered Materials.

Disorder is more the rule than the exception in natural and synthetic materials. Nonetheless, wave propagation within inhomogeneously disordered materials has received scant attention. We combine microwave experiments and theory to find the spatial variation of generic wave propagation quantities in inhomogeneously disordered materials. We demonstrate that wave statistics within samples of any dimension are independent of the detailed structure of a material and depend only on the net strengths of distributed scattering and reflection between the observation point and each of the boundaries.

Concentration-of-Measure Theory for Structures and Fluctuations of Waves.

The emergence of nonequilibrium phenomena in individual complex wave systems has long been of fundamental interest. Its analytic studies remain notoriously difficult. Using the mathematical tool of the concentration of measure, we develop a theory for structures and fluctuations of waves in individual disordered media. We find that, for both diffusive and localized waves, fluctuations associated with the change in incoming waves ("wave-to-wave" fluctuations) exhibit a new kind of universality, which does not exist in conventional mesoscopic fluctuations associated with the change in disorder realizations ("sample-to-sample" fluctuations), and originates from the coherence between the natural channels of waves-the transmission eigenchannels. Using the results obtained for wave-to-wave fluctuations, we find the criterion for almost all stationary scattering states to exhibit the same spatial structure such as the diffusive steady state. We further show that the expectations of observables at stationary scattering states are independent of incoming waves and are given by their averages with respect to eigenchannels. This suggests the possibility of extending the studies of thermalization of closed systems to open systems, which provides new perspectives for the emergence of nonequilibrium statistical phenomena.

Experimental Observation of a Time-Driven Phase Transition in Quantum Chaos.

We report the first experimental observation of the time-driven phase transition in a canonical quantum chaotic system, the quantum kicked rotor. The transition bears a firm analogy to a thermodynamic phase transition, with the time mimicking the temperature and the quantum expectation of the rotor's kinetic energy mimicking the free energy. The transition signals a sudden change in the system's memory behavior: before the critical time, the system undergoes chaotic motion in phase space and its memory of initial states is erased in the course of time; after the critical time, quantum interference enhances the probability for a chaotic trajectory to return to the initial state, and thus the system's memory is recovered.

Universal structure of transmission eigenchannels inside opaque media.

As the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on the transmission matrix of the wave field. This matrix gives the fullest account of transmission and conductance and enables the control of the transmitted flux; however, it cannot address the fundamental issue of the spatial profile of eigenchannels of the transmission matrix inside the sample. Here we obtain a universal expression for the average disposition of energy of transmission eigenchannels within random diffusive systems in terms of auxiliary localization lengths determined by the corresponding transmission eigenvalues. The spatial profile of each eigenchannel is shown to be a solution of a generalized diffusion equation. These results reveal the rich structure of transmission eigenchannels and enable the control of the energy distribution inside random media.

Planck's quantum-driven integer quantum Hall effect in chaos.

We find in a canonical chaotic system, the kicked spin-1/2 rotor, a Planck's quantum(he)-driven phenomenon bearing a close analogy to the integer quantum Hall effect but of chaos origin. Specifically, the rotor's energy growth is unbounded ("metallic" phase) for a discrete set of critical values of he, but otherwise bounded ("insulating" phase). The latter phase is topological and characterized by a quantum number ("quantized Hall conductance"). The number jumps by unity whenever he passes through each critical value as it decreases. Our findings indicate that rich topological quantum phenomena can emerge from chaos.

Strong correlation induced charge localization in antiferromagnets.

The fate of a hole injected in an antiferromagnet is an outstanding issue of strongly correlated physics. It provides important insights into doped Mott insulators closely related to high-temperature superconductivity. Here, we report a systematic numerical study of t-J ladder systems based on the density matrix renormalization group. It reveals a surprising result for the single hole's motion in an otherwise well-understood undoped system. Specifically, we find that the common belief of quasiparticle picture is invalidated by the self-localization of the doped hole. In contrast to Anderson localization caused by disorders, the charge localization discovered here is an entirely new phenomenon purely of strong correlation origin. It results from destructive quantum interference of novel signs picked up by the hole, and since the same effect is of a generic feature of doped Mott physics, our findings unveil a new paradigm which may go beyond the single hole doped system.

Theory of the Anderson transition in the quasiperiodic kicked rotor.

We present the first microscopic theory of transport in quasiperiodically driven environments ("kicked rotors"), as realized in recent atom optic experiments. We find that the behavior of these systems depends sensitively on the value of a dimensionless Planck constant h: for irrational values of h/(4π) they fall into the universality class of disordered electronic systems and we describe the corresponding localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite (static) conductivity and turns into a "supermetal." We discuss the ensuing possibility of a metal-supermetal quantum phase transition.

Confinement-deconfinement interplay in quantum phases of doped Mott insulators.

In the t-J model, the electron fractionalization is dictated by the phase string effect. We find that in the underdoped regime, the antiferromagnetic and superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and vice versa in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined. A pair of Wilson loops was found to constitute a complete set of order parameters determining this zero-temperature phase diagram. The quantum phase transitions between these phases are suggested to be of non-Landau-Ginzburg-Wilson type.

Local diffusion theory for localized waves in open media.

We report a first-principles study of static transport of localized waves in quasi-one-dimensional open media. We find that such transport, dominated by disorder-induced resonant transmissions, displays novel diffusive behavior. Our analytical predictions are entirely confirmed by numerical simulations. We show that the prevailing self-consistent localization theory [B. A. van Tiggelen, Phys. Rev. Lett. 84, 4333 (2000)] is valid only if disorder-induced resonant transmissions are negligible. Our findings open a new direction in the study of Anderson localization in open media.

Competition between weak localization and ballistic transport.

High-frequency transport in perfect periodic dielectric cylinder arrays is studied. We analytically calculate the diffusive-ballistic transport crossover, which displays the competition between weak localization and ballistic transport.

Interplay of Ehrenfest and dephasing times in ballistic conductors.

Quantum interference corrections in ballistic conductors require a minimal time: the Ehrenfest time. In this Letter, we investigate the fate of the interference corrections to quantum transport in bulk ballistic conductors if the Ehrenfest time and the dephasing time are comparable.

Spectral form factor near the Ehrenfest time.

We calculate the Ehrenfest-time dependence of the leading quantum correction to the spectral form factor of a ballistic chaotic cavity using periodic orbit theory. For the case of broken time-reversal symmetry, when the quantum correction to the form factor involves two small-angle encounters of classical trajectories, our result differs from that previously obtained using field-theoretic methods [Tian and Larkin, Phys. Rev. B 70, 035305 (2004)]. While we believe that the existing field-theoretic calculation is technically flawed, the question whether the field theoretic and periodic-orbit approaches agree when more than one small-angle encounter of classical orbits is involved remains unanswered.

Anderson localization from the replica formalism.

We study Anderson localization in quasi-one-dimensional disordered wires within the framework of the replica sigma model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the context of supersymmetry by Lamacraft, Simons, and Zirnbauer, we compute the exact density of transmission matrix eigenvalues of superconducting wires (of symmetry class CI.) For the unitary class of metallic systems (class A) we are able to obtain the density function, save for its large transmission tail.