Universality of Entanglement Transitions from Stroboscopic to Continuous Measurements.

Measurement-driven transitions between extensive and subextensive scaling of the entanglement entropy receive interest as they illuminate the intricate physics of thermalization and control in open interacting quantum systems. While this transition is well established for stroboscopic measurements in random quantum circuits, a crucial link to physical settings is its extension to continuous observations, where for an integrable model it has been shown that the transition changes its nature and becomes immediate. Here, we demonstrate that the entanglement transition at finite coupling persists if the continuously measured system is randomly nonintegrable, and show that it is smoothly connected to the transition in the stroboscopic models. This provides a bridge between a wide range of experimental settings and the wealth of knowledge accumulated for the latter systems.

Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling.

We study exciton polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from S and P_{x,y} photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our Letter shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom, and interactions.

Effect of chiral symmetry on chaotic scattering from Majorana zero modes.

In many of the experimental systems that may host Majorana zero modes, a so-called chiral symmetry exists that protects overlapping zero modes from splitting up. This symmetry is operative in a superconducting nanowire that is narrower than the spin-orbit scattering length, and at the Dirac point of a superconductor-topological insulator heterostructure. Here we show that chiral symmetry strongly modifies the dynamical and spectral properties of a chaotic scatterer, even if it binds only a single zero mode. These properties are quantified by the Wigner-Smith time-delay matrix Q=-iℏS^{†}dS/dE, the Hermitian energy derivative of the scattering matrix, related to the density of states by ρ=(2πℏ)^{-1}TrQ. We compute the probability distribution of Q and ρ, dependent on the number ν of Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral symmetry is essential for a significant ν dependence.

Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect.

The helical edge state of a quantum spin-Hall insulator can carry a supercurrent in equilibrium between two superconducting electrodes (separation L, coherence length ξ). We calculate the maximum (critical) current I(c) that can flow without dissipation along a single edge, going beyond the short-junction restriction L << ξ of earlier work, and find a dependence on the fermion parity of the ground state when L becomes larger than ξ. Fermion-parity conservation doubles the critical current in the low-temperature, long-junction limit, while for a short junction I(c) is the same with or without parity constraints. This provides a phase-insensitive, dc signature of the 4 π-periodic Josephson effect.

Pseudospin valve in bilayer graphene: towards graphene-based pseudospintronics.

We propose a nonmagnetic, pseudospin-based version of a spin valve, in which the pseudospin polarization in neighboring regions of a graphene bilayer is controlled by external gates. Numerical calculations demonstrate a large on-off ratio of such a device. This finding holds promise for the realization of pseudospintronics: a form of electronics based upon the manipulation of pseudospin analogous to the control of physical spin in spintronics applications.

Asymptotic-boundary-layer method for unstable trajectories: semiclassical expansions for individual scar wave functions.

We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field.

Long-time signatures of short-time dynamics in decaying quantum-chaotic systems.

We analyze the decay of classically chaotic quantum systems in the presence of fast ballistic escape routes on the Ehrenfest time scale. For a continuous excitation process, the form factor of the decay cross section deviates from the universal random-matrix result on the Heisenberg time scale, i.e., for times much larger than the time for ballistic escape. We derive an exact analytical description and compare our results with numerical simulations for a dynamical model.

Nonuniversality of anderson localization in short-range correlated disorder.

We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief, we demonstrate that already next-neighbor statistical correlations in the potential can give rise to strong anomalies in the localization length and the density of states, and to the complete violation of single-parameter scaling. Such anomalies originate in additional symmetries of the lattice model in the limit of weak disorder. The results of numerical simulations are in full agreement with our theory, with no adjustable parameters.

Exponential sensitivity to dephasing of electrical conduction through a quantum dot.

According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish proportional to (tau(phi)/tau(D))(p) when the dephasing time tau(phi) becomes small compared to the mean dwell time tau(D). Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression proportional to exp((-tau(E)/tau(phi)) when tau(phi) drops below the Ehrenfest time tau(E). We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression proportional to exp((-tau(E)/tau(D)) in the absence of dephasing--which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations.

Antibunched photons emitted by a quantum point contact out of equilibrium.

Motivated by the experimental search for "GHz nonclassical light," we identify the conditions under which current fluctuations in a narrow constriction generate sub-Poissonian radiation. Antibunched electrons generically produce bunched photons, because the same photon mode can be populated by electrons decaying independently from a range of initial energies. Photon antibunching becomes possible at frequencies close to the applied voltage V x e/variant Planck's over 2pi, when the initial energy range of a decaying electron is restricted. The condition for photon antibunching in a narrow frequency interval below eV/variant Planck's over 2pi reads [SigmanTn(1-Tn)]2<2Sigman[Tn(1-Tn)]2, with Tn an eigenvalue of the transmission matrix. This condition is satisfied in a quantum point contact, where only a single Tn differs from 0 or 1. The photon statistics is then a superposition of binomial distributions.

Anomalous wave function statistics on a one-dimensional lattice with power-law disorder.

Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wavelength to lattice constant. Power-law rather than log-normal tails dominate the short-distance wave-function statistics.

Quantum Andreev map: a paradigm of quantum chaos in superconductivity.

We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for a large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time.

Shot noise in ballistic quantum dots with a mixed classical phase space.

We investigate shot noise for quantum dots whose classical phase space consists of both regular and chaotic regions. The noise is systematically suppressed below the universal value of fully chaotic systems, by an amount which varies with the positions of the leads. We analyze the dynamical origin of this effect by a novel way to incorporate diffractive impurity scattering. The dependence of the shot noise on the scattering rate shows that the suppression arises due to the deterministic nature of transport through regular regions and along short chaotic trajectories. Shot noise can be used to probe phase-space structures of quantum dots with generic classical dynamics.

Statistics of finite-time Lyapunov exponents in a random time-dependent potential.

The sensitivity of trajectories over finite-time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M(ij) of the stability matrix M. For globally chaotic dynamics, lambda tends to a unique value (the usual Lyapunov exponent lambda(infinity)) for almost all trajectories as t is sent to infinity, but for finite t it depends on the initial conditions of the trajectory and can be considered as a statistical quantity. We compute for a particle moving in a randomly time-dependent, one-dimensional potential how the distribution function P(lambda;t) approaches the limiting distribution P(lambda; infinity)=delta(lambda-lambda(infinity)). Our method also applies to the tail of the distribution, which determines the growth rates of moments of M(ij). The results are also applicable to the problem of wave-function localization in a disordered one-dimensional potential.

Quality of life in cirrhotics with minimal hepatic encephalopathy.

Minimal hepatic encephalopathy (HE) is a major cause of premature retirement in cirrhotics. The decision on the earning capability of a patient is usually based on clinical judgement, considering the patient's complaints and clinical findings such as nervousness and depression. In a comprehensive psychometric study we were able to show that cirrhotic patients, who are considered to be unable to earn their living, differ significantly from those who are working, in tests evaluating psychomotor function and in personality and subjective well-being scores representing nervousness, aggressiveness, depression. The latter scores are considered to represent the individual discrepancies between professional demands and cerebral performance. Since minimal HE affects psychomotor function but not verbal abilities this discrepancy exists predominantly in "blue collar workers." In accordance with this 60% of "blue collar" (in contrast to 20% of "white collar") workers of our patient group were considered unfit for work. Working ability is an essential element of quality of life in Western societies. Thus, an impairment of working capability is of major impact on quality of life in cirrhotics.

Transmission delay times of localized waves.

We investigate the effects of wave localization on the delay time tau (frequency sensitivity of the scattering phase shift) of a wave transmitted through a disordered waveguide. Localization results in a separation tau=chi+chi(') of the delay time into two independent but equivalent contributions, associated to the left and right end of the waveguide. For N=1 propagating modes, chi and chi(') are identical to half the reflection delay time of each end of the waveguide. In this case the distribution function P(tau) in an ensemble of random disorder can be obtained analytically. For N>1 propagating modes the distribution function can be approximated by a simple heuristic modification of the single-channel problem. We find a strong correlation between channels with long reflection delay times and the dominant transmission channel.

Limits to error correction in quantum chaos.

We study the correction of errors that have accumulated in an entangled state of spins as a result of unknown local variations in the Zeeman energy ( B) and spin-spin interaction energy ( J). A nondegenerate code with error rate kappa can recover the original state with high fidelity within a time t(R) approximately Planck's over 2pikappa(1/2)/max(B,J)-independent of the number of encoded qubits. Whether the Hamiltonian is chaotic or not does not affect this time scale, but it does affect the complexity of the error-correcting code.

Semiclassical singularities from bifurcating orbits.

We investigated numerically, for a generic quantum system (a kicked top), how the singular behavior of classical systems at bifurcations is reflected by their quantum counterpart. Good agreement is found with semiclassical predictions.

Localization-induced coherent backscattering effect in wave dynamics.

We investigate the statistics of single-mode delay times of waves reflected from a disordered waveguide in the presence of wave localization. The distribution of delay times is qualitatively different from the distribution in the diffusive regime, and sensitive to coherent backscattering: The probability of finding small delay times is enhanced by a factor close to sqrt[2] for reflection angles near the angle of incidence. This dynamic effect of coherent backscattering disappears in the diffusive regime.