Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence of noise, the asymptotic phase is no longer well defined. We introduce a new definition of asymptotic phase in terms of the slowest decaying modes of the Kolmogorov backward operator. Our stochastic asymptotic phase is well defined for noisy oscillators, even when the oscillations are noise dependent. It reduces to the classical asymptotic phase in the limit of vanishing noise. The phase can be obtained either by solving an eigenvalue problem, or by empirical observation of an oscillating density’s approach to its steady state.

Rapidly rotating Rayleigh-Bénard convection is studied by combining results from direct numerical simulations (DNS), laboratory experiments, and asymptotic modeling. The asymptotic theory is shown to provide a good description of the bulk dynamics at low, but finite Rossby number. However, large deviations from the asymptotically predicted heat transfer scaling are found, with laboratory experiments and DNS consistently yielding much larger Nusselt numbers than expected. These deviations are traced down to dynamically active Ekman boundary layers, which are shown to play an integral part in controlling heat transfer even for Ekman numbers as small as $10^{-7}$. By adding an analytical parametrization of the Ekman transport to simulations using stress-free boundary conditions, we demonstrate that the heat transfer jumps from values broadly compatible with the asymptotic theory to states of strongly increased heat transfer, in good quantitative agreement with no-slip DNS and compatible with the experimental data. Finally, similarly to nonrotating convection, we find no single scaling behavior, but instead that multiple well-defined dynamical regimes exist in rapidly rotating convection systems.

We investigate the mechanism by which relativistic electron bunches created at the surface of a target irradiated by a very short and intense laser pulse transfer energy to the deeper parts of the target. In existing theories, the dominant heating mechanism is that of resistive heating by the neutralizing return current. In addition to this, we find that large amplitude plasma waves are induced in the plasma in the wake of relativistic electron bunches. The subsequent collisional damping of these waves represents a source of heating that can exceed the resistive heating rate. As a result, solid targets heat significantly faster than has been previously considered. A new hybrid model, capable of reproducing these results, is described.

Recently, the long-sough quantum anomalous Hall effect was realized in a magnetic topological insulator. However, the requirement of an extremely low temperature (approximately 30 mK) hinders realistic applications. Based on ab initio band structure calculations, we propose a quantum anomalous Hall platform with a large energy gap of 0.34 and 0.06 eV on honeycomb lattices comprised of Sn and Ge, respectively. The ferromagnetic (FM) order forms in one sublattice of the honeycomb structure by controlling the surface functionalization rather than dilute magnetic doping, which is expected to be visualized by spin polarized STM in experiment. Strong coupling between the inherent quantum spin Hall state and ferromagnetism results in considerable exchange splitting and, consequently, an FM insulator with a large energy gap. The estimated mean-field Curie temperature is 243 and 509 K for Sn and Ge lattices, respectively. The large energy gap and high Curie temperature indicate the feasibility of the quantum anomalous Hall effect in the near-room-temperature and even room-temperature regions.

Recently, it has been realized that dissipative processes can be harnessed and exploited to the end of coherent quantum control and information processing. In this spirit, we consider strongly dissipative quantum systems admitting a nontrivial manifold of steady states. We show how one can enact adiabatic coherent unitary manipulations, e.g., quantum logical gates, inside this steady-state manifold by adding a weak, time-rescaled, Hamiltonian term into the system’s Liouvillian. The effective long-time dynamics is governed by a projected Hamiltonian which results from the interplay between the weak unitary control and the fast relaxation process. The leakage outside the steady-state manifold entailed by the Hamiltonian term is suppressed by an environment-induced symmetrization of the dynamics. We present applications to quantum-computation in decoherence-free subspaces and noiseless subsystems and numerical analysis of nonadiabatic errors.

We study the extended Hubbard model on the triangular lattice as a function of filling and interaction strength. The complex interplay of kinetic frustration and strong interactions on the triangular lattice leads to exotic phases where long-range charge order, antiferromagnetic order, and metallic conductivity can coexist. Variational Monte Carlo simulations show that three kinds of ordered metallic states are stable as a function of nearest neighbor interaction and filling. The coexistence of conductivity and order is explained by a separation into two functional classes of particles: part of them contributes to the stable order, while the other part forms a partially filled band on the remaining substructure. The relation to charge ordering in charge transfer salts is discussed.

Recent simulations have indicated that the traditional model for topographical fluctuations in biomembranes should be enriched to include molecular tilt. Here we report the first experimental data supporting this enrichment. Utilizing a previously posited tilt-dependent model, a height-height correlation function was derived. The x-ray scattering from a liquid crystalline stack of oriented fluid phase lipid bilayers was calculated and compared with experiment. By fitting the measured scattering intensity, both the bending modulus $K_c=8.3\pm 0.6\times {10}^{-20}\mathrm{J}$ and the tilt modulus $K_{\theta }=95\pm 7\mathrm{mN}/\mathrm{m}$ were determined for DOPC lipid bilayers at $30°\mathrm{C}$.

The T2K off-axis near detector ND280 is used to make the first differential cross-section measurements of electron neutrino charged current interactions at energies $\sim 1\mathrm{GeV}$ as a function of electron momentum, electron scattering angle, and four-momentum transfer of the interaction. The total flux-averaged ${\nu }_e$ charged current cross section on carbon is measured to be $⟨\sigma {⟩}_{\varphi }=1.11\pm 0.10(\text{stat})\pm 0.18(\text{syst})\times 10^{-38}{\mathrm{cm}}^2/\text{nucleon}$. The differential and total cross-section measurements agree with the predictions of two leading neutrino interaction generators, NEUT and GENIE. The NEUT prediction is $1.23\times 10^{-38}{\mathrm{cm}}^2/\text{nucleon}$ and the GENIE prediction is $1.08\times 10^{-38}{\mathrm{cm}}^2/\text{nucleon}$. The total ${\nu }_e$ charged current cross-section result is also in agreement with data from the Gargamelle experiment.

We report the breakdown of the electric dipole approximation in the long-wavelength limit in strong-field ionization with linearly polarized few-cycle mid-infrared laser pulses at intensities on the order of $10^{13}\mathrm{W}/{\mathrm{cm}}^2$. Photoelectron momentum distributions were recorded by velocity map imaging and projected onto the beam propagation axis. We observe an increasing shift of the peak of this projection opposite to the beam propagation direction with increasing laser intensities. From a comparison with semiclassical simulations, we identify the combined action of the magnetic field of the laser pulse and the Coulomb potential as the origin of our observations.

Systems of strongly interacting dipoles offer an attractive platform to study many-body localized phases, owing to their long coherence times and strong interactions. We explore conditions under which such localized phases persist in the presence of power-law interactions and supplement our analytic treatment with numerical evidence of localized states in one dimension. We propose and analyze several experimental systems that can be used to observe and probe such states, including ultracold polar molecules and solid-state magnetic spin impurities.

We show that a purely dielectric structure made of alternating layers of deep subwavelength thicknesses exhibits novel transmission effects which completely contradict conventional effective medium theories exactly in the regime in which those theories are commonly used. We study waves incident at the vicinity of the effective medium’s critical angle for total internal reflection and show that the transmission through the multilayer structure depends strongly on nanoscale variations even at layer thicknesses smaller than $\lambda /50$. In such deep subwavelength structures, we demonstrate dramatic changes in the transmission for variations in properties such as periodicity, order of the layers, and their parity. In addition to its conceptual importance, such sensitivity has important potential applications in sensing and switching.

We study hollow plasma channels with smooth boundaries for laser-driven electron acceleration in the bubble regime. Contrary to the uniform plasma case, the laser forms no optical shock and no etching at the front. This increases the effective bubble phase velocity and energy gain. The longitudinal field has a plateau that allows for monoenergetic acceleration. We observe as low as ${10}^{-3}$ rms relative witness beam energy uncertainty in each cross section and 0.3% total energy spread. By varying the plasma density profile inside a deep channel, the bubble fields can be adjusted to balance the laser depletion and dephasing lengths. Bubble scaling laws for the deep channel are derived. Ultrashort pancakelike laser pulses lead to the highest energies of accelerated electrons per Joule of laser pulse energy.

We show that in deeply supercooled liquids, structural relaxation proceeds via the accumulation of Eshelby events, i.e. local rearrangements that create long-ranged and anisotropic stresses in the surrounding medium. Such events must be characterized using tensorial observables and we construct an analytical framework to probe their correlations using local stress data. By analyzing numerical simulations, we then demonstrate that events are power-law correlated in space, with a time-dependent amplitude which peaks at the alpha relaxation time ${\tau }_{\alpha }$. This effect, which becomes stronger near the glass transition, results from the increasingly important role of local stress fluctuations in facilitating relaxation events. Our finding precludes the existence of any length scale beyond which the relaxation process decorrelates.

An atomistic method of calculating the spin-lattice relaxation times ($T_1$) is presented for donors in silicon nanostructures comprising of millions of atoms. The method takes into account the full band structure of silicon including the spin-orbit interaction. The electron-phonon Hamiltonian, and hence, the deformation potential, is directly evaluated from the strain-dependent tight-binding Hamiltonian. The technique is applied to single donors and donor clusters in silicon, and explains the variation of $T_1$ with the number of donors and electrons, as well as donor locations. Without any adjustable parameters, the relaxation rates in a magnetic field for both systems are found to vary as $B^5$, in excellent quantitative agreement with experimental measurements. The results also show that by engineering electronic wave functions in nanostructures, $T_1$ times can be varied by orders of magnitude.

We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from self-consistent extended dynamical mean-field theory and include nonlocal dynamical vertex corrections through a ladder approximation to the polarization operator. This is necessary to fulfill charge conservation and to describe plasmons in the correlated state. The calculated plasmon spectra are qualitatively different from those in the random-phase approximation: they exhibit a spectral density transfer and a renormalized dispersion with enhanced deviation from the canonical $\sqrt{q}$ behavior. Both features are reminiscent of interaction induced changes found in single-electron spectra of strongly correlated systems.

In two-dimensional electron systems confined to GaAs quantum wells, as a function of either tilting the sample in a magnetic field or increasing density, we observe multiple spin-polarization transitions of the fractional quantum Hall states at filling factors $\nu =4/5$ and $5/7$. The number of observed transitions provides evidence that these are fractional quantum Hall states of interacting two-flux composite fermions. Moreover, the fact that the reentrant integer quantum Hall effect near $\nu =4/5$ always develops following the transition to full spin polarization of the $\nu =4/5$ fractional quantum Hall state links the reentrant phase to a pinned ferromagnetic Wigner crystal of composite fermions.