The 6D quantum Hall effect and 3D topological pumps

Modern technological advances allow for the study of systems with additional synthetic dimensions. Using such approaches, higher-dimensional physics that was previously deemed to be of purely theoretical interest has now become an active field of research. In this work, we derive from first principles using a semiclassical equation of motions approach, the bulk response of a six-dimensional Chern insulator. We find that in such a system a quantized bulk response appears with a quantization originating from a six-dimensional topological index -- the 3rd Chern number. Alongside this novel six-dimensional response, we rigorously describe the lower even-dimensional Chern-like responses that can occur due to nonvanishing 1st and 2nd Chern numbers in sub-spaces of the six-dimensional space. Last, we propose how to realize such a bulk response using three-dimensional topological charge pumps in cold atomic systems.Comment: 12 pages + 13 pages of supporting material, 2 figures, published versio

Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model

One-dimensional quasiperiodic systems, such as the Harper model and the Fibonacci quasicrystal, have long been the focus of extensive theoretical and experimental research. Recently, the Harper model was found to be topologically nontrivial. Here, we derive a general model that embodies a continuous deformation between these seemingly unrelated models. We show that this deformation does not close any bulk gaps, and thus prove that these models are in fact topologically equivalent. Remarkably, they are equivalent regardless of whether the quasiperiodicity appears as an on-site or hopping modulation. This proves that these different models share the same boundary phenomena and explains past measurements. We generalize this equivalence to any Fibonacci-like quasicrystal, i.e., a cut and project in any irrational angle.Comment: 7 pages, 2 figures, minor change

"Quantum phase transitions" in classical nonequilibrium processes

Diffusion limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed-point. This fixed-point becomes unstable due to discretization effects, a scenario similar to quantum phase transitions. As a result, the long-time asymptotic behavior of the system changes and the dynamics flows into a limit cycle. The results are verified by numerical simulations.Comment: 9 pages, 3 figures include

The role of symmetry in driven propulsion at low Reynolds number

We theoretically and experimentally investigate low-Reynolds-number propulsion of geometrically achiral planar objects that possess a dipole moment and that are driven by a rotating magnetic field. Symmetry considerations (involving parity, $\widehat{P}$, and charge conjugation, $\widehat{C}$) establish correspondence between propulsive states depending on orientation of the dipolar moment. Although basic symmetry arguments do not forbid individual symmetric objects to efficiently propel due to spontaneous symmetry breaking, they suggest that the average ensemble velocity vanishes. Some additional arguments show, however, that highly symmetrical ($\widehat{P}$-even) objects exhibit no net propulsion while individual less symmetrical ($\widehat{C}\widehat{P}$-even) propellers do propel. Particular magnetization orientation, rendering the shape $\widehat{C}\widehat{P}$-odd, yields unidirectional motion typically associated with chiral structures, such as helices. If instead of a structure with a permanent dipole we consider a polarizable object, some of the arguments have to be modified. For instance, we demonstrate a truly achiral ($\widehat{P}$- and $\widehat{C}\widehat{P}$-even) planar shape with an induced electric dipole that can propel by electro-rotation. We thereby show that chirality is not essential for propulsion due to rotation-translation coupling at low Reynolds number.Comment: 5 pages, 5 figure

Sediment Management for Southern California Mountians, Coastal Plains and Shoreline. Part D: Special Inland Studies

In southern California the natural environmental system involves the continual relocation of sedimentary materials. Particles are eroded from inland areas where there is sufficient relief and, precipitation. Then, with reductions in hydraulic gradient along the stream course and at the shoreline, the velocity of surface runoff is reduced and there is deposition. Generally, coarse sand, gravel and larger particles are deposited near the base of the eroding surfaces (mountains and hills) and the finer sediments are deposited on floodplains, in bays or lagoons, and at the shoreline as delta deposits. Very fine silt and clay particles, which make up a significant part of the eroded material, are carried offshore where they eventually deposit in deeper areas. Sand deposited at the shoreline is gradually moved along the coast by waves and currents, and provides nourishment for local beaches. However, eventually much of this littoral material is also lost to offshore areas. Human developments in the coastal region have substantially altered the natural sedimentary processes, through changes in land use, the harvesting of natural resources (logging, grazing, and sand and gravel mining); the construction and operation of water conservation facilities and flood control structures; and coastal developments. In almost all cases these developments have grown out of recognized needs and have well served their primary purpose. At the time possible deleterious effects on the local or regional sediment balance were generally unforeseen or were felt to be of secondary importance. In 1975 a large-scale study of inland and coastal sedimentation processes in southern California was initiated by the Environmental Quality Laboratory at the California Institute of Technology and the Center for Coastal Studies at Scripps Institution of Oceanography. This volume is one of a series of reports from this study. Using existing data bases, this series attempts to define quantitatively inland and coastal sedimentation processes and identify the effects man has had on these processes. To resolve some issues related to long-term sediment management, additional research and data will be needed. In the series there are four Caltech reports that provide supporting studies for the summary report (EQL Report No. 17). These reports include: EQL Report 17-A Regional Geological History EQL Report 17-B Inland Sediment Movements by Natural Processes EQL Report 17-C Coastal Sediment Delivery by Major Rivers in Southern California EQL Report 17-D -- Special Inland Studies Additional supporting reports on coastal studies (shoreline sedimentation processes, control structures, dredging, etc.) are being published by the Center for Coastal Studies at Scripps Institution of Oceanography, La Jolla, California

Superlubricity - a new perspective on an established paradigm

Superlubricity is a frictionless tribological state sometimes occurring in nanoscale material junctions. It is often associated with incommensurate surface lattice structures appearing at the interface. Here, by using the recently introduced registry index concept which quantifies the registry mismatch in layered materials, we prove the existence of a direct relation between interlayer commensurability and wearless friction in layered materials. We show that our simple and intuitive model is able to capture, down to fine details, the experimentally measured frictional behavior of a hexagonal graphene flake sliding on-top of the surface of graphite. We further predict that superlubricity is expected to occur in hexagonal boron nitride as well with tribological characteristics very similar to those observed for the graphitic system. The success of our method in predicting experimental results along with its exceptional computational efficiency opens the way for modeling large-scale material interfaces way beyond the reach of standard simulation techniques.Comment: 18 pages, 7 figure

Non-ohmicity and energy relaxation in diffusive 2D metals

We analyze current-voltage characteristics taken on Au-doped indium-oxide films. By fitting a scaling function to the data, we extract the electron-phonon scattering rate as function of temperature, which yields a quadratic dependence of the electron-phonon scattering rate on temperature from 1K down to 0.28K. The origin of this enhanced electron-phonon scattering rate is ascribed to the mechanism proposed by Sergeev and Mitin.Comment: 7 pages, 6 figure

KPZ in one dimensional random geometry of multiplicative cascades

We prove a formula relating the Hausdorff dimension of a subset of the unit interval and the Hausdorff dimension of the same set with respect to a random path matric on the interval, which is generated using a multiplicative cascade. When the random variables generating the cascade are exponentials of Gaussians, the well known KPZ formula of Knizhnik, Polyakov and Zamolodchikov from quantum gravity appears. This note was inspired by the recent work of Duplantier and Sheffield proving a somewhat different version of the KPZ formula for Liouville gravity. In contrast with the Liouville gravity setting, the one dimensional multiplicative cascade framework facilitates the determination of the Hausdorff dimension, rather than some expected box count dimension.Comment: 14 page