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We consider s-wave pairing in a double layer of two chiral metals due to Coulomb interaction, and study the Josephson effect near a domain wall, where the sign of the order parameter jumps. The domain wall creates two zero energy modes, whose superposition is associated with a current that flows in different direction in the two layers. Assuming a toroidal geometry, the effective Josephson currents winds around the domain walls, whose winding number is determined by the coefficients of the superimposed zero energy modes. This result can be understood as a competition of the conventional Josephson current perpendicular and the edge current parallel to a domain wall in a double layer of two chiral metals. As a realization we suggest the surface of a ring-shaped topological insulator. The duality between electron-electron and electron-hole double layers indicates that this effect should also be observable in excitonic double layers., Comment: 6 pages, 2 figures

Randomly repeated measurements during the evolution of a closed quantum system create a sequence of probabilities for the first detection of a certain quantum state. The related discrete monitored evolution for the return of the quantum system to its initial state is investigated. We found that the mean number of measurements until the first detection is an integer, namely the dimensionality of the accessible Hilbert space. Moreover, the mean first detected return time is equal to the average time step between successive measurements times the mean number of measurements. Thus, the mean first detected return time scales linearly with the dimensionality of the accessible Hilbert space. The main goal of this work is to explain the quantization of the mean return time in terms of a quantized Berry phase., Comment: 21 pages, 3 figures

We propose an approach to process data from interferometric measurements on a closed quantum system at random times. For this purpose a time correlation matrix is introduced which enables us to extract dynamical properties of the quantum system. After defining a generalized expectation value we obtain a distribution of time scales, an average transition time and a correlation time. A classical limit exists which is separated from the quantum fluctuations. The latter are characterized by resonances associated with poles of the generalized expectation value. Its analytic behavior is studied and some generic properties are linked to a quantized Berry phase., Comment: 11 pages, 2 figures

We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/\tau$. A general formula for the mean first detected transition time is obtained for a quantum walk in a finite-dimensional Hilbert space where the initial state $|\psi_{\rm in}\rangle$ of the walker is orthogonal to the detected state $|\psi_{\rm d}\rangle$. We focus on diverging mean transition times, where the total detection probability exhibits a discontinuous drop of its value, by mapping the problem onto a theory of fields of classical charges located on the unit disk. Close to the critical parameter of the model, which exhibits a blow-up of the mean transition time, we get simple expressions for the mean transition time. Using previous results on the fluctuations of the return time, corresponding to $|\psi_{\rm in}\rangle = |\psi_{\rm d}\rangle$, we find close to these critical parameters that the mean transition time is proportional to the fluctuations of the return time, an expression reminiscent of the Einstein relation.

We propose to control of an electron-hole superfluid in semiconductor coupled quantum wells and double layers of two-dimensional (2D) material by an external periodic field. This can either be created by the gates periodically located and attached to the quantum wells or double layers of 2D material or by the Moir\'e pattern of two twisted layers. The dependence of the electron-hole pairing order parameter on the temperature, the charge carrier density, and the gate parameters is obtained by minimization of the mean-field free energy. The second order phase transition between superfluid and electron-hole plasma, controlled by the external periodic gate field, is analyzed for different parameters., Comment: 10 pages, 4 figures

The properties of zero modes in particle-hole symmetric systems are analyzed in the presence of strong random scattering by a disordered environment. The study is based on the calculation of the time-averaged density distribution on a lattice. In particular, a flat distribution is found for strong random scattering. This result is compared with a decaying distribution for weak random scattering by an analysis of the scattering paths. In the calculation we consider the invariant measure of the average two-particle Green's function, which is related to lattice-covering self-avoiding (LCSA) strings. In particular, strong scattering is associated with LCSA loops, whereas weaker scattering is associated with open LCSA strings. Our results are a generalization of the delocalized state observed at the band center of a one-dimensional tight-binding model with random hopping by Dyson in 1953., Comment: 12 pages, 3 figures

A finite photonic lattice with two bands and a random gap is considered. Using a two-dimensional Dirac equation, the effect of a random sign of the Dirac mass is studied numerically. The edge state at the sample boundary has a strong influence on the electromagnetic field and its polarization inside the sample. The creation of edge states through a randomly fluctuating sign of the Dirac mass defeats Anderson localization and allows the electromagnetic field to distribute over the entire sample. The width of the distribution increases with an increasing gap due to increasing sharpness of the edge states. These results are compared with those of a random one-band Helmholtz equation. In contrast to the Dirac model, the one-band model displays a clear signature of Anderson localization., Comment: 12 pages, 12 figures

The average density of states of two- and three-dimensional Weyl fermions is studied in the self-consistent Born approximation (SCBA) and its corrections. The latter have been organized in terms of a 1/N expansion. It turns out that an expansion in terms of the disorder strength is not applicable, as previously mentioned by other authors. Nevertheless, the 1/N expansion provides a justification of the SCBA as the large N limit of Weyl fermions., Comment: 12 pages, 4 figures, Phys. Rev. B (2017)

The average density of states in a disordered three-dimensional Weyl system is discussed in the case of a continuous distribution of random scattering. Our result clearly indicate that the average density of states does not vanish, reflecting the absence of a critical point for a metal-insulator transition. This calculation supports recent suggestions of an avoided quantum critical point in the disordered three-dimensional Weyl semimetal. However, the effective density of states can be very small such that the saddle-approximation with a vanishing density of states might be valid for practical cases., Comment: 5 pages, 2 figures, minor changes, additional supplement

Edge states are studied for the two-dimensional Dirac equation in a circular geometry. The properties of the two-component electromagnetic field are discussed in terms of the three-component polarization field, which can form a vortex structure near the Dirac node with a vorticity changing with the sign of the Dirac mass. The Berry curvature of the polarization field is related to the Berry curvature of the Dirac spinor state. This quantity is sensitive to a change of boundary conditions. In particular, it vanishes for a geometry with a single boundary but not for a geometry with two boundaries. This effect is robust against the creation of a step-like edge inside the sample., Comment: 8 pages, 5 figures

The topology of the band structure, which is determined by the lattice symmetries, has a strong influence on the transport properties. Here we consider an anisotropic honeycomb lattice and study the effect of a continuously deformed band structure on the optical conductivity and on diffusion due to quantum fluctuations. In contrast to the behavior at an isotropic node we find super- and subdiffusion for the anisotropic node. The spectral saddle points create van Hove singularities in the optical conductivity, which could be used to characterize the spectral properties experimentally., Comment: 9 pages, 6 figures. Slightly extended version, e.g. Eq.(12) included

We consider excitons in a two-dimensional periodic potential and study the linear response of the excitonic superfluid to an electromagnetic wave at low and high densities. It turns out that the static structure factor for small wavevectors is very sensitive to a change of density and temperature. It is a consequence of the fact that thermal fluctuations play a crucial role at small wavevectors, since exchanging the order of the two limits, zero temperature and vanishing wavevector, leads to different results for the structure factor. This effect could be used for high accuracy measurements in the superfluid exciton phase, which might be realized by a gated electron-hole gas. The transition of the exciton system from the superfluid state to a non-superfluid state and its manifestation by light scattering are discussed., Comment: 9 pages, 5 figures

The influence of collective phonon excitations, due to intersite atomic interactions, on the stability of optical lattices is analyzed. These phonon excitations are shown to essentially reduce the ability of atoms to be localized. The states that seem to be insulating in the absence of the phonon excitations can become delocalized when the latter are present. The delocalization effect exists for both long-range as well as local atomic interactions., Comment: Latex file, 9 pages, 1 figure

We analyze the evolution of an entangled many-body state in a Josephson tunneling junction. A N00N state, which is a superposition of two complementary Fock states, appears in the evolution with sufficient probability only for a moderate many-body interaction on an intermediate time scale. This time scale is inversely proportional to the tunneling rate. Interaction between particles supports entanglement: The probability for creating an entangled state decays exponentially with the number of non-interacting particles, whereas it decays only like the inverse square root of the number of interacting particles., Comment: 9 pages, 5 figures

An exciton gas on a lattice is analyzed in terms of a convergent hopping expansion. For a given chemical potential our calculation provides a sufficient condition for the hopping rate to obtain an exponential decay of the exciton correlation function. This result indicates the existence of a Mott phase in which strong fluctuations destroy the long range correlations in the exciton gas at any temperature, either by thermal or by quantum fluctuations., Comment: 5 pages, 1 figure

We cross-match galaxy cluster candidates selected via their Sunyaev-Zel'dovich effect (SZE) signatures in 129.1 deg$^2$ of the South Pole Telescope 2500d SPT-SZ survey with optically identified clusters selected from the Dark Energy Survey (DES) science verification data. We identify 25 clusters between $0.1\lesssim z\lesssim 0.8$ in the union of the SPT-SZ and redMaPPer (RM) samples. RM is an optical cluster finding algorithm that also returns a richness estimate for each cluster. We model the richness $\lambda$-mass relation with the following function $\langle\ln\lambda|M_{500}\rangle\propto B_\lambda\ln M_{500}+C_\lambda\ln E(z)$ and use SPT-SZ cluster masses and RM richnesses $\lambda$ to constrain the parameters. We find $B_\lambda= 1.14^{+0.21}_{-0.18}$ and $C_\lambda=0.73^{+0.77}_{-0.75}$. The associated scatter in mass at fixed richness is $\sigma_{\ln M|\lambda} = 0.18^{+0.08}_{-0.05}$ at a characteristic richness $\lambda=70$. We demonstrate that our model provides an adequate description of the matched sample, showing that the fraction of SPT-SZ selected clusters with RM counterparts is consistent with expectations and that the fraction of RM selected clusters with SPT-SZ counterparts is in mild tension with expectation. We model the optical-SZE cluster positional offset distribution with the sum of two Gaussians, showing that it is consistent with a dominant, centrally peaked population and a sub-dominant population characterized by larger offsets. We also cross-match the RM catalog with SPT-SZ candidates below the official catalog threshold significance $\xi=4.5$, using the RM catalog to provide optical confirmation and redshifts for additional low-$\xi$ SPT-SZ candidates.In this way, we identify 15 additional clusters with $\xi\in [4,4.5]$ over the redshift regime explored by RM in the overlapping region between DES science verification data and the SPT-SZ survey., Comment: 15 pages, 8 Figures, submitted to MNRAS

In the presence of strong random scattering the behavior of particles with degenerate spectra is quite different from Anderson localization of particles in a single band: it creates geometric states rather than confining the particles to an area of the size of the localization length. These states are subject to a Fokker-Planck dynamics with universal drift velocity and disorder dependent diffusion coefficient. This behavior has some similarity with the unidirectionally propagating edge states in quantum Hall systems., Comment: 5 pages, 3 figures

The role of collective phonon excitations on the properties of cold atoms in optical lattices is investigated. These phonon excitations are collective excitations, whose appearance is caused by intersite atomic interactions correlating the atoms, and they do not arise without such interactions. These collective excitations should not be confused with lattice vibrations produced by an external force. No such a force is assumed. But the considered phonons are purely self-organized collective excitations, characterizing atomic oscillations around lattice sites, due to intersite atomic interactions. It is shown that these excitations can essentially influence the possibility of atoms to be localized. The states that would be insulating in the absence of phonon excitations can become delocalized when these excitations are taken into account. This concerns long-range as well as local atomic interactions. To characterize the region of stability, the Lindemann criterion is used., Comment: Latex file, 27 pages, 1 figure

We calculate the transport properties of three-dimensional Weyl fermions in a disordered environment. The resulting conductivity depends only on the Fermi energy and the scattering rate. First we study the conductivity at the spectral node for a fixed scattering rate and obtain a continuous transition from an insulator at weak disorder to a metal at stronger disorder. In the self-consistent Born approximation the scattering rate depends on the Fermi energy. Then it is crucial that the limits of the conductivity for a vanishing Fermi energy and a vanishing scattering rate do not commute. As a result, there is also metallic behavior in the phase with vanishing scattering rate and only a quantum critical point remains as an insulating state., Comment: 9 pages, 5 figures

Anderson localization is studied for two-dimensional Dirac fermions in the presence of strong random scattering. Averaging with respect to the latter leads to a graphical representation of the correlation function with entangled random walks and three-vertices which connect three different types of propagators. This approach indicates Anderson localization along a semi-infinite line, where the localization length is inversely proportional to the scattering rate., Comment: 8 pages, 2 figures

The aubrites are a unique group of differentiated meteorites that formed on parent bodies with oxygen fugacities (ƒO2) from ~2 to ~6 log units below the iron-wustite buffer. At these highly reduced condi- tions, elements deviate from the geochemical behavior exhibited at terrestrial ƒO2, and may form FeO-poor silicates, Si-bearing metals, and exotic sulfides. Geochemical examinations of aubrites, such as mineral major-element compositions, bulk-rock compositions, O isotopes, and crystallization ages, are crucial to understand their formation and evolution at extreme ƒO2 conditions. In this study, we determine partitioning relationships of elements between bulk silicate, sulfide, and metal phases within aubrites, and compare the results to partition coefficients determined from petrologic experiments run under mercurian conditions. While previous studies have described the petrology and 2D modal abundances of aubrites, this work provides the first 3D view of aubritic mineralogies, which are com- pared to the available 2D data. Constraints of 3D modal abundances will increase the accuracy of computed bulk distribution coefficients; therefore, 3D scans of aubrite samples are imperative. We utilize X-ray computed tomogra- phy (XCT) to non-destructively analyze the distribution and abundances of mineral phases in aubrites and locate composite clasts of sulfide grains for future analysis.

The aubrites (~30 known meteorites) are a unique group of differentiated meteorites that formed on asteroids with oxygen fugacities (ƒO2) from ~2 to ~6 log units below the iron-wüstite buffer [1–2]. At these highly reduced conditions, elements deviate from the geochemical behavior exhibited at terrestrial ƒO2, forming FeO-poor silicates, Si-bearing metals, and exotic sulfides [3]. Here we examine the 3D mineralogy and the geochemistry of fourteen aubrites, including mineral major element compositions, bulk-rock compositions, and oxygen isotopic compositions to understand their formation and evolution at extreme ƒO2 conditions. While previous studies have described the petrology and 2D modal abundances of aubrites, this work investigates the 3D modal mineralogies of silicate, metal, and sulfide phases in aubrite samples, which are then com-pared to the available 2D data. We utilize X-ray computed tomography (XCT) to non-destructively analyze the distribution and abundances of mineral phases in aubrites and locate composite clasts of sulfide grains for future analysis.

There is excellent evidence that a dynamical instability in the early solar system led to gravitational interactions between the giant planets and trans-Neptunian objects (TNOs). Giant planetary migration triggered by the instability dispersed a disk of primordial TNOs and created a number of small body reservoirs (e.g. the Kuiper Belt, scattered disk, irregular satellites, and the Jupiter/Neptune Trojan populations). It also injected numerous bodies into the main asteroid belt, where modeling shows they can successfully reproduce the observed P and D-type asteroid populations. During the injection era and after implantation, some of these “main belt TNOs” would have collided with S-class asteroids. Some of this material may have survived as a component of asteroid regolith breccias. Thus, we have been searching for evidence of these impact events in the form of carbonaceous xenoliths in brecciated ordinary chondrites. These xenoliths would have experienced a wide range of impact velocities, and therefore we should expect to see everything between relatively unaltered material to completely shock-melted lithologies. This material might also be different from the carbonaceous chondrites that represent standard C-complex asteroids. A goal of this research is to define useful criteria for distinguishing between these two classes of materials, including O, Cr, N and C isotopes, petrographic characteristics, and chronology.

There is excellent evidence that a dynamical instability in the early solar system led to gravitational interactions between the giant planets and trans-Neptunian planetesimals. Giant planetary migration triggered by the instability dispersed a disk of primordial trans-Neptunian object (TNOs) and created a number of small body reservoirs (e.g. the Kuiper Belt, scattered disk, irregular satellites, and the Jupiter/Neptune Trojan populations). It also injected numerous bodies into the main asteroid belt, where modeling shows they can successfully reproduce the observed P and D-type asteroid populations.

Up until recently the orthopyroxenite ALH 84001, a singleton martian meteorite type, was the only sample that did not fit within the common SNC types. However with the discovery of the unique basaltic breccia NWA 7034 pairing group [1] the diversity of martian meteorites beyond SNC types was expanded, and now with Northwest Africa (NWA) 8159, and its possible pairing NWA 7635 [2], the diversiy is expanded further with a third unique non-SNC meteorite type. The existence of meteorite types beyond the narrow range seen in SNCs is what might be expected from a random cratering sampling of a geologically long-lived and complex planet such as Mars.