Band twisting and resilience to disorder in long-range topological superconductors

Planar topological superconductors with power-law-decaying pairing display different kinds of topological phase transitions where quasiparticles dubbed nonlocal-massive Dirac fermions emerge. These exotic particles form through long-range interactions between distant Majorana modes at the boundary of the system. We show how these propagating-massive Dirac fermions neither mix with bulk states nor Anderson-localize up to large amounts of static disorder despite being finite energy. Analyzing the density of states (DOS) and the band spectrum of the long-range topological superconductor, we identify the formation of an edge gap and a surprising double peak structure in the DOS which can be linked to a twisting of energy bands with nontrivial topology. Our findings are amenable to experimental verification in the near future using atom arrays on conventional superconductors, planar Josephson junctions on two-dimensional electron gases, and Floquet driving of topological superconductors.Comment: 9 pages, 8 figure

Fate of the Quasi-condensed State for Bias-driven Hard-Core Bosons in one Dimension

Bosons in one dimension display a phenomenon called quasi-condensation, where correlations decay in a powerlaw fashion. We study the fate of quasi-condensation in the non-equilibrium steady-state of a chain of hard-core bosons coupled to macroscopic leads which are held at different chemical potentials. It is found that a finite bias destroys the quasi-condensed state and the critical scaling function of the quasi-condensed fraction, near the zero bias transition, is determined. Associated critical exponents are determined and numerically verified. Away from equilibrium, the system exhibits exponentially decaying correlations that are characterized by a bias-dependent correlation length that diverges in equilibrium. In addition, power-law corrections are found, which are characterized by an exponent that depends on the chain-leads coupling and is non-analytic at zero bias. This exactly-solvable nonequilibrium strongly-interacting system has the remarkable property that, the near-equilibrium state at infinitesimal bias, cannot be obtained within linear response. These results aid in unraveling the intricate properties spawned by strong interactions once liberated from equilibrium constraints.Comment: 7 pages, 4 figure

A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strictly convex and $a1 > a2$ . As a consequence of this inequality, uniqueness and Lip- schitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coefficient from a single time-dependent Neumann boundary measurement