Vortex pinning and non-Hermitian quantum mechanics

Abstract

A delocalization phenomenon is studied in a class of non-Hermitian random quantum-mechanical problems. Delocalization arises in response to a sufficiently large constant imaginary vector potential. The transition is related to depinning of flux lines from extended defects in type-II superconductors subject to a tilted external magnetic field. The physical meaning of the complex eigenvalues and currents of the non-Hermitian system is elucidated in terms of properties of tilted vortex lines. The singular behavior of the penetration length describing stretched exponential screening of a perpendicular magnetic field (transverse Meissner effect), the surface transverse magnetization, and the trapping length are determined near the flux-line depinning point.

Spectral Theory of Pseudo-Ergodic Operators

“…Recent papers have obtained some striking results concerning the spectral properties of the non-self-adjoint (nsa) Anderson model, which models the growth of bacteria in an inhomogeneous environment, [10,11,12,13,5]. To be more precise the authors have determined the asymptotic limit of the spectrum of a nsa random finite periodic chain almost surely as the length of the chain increases to infinity.…”

Timelike boundary Liouville theory

“…This relation will be further discussed in section 2. Non-hermitian boundary interactions of the general variety S NH (1.4) are realized in a variety of condensed matter systems [22]. S NH itself arises in the infrared limit of a 2d…”

Regular Spacings of Complex Eigenvalues in the One-Dimensional Non-Hermitian Anderson Model

“…(A much more detailed description of the spectrum of the limiting operator can be found in [3].) However, numerical experiments reproduce pictures like that in Fig.1 with remarkable stability also for large values of n (in [5,6] n = 1000). They clearly show that the eigenvalues of H g n have no tendency to spread over any two-dimensional region but rather tend to belong to smooth curves.…”

“…✷ Define θ n (x) = −V n (x, y j,n (x)) and θ(x) = −V (x, y j (x)) for x ∈ [α, β] ⊂ (a j , b j ) and n > n 1 with n 1 as in part (ii) of Theorem 3.3. As before, V n (x, y) and V (x, y) are the imaginary parts of the analytic functions F n (z and F (z), see (6) and (7). In view of Theorem 3.3 and Proposition 3.1, we have that…”