Solving generic nonarchimedean semidefinite programs using stochastic game algorithms

A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility problems given by generic matrices. Our approach is based on tropical geometry. It relies on tropical spectrahedra, which are defined as the images by the valuation of nonarchimedean spectrahedra. We establish a correspondence between generic tropical spectrahedra and zero-sum stochastic games with perfect information. The latter have been well studied in algorithmic game theory. This allows us to solve nonarchimedean semidefinite feasibility problems using algorithms for stochastic games. These algorithms are of a combinatorial nature and work for large instances.Comment: v1: 25 pages, 4 figures; v2: 27 pages, 4 figures, minor revisions + benchmarks added; v3: 30 pages, 6 figures, generalization to non-Metzler sign patterns + some results have been replaced by references to the companion work arXiv:1610.0674

A quotient of the Lubin-Tate tower II

In this article we construct the quotient M_1/P(K) of the infinite-level Lubin-Tate space M_1 by the parabolic subgroup P(K) of GL(n,K) of block form (n-1,1) as a perfectoid space, generalizing results of one of the authors (JL) to arbitrary n and K/Q_p finite. For this we prove some perfectoidness results for certain Harris-Taylor Shimura varieties at infinite level. As an application of the quotient construction we show a vanishing theorem for Scholze's candidate for the mod p Jacquet-Langlands and the mod p local Langlands correspondence. An appendix by David Hansen gives a local proof of perfectoidness of M_1/P(K) when n = 2, and shows that M_1/Q(K) is not perfectoid for maximal parabolics Q not conjugate to P.Comment: with an appendix by David Hanse

Microscopic origin of the mobility enhancement at a spinel/perovskite oxide heterointerface revealed by photoemission spectroscopy

The spinel/perovskite heterointerface $\gamma$-Al$_2$O$_3$/SrTiO$_3$ hosts a two-dimensional electron system (2DES) with electron mobilities exceeding those in its all-perovskite counterpart LaAlO$_3$/SrTiO$_3$ by more than an order of magnitude despite the abundance of oxygen vacancies which act as electron donors as well as scattering sites. By means of resonant soft x-ray photoemission spectroscopy and \textit{ab initio} calculations we reveal the presence of a sharply localized type of oxygen vacancies at the very interface due to the local breaking of the perovskite symmetry. We explain the extraordinarily high mobilities by reduced scattering resulting from the preferential formation of interfacial oxygen vacancies and spatial separation of the resulting 2DES in deeper SrTiO$_3$ layers. Our findings comply with transport studies and pave the way towards defect engineering at interfaces of oxides with different crystal structures.Comment: Accepted as Rapid Communications in Physical Review

Gate-tunable, normally-on to normally-off memristance transition inpatterned LaAlO3/SrTiO3 interfaces

The authors gratefully acknowledge the support from the state of Bavaria as well as from the Deutsche Forschungsgemeinschaft (FOR1162 and SFB1170).We report gate-tunable memristive switching in patterned LaAlO3/SrTiO3 interfaces at cryogenic temperatures. The application of voltages in the order of a few volts to the back gate of the device allows controlling and switching on and -off the inherent memory functionality (memristance). For large and small gate voltages a simple non-linear resistance characteristic is observed while a pinched hysteresis loop and memristive switching occurs in an intermediate voltage range. The memristance is further controlled by the density of oxygen vacancies, which is tuned by annealing the sample at 300 °C in nitrogen atmosphere. Depending on the annealing time the memristance at zero gate voltage can be switched on and off leading to normally-on and normally-off memristors. The presented device offers reversible and irreversible control of memristive characteristics by gate voltages and annealing, respectively, which may allow to compensate fabrication variabilities of memristors that complicate the realization of large memristor-based neural networks.PostprintPeer reviewe