5,657 research outputs found
Bounded Context Switching for Valence Systems
We study valence systems, finite-control programs over infinite-state memories modeled in terms of graph monoids. Our contribution is a notion of bounded context switching (BCS). Valence systems generalize pushdowns, concurrent pushdowns, and Petri nets. In these settings, our definition conservatively generalizes existing notions. The main finding is that reachability within a bounded number of context switches is in NPTIME, independent of the memory (the graph monoid). Our proof is genuinely algebraic, and therefore contributes a new way to think about BCS. In addition, we exhibit a class of storage mechanisms for which BCS reachability belongs to PTIME
Reversible carrier-type transition in gas-sensing oxides and nanostructures
Despite many important applications of a-Fe2O3 and Fe doped SnO2 in
semiconductors, catalysis, sensors, clinical diagnosis and treatments, one
fundamental issue that is crucial to these applications remains theoretically
equivocal- the reversible carrier-type transition between n- and p-type
conductivities during gas-sensing operations. Here, we give unambiguous and
rigorous theoretical analysis in order to explain why and how the oxygen
vacancies affect the n-type semiconductors, a-Fe2O3 and Fe doped SnO2 in which
they are both electronically and chemically transformed into a p-type
semiconductor. Furthermore, this reversible transition also occurs on the oxide
surfaces during gas-sensing operation due to physisorbed gas molecules (without
any chemical reaction). We make use of the ionization energy theory and its
renormalized ionic displacement polarizability functional to reclassify,
generalize and to explain the concept of carrier-type transition in solids, and
during gas-sensing operation. The origin of such a transition is associated to
the change in ionic polarizability and the valence states of cations in the
presence of (a) oxygen vacancies and (b) physisorped gas molecules.Comment: To be published in ChemPhysChe
Scope-Bounded Reachability in Valence Systems
Multi-pushdown systems are a standard model for concurrent recursive programs, but they have an undecidable reachability problem. Therefore, there have been several proposals to underapproximate their sets of runs so that reachability in this underapproximation becomes decidable. One such underapproximation that covers a relatively high portion of runs is scope boundedness. In such a run, after each push to stack i, the corresponding pop operation must come within a bounded number of visits to stack i.
In this work, we generalize this approach to a large class of infinite-state systems. For this, we consider the model of valence systems, which consist of a finite-state control and an infinite-state storage mechanism that is specified by a finite undirected graph. This framework captures pushdowns, vector addition systems, integer vector addition systems, and combinations thereof. For this framework, we propose a notion of scope boundedness that coincides with the classical notion when the storage mechanism happens to be a multi-pushdown.
We show that with this notion, reachability can be decided in PSPACE for every storage mechanism in the framework. Moreover, we describe the full complexity landscape of this problem across all storage mechanisms, both in the case of (i) the scope bound being given as input and (ii) for fixed scope bounds. Finally, we provide an almost complete description of the complexity landscape if even a description of the storage mechanism is part of the input
Quantum Many-Body Dynamics of Coupled Double-Well Superlattices
We propose a method for controllable generation of non-local entangled pairs
using spinor atoms loaded in an optical superlattice. Our scheme iteratively
increases the distance between entangled atoms by controlling the coupling
between the double wells. When implemented in a finite linear chain of 2N
atoms, it creates a triplet valence bond state with large persistency of
entanglement (of the order of N). We also study the non-equilibrium dynamics of
the one-dimensional ferromagnetic Heisenberg Hamiltonian and show that the time
evolution of a state of decoupled triplets on each double well leads to the
formation of a highly entangled state where short-distance antiferromagnetic
correlations coexist with longer-distance ferromagnetic ones. We present
methods for detection and characterization of the various dynamically generated
states. These ideas are a step forward towards the use of atoms trapped by
light as quantum information processors and quantum simulators.Comment: 13 pages, 10 figures, references adde
Rips Induction: Index of the dual lamination of an -tree
Let be a -tree in the boundary of the Outer Space CV, with dense
orbits. The -index of is defined by means of the dual lamination of .
It is a generalisation of the Euler-Poincar\'e index of a foliation on a
surface. We prove that the -index of is bounded above by , and we
study the case of equality. The main tool is to develop the Rips Machine in
order to deal with systems of isometries on compact -trees. Combining our
results on the \CQ-index with results on the classical geometric index of a
tree, we obtain a beginning of classification of trees. As a consequence, we
give a classification of iwip outer automorphisms of the free group, by
discussing the properties of their attracting and repelling trees.Comment: 33 pages. The previous version has been splitted in two disjoint
papers. See also Botanic of irreducible automorphisms of free group
Surface theorem for the Chern-Simons axion coupling
The Chern-Simons axion coupling of a bulk insulator is only defined modulo a
quantum of e^2/h. The quantized part of the coupling is uniquely defined for a
bounded insulating sample, but it depends on the specific surface termination.
Working in a slab geometry and representing the valence bands in terms of
hybrid Wannier functions, we show how to determine that quantized part from the
excess Chern number of the hybrid Wannier sheets located near the surface of
the slab. The procedure is illustrated for a tight-binding model consisting of
coupled quantum anomalous Hall layers. By slowly modulating the model
parameters, it is possible to transfer one unit of Chern number from the bottom
to the top surface over the course of a cyclic evolution of the bulk
Hamiltonian. When the evolution of the surface Hamiltonian is also cyclic, the
Chern pumping is obstructed by chiral touchings between valence and conduction
surface bands.Comment: 15 page
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