Quantum backflow for many-particle systems

Quantum backflow is the classically-forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to many-particle systems. We give a general formulation of quantum backflow for systems formed of $N$ free nonrelativistic structureless particles, either identical or distinguishable. Restricting our attention to bosonic systems where the $N$ identical bosons are in the same one-particle state allows us in particular to analytically show that the maximum achievable amount of quantum backflow in this case becomes arbitrarily small for large values of $N$.Comment: 12 pages, 2 figure

Anomalous Surface Segregation Profiles in Ferritic FeCr Stainless Steel

The iron-chromium alloy and its derivatives are widely used for their remarkable resistance to corrosion, which only occurs in a narrow concentration range around 9 to 13 atomic percent chromium. Although known to be due to chromium enrichment of a few atoms thick layer at the surfaces, the understanding of its complex atomistic origin has been a remaining challenge. We report an investigation of the thermodynamics of such surfaces at the atomic scale by means of Monte Carlo simulations. We use a Hamiltonian which provides a parameterization of previous ab initio results and successfully describes the alloy's unusual thermodynamics. We report a strong enrichment in Cr of the surfaces for low bulk concentrations, with a narrow optimum around 12 atomic percent chromium, beyond which the surface composition decreases drastically. This behavior is explained by a synergy between (i) the complex phase separation in the bulk alloy, (ii) local phase transitions that tune the layers closest to the surface to an iron-rich state and inhibit the bulk phase separation in this region, and (iii) its compensation by a strong and non-linear enrichment in Cr of the next few layers. Implications with respect to the design of prospective nanomaterials are briefly discussed.Comment: 6 pages, 4 figure

Lexicographic identifying codes

An identifying code in a graph is a set of vertices which intersects all the symmetric differences between pairs of neighbourhoods of vertices. Not all graphs have identifying codes; those that do are referred to as twin-free. In this paper, we design an algorithm that finds an identifying code in a twin-free graph on n vertices in O(n^3) binary operations, and returns a failure if the graph is not twin-free. We also determine an alternative for sparse graphs with a running time of O(n^2d log n) binary operations, where d is the maximum degree. We also prove that these algorithms can return any identifying code with minimum cardinality, provided the vertices are correctly sorted

Entropy of Closure Operators

The entropy of a closure operator has been recently proposed for the study of network coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank functions for a given closure operator, which determine bounds on the entropy of that operator. This yields new axioms for matroids based on their closure operators. We also determine necessary conditions for a large class of closure operators to be solvable. We then define the Shannon entropy of a closure operator, and use it to prove that the set of closure entropies is dense. Finally, we justify why we focus on the solvability of closure operators only.Comment: arXiv admin note: substantial text overlap with arXiv:1209.655