Generalized Arf invariants in algebraic L-theory

The difference between the quadratic L-groups L_*(A) and the symmetric L-groups L^*(A) of a ring with involution A is detected by generalized Arf invariants. The special case A=Z[x] gives a complete set of invariants for the Cappell UNil-groups UNil_*(Z;Z,Z) for the infinite dihedral group D_{\infty}=Z_2*Z_2, extending the results of Connolly and Ranicki (math.AT/0304016) and Connolly and Davis.Comment: 90 pages, LATE

Entanglement Energetics at Zero Temperature

We show how many-body ground state entanglement information may be extracted from sub-system energy measurements at zero temperature. Generically, the larger the measured energy fluctuations are, the larger the entanglement is. Examples are given with the two-state system and the harmonic oscillator. Comparisons made with recent qubit experiments show this type of measurement provides another method to quantify entanglement with the environment.Comment: 4 pages, 2 figure

Fibonacci-Lucas SIC-POVMs

We present a conjectured family of SIC-POVMs which have an additional symmetry group whose size is growing with the dimension. The symmetry group is related to Fibonacci numbers, while the dimension is related to Lucas numbers. The conjecture is supported by exact solutions for dimensions d=4,8,19,48,124,323, as well as a numerical solution for dimension d=844.Comment: The fiducial vectors can be obtained from http://sicpovm.markus-grassl.de as well as from the source files. v2: precision for the numerical solution in dimension 844 increased to 150 digits and new exact solution for dimension 323 adde

Selectivity in binary fluid mixtures: static and dynamical properties

Selectivity of particles in a region of space can be achieved by applying external potentials to influence the particles in that region. We investigate static and dynamical properties of size selectivity in binary fluid mixtures of two particles sizes. We find that by applying an external potential that is attractive to both kinds of particles, due to crowding effects, this can lead to one species of particles being expelled from that region, whilst the other species is attracted into the region where the potential is applied. This selectivity of one species of particle over the other in a localized region of space depends on the density and composition of the fluid mixture. Applying an external potential that repels both kinds of particles leads to selectivity of the opposite species of particles to the selectivity with attractive potentials. We use equilibrium and dynamical density functional theory to describe and understand the static and dynamical properties of this striking phenomenon. Selectivity by some ion-channels is believed to be due to this effect.Comment: 11 pages, 9 figure

Continuous quantum measurement with independent detector cross-correlations

We investigate the advantages of using two independent, linear detectors for continuous quantum measurement. For single-shot quantum measurement, the measurement is maximally efficient if the detectors are twins. For weak continuous measurement, cross-correlations allow a violation of the Korotkov-Averin bound for the detector's signal-to-noise ratio. A vanishing noise background provides a nontrivial test of ideal independent quantum detectors. We further investigate the correlations of non-commuting operators, and consider possible deviations from the independent detector model for mesoscopic conductors coupled by the screened Coulomb interaction.Comment: 4 pages, 2 figure