Neural Network Model for Apparent Deterministic Chaos in Spontaneously Bursting Hippocampal Slices

A neural network model that exhibits stochastic population bursting is studied by simulation. First return maps of inter-burst intervals exhibit recurrent unstable periodic orbit (UPO)-like trajectories similar to those found in experiments on hippocampal slices. Applications of various control methods and surrogate analysis for UPO-detection also yield results similar to those of experiments. Our results question the interpretation of the experimental data as evidence for deterministic chaos and suggest caution in the use of UPO-based methods for detecting determinism in time-series data.Comment: 4 pages, 5 .eps figures (included), requires psfrag.sty (included

B\"acklund Transformations of MKdV and Painlev\'e Equations

For $N\ge 3$ there are $S_N$ and $D_N$ actions on the space of solutions of the first nontrivial equation in the $SL(N) MKdV hierarchy, generalizing the two$Z_2$ actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painlev\'e equations.Comment: 8 pages, plain te

Theory of valley-orbit coupling in a Si/SiGe quantum dot

Electron states are studied for quantum dots in a strained Si quantum well, taking into account both valley and orbital physics. Realistic geometries are considered, including circular and elliptical dot shapes, parallel and perpendicular magnetic fields, and (most importantly for valley coupling) the small local tilt of the quantum well interface away from the crystallographic axes. In absence of a tilt, valley splitting occurs only between pairs of states with the same orbital quantum numbers. However, tilting is ubiquitous in conventional silicon heterostructures, leading to valley-orbit coupling. In this context, "valley splitting" is no longer a well defined concept, and the quantity of merit for qubit applications becomes the ground state gap. For typical dots used as qubits, a rich energy spectrum emerges, as a function of magnetic field, tilt angle, and orbital quantum number. Numerical and analytical solutions are obtained for the ground state gap and for the mixing fraction between the ground and excited states. This mixing can lead to valley scattering, decoherence, and leakage for Si spin qubits.Comment: 18 pages, including 4 figure

Tautomeric mutation: A quantum spin modelling

A quantum spin model representing tautomeric mutation is proposed for any DNA molecule. Based on this model, the quantum mechanical calculations for mutational rate and complementarity restoring repair rate in the replication processes are carried out. A possible application to a real biological system is discussed.Comment: 7 pages (no figures

Upsilon Dissociation in Quark-Gluon Plasma

I consider the dissociation of the upsilon meson due to absorption of a thermal gluon. I discuss the dissociation rate in terms of the energy density, the number density, and the temperature of the quark-gluon plasma. I compare this to the effect due to screening.Comment: 5 pages, added calculations on screening; added figur

A comparative study of some models of incoherence at the mesoscopic scale

The pre-existing literature on phenomena at the mesoscopic scale is concerned among other things with phase coherent transport. Phase coherent transport dominates at very low temperatures. With increase in temperature, as the system size becomes comparable to the inelastic mean free path phase incoherence sets in. This incoherence further leads to dephasing, and as a consequence purely quantum effects in electron transport give way to classical macroscopic behavior. In this work we consider two distinct phenomenological models of incoherent transport, the Coherent Absorption and Wave Attenuation models. We reveal some physical problems in the Coherent Absorption model as opposed to the Wave Attenuation model. We also compare our proposed model with experiments in case of the much studied peak to valley ratios in resonant tunneling diodes, magneto-conductance oscillations and Fano resonances in case of Aharonov-Bohm rings.Comment: 20 pages, 9 figure