Testable non-linearity through entanglement measurement

A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the proposals for the gravitationally induced collapse of wave function. Here, it is shown that the consequence of the connection demonstrates a possible deviation of the theory from the standard formulation of quantum mechanics in the probability prediction of experiments. The links are identified from the fact that the analytic solution of the equation is given by Dirichlet eigenvalues which can be expressed by generalized trigonometric function. Consequently, modified formulation of Born's rule is obtained by relating the event probability of the measuement to an arbitrary exponent of the modulus of the eigenvalue solution. Such system, which is subject to the non-linear dynamic equation, illustrates the violation of the Clauser-Hore-Shimony-Holt inequality proportional to the degree of the non-linearity as it can be tested by a real experiment. Depending upon the degree, it is found that the violation can go beyond Tsirelson bound $2\sqrt{2}$ and reaches to the value of nonlocal box.Comment: 3 figure

Substitutions, tiling dynamical systems and minimal self-joinings

We investigate substitution subshifts and tiling dynamical systems arising from the substitutions (1) \theta : 0 \rightarrow 001,1 \rightarrow 11001 and (2) \eta : 0 \rightarrow 001,1 \rightarrow 11100. We show that the substitution subshifts arising from \theta and \eta have minimal self-joinings and are mildly mixing. We also give a criterion for 1-dimensional tiling systems arising from \theta or \eta to have minimal self-joinings. We apply this to obtain examples of mildly mixing 1-dimensional tiling systems

Entropy Maximization and Instability of Uniformly Magnetized Plasma

A regime where a uniformly magnetized plasma could be unstable to a spatial perturbation in the magnetic field is explored. In this regime, a uniformly magnetized state does not maximize the entropy. The physical implication is discussed in the context of the current generation, the magnetic reconnection, and the dynamo effect

Comment on "Is There a "Most Perfect Fluid" Consistent with Quantum Field Theory?"

This is a comment on hep-th/0702136Comment: 1 page, comment on hep-th/070213

On conformally flat circle bundles over surfaces

We study surface groups $\Gamma$ in $SO(4,1)$, which is the group of Mobius tranformations of $S^3$, and also the group of isometries of $\mathbb{H}^4$. We consider such $\Gamma$ so that its limit set $\Lambda_\Gamma$ is a quasi-circle in $S^3$, and so that the quotient $(S^3 - \Lambda_\Gamma) / \Gamma$ is a circle bundle over a surface. This circle bundle is said to be conformally flat, and our main goal is to discover how twisted such bundle may be by establishing a bound on its Euler number. By combinatorial approaches, we have two soft bounds in this direction on certain types of nice structures. In this article we also construct new examples, a "grafting" type path in the space of surface group representations into $SO(4,1)$: starting inside the quasi-Fuschsian locus, going through non-discrete territory and back.Comment: 28 pages, 7 figures. Updated from Thesis version: more correct bound of (3/2)n^2, updated exposition in section 3.