Tipping time of a quantum rod

The behaviour of a quantum rod, pivoted at its lower end on an impenetrable floor and restricted to moving in the vertical plane under the gravitational potential is studied analytically under the approximation that the rod is initially localised to a small-enough neighbourhood around the point of classical unstable equilibrium. It is shown that the rod evolves out of this neighbourhood. The time required for this to happen, i.e., the tipping time is calculated using the semi-classical path integral. It is shown that equilibrium is recovered in the classical limit, and that our calculations are consistent with the uncertainty principle.Comment: 10 pages, 1 figure, To appear in Euro. J. Phy

Characterization in bi-parameter space of a non-ideal oscillator

The authors thank scientific agencies CAPES, CNPq (112952/2015-1), and FAPESP (2011/ 19269-11). M. S. Baptista also thanks EPSRC (EP/I03 2606/1).Peer reviewedPostprin

Quantum Phase Diagram of the t-Jz Chain Model

We present the quantum phase diagram of the one-dimensional $t$-$J_z$ model for arbitrary spin (integer or half-integer) and sign of the spin-spin interaction $J_z$, using an {\it exact} mapping to a spinless fermion model that can be solved {\it exactly} using the Bethe ansatz. We discuss its superconducting phase as a function of hole doping $\nu$. Motivated by the new paradigm of high temperature superconductivity, the stripe phase, we also consider the effect the antiferromagnetic background has on the $t$-$J_z$ chain intended to mimic the stripe segments.Comment: 4 pages, 2 figure