Witnessing a Poincar\'e recurrence with Mathematica

The often elusive Poincar\'e recurrence can be witnessed in a completely separable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple numbers. The latter problem then can be somewhat satisfactorily solved by using the famous Lenstra-Lenstra-Lov\'{a}sz (LLL) algorithm, which is implemented in the Mathematica built-in function \verb"LatticeReduce". The procedure is illustrated with a harmonic chain. The incredibly large recurrence times are obtained exactly. They follow the expected scaling law very well.Comment: 8 pages, 5 figure

Hadron-quark phase transition in asymmetric matter with dynamical quark masses

The two-Equation of State (EoS) model is used to describe the hadron-quark phase transition in asymmetric matter formed at high density in heavy-ion collisions. For the quark phase, the three-flavor Nambu--Jona-Lasinio (NJL) effective theory is used to investigate the influence of dynamical quark mass effects on the phase transition. At variance to the MIT-Bag results, with fixed current quark masses, the main important effect of the chiral dynamics is the appearance of an End-Point for the coexistence zone. We show that a first order hadron-quark phase transition may take place in the region T=(50-80)MeV and \rho_B=(2-4)\rho_0, which is possible to be probed in the new planned facilities, such as FAIR at GSI-Darmstadt and NICA at JINR-Dubna. From isospin properties of the mixed phase somepossible signals are suggested. The importance of chiral symmetry and dynamical quark mass on the hadron-quark phase transition is stressed. The difficulty of an exact location of Critical-End-Point comes from its appearance in a region of competition between chiral symmetry breaking and confinement, where our knowledge of effective QCD theories is still rather uncertain.Comment: 13 pages, 16 figures (revtex

Phonon-Assisted Gain in a Semiconductor Double Quantum Dot Maser

We develop a microscopic model for the recently demonstrated double quantum dot (DQD) maser. In characterizing the gain of this device we find that, in addition to the direct stimulated emission of photons, there is a large contribution from the simultaneous emission of a photon and a phonon, i.e., the phonon sideband. We show that this phonon-assisted gain typically dominates the overall gain which leads to masing. Recent experimental data are well fit with our model.Comment: v1: 6 pgs, 2 figures; v2: 6 pgs, 3 figures, added Fig 2b and Fig. 3b, modified main text; v3: 6+ pgs, 3 figures, modified main tex

Lattice Gluon Propagator in the Landau Gauge: A Study Using Anisotropic Lattices

Lattice gluon propagators are studied using tadpole and Symanzik improved gauge action in Landau gauge. The study is performed using anisotropic lattices with asymmetric volumes. The Landau gauge dressing function for the gluon propagator measured on the lattice is fitted according to a leading power behavior: $Z(q^2)\simeq (q^2)^{2\kappa}$ with an exponent $\kappa$ at small momenta. The gluon propagators are also fitted using other models and the results are compared. Our result is compatible with a finite gluon propagator at zero momentum in Landau gauge.Comment: 14 pages, 4 figure

Microwave detection of electron-phonon interactions in a cavity-coupled double quantum dot

Quantum confinement leads to the formation of discrete electronic states in quantum dots. Here we probe electron-phonon interactions in a suspended InAs nanowire double quantum dot (DQD) that is electric-dipole coupled to a microwave cavity. We apply a finite bias across the wire to drive a steady state population in the DQD excited state, enabling a direct measurement of the electron-phonon coupling strength at the DQD transition energy. The amplitude and phase response of the cavity field exhibit features that are periodic in the DQD energy level detuning due to the phonon modes of the nanowire. The observed cavity phase shift is consistent with theory that predicts a renormalization of the cavity center frequency by coupling to phonons