Isospin-dependent pion in-medium effects on charged pion ratio in heavy ion collisions

Using results from the chiral perturbation theory for the s-wave interaction and the delta-resonance model for the p-wave interaction of pions with nucleons, we have evaluated the spectral functions of pions in asymmetric nuclear matter with unequal proton and neutron densities. We find that in hot dense neutron-rich matter the strength of the spectral function of positively charged pion at low energies is somewhat larger than that of negatively charged pion. In a thermal model, this isospin-dependent effect slightly reduces the ratio of negatively charged to positively charged pions that are produced in heavy ion collisions induced by radioactive beams. Relevance of our results to the determination of the nuclear symmetry energy from measured ratio of negatively to positively charged pions produced in heavy ion collisions is discussed.Comment: 7 pages, 4 figures, pion-nucleon s-wave interaction include

Entanglement distribution over the subsystems and its invariance

We study the entanglement dynamics of two qubits, each of which is embedded into its local amplitude-damping reservoir, and the entanglement distribution among all the bipartite subsystems including qubit-qubit, qubit-reservoir, and reservoir-reservoir. It is found that the entanglement can be stably distributed among all components, which is much different to the result obtained under the Born-Markovian approximation by C. E. L\'{o}pez {\it et al.} [Phys. Rev. Lett. \textbf{101}, 080503 (2008)], and particularly it also satisfies an identity. Our unified treatment includes the previous results as special cases. The result may give help to understand the physical nature of entanglement under decoherence.Comment: 6 pages, 5 figure

Fractality of profit landscapes and validation of time series models for stock prices

We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters $p$ and $q$, and the sell (buy) decision is made when the log return is larger (smaller) than $p$ ($-q$). We discretize the unit square $(p, q) \in [0, 1] \times [0, 1]$ into the $N \times N$ square grid and the profit $\Pi (p, q)$ is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: The number M of local maxima follows the power-law form $M \sim N^{a}$, but the scaling exponent $a$ is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent $a \approx 1.6$ observed for real stock markets. We suggest that the fractality of profit landscape characterized by $a \approx 1.6$ can be a useful measure to validate time series model for stock prices.Comment: 10pages, 6figure

Generating Many Majorana Modes via Periodic Driving: A Superconductor Model

Realizing Majorana modes (MMs) in condensed-matter systems is of vast experimental and theoretical interests, and some signatures of MMs have been measured already. To facilitate future experimental observations and to explore further applications of MMs, generating many MMs at ease in an experimentally accessible manner has become one important issue. This task is achieved here in a one-dimensional $p$-wave superconductor system with the nearest- and next-nearest-neighbor interactions. In particular, a periodic modulation of some system parameters can induce an effective long-range interaction (as suggested by the Baker-Campbell-Hausdorff formula) and may recover time-reversal symmetry already broken in undriven cases. By exploiting these two independent mechanisms at once we have established a general method in generating many Floquet MMs via periodic driving.Comment: 5 pages, 3 figures. To appear in Phys. Rev. B as a Rapid Communicatio

Medium effects on charged pion ratio in heavy ion collisions

We have recently studied in the delta-resonance--nucleon-hole model the dependence of the pion spectral function in hot dense asymmetric nuclear matter on the charge of the pion due to the pion p-wave interaction in nuclear medium. In a thermal model, this isospin-dependent effect enhances the ratio of negatively charged to positively charged pions in neutron-rich nuclear matter, and the effect is comparable to that due to the uncertainties in the theoretically predicted stiffness of nuclear symmetry energy at high densities. This effect is, however, reversed if we also take into account the s-wave interaction of the pion in nuclear medium as given by chiral perturbation theory, resulting instead in a slightly reduced ratio of negatively charged to positively charged pions. Relevance of our results to the determination of the nuclear symmetry energy from the ratio of negatively to positively charged pions produced in heavy ion collisions is discussed.Comment: 11 pages, 4 figures, contribution to The International Workshop on Nuclear Dynamics in Heavy-Ion Reactions and the Symmetry Energy (IWND2009), Shanghai, China, 22-25 August, 200