Generalization of correlated electron-ion dynamics from nonequilibrium Green's functions

We present a new formulation of the correlated electron-ion dynamics (CEID) by using equations of motion for nonequilibrium Green's functions, which generalizes CEID to a general nonequilibrium statistical ensemble that allows for a variable total number of electrons. We make a rigorous connection between CEID and diagrammatic perturbation theory, which furthermore allows the key approximations in CEID to be quantified in diagrammatic terms, and, in principle, improved. We compare analytically the limiting behavior of CEID and the self-consistent Born approximation (SCBA) for a general dynamical nonequilibrium state. This comparison shows that CEID and SCBA coincide in the weak electron-phonon coupling limit, while they differ in the large ionic mass limit where we can readily quantify their difference. In particular, we illustrate the relation between CEID and SCBA by perturbation theory at the fourth-order in the coupling strength.Comment: 21 pages, 2 figure

Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds

By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of stochastic differential equations with multiplicative noise. These inequalities are applied to the study of heat kernel upper bound and contractivity properties of the semigroup. The main results are also extended to reflecting diffusion processes on Riemannian manifolds with nonconvex boundary.Comment: Published in at http://dx.doi.org/10.1214/10-AOP600 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Generating coherent state of entangled spins

A coherent state of many spins contains quantum entanglement which increases with a decrease in the collective spin value. We present a scheme to engineer this class of pure state based on incoherent spin pumping with a few collective raising/lowering operators. In a pumping scenario aimed for maximum entanglement, the steady-state of N pumped spin qubits realizes the ideal resource for the 1 to N/2 quantum telecloning. We show how the scheme can be implemented in a realistic system of atomic spin qubits in optical lattice. Error analysis show that high fidelity state engineering is possible for N ~ O(100) spins in the presence of decoherence. The scheme can also prepare a resource state for the secret sharing protocol and for the construction of large scale Affleck-Kennedy-Lieb-Tasaki (AKLT) state.Comment: updated version to appear on Phys. Rev.

Harnack inequality and applications for stochastic generalized porous media equations

By using coupling and Girsanov transformations, the dimension-free Harnack inequality and the strong Feller property are proved for transition semigroups of solutions to a class of stochastic generalized porous media equations. As applications, explicit upper bounds of the $L^p$-norm of the density as well as hypercontractivity, ultracontractivity and compactness of the corresponding semigroup are derived.Comment: Published at http://dx.doi.org/10.1214/009117906000001204 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Factorization, resummation and sum rules for heavy-to-light form factors

Precision calculations of heavy-to-light form factors are essential to sharpen our understanding towards the strong interaction dynamics of the heavy-quark system and to shed light on a coherent solution of flavor anomalies. We briefly review factorization properties of heavy-to-light form factors in the framework of QCD factorization in the heavy quark limit and discuss the recent progress on the QCD calculation of $B \to \pi$ form factors from the light-cone sum rules with the $B$-meson distribution amplitudes. Demonstration of QCD factorization for the vacuum-to-$B$-meson correlation function used in the sum-rule construction and resummation of large logarithms in the short-distance functions entering the factorization theorem are presented in detail. Phenomenological implications of the newly derived sum rules for $B \to \pi$ form factors are further addressed with a particular attention to the extraction of the CKM matrix element $|V_{ub}|$.Comment: 6 pages, 3 figures, proceedings prepared for the "QCD@work 2016", (27-30 June 2016, Martina Franca, Italy