Poisson sigma models and symplectic groupoids

We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in the Hamiltonian formalism. The phase space is the space of leaves of a Hamiltonian foliation and has a natural groupoid structure. If it is a manifold then it is a symplectic groupoid for the given Poisson manifold. We study various families of examples. In particular, a global symplectic groupoid for a general class of two-dimensional Poisson domains is constructed.Comment: 34 page

Current saturation and Coulomb interactions in organic single-crystal transistors

Electronic transport through rubrene single-crystal field effect transistors (FETs) is investigated experimentally in the high carrier density regime (n ~ 0.1 carrier/molecule). In this regime, we find that the current does not increase linearly with the density of charge carriers, and tends to saturate. At the same time, the activation energy for transport unexpectedly increases with increasing n. We perform a theoretical analysis in terms of a well-defined microscopic model for interacting Frohlich polarons, that quantitatively accounts for our experimental observations. This work is particularly significant for our understanding of electronic transport through organic FETs.Comment: Extended version with 1 additional figure and an appendix explaining the consistency of the theoretical calculatio

Suppression of Decoherence and Disentanglement by the Exchange Interaction

Entangled qubit pairs can serve as a quantum memory or as a resource for quantum communication. The utility of such pairs is measured by how long they take to disentangle or decohere. To answer the question of whether qubit-qubit interactions can prolong entanglement, we calculate the dissipative dynamics of a pair of qubits coupled via the exchange interaction in the presence of random telegraph noise and $1/f$ noise. We show that for maximally entangled (Bell) states, the exchange interaction generally suppresses decoherence and disentanglement. This suppression is more apparent for random telegraph noise if the noise is non-Markovian, whereas for $1/f$ noise the exchange interaction should be comparable in magnitude to strongest noise source. The entangled singlet-triplet superposition state of 2 qubits ($\psi_{\pm}$ Bell state) can be protected by the interaction, while for the triplet-triplet state ($\phi_{\pm}$ Bell state), it is less effective. Thus the former is more suitable for encoding quantum information

Phonon-affected steady-state transport through molecular quantum dots

We consider transport through a vibrating molecular quantum dot contacted to macroscopic leads acting as charge reservoirs. In the equilibrium and nonequilibrium regime, we study the formation of a polaron-like transient state at the quantum dot for all ratios of the dot-lead coupling to the energy of the local phonon mode. We show that the polaronic renormalization of the dot-lead coupling is a possible mechanism for negative differential conductance. Moreover, the effective dot level follows one of the lead chemical potentials to enhance resonant transport, causing novel features in the inelastic tunneling signal. In the linear response regime, we investigate the impact of the electron-phonon interaction on the thermoelectrical properties of the quantum dot device.Comment: 11 pages, 7 figures, FQMT11 Proceeding

Interaction of strongly correlated electrons and acoustical phonons

We investigate the interaction of correlated electrons with acoustical phonons using the extended Hubbard-Holstein model in which both, the electron-phonon interaction and the on-site Coulomb repulsion are considered to be strong. The Lang-Firsov canonical transformation allows to obtain mobile polarons for which a new diagram technique and generalized Wick's theorem is used. This allows to handle the Coulomb repulsion between the electrons emerged into a sea of phonon fields (\textit{phonon clouds}). The physics of emission and absorption of the collective phonon-field mode by the polarons is discussed in detail. Moreover, we have investigated the different behavior of optical and acoustical phonon clouds when propagating through the lattice. In the strong-coupling limit of the electron-phonon interaction, and in the normal as well as in the superconducting phase, chronological thermodynamical averages of products of acoustical phonon-cloud operators can be expressed by one-cloud operator averages. While the normal one-cloud propagator has the form of a Lorentzian, the anomalous one is of Gaussian form and considerably smaller. Therefore, the anomalous electron Green's functions can be considered to be more important than corresponding polarons functions, i.e., pairing of electrons without phonon-clouds is easier to achieve than pairing of polarons with such clouds.Comment: : 28 pages, 9 figures, revtex4. Invited paper for a special issue of Low Temperature Physics dedicated to the 20th anniversary of HTS

Phase transition and phase diagram at a general filling in the spinless one-dimensional Holstein Model

Among the mechanisms for lattice structural deformation, the electron-phonon interaction mediated Peierls charge-density-wave (CDW) instability in single band low-dimensional systems is perhaps the most ubiquitous. The standard mean-field picture predicts that the CDW transition occurs at all fillings and all values of the electron-phonon coupling $g$ and the adiabaticity parameter $t/\omega_0$. Here, we correct the mean-field expression for the Peierls instability condition by showing that the non-interacting static susceptibility, at twice the Fermi momentum, should be replaced by the dynamic one. We derive the Luttinger liquid (LL) to CDW transition condition, {\it exact to second order in a novel blocked perturbative approach}, for the spinless one-dimensional Holstein model in the adiabatic regime. The small parameter is the ratio $g \omega_0/t$. We present the phase diagram at non-half-filling by obtaining the surprising result that the CDW occurs in a more restrictive region of a two parameter ($g^2 \omega_0/t$ and $t/\omega_0$) space than at half-filling.Comment: Made changes in the appendices and also in notatio

The anomaly-free quantization of two-dimensional relativistic string. I

An anomaly-free quantum theory of a relativistic string is constructed in two-dimensional space-time. The states of the string are found to be similar to the states of a massless chiral quantum particle. This result is obtained by generalizing the concept of an ``operator'' in quantum field theory.Comment: LaTeX, 19 pages, no figure