Growth in systems of vesicles and membranes

We present a theoretical study for the intermediate stages of the growth of membranes and vesicles in supersaturated solutions of amphiphilic molecules. The problem presents important differences with the growth of droplets in the classical theory of Lifshitz-Slyozov-Wagner, because the aggregates are extensive only in two dimensions, but still grow in a three dimensional bath. The balance between curvature and edge energy favours the nucleation of small planar membranes, but as they grow beyond a critical size they close themselves to form vesicles. We obtain a system of coupled equations describing the growth of planar membranes and vesicles, which is solved numerically for different initial conditions. Finally, the range of parameters relevant in experimental situations is discussed.Comment: 13 pages and 5 postscript figures. To appear in Phys. Rev

Dynamics of coherence, localization and excitation transfer in disordered nanorings

Self-assembled supramolecular aggregates are excellent candidates for the design of efficient excitation transport devices. Both artificially prepared and natural photosynthetic aggregates in plants and bacteria present an important degree of disorder that is supposed to hinder excitation transport. Besides, molecular excitations couple to nuclear motion affecting excitation transport in a variety of ways. We present an exhaustive study of exciton dynamics in disordered nanorings with long-range interactions under the influence of a phonon bath and take the LH2 system of purple bacteria as a model. Nuclear motion is explicitly taken into account by employing the Davydov ansatz description of the polaron and quantum dynamics are obtained using a time-dependent variational method. We reveal an optimal exciton-phonon coupling that suppresses disorder-induced localization and facilitate excitation de-trapping. This excitation transfer enhancement, mediated by environmental phonons, is attributed to energy relaxation toward extended, low-energy excitons provided by the precise LH2 geometry with anti-parallel dipoles and long-range interactions. An analysis of localization and spectral statistics is followed by dynamical measures of coherence and localization, transfer efficiency and superradiance. Linear absorption, 2D photon-echo spectra and diffusion measures of the exciton are examined to monitor the diffusive behavior as a function of the strengths of disorder and exciton-phonon coupling.Comment: 18 pages, 13 figure

Emergent SO(5)SO(5) Symmetry at the N\'eel to Valence-Bond-Solid Transition

We show numerically that the `deconfined' quantum critical point between the N\'eel antiferromagnet and the columnar valence-bond-solid, for a square lattice of spin-1/2s, has an emergent $SO(5)$ symmetry. This symmetry allows the N\'eel vector and the valence-bond-solid order parameter to be rotated into each other. It is a remarkable 2+1-dimensional analogue of the $SO(4)= [SU(2)\times SU(2)]/Z_2$ symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent $SO(5)$ is strong evidence that the phase transition in the 2+1D system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (non-compact $CP^1$ model). The result indicates that in three dimensions there is an $SO(5)$-symmetric conformal field theory which has no relevant singlet operators, so is radically different to conventional Wilson-Fisher-type conformal field theories.Comment: 4+epsilon pages, 6 figure

Effects of many-electron jumps in relaxation and conductivity of Coulomb glasses

A numerical study of the energy relaxation and conductivity of the Coulomb glass is presented. The role of many-electron transitions is studied by two complementary methods: a kinetic Monte Carlo algorithm and a master equation in configuration space method. A calculation of the transition rate for two-electron transitions is presented, and the proper extension of this to multi-electron transitions is discussed. It is shown that two-electron transitions are important in bypassing energy barriers which effectively block sequential one-electron transitions. The effect of two-electron transitions is also discussed.Comment: 8 pages, 6 figure