Homologous non-isotopic symplectic tori in a K3-surface

For each member of an infinite family of homology classes in the K3-surface E(2), we construct infinitely many non-isotopic symplectic tori representing this homology class. This family has an infinite subset of primitive classes. We also explain how these tori can be non-isotopically embedded as homologous symplectic submanifolds in many other symplectic 4-manifolds including the elliptic surfaces E(n) for n>2.Comment: 15 pages, 9 figures; v2: extended the main theorem, gave a second construction of symplectic tori, added a figure, added/updated references, minor changes in figure

Ergodic property of Markovian semigroups on standard forms of von Neumann algebras

We give sufficient conditions for ergodicity of the Markovian semigroups associated to Dirichlet forms on standard forms of von Neumann algebras constructed by the method proposed in Refs. [Par1,Par2]. We apply our result to show that the diffusion type Markovian semigroups for quantum spin systems are ergodic in the region of high temperatures where the uniqueness of the KMS-state holds.Comment: 25 page

Polymer Release out of a Spherical Vesicle through a Pore

Translocation of a polymer out of curved surface or membrane is studied via mean first passage time approach. Membrane curvature gives rise to a constraint on polymer conformation, which effectively drives the polymer to the outside of membrane where the available volume of polymer conformational fluctuation is larger. Considering a polymer release out of spherical vesicle, polymer translocation time $\tau$ is changed to the scaling behavior $\tau\sim L^2$ for $R<R_G$, from $\tau\sim L^3$ for $R\gg R_G$, where $L$ is the polymer contour length and $R$, $R_G$ are vesicle radius and polymer radius of gyration respectively. Also the polymer capture into a spherical budd is studied and possible apparatus for easy capture is suggested.Comment: 14 pages RevTeX, 6 postscript figures, published in Phys. Rev. E 57, 730 (1998

Structural Anomalies at the Magnetic and Ferroelectric Transitions in RMn2O5RMn_2O_5 (R=Tb, Dy, Ho)

Strong anomalies of the thermal expansion coefficients at the magnetic and ferroelectric transitions have been detected in multiferroic $RMn_2O_5$. Their correlation with anomalies of the specific heat and the dielectric constant is discussed. The results provide evidence for the magnetic origin of the ferroelectricity mediated by strong spin-lattice coupling in the compounds. Neutron scattering data for $HoMn_2O_5$ indicate a spin reorientation at the two low-temperature phase transitions

Entropy of the FRW universe based on the generalized uncertainty principle

The statistical entropy of the FRW universe described by time-dependent metric is newly calculated using the brick wall method based on the general uncertainty principle with the minimal length. We can determine the minimal length with the Plank scale to obtain the entropy proportional to the area of the cosmological apparent horizon.Comment: 10 pages, accepted in Modern Physics Letters