Related papers: Branched Polymers with Loops
The first aim is to construct generalizations of Polya type point process by applying a branching mechanism to these point processes. Conditions are given under which these point processes satisfy an integration by parts formula.…
We study the order statistics of one dimensional branching Brownian motion in which particles either diffuse (with diffusion constant $D$), die (with rate $d$) or split into two particles (with rate $b$). At the critical point $b=d$ which…
We apply the framework of Cauchy Slice Holography to the quantization of gravity on closed slices with $\Lambda>0$ (with a focus on $2+1$ dimensions for concreteness). We obtain solutions to the Wheeler-DeWitt equation in a basis of…
We study the conformational properties of complex polymer macromolecules, consisting in general of $n$ subsequently connected chains (blocks) of different lengths and distinct chemical structure. Depending on the solvent conditions, the…
Four-dimensional (4D) simplicial quantum gravity coupled to U(1) gauge fields has been studied using Monte-Carlo simulations. A negative string susceptibility exponent is observed beyond the phase-transition point, even if the number of…
The minimal energy variations of a directed polymer with tilted columnar disorder in two dimensions are shown numerically to obey a multiscaling at short distances which crosses over to global simple scaling at large distances. The scenario…
We compute the generating function of random planar quadrangulations with three marked vertices at prescribed pairwise distances. In the scaling limit of large quadrangulations, this discrete three-point function converges to a simple…
Two popular attempts to understand the quantum physics of gravitation are critically assessed. The talk on which this paper is based was intended for a general particle-physics audience.
Type IIA string theory compactified on an elliptic CY3-fold gives rise to N=2 U(1) gauge theory with an adjoint hypermultiplet. We study the refined open and closed topological string partition functions of this geometry using the refined…
The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann…
We consider a nonlinear generalization of Cauchy-Riemann eqs. to the algebra of biquaternions. From here we come to "universal generating equations" (1) which deal with 2-spinor and gauge fields and form the basis of some unified algebraic…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
Four-dimensional simplicial quantum gravity is modified either by coupling it to U(1) gauge fields or by introducing a measure weighted by the orders of the triangles. Strong coupling expansion and Monte Carlo simulations are used. Although…
The structure of flexible polymers endgrafted in cylindrical pores of diameter D is studied as a function of chain length N and grafting density \sigma, assuming good solvent conditions. A phenomenological scaling theory, describing the…
We have used the Topological String Theory partition function in the scaling limit, to relate the Black Hole partition function and Topological String Theory partition function.
We equip the categorified quantum group attached to a KLR algebra and an arbitrary choice of scalars with duality functor which is cyclic, that is, such that f=f^** for all 2-morphisms f. This is accomplished via a modified diagrammatic…
For $m=2$ and $m=3$ we prove that any connected, oriented, open manifold $M^m$ admits a simple branched covering map over $\mathbb{R}^m$. When $M$ has $k$ ends and $k$ is finite, the degree of the cover can be taken to be $mk$. Regardless…
The equilibrium partitioning of linear polymer chains into flexible polymer networks is governed by intricate entropic constraints arising from configurational degrees of freedom of both chains and network, yet a quantitative understanding…
The search for a mathematical foundation for the path integral of Euclidean quantum gravity calls for the construction of random geometry on the spacetime manifold. Following developments in physics on the two-dimensional theory, random…
We study universal aspects of polymer conformations and transverse fluctuations for a single swollen chain characterized by a contour length $L$ and a persistence length $\ell_p$ in two dimensions (2D) and in three dimensions (3D) in the…