# Thermal Excitations of Warped Membranes

 Title: Thermal Excitations of Warped Membranes Author: Kosmrlj, Andrej; Nelson, David R. Note: Order does not necessarily reflect citation order of authors. Citation: Kosmrlj, Andrej, and David R. Nelson. 2014. "Thermal Excitations of Warped Membranes." Physical Review E 89 (2): 022126. Full Text & Related Files: 1312.4089v1.pdf (232.9Kb; PDF) Abstract: We explore thermal fluctuations of thin planar membranes with a frozen spatially varying background metric and a shear modulus. We focus on a special class of D-dimensional “warped membranes” embedded in a d-dimensional space with d≥D+1 and a preferred height profile characterized by quenched random Gaussian variables $$\{h_\alpha(q)\}$$, $$\alpha=D+1,...,d$$, in Fourier space with zero mean and a power-law variance $$\over{h\alpha(q_1)h_\beta(q_2)}$$ $$\sim \delta_{\alpha,\beta} \delta_{q_1,−q_2} q_1^{-d_h}$$. The case D=2, d=3, with $$d_h=4$$ could be realized by flash-polymerizing lyotropic smectic liquid crystals. For $$D\lt max\{4,d_h\}$$ the elastic constants are nontrivially renormalized and become scale dependent. Via a self-consistent screening approximation we find that the renormalized bending rigidity increases for small wave vectors q as $$\kappa_R \sim q^{−\eta_f}$$, while the in-hyperplane elastic constants decrease according to $$\lambda_R, \mu_R \sim q^{+\eta_u}$$. The quenched background metric is relevant (irrelevant) for warped membranes characterized by exponent $$d_h\gt 4−\eta^{(F)}_f (d_h\lt 4−\eta ^{(F)}_f)$$, where $$\eta^{(F)}_f$$ is the scaling exponent for tethered surfaces with a flat background metric, and the scaling exponents are related through $$\eta_u+\eta_f=d_h−D (\eta_u+2\eta_f=4−D)$$. Published Version: doi:10.1103/PhysRevE.89.022126 Other Sources: http://arxiv.org/pdf/1312.4089v1.pdf Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:13457872 Downloads of this work: