Fermion Mapping for Orthogonal and Symplectic Ensembles
The circular orthogonal and circular symplectic ensembles are mapped onto free, non-hermitian fermion systems. As an illustration, the two-level form factors are calculated.
cond-mat.dis-nn↗
arXiv subjects
M. B. Hastings
Publications and source records attributed to M. B. Hastings.
Bragg resonances for tunneling between edges of a 2D Quantum Hall system
A theory is presented for tunneling between compressible regions on the sides of a narrow incompressible Quantum Hall strip. Assuming that electron interactions lead to formation of a Wigner crystal on the edges of the compressible regions, we consider the situation when the non-conservation of electron momentum required for transport is provided, in the absence of disorder, by umklapp scattering on the crystal. The momentum given to the crystal is quantized due to the Bragg condition, which leads to resonances in tunneling conductivity as a function of the incompressible strip width, similar to those reported recently by N. Zhitenev, M. Brodsky, R. Ashoori, and M. Melloch.
cond-mat↗
Laplacian growth as one-dimensional turbulence
A new model of Laplacian stochastic growth is formulated using conformal mappings. The model describes two growth regimes, stable and turbulent, separated by a sharp phase transition. The first few Fourier components of the mapping define the web, an envelope of the cluster. The web is used to study the transition and the dynamics of large-scale features of the cluster characterized by evolution from macro- to micro-scales. Also, we derive scaling laws for the cluster size.
cond-mat↗