Related papers: Elliptic mirror of the quantum Hall effect
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
One encounters iterated elliptic integrals in the study of Hall effect devices, as a result of conformal mappings of Schwarz--Christoffel type. Some of these double elliptic integrals possess amazing symmetries with regard to the physical…
The conductance of a two-dimensional electron gas at the transition from one quantum Hall plateau to the next has sample-specific fluctuations as a function of magnetic field and Fermi energy. Here we identify a universal feature of these…
Temperature dependence of the longitudinal and Hall resistance is studied in the regime of localization-delocalization transition. We carry out measurements of a scaling exponent $\kappa$ in the Landau level mixing region at several filling…
Numerical simulations of the evolution of a global topological defect field have two characteristic length scales --- one macrophysical, of order the field correlation length, and the other microphysical, of order the field width. The…
The possibility of having a delocalization transition in the 1D de Moura-Lyra class of models (having a power-spectrum $\propto q^{-\alpha})$ has been the object of a long standing discussion in the literature, filled with ambiguities. In…
Nontrivial bulk topological invariants of quantum materials can leave their signatures on charge, thermal and spin transports. In two dimensions, their imprints can be experimentally measured from well-developed multiterminal Hall bar…
The well-known fact that all elliptic curves are modular, proven by Wiles, Taylor, Breuil, Conrad and Diamond, leaves open the question whether there exists a 'nice' representation of the modular form associated to each elliptic curve. Here…
Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, thes elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the…
The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality…
Generic 2D Hamiltonian systems possess partial barriers in their chaotic phase space that restrict classical transport. Quantum mechanically the transport is suppressed if Planck's constant h is large compared to the classical flux, h >>…
Computer modelling of the integer quantum Hall effect based on self-consistent Hartee-Fock calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of…
Kostant gave a model for the real geometric quantization associated to polarizations via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This model is well-adapted for real polarizations given by…
The moduli space of isometry classes of Riemannian structures on a smooth manifold was emphasized by J.A.Wheeler in his superspace formalism of quantum gravity. A natural question concerning it is: What is a natural topology on such moduli…
A numerical simulation is performed of the gravitational collapse of a spherically symmetric scalar field. The algorithm uses the null initial value formulation of the Einstein-scalar equations, but does {\it not} use adaptive mesh…
We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contribution of the susceptibility of the Ising model for $\, n \le 6$, are operators "associated with elliptic curves". Beyond the…
The jamming transition of particles with finite-range interactions is characterized by a variety of critical phenomena, including power law distributions of marginal contacts. We numerically study a recently proposed simple model of…
The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
We perform numerical simulations of the gravitational collapse of a spherically symmetric scalar field. For those data that just barely do not form black holes we find the maximum curvature at the position of the central observer. We find a…