Related papers: (4+1)-Dimensional Quantum Hall Effect & Applicatio…
The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic…
The problem of unification of Gravitation and Electromagnetism in four dimensions; some new ideas involving mixtures of commuting and anti-commuting co-ordinates. Maxwell's equations are extracted in terms of the curvature of the…
The recent model of Quantum Mechanical Black Holes is discussed and its implications for cosmology, particle structure, low dimensionality and other issues are examined.
We study the possible phase transitions between (2+1)-dimensional abelian Chern-Simons theories. We show that they may be described by non-unitary rational conformal field theories with c_eff = 1. As an example we choose the fractional…
The basic problem of quantum cosmology is the definition of the quantum state of the universe, with appropriate boundary conditions on Riemannian three-geometries. This paper describes recent progress in the corresponding analysis of…
Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex $\mathrm{SL}(2,\mathbb{C})$ Chern-Simons theory we include a cosmological…
We construct higher dimensional quantum Hall systems based on fuzzy spheres. It is shown that fuzzy spheres are realized as spheres in colored monopole backgrounds. The space noncommutativity is related to higher spins which is originated…
Recently by us was proposed the model where Einstein's equation on the brane was connected with Maxwell's multi-dimensional equations in pseudo-Euclidean space. Based on this idea unification of 4-dimensional gravity and electromagnetism in…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
We study theoretically the parallel quantum wires of the experiment by Auslaender et al. [Science 308, 88 (2005)] at low electron density. It is shown that a Hall effect as observed in two- or three-dimensional electron systems develops as…
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise…
We construct a generalization of the quantum Hall effect where particles move in an eight dimensional space under an SO(8) gauge field. The underlying mathematics of this particle liquid is that of the last normed division algebra, the…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
We apply the background field method and the effective action formalism to describe the four-dimensional dynamical Casimir effect. Our picture corresponds to the consideration of quantum cosmology for an expanding FRW universe (the boundary…
In this contribution, we present an introduction to the physical principles underlying the quantum Hall effect. The field theoretic approach to the integral and fractional effect is sketched, with some emphasis on the mechanism of…
In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects,…
The Laughlin function of quantum Hall effect is shown to satisfy Hirota's bilinear difference equation with certain coefficients a little different from the KP hierarchy. Vertex operators which constitute blocks of solutions generate a…
We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological…