Related papers: Fuzzy spaces, the M(atrix) model and the quantum H…
We explore a new way to simulate quantum field theory, without introducing a spatial lattice. As a pilot study we apply this method to the 3d \lambda \phi^4 model. The regularisation consists of a fuzzy sphere with radius R for the two…
Quantum-gravity effects may introduce relevant consequences for the propagation and interaction of high energy cosmic rays particles. Assuming the space-time foamy structure results in an intrinsic uncertainty of energy and momentum of…
The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic…
We show that fuzzy spheres are solutions of ${\it Lorentzian}$ IKKT matrix models. The fuzzy sphere solutions serve as toy models of closed noncommutative cosmologies where big bang/crunch singularities appear only after taking the…
We review recent literature on the connection between quantum entanglement and cosmology, with an emphasis on the context of expanding universes. We discuss recent theoretical results reporting on the production of entanglement in quantum…
Quantum entanglement is closely related to the structure of spacetime in quantum gravity. For quantum field theories or statistical models, we usually consider base space entanglement. However, target space instead of base space sometimes…
To probe the nature of the even-fraction quantum Hall system, we have investigated the low-lying excitation spectrum by means of exact diagonalization for finite systems. We have found (i) a striking one-to-one correspondence (i.e., a shell…
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…
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…
The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides…
We describe how a model of effective interactions between quantum fluctuations under certain assumptions can be constructed in a way so that the large-scale limit gives an effective theory that matches general relativity in vacuum regions.…
We consider the quantum computational process as viewed by an insider observer: this is equivalent to an isomorphism between the quantum computer and a quantum space, namely the fuzzy sphere. The result is the formulation of a reversible…
We present here a complete microscopic theory of a family of neutral excitations in the fractional quantum Hall fluids, related to the geometric fluctuations of the quantum Hall ground states. Many of the physical properties of such…
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of…
Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1/3 liquid directly by resonant inelastic light…
This paper is concerned with the study of fuzzy dynamical systems. Let (X;M; *) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map defined on X. We…
A two dimensional array of Josephson junctions in a magnetic field is considered. It is shown that the dynamics of the vortices in the array resembles that of electrons on a two--dimensional lattice put in a magnetic field perpendicular to…
We present a theory of composite fermion edge states and their transport properties in the fractional and integer quantum Hall regimes. We show that the effective electro-chemical potentials of composite fermions at the edges of a Hall bar…
The fractional quantum Hall effect has been considered as a puzzling quantum many-body phenomenon that has yet to be fully explained. The plateau width and excitation energy gap are particularly problematic. We report here that those two…
The article demonstrates the nontrivial manifestation of quantum shell effects in a compressed mesoscopic system. It is shown that there are two spatial scales in the distribution of degenerate electrons in a spherical well. The first scale…