arXiv subjects

J. -C. Wallet

Publications and source records attributed to J. -C. Wallet.

7 recordsLinked to original sources

arXiv2018

$κ$-Poincaré invariant quantum field theories with KMS weight

A natural star product for 4-d $κ$-Minkowski space is used to investigate various classes of $κ$-Poincaré invariant scalar field theories with quartic interactions whose commutative limit coincides with the usual $ϕ^4$ theory. $κ$-Poincaré invariance forces the integral involved in the actions to be a twisted trace, thus defining a KMS weight for the noncommutative (C*-)algebra modeling the $κ$-Minkowski space. The associated modular group and Tomita modular operator are characterized. In all the field theories, the twist generates different planar one-loop contributions to the 2-point function which are at most UV linearly diverging. Some of these theories are free of UV/IR mixing. In the others, UV/IR mixing shows up in non-planar contributions to the 2-point function as a polynomial singularity at exceptional zero external momenta while staying finite at non-zero external momenta. These results are discussed together with the possibility for the KMS weight relative to the quantum space algebra to trigger the appearance of KMS state on the algebra of observables.

hep-th↗

arXiv2004

Quantum Hall Conductivity in a Landau Type Model with a Realistic Geometry II

We use a mathematical framework that we introduced in a previous paper to study geometrical and quantum mechanical aspects of a Hall system with finite size and general boundary conditions. Geometrical structures control possibly the integral or fractionnal quantization of the Hall conductivity depending on the value of $NB/2π$ ($N$ is the number of charge carriers and $B$ is the magnetic field). When $NB/2π$ is irrationnal, we show that monovalued wave functions can be constructed only on the graph of a free group with two generators. When $NB/2π$ is rationnal, the relevant space becomes a puncturated Riemann surface. We finally discuss our results from a phenomenological viewpoint.

cond-mat.mes-hall↗

arXiv2003

Quantum Hall Conductivity in a Landau Type Model with a Realistic Geometry

In this paper, we revisit some quantum mechanical aspects related to the Quantum Hall Effect. We consider a Landau type model, paying a special attention to the experimental and geometrical features of Quantum Hall experiments. The resulting formalism is then used to compute explicitely the Hall conductivity from a Kubo formula.

cond-mat.mes-hall↗

arXiv2000

Self-duality in Maxwell-Chern-Simons theories with non minimal coupling with field

We consider a general class of non-local MCS models whose usual minimal coupling to a conserved current is supplemented with a (non-minimal) magnetic Pauli-type coupling. We find that the considered models exhibit a self-duality whenever the magnetic coupling constant reaches a special value: the partition function is invariant under a set of transformations among the parameter space (the duality transformations) while the original action and its dual counterpart have the same form. The duality transformations have a structure similar to the one underlying self-duality of the (2+1)-dimensional Zn-abelian Higgs model with Chern-Simons and bare mass term.

cond-mat.mes-hall↗

arXiv1999

Visibility diagrams and experimental stripe structure in the quantum Hall effect

We analyze various properties of the visibility diagrams that can be used in the context of modular symmetries and confront them to some recent experimental developments in the Quantum Hall Effect. We show that a suitable physical interpretation of the visibility diagrams which permits one to describe successfully the observed architecture of the Quantum Hall states gives rise naturally to a stripe structure reproducing some of the experimental features that have been observed in the study of the quantum fluctuations of the Hall conductance. Furthermore, we exhibit new properties of the visibility diagrams stemming from the structure of subgroups of the full modular group.

cond-mat.mes-hall↗

arXiv1999

$Γ(2)$ modular symmetry, renormalization, group flow and the quantum Hall effect

We construct a family of holomorphic $β$-functions whose RG flow preserves the $Γ(2)$ modular symmetry and reproduces the observed stability of the Hall plateaus. The semi-circle law relating the longitudinal and Hall conductivities that has been observed experimentally is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules encoded in the flow diagram. The generic scale dependance of the conductivities is found to agree qualitatively with the present experimental data. The existence of a crossing point occuring in the crossover of the permitted transitions is discussed.

cond-mat.mes-hall↗

arXiv1995

Linear Connections on the Two Parameter Quantum Plane

We apply a recently proposed definition of a linear connection in non commutative geometry based on the natural bimodule structure of the algebra of differential forms to the case of the two-parameter quantum plane. We find that there exists a non trivial family of linear connections only when the two parameters obeys a specific relation.

q-alg↗