arXiv subjects

Jon Magne Leinaas

Publications and source records attributed to Jon Magne Leinaas.

24 records · Page 2Linked to original sources

arXiv1998

Accelerated Electrons and the Unruh Effect

Quantum effects for electrons in a storage ring are studied in a co-moving, accelerated frame. The polarization effect due to spin flip synchrotron radiation is examined by treating the electron as a simple quantum mechanical two-level system coupled to the orbital motion and to the radiation field. The excitations of the spin system are related to the Unruh effect, i.e. the effect that an accelerated radiation detector is thermally excited by vacuum fluctuations. The importance of orbital fluctuations is pointed out and the vertical fluctuations are examined.

hep-th↗

arXiv1997

Bulk and edge properties of the Chern-Simons Ginzburg-Landau theory for the fractional quantum Hall effect

The Chern-Simons Ginzburg-Landau theory for the fractional Quantum Hall effect is studied in the presence of a confining potential. We review the bulk properties of the model and discuss how the plateau formation emerges without any impurity potential. The effect is related to changes, by accumulation of charge, at the edge when the chemical potential is changed. Fluctuations about the ground state are examined and an expression is found for the velocity of the massless edge mode in terms of the confining potential. The effect of including spin is examined for the case when the system is fully polarized in the bulk. In general a spin texture may appear at the edge, and we examine this effect in the case of a small spin down component. The low frequency edge modes are examined and a third order equation is found for velocities which indicates the presence of three different modes. The discussions are illustrated by numerical studies of the ground states, both for the one- and two-component cases.

cond-mat.mes-hall↗

arXiv1997

Algebra of Observables for Identical Particles in One Dimension

The algebra of observables for identical particles on a line is formulated starting from postulated basic commutation relations. A realization of this algebra in the Calogero model was previously known. New realizations are presented here in terms of differentiation operators and in terms of SU(N)-invariant observables of the Hermitian matrix models. Some particular structure properties of the algebra are briefly discussed.

hep-th↗

arXiv1996

Generalized statistics and the algebra of observables

A short review is given of how to apply the algebraic Heisenberg quantization scheme to a system of identical particles. For two particles in one dimension the approach leads to a generalization of the Bose and Fermi description which can be expressed in the form of a 1/x^2 statistics interaction between the particles. For an N-particle system it is shown how a particular infinite-dimensional algebra arises as a generalization of the su(1,1) algebra which is present for the two-particle system.

hep-th↗

arXiv1996

On the anyon description of the Laughlin hole states

We examine the anyon representation of the Laughlin quasi-holes, in particular the one-dimensional, algebraic aspects of the representation. For the cases of one and two quasi-holes an explicit mapping to anyon systems is given, and the connection between the hole-states and coherent states of the fundamental algebras of observables is examined. The quasi-electron case is discussed more briefly, and some remaining questions are pointed out.

cond-mat↗

arXiv1995

Algebra of one-particle operators for the Calogero model

An algebra ${\cal G}$ of symmetric {\em one-particle} operators is constructed for the Calogero model. This is an infinite-dimensional Lie-algebra, which is independent of the interaction parameter $λ$ of the model. It is constructed in terms of symmetric polynomials of raising and lowering operators which satisfy the commutation relations of the $S_N$-{\em extended} Heisenberg algebra. We interpret ${\cal G}$ as the algebra of observables for a system of identical particles on a line. The parameter $λ$, which characterizes (a class of) irreducible representations of the algebra, is interpreted as a statistics parameter for the identical particles.

hep-th↗