Properties of a discretized coherent state representation (DCSR) and its connection to Gabor frame analysis are discussed. The DCSR approach was recently shown (Andersson L M 2001 J. Chem. Phys. 115 1158) to yield a practical computational scheme for quantum dynamics, and an iterative scheme for finding the identity operator was proposed. In the present work, we suggest a proof of fast convergence of the iterative scheme for computing the canonical dual to any given countable frame in a Hilbert space. The method of frames is concerned with the use of a non-orthogonal, over-complete set of functions for expansion of an arbitrary function. We also introduce the concept of 'representations of the identity operator' and show how to expand arbitrary vectors using the frame elements, without explicit diagonalization to an orthonormal basis. Numerical examples that illustrate the method are shown.

2. Faddeev, Ludwig D.

et al.

Freyhult, Lisa

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.

Niemi, Antti J.

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.

Rajan, Peter

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.

Shafranov's virial theorem implies that nontrivial magnetohydrodynamical equilibrium configurations must be supported by externally supplied currents. Here we extend the virial theorem to field theory, where it relates to Derrick's scaling argument on soliton stability. We then employ virial arguments to investigate a realistic field theory model of a two-component plasma, and conclude that stable localized solitons can exist in the bulk of a finite density plasma. These solitons entail a nontrivial electric field, which implies that purely magnetohydrodynamical arguments are insufficient for describing stable, nontrivial structures within the bulk of a plasma.

Two chiral aspects of the SL(2,R) WZW model in an operator formalism are investigated. First, the meaning of duality, or conjugation, of primary fields is clarified. On a class of modules obtained from the discrete series it is shown, by looking at spaces of two-point conformal blocks, that a natural definition of contragredient module provides a suitable notion of conjugation of primary fields, consistent with known two-point functions. We find strong indications that an apparent contradiction with the Clebsch-Gordan series of SL(2,R), and proposed fusion rules, is explained by nonsemisimplicity of a certain category. Second, results indicating an infinite cyclic simple current group, corresponding to spectral flow automorphisms, are presented. In particular, the subgroup corresponding to even spectral flow provides part of a hypothetical extended chiral algebra resulting in proposed modular invariant bulk spectra.

New symmetries of the chiral Potts model2012In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 45Article in journal (Refereed)

Abstract [en]

In this paper a hithertho unknown symmetry of the three-state chiral Potts model is found consisting of two coupled Temperley-Lieb algebras. From these we can construct new superintegrable models. One realisation is in terms of a staggered isotropic XY spin chain. Further we investigate the importance of the algebra for the existence of mutually commuting charges. This leads us to a natural generalisation of the boost-operator, which generates the charges.

In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase (2004 J. Phys. A: Math. Gen.37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions.

Previously, it has been shown that in a spin-charge separated SU(2) Yang– Mills theory, (Euclidean) spacetime rotation invariance can be broken by an inﬁnitesimal 1-cocycle that appears in the S O(4) boosts. Here we study in detail the structure of this 1-cocycle. In particular, we show that its non- triviality relates to the presence of a (Dirac) magnetic monopole bundle. We also compute the ﬁnite version of the cocycle.

It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions (Fu L-B and Chen J-L 2004 J. Phys. A: Math. Gen.37 3699) is gauge dependent.

Berry phases and quantum fidelities for interacting spins have attracted considerable attention, particularly in relation to entanglement properties of spin systems and quantum phase transitions. These efforts mainly focus either on spin pairs or the thermodynamic infinite spin limit, while studies of the multi-partite case of a finite number of spins are rare. Here we analyze Berry phases and quantum fidelities of the ground state of a Lipkin–Meshkov–Glick model consisting of three spin-1/2 particles (qubits). We find explicit expressions for the Berry phase and fidelity susceptibility of the full system as well as the mixed-state Berry phase and partial-state fidelity susceptibility of its one- and two-qubit subsystems. We demonstrate a realization of a nontrivial magnetic monopole structure associated with local, coordinated rotations of the three-qubit system around the external magnetic field.

We are interested in a gauge invariant coupling between four dimensional Yang-Mills ﬁeld and a three brane that can ﬂuctuate into higher dimensions. For this we interpret the Yang-Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge ﬁeld in a manner that displays the original gauge symmetry as an isometry. The brane moves in this higher dimensional space-time under the inﬂuence of its bulk gravity, with dynamics determined by the Nambu action. This introduces the desired interaction between the brane and the gauge ﬁeld in a way that preserves the original gauge invariance as an isometry of the induced metric. After a prudent change of variables the result can be interpreted as a gauge invariant and massive vector ﬁeld that propagates in the original space-time R4 : The presence of the brane becomes entirely invisible, except for the mass.We are interested in a gauge invariant coupling between four dimensional Yang-Mills ﬁeld and a three brane that can ﬂuctuate into higher dimensions. For this we interpret the Yang-Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge ﬁeld in a manner that displays the original gauge symmetry as an isometry. The brane moves in this higher dimensional space-time under the inﬂuence of its bulk gravity, with dynamics determined by the Nambu action. This introduces the desired interaction between the brane and the gauge ﬁeld in a way that preserves the original gauge invariance as an isometry of the induced metric. After a prudent change of variables the result can be interpreted as a gauge invariant and massive vector ﬁeld that propagates in the original space-time R4 : The presence of the brane becomes entirely invisible, except for the mass.