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A. Sudbery

Publications and source records attributed to A. Sudbery.

10 recordsLinked to original sources
arXiv2010

Entanglement and density-functional theory: testing approximations on Hooke's atom

We present two methods of calculating the spatial entanglement of an interacting electron system within the framework of density-functional theory. These methods are tested on the model system of Hooke's atom for which the spatial entanglement can be calculated exactly. We analyse how the strength of the confining potential affects the spatial entanglement and how accurately the methods that we introduced reproduce the exact trends. We also compare the results with the outcomes of standard first-order perturbation methods. The accuracies of energies and densities when using these methods are also considered.

quant-ph↗
arXiv2008

Quantum supergroups of $GL(n|m)$ type: differential forms, Koszul complexes and Berezinians

We introduce and study the Koszul complex for a Hecke $R$-matrix. Its cohomologies, called the Berezinian, are used to define quantum superdeterminant for a Hecke $R$-matrix. Their behaviour with respect to Hecke sum of $R$-matrices is studied. Given a Hecke $R$-matrix in $n$-dimensional vector space, we construct a Hecke $R$-matrix in $2n$-dimensional vector space commuting with a differential. The notion of a quantum differential supergroup is derived. Its algebra of functions is a differential coquasitriangular Hopf algebra, having the usual algebra of differential forms as a quotient. Examples of superdeterminants related to these algebras are calculated. Several remarks about Woronowicz's theory are made.

hep-th↗
arXiv2002

Multipartite generalisation of the Schmidt decomposition

We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For identical particles they are invariant under permutations of the particles. As an application, we find the dimension of the generic local equivalence class.

quant-ph↗
arXiv2002

Magic Squares of Lie Algebras

An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.

math.RA↗
arXiv2000

How entangled can two couples get?

We describe a pure state of four qubits whose single-qubit density matrices are all maximally mixed and whose average entanglement as a system of two pairs of qubits appears to be maximal.

quant-ph↗
arXiv1998

Representations of the Generalized Lie Algebra sl(2)_q

We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra $\ssll (2)_q$ introduced by Lyubashenko and the second named author. We consider separately the cases of $q$ generic and $q$ at roots of unity. Some of the representations have no classical analog even for generic $q$. Some of the representations have no analog to the finite-dimensional representations of the quantised enveloping algebra $U_q(sl(2))$, while in those that do there are different matrix elements.

math.QA↗
arXiv1998

Non-local properties of multi-particle density matrices

As far as entanglement is concerned, two density matrices of $n$ particles are equivalent if they are on the same orbit of the group of local unitary transformations, $U(d_1)\times...\times U(d_n)$ (where the Hilbert space of particle $r$ has dimension $d_r$). We show that for $n$ greater than or equal to two, the number of independent parameters needed to specify an $n$-particle density matrix up to equivalence is $Π_r d_r^2 - \sum_r d_r^2 + n - 1$. For $n$ spin-${1\over 2}$ particles we also show how to characterise generic orbits, both by giving an explicit parametrisation of the orbits and by finding a finite set of polynomial invariants which separate the orbits.

quant-ph↗
arXiv1995

Yangian Construction of the Virasoro Algebra

We show that a Yangian construction based on the algebra of an infinite number of harmonic oscillators (i.e. a vibrating string) terminates after one step, yielding the Virasoro algebra.

q-alg↗
arXiv1994

The quantum orthogonal mystery

This is (hopefully) a Latexable version of a talk given at the XXX Winter School in Theoretical Physics at Karpacz in February 1994. It discusses the use of non-commutative differential calculus to construct a Lie algebra of a quantum group. Usually the result has a different dimension from the classical Lie algebra. This is illustrated by menas of the orthogonal quantum group, and various other possible ways of constructing an orthogonal Lie algebra are described.

hep-th↗