The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier work). It is illustrated how such coalgebras-on-algebras can be understood as bases, decomposing each element x into primitives elements from which x can be reco...

We describe a universal information compression scheme that compresses any pure quantum i.i.d. source asymptotically to its von Neumann entropy, with no prior knowledge of the structure of the source. We introduce a diagonalisation procedure that enables any classical compression algorithm to be utilised in a quantum context. Our scheme is then based on the corresponding quantum translation of ...

We present a Bayesian scheme for the approximate diagonalisation of several square matrices which are not necessarily symmetric. A Gibbs sampler is derived to simulate samples of the common eigenvectors and the eigenvalues for these matrices. Several synthetic examples are used to illustrate the performance of the proposed Gibbs sampler and we then provide comparisons to several other joint dia...

A Universal Compression scheme is presented, to compress sequences of quantum information from unknown quantum sources (i.e. described by unknown density matrix ρ) asymptotically to S(ρ), with fidelity bounded toward unity. The introduction of a“B-diagonalisation” process allows us to treat the input as if it were diagonal in a known basis B. Applying a version of the Lempel-Ziv algorithm in th...

The molecular (and antimolecular) properties of a large number of intrashell and intershell doubly excited states of C4+ and He are studied. By comparing a number of expectation values using wavefunctions calculated by the truncated diagonalisation method (TDM) and the group theoretic doubly excited symmetry basis (DESB) functions, the origin of the molecular properties of doubly excited states...

We investigate the Laplacian Abelian gauge on the sphere S in the background of a single ‘t Hooft instanton. To this end we solve the eigenvalue problem of the covariant Laplace operator in the adjoint representation. The ground state wave function serves as an auxiliary Higgs field. We find that the ground state is always degenerate and has nodes. Upon diagonalisation, these zeros induce toplo...

It is remarkable how the Fröhlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since ∼ 1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-ana...

A discrete nonlinear system is analysed in case of open chain boundary conditions at the ends. It is shown that the integrability of the system remains intact, by obtaining a modified set of Lax equations which automatically take care of the boundary conditions. The same Lax pair also conforms to the conditions stipulated by Sklyanin [5]. The quantum inverse problem is set up and the diagonalis...

We show how to determine the lowest order mixing of all scalar with twofermion two impurity BMN operators in the antisymmetric representation of SO(4). Differentiation on harmonic superspace allows one to derive two-loop anomalous dimensions of gauge invariant operators from this knowledge: the value for the second anomalous correction to the dimension is essentially the square of the two-fermi...

We have obtained new inelastic neutron scattering (INS) data for the molecular magnet Mn12-acetate which exhibit at least six magnetic peaks in the energy range 5–35meV. These are compared with a microscopic Heisenberg model for the 12 quantum spins localised on the Mn ions, coupled by four inequivalent magnetic exchange constants. A fit to the magnetic susceptibility under the constraint that ...