Related papers: Parametrization of degenerate density matrices

One studies certain degenerations of the generic square matrix over a field $k$ along with its main related structures, such as the determinant of the matrix, the ideal generated by its partial derivatives, the polar map defined by these…

Degeneracies near the real axis in a complex-extended parameter space of a hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in…

Degeneracies in the energy spectra of physical systems are commonly considered to be either of accidental character or induced by symmetries of the Hamiltonian. We develop an approach to explain degeneracies by tracing them back to…

This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces…

In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian…

We consider the problem of recovering a unitary eigendecomposition of a complex unitary matrix from that of its embedded real-valued formulation. Such formulations arise naturally in scientific computing workflows that employ…

The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…

We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape design. While one-dimensional degenerate models have been…

Permutation symmetries of multipartite quantum states are defined only when the constituent subsystems are of equal dimensions. In this work we extend this notion of permutation symmetry to heterogeneous systems, that is, systems composed…

We study the renormalization of normal mixing matrices, which includes hermitian and unitary matrices as particular cases. We give a minimal, multiplicative parametrization of counterterms, and compute the renormalized Lagrangian to…

The standard cold dark matter cosmological model, while successful in explaining the observed large scale structure of the Universe, tends to overpredict structure on small scales. It has been proposed this problem may be alleviated in a…

While dealing with the nontrivial task of classifying Mueller matrices, of special interest is the study of the degenerate Mueller matrices (matrices with vanishing determinant, for which the law of multiplication holds, but there exists no…

In this paper we construct coherent states for the two-dimensional Morse potential. We find the dependence of the spectrum on the physical parameters and use this to understand the emergence of accidental degeneracies. It is observed that,…

We revisit the dark degeneracy that arises from the Einstein equations relating geometry to the total cosmic substratum but not resolving its individual components separately. We establish the explicit conditions for the dark degeneracy in…

Spectral projectors of Hermitian matrices play a key role in many applications, and especially in electronic structure computations. Linear scaling methods for gapped systems are based on the fact that these special matrix functions are…

This paper deals with a unifying approach to the problems of computing the admissible sets of parametrical multi perturbations in appropriate bounded sets such that some fundamental properties of parameter-varying linear dynamic systems are…

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. This representation is based upon a triangular matrix of transition rates. We expand the state vector of mass multiplicities, which…

Tensors are often studied by introducing preorders such as restriction and degeneration: the former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local…

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…

In this paper, we introduce properly-invariant diagonality measures of Hermitian positive-definite matrices. These diagonality measures are defined as distances or divergences between a given positive-definite matrix and its diagonal part.…