Related papers: Parametrization of degenerate density matrices
Cosmological background observations cannot fix the dark energy equation of state, which is related to a degeneracy in the definition of the dark sector components. Here we show that this degeneracy can be broken at perturbation level by…
We propose for the spin density matrix two parametrizations which automatically fulfil the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and…
A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the…
We give a complete structural characterisation of the map the positive branch of a one-way pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition, which is then further analysed…
We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…
We consider the recovery of a low rank $M \times N$ matrix $S$ from its noisy observation $\tilde{S}$ in two different regimes. Under the assumption that $M$ is comparable to $N$, we propose two consistent estimators for $S$. Our analysis…
We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric…
Using the density matrix renormalization group method (DMRG) we calculate the magnetization of frustrated S=1/2 Heisenberg chains for various modulation patterns of the nearest neighbour coupling: commensurate, incommensurate with…
At present the three major unknowns in neutrino oscillation parameters are the mass hierarchy, the octant of $\theta_{23}$ and the CP phase $\delta_{CP}$. It is well known that the presence of hierarchy$-\delta_{CP}$ and octant degeneracies…
We study tridimensional tensors on the complex field from the point of view of hypermatrices, taking into consideration the problem of determining whether they are degenerate or not, concise or not, what is their essential format if they…
We examine the dark energy and matter densities allowed by precision measurements of distances out to various redshifts, in the presence of spatial curvature and (near) arbitrary behavior of the dark energy equation of state. Degeneracies…
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
Degeneracies in the spectrum of an adiabatically transported quantum system are important to determine the geometrical phase factor, and may be interpreted as magnetic monopoles. We investigate the mechanism by which constraints acting on…
The $1/x^{2}$ deformed $c=1$ matrix model is studied at finite radius and non-zero cosmological constant. Calculational techniques are presented and illustrated in some examples. Furthermore, a new kind of $R \rightarrow 1/R$ duality is…
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter…
We give new characterizations for the class of uniformly dense matroids and study applications of these characterizations to graphic and real representable matroids. We show that a matroid is uniformly dense if and only if its base polytope…
This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear…
In systems subject to periodic boundary conditions, Haldane has shown that states at arbitrary filling fraction possess a degeneracy with respect to center of mass translations. An analysis is carried out for multi-component electron…
In this work we consider the Takagi factorization of a matrix valued function depending on parameters. We give smoothness and genericity results and pay particular attention to the concerns caused by having either a singular value equal to…
We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter $\mu_a>0$. We establish observability inequalities for weakly (when…