相关论文: Linear Parameters and the Decoupling Matrix for Li…
Explicit separability of general two qubits density matrices is related to Lorentz transformations. We use the 4-dimensional form R(u,v=0,1,2,3) of the Hilbert-Schmidt (HS) decomposition of the density matrix. For the generic case in which…
Over the next decade, improvements in cosmological parameter constraints will be driven by surveys of large-scale structure. Its inherent non-linearity suggests that significant information will be embedded in higher correlations beyond the…
We propose a simple mathematical model that describes a pairing-induced motion of active and passive particles in a two-dimensional system, which is motivated by our previous paper [Ishikawa et al., Phys. Rev. E \textbf{106} (2022) 024604].…
In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple…
We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement…
Based on the partition of parameter space, two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Unlike the rational univariate representation of…
The continuous phase transition, indicated by the macroscopic order parameter and the occurrence of the spontaneous symmetry breaking, is well illustrated based on the Ginzburg-Landau's paradigm. In systems described by one order parameter,…
We consider a hierarchy of the natural type Hamiltonian systems of $n$ degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. We give a Lax representation in terms of $2\times 2$…
The transition matrix elements between the correlated $N$ and $N\!+\!1$ electron states of a quantum dot are calculated by numerical diagonalization. They are the central ingredient for the linear and non--linear transport properties which…
I present a new formalism of the R-matrix theory where the formal parameters for the resonance energies and widths are identical to the observed values. By allowing the boundary condition parameters to vary from level to level, the freedom…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…
This paper presents a parametrization of a degenerate density matrix. The problem needs to be approached first with a diagonalized form (the spectral representation) to deal with degeneracy. Such a form is useful for this parametrization in…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
Assume we are given a sum of linear measurements of $s$ different rank-$r$ matrices of the form $y = \sum_{k=1}^{s} \mathcal{A}_k ({X}_k)$. When and under which conditions is it possible to extract (demix) the individual matrices ${X}_k$…
A promising step from linear towards nonlinear data-driven control is via the design of controllers for linear parameter-varying (LPV) systems, which are linear systems whose parameters are varying along a measurable scheduling signal.…
Recent progress in understanding the physics of magnetic reconnection is conveniently summarized in terms of a phase diagram which organizes the essential dynamics for a wide variety of applications in heliophysics, laboratory and…
Time-dependent quantities are calculated in the linear response limit for a correlated one dimensional model atom driven by an external quadrupolar time-dependent field. Besides the analysis of the time-evolving energy change in the…
Modeling matrix-valued time series is an interesting and important research topic. In this paper, we extend the method of Chang et al. (2017) to matrix-valued time series. For any given $p\times q$ matrix-valued time series, we look for…
Two distinct systems of commutative complex numbers in 6 dimensions of the polar and planar types of the form u=x_0+h_1x_1+h_2x_2+h_3x_3+h_4x_4+h_5x_5 are described in this work, where the variables x_0, x_1, x_2, x_3, x_4, x_5 are real…