Related papers: Hyper-sparsity of the density matrix in a wavelet …
To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the $\textit{flat-sky approximation}$ has been sufficiently satisfied. However, with Stage IV surveys ($\textit{e.g. LSST}$ and…
Context. Galaxy cluster masses are usually defined as the mass within a spherical region enclosing a given matter overdensity (in units of the critical density). Converting masses from one overdensity definition to another can have several…
We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models.…
Carpet-type structures constitute an ideal laboratory to study and analyze the robustness of the interference process that underlies this phenomenon against the harmful effects of decoherence. Here, without losing any generality, for…
At early times dark matter has a thermal velocity dispersion of unknown amplitude which, for warm dark matter models, can influence the formation of nonlinear structure on observable scales. We propose a new scheme to simulate cosmologies…
Decoherence phenomena are pervasive in the arena of nanostructures but perhaps even more so in the study of the fundamentals of quantum mechanics and quantum computation. Since there has been little overlap between the studies in both…
We present an analytical study of the spatial decay rate $\gamma$ of the one-particle density matrix $\rho(\vec r,\vec r')\sim\exp(-\gamma|\vec r-\vec r'|)$ for systems described by single particle orbitals in periodic potentials in…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
We introduce matrix quantum phase-space distributions. These extend the idea of a quantum phase-space representation via projections onto a density matrix of global symmetry variables. The method is applied to verification of low-loss…
We examine the reduced density matrix of the centre of mass on position basis considering a one-dimensional system of $N$ non-interacting distinguishable particles in a infinitely deep square potential well. We find a class of pure states…
A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
By absorbing fluctuations into a local background, separate universe simulations provide a powerful technique to characterize the response of small-scale observables to the long-wavelength density fluctuations, for example those of the…
We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite…
With the aim of measuring the sparsity of a real signal, Donoho and Logan introduced the concept of maximum Nyquist density, and used it to extend Bombieri's principle of the large sieve to bandlimited functions. This led to several…
Scattering-type scanning near-field optical microscopy is a powerful imaging technique for studying materials beyond the diffraction limit. However, interpreting near-field measurements poses challenges in mapping the response of…
We derive and analyze a hierarchy of approximations to the strongly correlated limit of the Hohenberg-Kohn functional. These "density representability approximations" are obtained by first noting that in the strongly correlated limit,…
We introduce a novel application of the Hartmann sensor, traditionally designed for wavefront sensing, to measure the coherence properties of optical signals. By drawing an analogy between the coherence matrix and the density matrix of a…
Dark matter is theorised to form massive haloes, which could be further condensed into so-called spikes when a black hole grows at the centre of such a halo. The existence of these spikes is instrumental for several dark matter detection…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…