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The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
Quantum entanglement does not necessarily imply Einstein-Podolsky-Rosen steering. We identify a \emph{boundary mechanism} that closes this gap when an entangled state meets the boundary of the trusted state space in a nondegenerate way. The…
Identifying structural parameters in linear simultaneous-equation models is a longstanding challenge. Recent work exploits information in higher-order moments of non-Gaussian data. In this literature, the structural errors are typically…
Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal…
Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $\gamma $ were introduced recently which measure the non-homogeneity of…
The complexity of a well-quasi-order (wqo) can be measured through three ordinal invariants: the width as a measure of antichains, height as a measure of chains, and maximal order type as a measure of bad sequences. We study these ordinal…
We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some…
We present the attempt to study the problem of the estimates of higher-order perturbative corrections to physical quantities in the Euclidean region. Our considerations are based on the application of the scheme-invariant methods, namely…
We propose to use quantized Berry phases as local order parameters of gapped quantum liquids, which are invariant under some anti-unitary operation. After presenting a general prescription, the scheme is applied for Heisenberg models with…
We study the 2D Ginzburg-Landau theory for a type-II superconductor in an applied magnetic field varying between the second and third critical value. In this regime the order parameter minimizing the GL energy is concentrated along the…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
Molecular simulations as well as single molecule experiments have been widely analyzed in terms order parameters, the latter representing candidate probes for the relevant degrees of freedom. Notwithstanding this approach is very intuitive,…
In the weak disordered regime we provide analytical expressions for the electron localization lengths in quasi-one dimensional (Q1D) disordered quantum wire with hard wall and periodic boundary conditions. They are exact up to order $W^2$…
We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an…
In Ginzburg-Landau Theory of superconductivity, the density and location of the superconducting electrons are measured by a complex-valued wave function, the order parameter. In this paper, when the intensity of the applied magnetic field…
Novelty in materials discovery requires candidates to be distinct, non-redundant, and thermodynamically plausible. While crystallographic databases continue to expand in both size and complexity, making efficient and reliable novelty…
In perturbative quantum field theory one encounters certain, very specific geometries over the integers. These perturbative quantum geometries determine the number contents of the amplitude considered. In the article `Modular forms in…
Machine learning methods are being explored in many areas of science, with the aim of finding solution to problems that evade traditional scientific approaches due to their complexity. In general, an order parameter capable of identifying…
Recent diffraction experiments on metallic glasses have unveiled an unexpected non-cubic scaling law between density and average interatomic distance, which lead to the speculations on the presence of fractal glass order. Using X-ray…
Geometrically nontrivial quantum states can be defined as states that cannot be prepared by a constant depth geometrically local unitary circuit starting from a product state. However, for topological phases, as well as a large class of…