相关论文: Mining metrics for buried treasure

We analyze the effective content of countable, second countable topological spaces by directly calculating the complexity of several topologically defined index sets. We focus on the separation principles, calibrating an arithmetic…

We give a covariant definition of closeness between (time oriented) Lorentzian metrics on a manifold M, using a family of functions which measure the difference in volume form on one hand and the difference in causal structure relative to a…

We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is…

We introduce a definition for a 'hidden measurement system', i.e., a physical entity for which there exist: (i) 'a set of non-contextual states of the entity under study' and (ii) 'a set of states of the measurement context', and which are…

We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter "power-law" metrics we identify those parameters for which the spacetimes have classical…

One of the most fundamental questions of modern physics is the nature of spacetime. There are various propositions on the table, as the grand unified theory, quantum gravity, supersymmetry, string and superstring theories, and M theory.…

Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…

We investigate structure that describes physical data in gravitational systems that is, to one degree or another, independent of the metric and affine structure. We dub such structure surplus structure and seek to incorporate it into our…

We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…

Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…

Periodic structures are often found in various areas of nanoscience and nanotechnology with many of them being used for metrological purposes either to calibrate instruments, or forming the basis of measuring devices such as encoders.…

We study the quantum cosmology of a flat Friedmann-Lema\^{i}tre-Robertson-Walker universe filled with a (free) massless scalar field and a perfect fluid that represents radiation or a cosmological constant whose value is not fixed by the…

We present a model-theoretic property of finite structures, that can be seen to be a finitary analogue of the well-studied downward L\"owenheim-Skolem property from classical model theory. We call this property as the…

We consider fixed-point equations for probability distributions on isometry classes of measured metric spaces. The construction is required to be recursive and tree-like, but we allow loops for the geodesics between points in the support of…

We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries…

In the standard model of cosmology, the universe is described by a Robertson-Walker spacetime, while its matter/energy content is modeled by a perfect fluid with three components corresponding to matter/dust, radiation and a cosmological…

In order to use quantum devices for computations, it is necessary to understand the intricacies of the theoretical description. To this end, we provide several novel constructions useful for the comprehension of quantum mechanics from the…

We discuss hidden symmetries of M-theory, its feedback on the construction of the M-theory effective action, and a response of the effective action when locality is preserved. In particular, the locality of special symmetries of the…

We explore the features of gravity in its quantum regime in a mathematically rigorous way by carrying out the classical and quantum formulations of some two-Killing symmetry reductions of general relativity which admit an exact…

The \emph{flat deformation theorem} states that given a semi-Riemannian analytic metric $g$ on a manifold, locally there always exists a two-form $F$, a scalar function $c$, and an arbitrarily prescribed scalar constraint depending on the…