相关论文: Theoretical foundations of nonlinear electromagnet…

This paper investigates nonlinear bending and buckling behaviours of composite plates characterized by a thickness variation. Layer interfaces are described as functions of inplane coordinates. Top and bottom surfaces of the plate are…

We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry…

A two dimensional Finsler space associated with the differential equation $y''=Y_3 y'^3+Y_2 y'^2+Y_1 y'+Y_0$ is characterized by a tensor equation and called the Douglas space. An application to the Lorenz nonlinear dynamical equation is…

We study an observable-based notion of equilibration and its application to realistic systems like spin qubits in quantum dots. On the basis of the so-called distinguishability, we analytically derive general equilibration bounds, which we…

We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated…

Robotics research has found numerous important applications of Riemannian geometry. Despite that, the concept remain challenging to many roboticists because the background material is complex and strikingly foreign. Beyond {\em Riemannian}…

Two entangled electron spins, or qubits, are analyzed in terms of ordinary three-dimensional space geometric properties, as are the angles between their angular momenta. This formulation allows concurrence, a measure of quantum…

A quantum kinetic theory of the linear response to an electric field is provided from a controlled expansion of the Keldysh theory at leading order, for a multiband electron system with weak scalar disorder. The response is uniquely…

In 1933-1934 Born and Infeld constructed the first non-linear generalization of Maxwell's electrodynamics that turned out to be a remarkable theory in many respects. In 1935 Heisenberg and Euler computed a complete effective action…

Entanglement is generally considered necessary for achieving the Heisenberg limit in quantum metrology. We construct analogues of Dicke and GHZ states on a single $N+1$ dimensional qudit that achieve precision equivalent to symmetrically…

Nonlinear eigenvalue equations arise naturally in quantum information theory, particularly in the variational quantification of entanglement. In this work, we present a hybrid analytical and numerical framework for evaluating the geometric…

We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…

A theoretical framework bridging General Relativity (GR) and Quantum Dynamics (QD) is introduced through the application of Kripke semantics and linear logic. While conventional unification efforts often rely on structural or geometrical…

Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a…

Entanglement is one of the most fascinating concepts of modern physics. In striking contrast to its abstract, mathematical foundation, its practical side is, however, remarkably underdeveloped. Even for systems of just two orbitals or sites…

In quantum many-body problems, one of the main difficulties comes from the description of non-negligible interactions which require, at least in principle, an exponential amount of information. Recently, in the context of spin glasses and…

In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

We study an effective Einstein-Finsler theory on tangent Lorentz bundle constructed as a "minimal" extension of general relativity. Black ring and Kerr like ellipsoid exact solutions and soliton configurations are presented. In this…

A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…