相关论文: Information Metric on Instanton Moduli Spaces in N…
The so-called Darboux III oscillator is an exactly solvable $N$-dimensional nonlinear oscillator defined on a radially symmetric space with non-constant negative curvature. This oscillator can be interpreted as a smooth (super)integrable…
Let $X$ be a closed $6-$dimensional manifold with a half-closed $SU(3)-$structure. On the product manifold $X\times S^{1}$, with respect to the product $G_{2}-$structure and on a pullback vector bundle from $X$, we show that any…
We introduce a geometric scaling relation that characterizes the local scale behavior of correlations using the informational distance $d_E = K_0/\sqrt{I}$, where $I$ is the mutual information. We define a geometric conversion factor, $G…
The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time and space, for which an index theory has…
Quantum conditional mutual information (QCMI) is a versatile information theoretic measure. It is used to find the amount of correlations between two qubits from the perspective of a third qubit. In this work we characterise the QCMI of…
The diagonalization of the metrical Hamiltonian of a scalar field with an arbitrary coupling with a curvature in N-dimensional homogeneous isotropic space is performed. The energy spectrum of the corresponding quasiparticles is obtained.…
$\mathtt{d}$-dimensional hyperspherical quantum dot with either Dirichlet or Neumann boundary conditions (BCs) allows analytic solution of the Schr\"{o}dinger equation in position space and the Fourier transform of the corresponding wave…
Using D3/D(-1) brane set-up in type IIB string theory we introduce gauge-stringy instantons in N=2 U(N) supersymmetry theories with one matter multiplet in symmetric representation. In addition to the gauge and stringy moduli there exist…
We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference $2H_L(w) - H_{2L}(w)$ between entropies on cylinders of finite…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…
We compute and analyse the moduli space of those real projective structures on a hyperbolic 3-orbifold that are modelled on a single ideal tetrahedron in projective space. Parameterisations are given in terms of classical invariants,…
Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian,…
The moduli space of instantons on C^2 for any simple gauge group is studied using the Coulomb branch of N=4 gauge theories in three dimensions. For a given simple group G, the Hilbert series of such an instanton moduli space is computed…
The scaling properties of various composite information-theoretic measures (Shannon and R\'enyi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in…
Let ${\mathcal I}(n)$ denote the moduli space of rank $2$ instanton bundles of charge $n$ on ${\mathbb P}^3$. We know from several authors that ${\mathcal I}(n)$ is an irreducible, nonsingular and affine variety of dimension $8n-3$. Since…
We explore a relation between four-dimensional N=2 heterotic vacua induced by Mirror Symmetry via Heterotic/Type II duality. It allows us to compute the \alpha' corrections to the hypermultiplet moduli space of heterotic compactifications…
We investigate infra-red dynamics of the non-linear sigma model in de Sitter space. In the presence of minimally coupled massless scalar fields, the de Sitter symmetry is dynamically broken and physical constants become time dependent. We…
We show that in each dimension $4n+3$, $n\ge 1$, there exist infinite sequences of closed smooth simply connected manifolds $M$ of pairwise distinct homotopy type for which the moduli space of Riemannian metrics with nonnegative sectional…
Supersymmetric non-linear sigma-models are described by a field dependent Kaehler metric determining the kinetic terms. In general it is not guaranteed that this metric is always invertible. Our aim is to investigate the symmetry structure…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…