相关论文: Information Geometry and Phase Transitions
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…
A spherical model of skeleton with junctions is investigated by Monte Carlo simulations. The model is governed by one-dimensional bending energy. The results indicate that the model undergoes a first-order transition separating the smooth…
The relationship between micro-structure and macro-structure of complex systems using information geometry has been dealt by several authors. From this perspective, we are going to apply it as a geometrical structure connecting both…
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter $\omega$ which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
We define geometric critical exponents for systems that undergo continuous second order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…
Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
We study a geometrical representation of the quantum information metric in the gauge/gravity correspondence. We consider the quantum information metric that measures the distance between the ground states of two theories on the field theory…
We find the information geometry of tempered stable processes. Beginning with the derivation of $\alpha$-divergence between two tempered stable processes, we obtain the corresponding Fisher information matrices and the $\alpha$-connections…
Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…
Geometric phase (GP) independent of energy and time rely only on the geometry of state space. It has been argued to have potential fault tolerance and plays an important role in quantum information and quantum computation. We present the…
Using geomterothermodynamics (GTD), we investigate the phase transition of black hole in a metric independent way. We show that for any black hole, curvature scalar (of equilibrium state space geometry) is singular at the point where…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems…
Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…
Faceted interfaces are a key feature in self-resembling morphologies of many microstructures generated from solid state phase transformations. Interpretations, predictions and simulations of the faceted morphologies remain a challenge,…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…