Related papers: Information Geometry in Time Dependent Quantum Sys…
We reflect on the information paradigm in quantum and gravitational physics and on how it may assist us in approaching quantum gravity. We begin by arguing, using a reconstruction of its formalism, that quantum theory can be regarded as a…
We study the geometric phase of an open two-level quantum system under the influence of a squeezed, thermal environment for both non-dissipative as well as dissipative system-environment interactions. In the non-dissipative case, squeezing…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
The nature of phase transitions involving the questions why and how phase transitions take place has not been sufficiently touched in the literature. In contrast, the current attention to certain extent still focus on the description of…
Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…
In this paper, we investigate the geometric phase of the field interacting with $\Xi $-type moving three-level atom. The results show that the atomic motion and the field-mode structure play important roles in the evolution of the system…
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…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…
The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous, and also underline the physics of robust…
We study the general-setting quantum geometric phase acquired by a particle in a vibrating cavity. Solving the two-level theory with the rotating-wave approximation and the SU(2) method, we obtain analytic formulae that give excellent…
Quantum phase transitions in the one-dimensional extended quantum compass model in transverse field are studied by using the Jordan-Wigner transformation. This model is always gapful except at the critical surfaces where the energy gap…
We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of…
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…
The one-dimensional extended isotropic XY model (s=1/2) in a transverse field with uniform long-range interactions among the \textit{z} components of the spin is considered. The model is exactly solved by introducing the gaussian and…
The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold…
We take as a starting point an expression for the quantum geometric tensor recently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…