Bogar Díaz

In non-Hermitian systems, the bi-orthogonal Left-Right (LR) formulation introduces a fundamental ambiguity in the definition of the Quantum Metric Tensor (QMT). Using the cubic oscillator, we resolve this by showing that the fully complex LR metric naturally emerges from the Borel resummation of the divergent perturbative series of the Hermitian system. Thus, its complex nature is a strict consequence of analytic continuation, not merely a mathematical convention. Extending Borel resummation from complex energies to quantum geometry, we reconstruct the complex QMT of the associated dilated system from divergent perturbative series. Furthermore, we reveal a critical physical distinction: while ground-state energy resummation remains robust, geometric reconstruction breaks down earlier due to its spectral sum structure, which inherits the severe instability of the excited spectrum. Finally, we analytically extract the leading non-perturbative contributions, thereby proving that the imaginary components of the non-Hermitian metric are directly governed by the classical bounce action.

In this work, we analyze perturbative expansions of the quantum metric tensor (QMT) in anharmonic oscillators, focusing on quartic, sextic, and d -dimensional models. Using high-order perturbation theory, we show that the divergent QMT series exhibit factorial growth. Our analysis identifies universal non-perturbative scales, with coefficients displaying large-order behavior consistent with resurgence theory. Then, we apply Borel–Padé resummation to the QMT. Comparisons with numerical diagonalization confirm that Borel–Padé resummations yield accurate results, especially for the ground state. For completeness, we also present the analysis of the energy eigenvalues in the examples. Our findings extend resurgent techniques from energies to the QMT, highlighting the interplay between quantum geometry and non-perturbative physics.

In this paper, we analyze from a geometric perspective the Hamiltonian formulation of a recent modification of the Husain–Kuchař model where, while preserving the connection as a dynamical variable, the other field is restricted to be the exterior covariant derivative of a Lie algebra-valued function. We prove that three-dimensional diffeomorphisms can be accommodated among the local gauge transformations of the model in addition to the internal gauge symmetries.

In this work, we analyze perturbative expansions of the quantum metric tensor (QMT) in anharmonic oscillators, focusing on quartic, sextic, and $d$-dimensional models. Using high-order perturbation theory, we show that the divergent QMT series exhibit factorial growth. Our analysis identifies universal non-perturbative scales, with coefficients displaying large-order behavior consistent with resurgence theory. Then, we apply resurgence and Borel--Padé resummation to the QMT. Comparisons with exact diagonalization confirm that Borel--Padé resummations yield accurate results, especially for the ground state. For completeness, we also present the analysis of the energy eigenvalues in the examples. Our findings extend resurgent techniques from energies to the QMT, highlighting the interplay between quantum geometry and non-perturbative physics.

We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state by considering small variations in both time and wave function parameters. Compared to the standard quantum geometric tensor, this tensor introduces new temporal components, enabling the analysis of systems with non-time-separable or explicitly time-dependent quantum states and encoding new information about these systems. In particular, the time-time component of this tensor is related to the energy dispersion of the system. We applied this framework to a harmonic/inverted oscillator, a time-dependent harmonic oscillator, and a chain of generalized harmonic/inverted oscillators. We show some results on the scalar curvature associated with the time-dependent quantum geometric tensor and the generalized Berry curvature behavior on the transition from harmonic oscillators to inverted ones. Furthermore, we analyze the entanglement for the chain through purity analysis, obtaining that the purity for any excited state is zero in the mentioned transitions.

We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the standard quantum geometric tensor, this tensor introduces new temporal components, enabling the analysis of systems with non-time-separable or explicitly time-dependent quantum states and encoding new information about these systems. In particular, the time-time component of this tensor is related to the energy dispersion of the system. We applied this framework to a harmonic/inverted oscillator, a time-dependent harmonic oscillator, and a chain of generalized harmonic/inverted oscillators. We show some results on the scalar curvature associated with the time-dependent quantum geometric tensor and the generalized Berry curvature behavior on the transition from harmonic oscillators to inverted ones. Furthermore, we analyze the entanglement for the chain through purity analysis, obtaining that the purity for any excited state is zero in the mentioned transitions.

We perform a Hamiltonian analysis of unimodular gravity in its first-order formulation, specifically a modification of the Holst action. In order to simplify the analysis, prior studies on this theory have introduced (for several reasons) additional elements, such as parametrization, complex fields, or considering the Barbero–Immirzi parameter as imaginary. We show that, by using a geometric implementation of the Dirac algorithm, a comprehensive analysis of the theory can be conducted without relying on these additional ingredients. The resulting theory reproduces the behavior of metric unimodular gravity.

It has recently been proposed classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the corresponding quantum system is in a Gaussian state. We generalized these results by providing classical analogs of the generalized purities, Bastiaans-Tsallis entropies, Rényi entropies, and logarithmic negativity for classical integrable systems. These classical analogs are entirely characterized by the classical covariance matrix. We compute these classical analogs exactly in the cases of linearly coupled harmonic oscillators, a generalized harmonic oscillator chain, and a one-dimensional circular lattice of oscillators. In all of these systems, the classical analogs reproduce the results of their quantum counterparts whenever the system is in a Gaussian state. In this context, our results show that quantum information of Gaussian states can be reproduced by classical information.

We investigate the structure of the medium formed in heavy ion collisions using three different models: the Color String Percolation Model (CSPM), the Core–Shell-Color String Percolation Model (CSCSPM), and the Color Glass Condensate (CGC) framework. We analyze the radial distribution function of the transverse representation of color flux tubes in each model to determine the medium’s structure. Our results indicate that the CSPM behaves as an ideal gas, while the CSCSPM exhibits a structural phase transition from a gas-like to a liquid-like structure. Additionally, our analysis of the CGC framework suggests that it produces systems that behave like non-ideal gases for AuAu central collisions at RHIC energies and liquid-like structures for PbPb central collisions at LHC energies.

We investigate the structure of the medium formed in heavy ion collisions using three different models: the Color String Percolation Model (CSPM), the Core-Shell-Color String Percolation Model (CSCSPM), and the Color Glass Condensate (CGC) framework. We analyze the radial distribution function of the transverse representation of color flux tubes in each model to determine the medium's structure. Our results indicate that the CSPM behaves as an ideal gas, while the CSCSPM exhibits a structural phase transition from a gas-like to a liquid-like structure. Additionally, our analysis of the CGC framework suggests that it produces systems that behave like interacting gases for AuAu central collisions at RHIC energies and liquid-like structures for PbPb central collisions at LHC energies.