arXiv subjects

F. D. Picoli

Publications and source records attributed to F. D. Picoli.

3 recordsLinked to original sources

arXiv2026

Temporal structures of the X-ray photoemission problem

Theoretical studies of X-ray photoemission from simple metals have traditionally focused on the frequency domain, aiming to reproduce experimental spectra. Here, we investigate the same problem in the time domain in search of physical insight and methodological advances. Our results reveal prominent aspects of the problem that are inconspicuous in the frequency domain. The calculated $\mathcal{F}(t)$ exhibits a weakly damped harmonic oscillation that modulates the Doniach-Sunjic power-law decay of the photoemission rate, a behavior arising from the coherent interference between two classes of particle-hole excitations. From a methodological perspective, we advance the time-dependent numerical renormalization-group (NRG) approach by exploring the eNRG method, a real-space variant that is more flexible than Wilson's construction. Giving special attention to strong core-hole potentials, we compare the photocurrents obtained from two complementary time-dependent eNRG algorithms with (i) an analytical expression for $\mathcal{F}(t)$ that becomes highly accurate at moderately long times and (ii) results from numerical diagonalization of a tight-binding Hamiltonian, which covers the time interval in which our analytical expression is less precise. Anticipating extensions to correlated-impurity models, we identify the sources of deviation and discuss the virtues and drawbacks of the two algorithms.

cond-mat.mes-hall↗

arXiv2025

Analytical Diagonalization of Fermi Gas-like Hamiltonians using the Sommerfeld-Watson Transformation

The Sommerfeld-Watson transformation is a powerful mathematical technique widely used in physics to simplify summations over discrete quantum numbers by converting them into contour integrals in the complex plane. This method has applications in scattering theory, high-energy physics, quantum field theory, and electrostatics. A lesser-known but significant use is in the analytical diagonalization of specific Hamiltonians in condensed matter physics, such as the Fermi gas Hamiltonian and the single-impurity Anderson model with vanishing Coulomb repulsion. These models are used to describe important phenomena like conductance in metals, x-ray photoemission, and aspects of the Kondo problem. In this work, we provide a comprehensive explanation of the Sommerfeld-Watson transformation and its application in diagonalization procedures for these models, using modern notation to enhance clarity for new students. The analytical results were validated against the numerical diagonalization, showing excellent agreement. Furthermore, we extend the presented method to a more generalized non-interacting single-impurity Anderson model with variable couplings and arbitrary band dispersion. The procedure presented here successfully achieved the analytical diagonalization of this more complex model, providing a unified solution that encompasses simpler cases. To our knowledge, this general solution has not been previously reported.

cond-mat.str-el↗

arXiv2025

Tracking Adiabaticity in Non-Equilibrium Many-Body Systems: The Hard Case of the X-ray Photoemission in Metals

The level of adiabaticity determines many properties of time-dependent quantum systems. However, a reliable and easy-to-apply criterion to check and track it remains an open question, especially for complex many-body systems. Here we test techniques based on metrics which have been recently proposed to quantitatively characterize and track adiabaticity. We investigate the time evolution of x-ray photoemission in metals, which displays a strongly out-of-equilibrium character, continuum energy spectrum, and experiences the Anderson orthogonality catastrophe: a nightmarish scenario for this type of test. Our results show that the metrics-based methods remains valid. In particular, we demonstrate that the natural local density distance is able not only to track adiabaticity, but also to provide information not captured by the corresponding Bures' or trace distances about the system's dynamics. In the process, we establish an explicit upper limit for this local density distance in terms of the trace distance, and derive a simple analytical solution that accurately describes the time evolution of a Fermi gas with a localized scattering potential for a large range of parameters. We also demonstrate that, for x-ray photoemission, the quantum adiabatic criterion, as commonly used, fails to predict and track adiabaticity. The local particle density is typically much simpler to compute than the corresponding quantum state and it is experimentally measurable: this makes the method tested extremely appealing.

cond-mat.mes-hall↗