arXiv subjects

Cristian M. Le

Publications and source records attributed to Cristian M. Le.

3 recordsLinked to original sources

arXiv2024

Efficient time dependent Wannier functions for ultrafast dynamics

Time-dependent Wannier functions were initially proposed as a means for calculating the polarization current in crystals driven by external fields. In this work, we present a simple gauge where Wannier states are defined based on the maximally localized functions at the initial time, and are propagated using the time-dependent Bloch states obtained from established first-principles calculations, avoiding the costly Wannierization at ech time step. We show that this basis efficiently describes the time-dependent polarization of the laser driven system through the analysis of the motion of Wannier centers. We use this technique to analyze highly nonlinear and non-perturbative responses such as high harmonic generation in solids, using the hexagonal boron nitride as an illustrative example, and we show how it provides an intuitive picture for the physical mechanisms.

cond-mat.mtrl-sci↗

arXiv2022

The missing quantum number of the Floquet states

We reformulate the Floquet theory for periodically driven quantum systems following a perfect analogy with the proof of Bloch theorem. We observe that the current standard method for calculating the Floquet eigenstates by the quasi-energy alone is incomplete and unstable, and pinpoint an overlooked quantum number, the average energy. This new quantum number resolves many shortcomings of the Floquet method stemming from the quasi-energy degeneracy issues, particularly in the continuum limit. Using the average energy quantum number we get properties similar to those of the static energy, including a unique lower-bounded ordering of the Floquet states, from which we define a ground state, and a variational method for calculating the Floquet states. This is a first step towards reformulating Floquet first-principles methods, that have long been thought to be incompatible due to the limitations of the quasi-energy.

quant-ph↗

arXiv2020

Defining a well-ordered Floquet basis by the average energy

At the moment, the most efficient method to compute the state of a periodically driven quantum system is using Floquet theory and the Floquet eigenbasis. The wide application of this basis set method is limited by: a lack of unique ordering of the Floquet eigenfunctions, an ambiguity in their definition at resonance, and an instability against infinitesimal perturbation at resonance. We address these problems by redefining the eigenbasis using a revised definition of the average energy as a quantum number. As a result of this redefinition, we also obtain a Floquet-Ritz variational principle, and justify the truncation of the Hilbert space.

quant-ph↗