We report a linear-scaling numerical method for exploring nonequilibrium electron dynamics in systems of arbitrary complexity. Based on the Chebyshev expansion of the time evolution of the single-particle density matrix, the method gives access to nonperturbative excitation and relaxation phenomena in models of disordered materials with sizes on the experimental scale. After validating the method by applying it to saturable optical absorption in clean graphene, we uncover that disorder can enhance absorption in graphene and that the interplay between light, anisotropy, and disorder in nanoporous graphene might be appealing for sensing applications. Beyond the optical properties of graphenelike materials, the method can be applied to a wide range of large-area materials and systems with arbitrary descriptions of defects and disorder.
We report a linear-scaling numerical method for exploring nonequilibrium electron dynamics in systems of arbitrary complexity. Based on the Chebyshev expansion of the time evolution of the single-particle density matrix, the method gives access to nonperturbative excitation and relaxation phenomena in models of disordered materials with sizes on the experimental scale. After validating the method by applying it to saturable optical absorption in clean graphene, we uncover that disorder can enhance absorption in graphene and that the interplay between light, anisotropy, and disorder in nanoporous graphene might be appealing for sensing applications. Beyond the optical properties of graphenelike materials, the method can be applied to a wide range of large-area materials and systems with arbitrary descriptions of defects and disorder.
This paper addresses the challenge of modeling relaxation dynamics in quantum many-body systems, specifically focusing on electrons in graphene nanoflakes. While quantum many-body techniques effectively describe dynamics up to a few particles, these approaches become computationally intractable for large systems. Larger systems may be tackled with a single-particle approach that, however, struggles to incorporate relaxation effects. Existing relaxation models encounter issues such as an inability to capture system complexity and violation of the Pauli principle. In this paper, we propose a single-particle model that accounts for various relaxation effects at the crossroads of quantum optics and solid-state photonics, that overcomes the limitations of previous models. Our approach is rooted in the quantum-optical Lindblad model, where relaxation rates are deactivated once the target levels saturate due to the Pauli principle. This approach is referred to as the saturated-Lindblad model. To validate the predictions of the saturated-Lindblad model, we confront them against phenomenological and many-body physics models in low-dimensional systems, including atomic chains and graphene nanoflakes. Remarkably, the saturated-Lindblad model exhibits excellent agreement with few-body calculations, distinguishing itself from other existing approaches. Moreover, by assigning different relaxation rates to different transitions, we successfully reproduce cascade deexcitation dynamics and predict emission spectra. The saturated-Lindblad model offers the ability to describe dynamics in systems of practical sizes, encompassing a wide range of structures that can be effectively captured within the single-particle description.
In this work we will analyse the capabilities of several numerical techniques for the description of different physical systems. Thereby, the considered systems range from quantum over semiclassical to classical and from few- to many-particle systems. For each case we address an interesting, partly unsolved question. Despite the different topics we address in the individual chapters, the problems under study are somehow related because we focus on the time evolution of the system. In chapter 1 we investigate the behaviour of a single quantum particle in the presence of an external disordered background (static potentials). Starting from the quantum percolation problem, we address the fundamental question of a disorder induced (Anderson-) transition from extended to localised single-particle eigenstates. Distinguishing isolating from conducting states by applying a local distribution approach for the local density of states (LDOS), we detect the quantum percolation threshold in two- and three-dimensions. Extending the quantum percolation model to a quantum random resistor model, we comment on the possible relevance of our results to the influence of disorder on the conductivity in graphene sheets. Furthermore, we confirm the localisation properties of the 2D percolation model by calculating the full quantum time evolution of a given initial state. For the calculation of the LDOS as well as for the Chebyshev expansion of the time evolution operator, the kernel polynomial method (KPM) is the key numerical technique. In chapter 2 we examine how a single quantum particle is influenced by retarded bosonic fields that are inherent to the system. Within the Holstein model, these bosonic degrees of freedom (phonons) give rise to an infinite dimensional Hilbert space, posing a true many-particle problem. Constituting a minimal model for polaron formation, the Holstein model allows us to study the optical absorption and activated transport in polaronic systems. Using a two-dimensional variant of the KPM, we calculate for the first time quasi-exactly the optical absorption and dc-conductivity as a function of temperature. Concerning the numerical technique, the close relation to the time evolution in the other chapters get clear if we identify temperature with an imaginary time. In chapter 3 we come back to the time evolution of a quantum particle in an external, static potential and investigate the capability of semiclassical approximations to it. Considering various one-dimensional geometries, we address basic quantum effects as tunneling, interference and anharmonicity. The question is, to which extend and at which numerical costs, several semiclassical methods can reproduce the exact result for the quantum dynamics, calculated by Chebyshev expansion. To this end we consider the linearised semiclassical propagator method, the Wigner-Moyal approach and the recently proposed quantum tomography. A conceptually very interesting aspect of the compared semiclassical methods is their relation to different representations of quantum mechanics (wave function/density matrix, Wigner function, quantum tomogram). Finally, in chapter 4 we calculate the dynamics of a classical many-particle system under the influence of external fields. Considering a low-temperature rf-plasma, we investigate the interplay of the plasma dynamics and the motion of dust particles, immersed into the plasma for diagnostic reasons. In addition to the huge number of involved particles, the numerical description of this systems faces the challenge of a large range of involved time and length scales. Exploiting the mass differences of plasma constituents and dust particles allows for separating the PIC description of the plasma from the MD simulation of the dust particles in the effective surrounding plasma.
Quasiparticles are fundamental in describing the complex many-body interactions underlying single-particle excitations, playing a key role in understanding the macroscopic properties of quantum materials. Recent advancements in ultrafast laser technology, combined with various detection methods, have enabled precise monitoring and manipulation of quantum states and their dynamic processes. These developments not only enhance our comprehension of quasiparticle excitation mechanisms but also facilitate driving materials into non-equilibrium states, uncovering novel physical phenomena and advancing the design and application of innovative functional materials. The computational approach based on real-time time-dependent density functional theory (rt-TDDFT) transcends the limitations of linear response theory, enabling first-principles simulations of the dynamic response of strongly coupled quasiparticles under non-equilibrium conditions. The proposed method provides accurate predictions of highly nonlinear phenomena induced by strong laser fields, offering deeper insights into the underlying physical mechanisms. These theoretical insights are crucial for optimizing the performance of optoelectronic devices. This paper introduces the theoretical foundations of Ehrenfest dynamics within the framework of rt-TDDFT and presents case studies on the evolution of various quasiparticles under laser excitation. The results demonstrate the significant potential of ultrafast lasers for probing and controlling the properties of quantum materials, while also underscoring the vital role of dynamic simulations for studying non-equilibrium states and their time-domain characteristics.
A nonequilibrium occupation distribution relaxes towards the Fermi-Dirac distribution due to electron-electron scattering even in finite Fermi systems. The dynamic evolution of this thermalization process assumed to result from an optical excitation is investigated numerically by solving a Boltzmann equation for the carrier populations using a one-dimensional disordered system. We focus on the short-time-scale behavior. The logarithmically long time scale associated with the glassy behavior of interacting electrons in disordered systems is not treated in our investigation. For weak disorder and short range interaction we recover the expected result that the relaxation rate is enhanced by disorder. For sufficiently strong disorder, however, we find an opposite trend due to the reduction of scattering probabilities originating from the strong localization of the single-particle states. Long-range interaction in this regime produces a similar effect. The relaxation rate is found to scale with the interaction strength, however, the interplay between the implicit and the explicit character of the interaction produces an anomalous exponent.
Abstract Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and viable quantum algorithms for simulating large-scale materials are still limited. We propose and implement random-state quantum algorithms to calculate electronic-structure properties of real materials. Using a random state circuit on a small number of qubits, we employ real-time evolution with first-order Trotter decomposition and Hadamard test to obtain electronic density of states, and we develop a modified quantum phase estimation algorithm to calculate real-space local density of states via direct quantum measurements. Furthermore, we validate these algorithms by numerically computing the density of states and spatial distributions of electronic states in graphene, twisted bilayer graphene quasicrystals, and fractal lattices, covering system sizes from hundreds to thousands of atoms. Our results manifest that the random-state quantum algorithms provide a general and qubit-efficient route to scalable simulations of electronic properties in large-scale periodic and aperiodic materials.