Theoretical Developments for the Real-Time Description and Control of Nanoscale Systems

In this thesis we focus on improvements of the description of the electron-electron correlation effects in nonequilibrium nanosystems. We mainly focus on developments of two nonequilibrium methods, namely the formalism of Nonequilibrium Green’s Function and Time Dependent Density Functional Theory and we explore the possibility to improve existing approximations in these theories. A smaller part of the thesis is devoted to the Exact Diagonalization method which provides a numerically exact description of small systems.Paper I: We review the current methods for description of correlated materials in nonequilibrium and their connection to pump-probe spectroscopy.Paper II: We propose a hybrid method for the real time dynamics of strongly correlated materials which includes memory effects beyond the adiabatic local density approximation.Paper III: We study the dynamics of desorption of a molecule from a surface with different levels of approximation for both the nuclear and the electronic part. We compare a full quantum mechanical treatment to the Ehrenfestapproximation for the molecule and perturbative approximations for the electrons.Paper IV: We develop a theory of current-induced forces within Adiabatic Ehrenfest Dynamics which includes effects of electron-electron interactions. We study a dependence of the electronic friction on interaction strength.We also benchmark it against nonadiabatic Ehrenfest dynamics.Paper V: We study the competition of interaction and disorder in systems with steady state currents - in transport and ring geometries. We exactly define the exchange-correlation screening of the disorder by the interactioneffects via Kohn–Sham construction of DFT.Paper VI: We study a competition between Kondo and RKKY interaction in small clusters of Periodic Anderson Model (ring geometries), we construct a nonequilibrium Doniach-phase like diagram. We then determine anoptimal pulse to induce transitions with the highest fidelity

Molecular junctions and molecular motors: Including Coulomb repulsion in electronic friction using nonequilibrium Green's functions

We present a theory of molecular motors based on the Ehrenfest dynamics for the nuclear coordinates and the adiabatic limit of the Kadanoff-Baym equations for the current-induced forces. Electron-electron interactions can be systematically included through many-body perturbation theory, making the nonequilibrium Green's functions formulation suitable for first-principles treatments of realistic junctions. The method is benchmarked against simulations via real-time Kadanoff-Baym equations, finding an excellent agreement. Results on a paradigmatic model of molecular motor show that correlations can change dramatically the physical scenario by, e.g. introducing a sizable damping in the self-sustained van der Pol oscillations.Comment: 7 pages , 3 figs + Suppl. Informatio

Scale invariant survival probability at eigenstate transitions

Understanding quantum phase transitions in highly-excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here we argue that a scaled survival probability, where time is measured in units of a typical Heisenberg time, exhibits a power-law decay that appears to be independent of system size at eigenstate transitions. We first demonstrate this property in two paradigmatic quadratic models, the one-dimensional Aubry-Andre model and three-dimensional Anderson model. Surprisingly, we then show that similar phenomenology emerges in the interacting avalanche model of ergodicity breaking phase transitions. This establishes an intriguing similarity between localization transition in quadratic systems and ergodicity breaking phase transition in interacting systems

Scale-invariant critical dynamics at eigenstate transitions

The notion of scale invariant dynamics is well established at late times in quantum chaotic systems, as illustrated by the emergence of a ramp in the spectral form factor (SFF). Building on the results of the preceding Letter [Phys. Rev. Lett. 131, 060404 (2023)], we explore features of scale invariant dynamics of survival probability and SFF at criticality, i.e., at eigenstate transitions from quantum chaos to localization. We show that, in contrast to the quantum chaotic regime, the quantum dynamics at criticality do not only exhibit scale invariance at late times, but also at much shorter times that we refer to as mid-time dynamics. Our results apply to both quadratic and interacting models. Specifically, we study Anderson models in dimensions three to five and power-law random banded matrices for the former, and the quantum sun model and the ultrametric model for the latter, as well as the Rosenzweig-Porter model

Similarity between a many-body quantum avalanche model and the ultrametric random matrix model

In the field of ergodicity-breaking phases, it has been recognized that quantum avalanches can destabilize many-body localization at a wide range of disorder strengths. This has in particular been demonstrated by the numerical study of a toy model, sometimes simply called the ''avalanche model'' or the ''quantum sun model'' [Phys. Rev. Lett. 129, 060602 (2022)], which consists of an ergodic seed coupled to a perfectly localized material. In this paper, we connect this toy model to a well-studied model in random matrix theory, the ultrametric ensemble. We conjecture that the models share the following features. 1) The location of the critical point is predicted sharply by analytics. 2) On the localized site, both models exhibit Fock space localization. 3) There is a manifold of critical points. On the critical manifold, the eigenvectors exhibit nontrivial multifractal behaviour that can be tuned by moving on the manifold. 4) The spectral statistics is intermediate between Poisson statistics and random matrix statistics, also tunable on the critical manifold. We confirm numerically these properties

Löwdin's symmetry dilemma within Green functions theory for the one‐dimensional Hubbard model

The energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix- renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many-body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the computation of the Hubbard gap. Here we present new GFMBA results that demonstrate that GFMBA simulations are capable of producing reliable data for the gap which agrees well with the DMRG benchmarks in 1D. An interesting observation is that the accuracy of the gap can be significantly increased when the simulations give up certain symmetry restriction of the exact system, such as spin symmetry and spatial homogeneity. This is seen as manifestation and generalization of the “symmetry dilemma” introduced by Löwdin for Hartree–Fock wave function calculations

Effect of the growth phase on the glucose activation of the H+-ATPase in the yeast Saccharomyces cerevisiae

Using the Saccharomyces cerevisiae AD1-3 strain, we tested the eect of glucose activation of H+-ATPase on value of the membrane potential. With the grow prole we described this yeast strain. Then using the method of dyeing curve based on uorescent dye diS-C3(3) we measured the size of glucose activation of H+-ATPase through three grow phase (exponencial, diauxic, postdiauxic). Finally, we studied impact of prolonged glucose treatment on activation of H+-ATPase

Nerovnovážná supravodivost

V předložené diplomové práci studujeme supravodivost v kovových nanotečkách pomocí příblížení založeného na dvoučásticové T-matici. Po zavedení korekcí známých z mnohačetného rozptylu do Galitského-Feynmanovy žebříčkové aprox- imace T-matice, lze touto metodou popsat popsat i supravodivý stav. Tato sjednocující teorie navíc popisuje supravodivý a normální stav na stejné úrovni přiblížení. Původní teorie pro rovnováhu je v této práci zobecněna na nerovnovážné systémy pomocí zobeněného Kadanoffova-Baymova formalizmu. Tato obecně nerovnovážná verze teorie je určená pro nekonečné systémy, kde moment hyb- nosti je dobré kvantové číslo. Pro nanosystémy, kde moment hybnosti už není dobré kvantové číslo, byla teorie přeformulována. Modifikace byla zaměřena na nanosféry, u nichž lze využít rozvoj do vlastních stavů momentu rotace. Velká degenerace energetických hladin umožňuje vysoké kritické teploty u nanosfér s magickým počtem elektronů a zlepšuje podmínky pro pozorování jevů za hranicí slabé vazby. Jako vhodnou experimentální techniku diskutujeme tunelovací spek- troskopii. 1In the present thesis we study superconductivity using approaches based on the two-particle T-matrix. With the multiple scattering corrections the Galitskii- Feynman ladder T-matrix approximation becomes applicable to the supercon- ducting state. This theory describes the superconducting and normal states within the same approximation. In this thesis, the original equilibrium theory is generalized to nonequilibrium systems using the generalized Kadanoff-Baym formalizm. The obtained theory of nonequilibrium superconductors is suitable for bulk systems where the momentum is a good quantum number. We have reformulated the theory for nanosystems, where the momentum is no longer a good quantum number. The modification was aimed at nanospheres, where one can benefit from the expansion in eigenstates of the angular momentum. High degeneracy of energy levels leads to high critical temperatures of sheres with a magical number of electrons, which makes them good candidates for observa- tion of phenomena beyond the weak coupling limit. As a suitable experimental technique we discuss the tunneling spectroscopy. 1Fyzikální ústav UKInstitute of Physics of Charles UniversityFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult