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This thesis is devoted to ab initio calculations of ground and excited state properties of different systems within density functional theory and time dependent density functional theory. From the numerical point of view we implemented an…
Recently, a novel bifurcation technique known as the deflated continuation method (DCM) was applied to the single-component nonlinear Schr\"odinger (NLS) equation with a parabolic trap in two spatial dimensions. The bifurcation analysis…
The purpose of the paper is to suggest a new method which allows one to study multiple coherent reflection/transmissions by partially transparent interfaces (e.g. in multi-layer mesoscopic structures or grain boundaries in high-Tc's) in the…
Topoelectrical circuits are meta-material realizations of topological features of condensed matter systems. In this work, we discuss experimental methods that allow a fast and straightforward detection of the spectral features of these…
We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The…
Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunneling, yield measurements of the…
The 2-D electron system (2DES) in Si metal-oxide field-effect transistors (MOSFETS) consists of two distinct electron fluids interacting with each other. We calculate the total energy as a function of the density $n$, and the spin…
Within the well-established optical response function formalism, a new strategy with the central idea of employing the forward-backward stochastic Schr\"{o}dinger equations in a segmented way to accurately obtain the two-dimensional (2D)…
The theory of a spinor field interacting with a pure Chern-Simons gauge field in 2+1 dimensions is quantized. Dynamical and nondynamical variables are separated in a gauge-independent way. After the nondynamical variables are dropped, this…
Multi-dimensional coherent spectroscopy (MDCS)1,2 is a powerful method for optical spectroscopy that has become an important tool for studying ultrafast dynamics in a wide range of systems. It is an optical analog of multidimensional…
We present a microscopic many-body calculation of the nonlinear two-dimensional coherent spectroscopy (2DCS) of trion-polaritons and exciton-polaritons in charge-tunable transition-metal-dichalcogenides monolayers placed in an optical…
We have developed a microscopic many-body theory of two-dimensional coherent spectroscopy (2DCS) for a model of polarons in one-dimensional (1D) materials. Our theory accounts for contributions from all three processes: excited-state…
Two-dimensional electronic spectroscopy (2DES) provides a detailed picture of electronically nonadiabatic dynamics that can be interpreted with the aid of simulations. Here, we develop and contrast trajectory-based nonadiabatic dynamics…
We demonstrate how dynamic correlations of heavy-hole and light-hole excitons in semiconductor quantum wells may be investigated by two dimensional correlation spectroscopy (2DCS). The coherent response to three femtosecond optical pulses…
We report a theoretical description and experimental implementation of a novel two-dimensional coherent excitation spectroscopy based on quasi-steady-state photoinduced absorption measurement of a long-lived nonlinear population. We have…
Correlation information in strongly correlated electron systems can be obtained using an extended Drude model. An interesting method related to the extended Drude model analysis of superconducting optical data was proposed recently, and it…
We demonstrate that spin-charge separation can occur in two dimensions and note its confluence with superconductivity, topology, gauge theory, and fault-tolerant quantum computation. We construct a microscopic Ising-like model and, at a…
Conformal invariance powerfully constrains the critical behavior of two-dimensional classical systems with short-range interactions and the critical theories in two-dimensions are parametrized by a dimensional number, termed central charge…
Detailed knowledge of the local environments of spin-defects in semiconductors, such as nitrogen vacancy (NV) centers in diamond or divacancies in silicon carbide, is crucial for optimizing control and entanglement protocols in quantum…
On-chip spectroscopy that could realize real-time fingerprinting with label-free and high-throughput detection of trace molecules is one of the 'holy grails" of sensing. Such miniaturized spectrometers would greatly enable applications in…