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The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a…
One of the challenges in diagrammatic simulations of nonequilibrium phenomena in lattice models is the large memory demand for storing momentum-dependent two-time correlation functions. This problem can be overcome with the recently…
We develop a causal optimization method that ensures causality in numerical calculations of Green's functions in interacting electron systems. Our method removes noncausality of numerical data by finding causal functions closest to the…
We develop nonequilibribrium Green's function based transport theory, which includes effects of nonadiabatic nuclear motion in the calculation of the electric current in molecular junctions. Our approach is based on the separation of slow…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
Standard derivations of the functional integral in non-equilibrium quantum field theory are based on the discrete time representation. In this work we derive the non-equilibrium functional integral for non-interacting bosons and fermions…
Nonequilibrium Green's functions represent underutilized means of studying the time evolution of quantum many-body systems. In view of a rising computer power, an effort is underway to apply the Green's functions formalism to the dynamics…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
Nonequilibrium Green's functions provide a powerful framework for studying quantum many-body dynamics including the laser-induced dynamics in solids. The Non-Equilibrium Systems Simulation package (NESSi) offers an efficient platform for…
In the nonequilibrium Green's function approach, the approximation of the correlation self-energy at the second-Born level is of particular interest, since it allows for a maximal speed-up in computational scaling when used together with…
We present a quantum Monte-Carlo algorithm for computing the perturbative expansion in power of the coupling constant $U$ of the out-of-equilibrium Green's functions of interacting Hamiltonians of fermions. The algorithm extends the one…
Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient…
We used methods of Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time Green's function generated in quantum Monte Carlo simulations to obtain the real-time Green's functions. For test…
We present a time-linear scaling method to simulate open and correlated quantum systems out of equilibrium. The method inherits from many-body perturbation theory the possibility to choose selectively the most relevant scattering processes…
This research demonstrates analytical time-dependent non-equilibrium green function (TD-NEGF) algorithms to investigate dynamical functionalities of quantum devices, especially for photon-assisted transports. Together with the lumped…
Discovering hidden partial differential equations (PDEs) and operators from data is an important topic at the frontier between machine learning and numerical analysis. This doctoral thesis introduces theoretical results and deep learning…
Quantum cascade lasers can be modeled within a hierarchy of different approaches: Standard rate equations for the electron densities in the levels, semiclassical Boltzmann equation for the microscopic distribution functions, and quantum…
Within the imaginary-time theory for nonequilibrium in quantum dot systems the calculation of dynamical quantities like Green's functions is possible via a suitable quantum Monte-Carlo algorithm. The challenging task is to analytically…
An acceleration of continuous time quantum Monte Carlo (CTQMC) methods is a potentially interesting branch of work as they are matchless as impurity solvers of a density functional theory in combination with a dynamical mean field theory…
The calculation of work distributions in a quantum many-body system is of significant importance and also of formidable difficulty in the field of nonequilibrium quantum statistical mechanics. To solve this problem, inspired by…