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Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nano-mechanical…
We present an approach for eliminating the gauge freedom for derivative couplings in nonadiabatic dynamics in the presence of geometric phase effects. This approach relies on a bottom-up construction of a parametric quantum Hamiltonian in…
The multilayer multiconfiguration time-dependent Hartree theory within second quantization representation of the Fock space is applied to study correlated electron transport in models of single-molecule junctions. Extending previous work,…
The t-J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson-Maleev transformation relating spin operators to…
Invariants at arbitrary and fixed energy (strongly and weakly conserved quantities) for 2-dimensional Hamiltonian systems are treated in a unified way. This is achieved by utilizing the Jacobi metric geometrization of the dynamics. Using…
Open quantum systems described by a non-Hermitian Hamiltonian exhibit rich dynamics due to the topology of their complex energy spectrum. By encircling an exceptional point degeneracy, this topology allows for topological state transport,…
The dynamics of exotic hypernuclei in heavy-ion collisions has been investigated thoroughly with a microscopic transport model. All possible channels on hyperon ($\Lambda$, $\Sigma$ and $\Xi$) production near threshold energies are…
We analyze the dynamical response functions of strongly interacting quantum critical states described by conformal field theories (CFTs). We construct a self-consistent holographic model that incorporates the relevant scalar operator…
The exact nondipole minimal-coupling Hamiltonian for an atom interacting with an explicitly time- and space-dependent laser field is transformed into the rest frame of a classical free electron in the laser field, i.e., into the…
We present a novel scheme for nuclear structure calculations based on realistic nucleon-nucleon potentials. The essential ingredient is the explicit treatment of the dominant interaction-induced correlations by means of the Unitary…
Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…
We study geometric energy transport in a slowly driven single-level quantum dot weakly coupled to electronic contacts and with strong onsite interaction, which can be either repulsive or attractive. Exploiting a recently discovered…
We present a means of studying rare reactive pathways in open quantum systems using Transition Path Theory and ensembles of quantum jump trajectories. This approach allows for elucidation of reactive paths for dissipative, nonadiabatic…
In this work, we investigate a Lagrangian model describing a particle constrained to move along non-degenerate conic sections, parameterized by the orbital eccentricity \( e \). In the non-relativistic regime, we apply the Dirac--Bergmann…
At low to moderate collision energies where the parton formation time $\tau_F$ is not small compared to the nuclear crossing time, the finite nuclear thickness significantly affects the energy density $\epsilon(t)$ and net conserved-charge…
A decomposition of the exact exchange-correlation potential of time-dependent density functional theory into an interaction component and a kinetic component offers a new starting point for non- adiabatic approximations. The components are…
This work identifies geometric effects on dynamics due to nonadiabatic couplings in Born Oppenheimer systems and provides a systematic method for deriving corrections to mixed quantum-classical methods. Specifically, an exact path integral…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
We study a deformation of the counterdiabatic-driving Hamiltonian as a systematic strategy for an adiabatic control of quantum states. Using a unitary transformation, we design a convenient form of the driver Hamiltonian. We apply the…
We consider a computational problem where the goal is to approximate the maximum eigenvalue of a two-local Hamiltonian that describes Heisenberg interactions between qubits located at the vertices of a graph. Previous work has shed light on…