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Modeling the orbital dynamics of objects in galactic disks is crucial to understanding the stability and evolution of disk galaxies. While studies of galactic orbits are largely dominated by $N$-body simulations, perturbative analytical…
The rapid development of ab initio nuclear structure methods towards doubly open-shell nuclei, heavy nuclei and greater accuracy occurs at the price of evermore increased computational costs, especially RAM and CPU time. While most of the…
Vortex-Induced Vibrations (VIVs) of cylindrical structures present significant challenges in various engineering applications, including marine risers, tall buildings, and renewable energy systems. Hence, it is vital to control…
This introductory work combines bottom-up and top-down approaches towards understanding the underlying categorical structure of possible unifying theories descending from string theory. Guided by well-established developments in the realm…
We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is that quadratic…
This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
We apply a time-dependent perturbation theory based on unitary transformations combined with averaging techniques, on molecular orientation dynamics by ultrashort pulses. We test the validity and the accuracy of this approach on LiCl…
The interaction of obliquely incident surface gravity waves with a vertical flexible permeable membrane wave barrier is investigated in the context of three-dimensional linear wave-structure interaction theory. A general formulation for…
In this paper, we start from the geometric relativistic foundations to define the basis upon which matter field theories are built, and their wave solutions are investigated, finding that they display repulsive interactions able to…
The Unitary Correlation Operator Method (UCOM) provides a means for nuclear structure calculations starting from realistic NN potentials. The dominant short-range central and tensor correlations are described explicitly by a unitary…
Conducting an open quantum system towards a desired steady state through reservoir engineering is a remarkable task that takes dissipation and decoherence as tools rather than impediments. Here we develop a collisional model to implement…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
Spin bases of relevance for quantum systems with cyclic symmetry as well as for quantum information and quantum computation are constructed from the theory of angular momentum. This approach is connected to the use of generalized Pauli…
This report presents a new approach for treating the coupling of electrons and nuclei in quantum mechanical calculations for molecules and condensed matter. It includes the standard "Born-Oppenheimer approximation" as a special case but…
We present a quantum mechanical theory of optically induced dynamic nuclear polarization applicable to quantum dots and other interacting spin systems. The exact steady state of the optically driven coupled electron-nuclear system is…
The development of the relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function are included to all orders of perturbation theory led to many important results for study…
An algebraic model based on Lie-algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. The local anharmonic effects are described by a Morse-like potential and corresponding anharmonic…
Strong, fast pulses, called ``bang-bang'' controls can be used to eliminate the effects of system-environment interactions. This method for preventing errors in quantum information processors is treated here in a geometric setting which…
After many years of development of the basic tools, quantum simulation with ultracold atoms has now reached the level of maturity where it can be used to investigate complex quantum processes. Planning of new experiments and upgrading…