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Ab initio simulations are capable of providing detailed information of material behavior at the nanoscale. Simulating experimentally relevant situations is, however, often computationally intense. Using hybrid approaches between ab initio…
The quantization of the kinetic energy of a deformed nucleus in curvilinear coordinates in the case of octupole oscillations of its surface firstly has been carried out. The obtained form of the Hamiltonian differs from the previously…
Electron density prediction stands as a cornerstone challenge in molecular systems, pivotal for various applications such as understanding molecular interactions and conducting precise quantum mechanical calculations. However, the scaling…
Three dimensional Dirac oscillator was considered in deformed space obeyed to deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations gives rise to appearance minimal uncertainty in position…
Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…
The electromagnetic interactions of a relativistic two-body bound state are formulated in three dimensions using an equal-time (ET) formalism. This involves a systematic reduction of four-dimensional dynamics to a three-dimensional form by…
We describe a new class of exact square integrable solutions of the Pauli and Dirac equation in rotating electromagnetic fields. Solutions obtained by putting equations in the stationary form with help of a coordinate transformation…
A fundamental goal in the manipulation of quantum systems is the achievement of many coherent oscillations within the characteristic dephasing time T2*[1]. Most manipulations of electron spins in quantum dots have focused on the…
Future X-ray missions, such as NICER and LOFT, together with gravitational-wave observations from ground-based detectors, will provide new insights into neutron stars. Interpreting accurate observations in the future will require accurate…
The document describes a numerical algorithm to simulate plasmas and fluids in the 3 dimensional space by the Euler method, in which the spatial meshes are fixed to the space. The plasmas and fluids move through the spacial Euler mesh…
A two-parameter deformation of the Lie algebra u$_2$ is used, in conjunction with the rotor system and the oscillator system, to generate a model for rotation-vibration spectroscopy of molecules and nuclei.
The manipulation of the motion of neutral molecules with electric or magnetic fields has seen tremendous progress over the last decade. Recently, these techniques have been extended to the manipulation of large and complex molecules. In…
Traditional methods in quantum chemistry rely on Hartree-Fock-based Slater-determinant (SD) representations, whose underlying zeroth-order picture assumes separability by particle. Here, we explore a radically different approach, based on…
This article introduces yet another representation of rotations in 3-space. The rotations form a 3-dimensional projective space, which fact has not been exploited in Computer Science. We use the four affine patches of this projective space…
Dielectric elastomers have significant potential for new technologies ranging from soft robots to biomedical devices, driven by their ability to display complex shape changes in response to electrical stimulus. However, an important…
During our previous modeling using all-atom molecular dynamics, we have identified several foldamers whose nanoscale behavior resembles that of classic bistable machines, namely the Euler archs and Duffing oscillators. However, time…
The paper provides mathematics and physics considerations concerning a special class of electron spin manipulating structures for future Electron-Ion Collider (EIC) projects. These structures, which we call Universal Synchronous Spin…
In this paper, we study the \texttt{Ehlers' transformation} (sometimes called gravitational duality rotation) for \texttt{reciprocal} static metrics. First we introduce the concept of reciprocal metric. We prove a theorem which shows how we…
The three-dimensional quantum Euclidean space is an example of a non-commutative space that is obtained from Euclidean space by $q$-deformation. Simultaneously, angular momentum is deformed to $so_q(3)$, it acts on the $q$-Euclidean space…
Quantum computing is one of the most promising technologies of the near future, and the simulation of quantum many-body systems is a natural application. In this work, we present classical simulations of the ground states of light atomic…