Related papers: Born-Oppenheimer approximation for an atom in cons…
We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in [26] to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a…
The major advantage of reduced magnetic vector potential formulations (RMVPs) is that complicated coil structures do not need to be resolved by a computational mesh. Instead, they are modeled by thin wires, whose source field is included…
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…
The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…
Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method…
We introduce a new method for representing the low energy subspace of a bosonic field theory on the qubit space of digital quantum computers. This discretization leads to an exponentially precise description of the subspace of the…
The modern semiclassical theory of a Bloch electron in a magnetic field encompasses the orbital magnetization and geometric phase. Beyond this semiclassical theory lies the quantum description of field-induced tunneling between…
We address the estimation of the magnetic field B acting on an ensemble of atoms with total spin J subjected to collective transverse noise. By preparing an initial spin coherent state, for any measurement performed after the evolution, the…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary…
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian…
Here, we propose a new modified quantum mechanics and its new algorithms of atomic fine-structure,asymmetric variational method based on hydrogen-like atom orbit. In addition, as we all know, the ab initio calculation of atomic…
A systematic study of energy spectra throughout the rare-earth region (even-even nuclei from $_{58}$Ce to $_{74}$W) is carried out in the framework of the interacting boson model (IBM), leading to an accurate description of the…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
We present a systematic numerical iteration approach to study the evolution properties of the spin-boson systems, which works well in whole coupling regime. This approach involves the evaluation of a set of coefficients for the formal…
When numerically simulating the unitary time evolution of an infinite-dimensional quantum system, one is usually led to treat the Hamiltonian $H$ as an "infinite-dimensional matrix" by expressing it in some orthonormal basis of the Hilbert…