Related papers: Quantum Mechanics on Manifolds Embedded in Euclide…
In summer 1999 an experiment at ILL, Grenoble was conducted. So-called ultra-cold neutrons (UCN) were trapped in the vertical direction between the Fermi-potential of a smooth mirror below and the gravitational potential of the earth above…
A geometric potential $V_C$ depending on the mean and Gaussian curvatures of a surface $\Sigma$ arises when confining a particle initially in a three-dimensional space $\Omega$ onto $\Sigma$ when the particle Hamiltonian $H_\Omega$ is taken…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
We derive the effective one-dimensional Schrodinger-Pauli equation for electrons constrained to move on a space curve. The electrons are confined using a double thin-wall quantization procedure with adiabatic separation of fast and slow…
We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
As a contribution to the ongoing discussion of trajectories of spinless particles in spaces with torsion we show that the geometry of such spaces can be induced by embedding their curves in a euclidean space without torsion. Technically…
4-manifolds have special topological properties which can be used to get a different view on quantum mechanics. One important property (connected with exotic smoothness) is the natural appearance of 3-manifold wild embeddings (Alexanders…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…
We propose a scalable analog quantum simulator for quantum electrodynamics (QED) in two spatial dimensions. The setup for the U(1) lattice gauge field theory employs inter-species spin-changing collisions in an ultra-cold atomic mixture…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…
This paper analyses quantum mechanics in multiply connected spaces. It is shown that the multiple connectedness of the configuration space of a physical system can determine the quantum nature of physical observables, such as the angular…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of an inverse-quadratic potential in 1D is…
We construct a quantum mechanics based on the hypothesis of existing compact extra dimensions for a particle that wants to detect it. By introducing a probability function, we express the transition of particle to the extra 2d window. The…