相关论文: Elliptic Rydberg states as direction indicators

The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…

Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…

We show that a highly-excited energy eigenfunction $\psi_{nlm}(\vec{r})$ of hydrogen atom can be approximated as an equal-weight superposition of classical elliptic orbits with energy $E_n$ and angular momentum $L=\sqrt{l(l+1)}\hbar$, and…

The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…

Molecular dynamics simulation is used to investigate the crystallization of a classical two-dimensional electron system, in which electrons interact with the Coulomb repulsion. From the positional and the orientational correlation…

We describe a mechanism for transport of energy in a mechanical system consisting of a pendulum and a rotator subject to a random perturbation. The perturbation that we consider is the product of a Hamiltonian vector field and a scalar,…

The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…

The dominantly orbital state description is applied to the study of light mesons. The effective Hamiltonian is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement.…

It is well-known that an electric charge under a uniform magnetic field has a bidimensional motion if its initial position and velocity are perpendicular to this magnetic field. Although some constants of motion, as the energy and angular…

We consider the class of spinning particle theories, whose quantization corresponds to the continuous helicity representation of the Poincare group. The classical trajectories of the particle are shown to lie on the parabolic cylinder with…

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…

The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the…

The lattice compact Abelian Higgs model is a non-perturbative regularized formulation of low-energy scalar quantum electrodynamics. In 1+1 dimensions, this model can be quantum simulated using a ladder-shaped optical lattice with…

General quantum-mechanical description of relativistic particles and nuclei with spin 1/2 channeled in bent crystals is performed with the use of the cylindrical coordinate system. The previously derived Dirac equation in this system is…

We consider the use of N spin-1/2 particles for indicating a direction in space. If N>2, their optimal state is entangled. For large N, the mean square error decreases as N^{-2} (rather than N^{-1} for parallel spins).

The appearance of tracks, close to classical orbits, left by charged quantum particles propagating inside a detector, such as a cavity periodically illuminated by light pulses, is studied for a family of idealized models. In the…

We show that an array of ultracold Rydberg atoms embedded in a laser driven background gas can serve as an aggregate for simulating exciton dynamics and energy transport with a controlled environment. Spatial disorder and decoherence…

The spatial Kepler problem with a perturbation satisfying the rotational symmetry w.r.t. the $z$-axis and the reflection symmetry w.r.t. the $(x, y)$-plane, can be reduced to an Hamiltonian system with 2 degrees of freedom after fixing the…

A new method for constructing of composite coherent states of the hydrogen atom, based on the dynamical group approach and various schemes of reduction to subgroups, is presented. A wide class of well-localized (Gaussian) hydrogenic wave…

In this paper, we introduced the 3D-Quantum Stationary Hamilton Jacobi Equation for a central potential, and established the 3D quantum law of motion of an electron in the presence of such a potential. We established a system of three…