相关论文: Elliptic Rydberg states as direction indicators

The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a…

We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In…

Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…

When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom a saddle point appears, which is called the Stark saddle point. For energies slightly above the saddle point energy one can find classical…

Rydberg atoms are ideal tools for quantum technologies. Due to their large size, their dipole-dipole interaction at micrometer-scale distances and their coupling to external fields are huge. Recent experiments vividly exhibit their interest…

The angular momentum formalism provides a powerful way to classify atomic states. Yet, requiring a spherical symmetry from the very first line, this formalism cannot be used for periodic systems, even though cubic semiconductor states are…

The Weyl-Wigner representations for canonical thermal equilibrium quantum states are obtained for the whole class of quadratic Hamiltonians through a Wick rotation of the Weyl-Wigner symbols of Heisenberg and metaplectic operators. The…

The angular momentum, angular velocity, Kelvin circulation, and vortex velocity vectors of a quantum Riemann rotor are proven to be either (1) aligned with a principal axis or (2) lie in a principal plane of the inertia ellipsoid. In the…

We consider a system of two particles in noncommutative space which is rotationally invariant. It is shown that the coordinates of the center-of-mass position and the coordinates of relative motion satisfy noncommutative algebra with…

We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…

Excitons, i.e. the bound states of an electron and a positively charged hole are the solid state analogue of the hydrogen atom. As such they exhibit a Rydberg series, which in cuprous oxide has been observed up to high principal quantum…

It is shown that electromagnetic vortices can act as beam guides for charged particles. The confinement in the transverse directions is due to the rotation of the electric and magnetic fields around the vortex line. Large class of exact…

We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…

Although hydrogen in external fields is a paradigm for the application of periodic orbits and the Gutzwiller trace formula to a real system, the trace formula has never been applied successfully to other Rydberg atoms. We show that spectral…

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…

Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…

A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples…

The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters.…

To solve the quantum-mechanical problem the procedure of mapping onto linear space $W$ of generators of the (sub)group violated by given classical trajectory is formulated. The formalism is illustrated by the plane H-atom model. The problem…

The invariance of the Lagrangian under time translations and rotations in Kepler's problem yields the conservation laws related to the energy and angular momentum. Noether's theorem reveals that these same symmetries furnish generalized…