Related papers: Spiked potentials and quantum toboggans
We study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this one dimension leads to an interesting…
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…
Using a representation of multichannel quantum defect theory in terms of a quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show, that…
We generalize the conformally invariant topological quantum mechanics of a particle propagating on a punctured plane by introducing a potential that breaks both the rotational and the conformal invariance down to a ${\bf Z}_2$…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…
Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can…
A taming symplectic structure provides an upper bound on the area of an approximately pseudoholomorphic curve in terms of its homology class. We prove that, conversely, an almost complex manifold with such an area bound admits a taming…
The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation…
A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a $\delta$-function potential, which appear naturally in the model.…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the…
The quantum scattering by smooth bodies is considered for small and large values of $kd$, with $k$ the wavenumber and $d$ the scale of the body. In both regimes, we prove that the forward scattering exceeds the backscattering. For high $k$,…
The motion of two attractively interacting atoms in an optical lattice is investigated in the presence of a scattering potential. The initial wavefunction can be prepared by using tightly bound exact two-particle eigenfunction for vanishing…
We study topological transport in the steady state of a quantum particle hopping on a one-dimensional lattice in the presence of dissipation. The model exhibits a rich phase structure, with the average particle velocity in the steady state…
We describe a broad class of bounded non-periodic potentials in one-dimensional stationary quantum mechanics having the same spectral properties as periodic potentials. The spectrum of the corresponding Schroedinger operator consists of a…
A phenomenological model of the time evolution of a particle wavepacket is presented that is subject to scattering event with small momentum transfer. It is suited for three dimensions and allows for an additional potential. For a random…
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walks are proving to be effective simulators of such phenomena. Here we report the realization of a…
Sturmian bound states emerging at a fixed energy and numbered by a complete set of real eigencouplings are considered. For Sturm-Schroedinger equations which are manifestly non-Hermitian we outline the way along which the correct…
Topological physics opens up a plethora of exciting phenomena allowing to engineer disorder-robust unidirectional flows of light. Recent advances in topological protection of electromagnetic waves suggest that even richer functionalities…
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…
Topological phase, a novel and fundamental role in matter, displays an extraordinary robustness to smooth changes in material parameters or disorder. A crossover between topological physics and quantum information may lead to inherent…