Quantum dynamics in a thin film, I. Propagation of localized perturbations

Constrained quantum systems as an adiabatic problem

“…[23], to a nonflat geometry. We note that the adiabatic nature of the problem was observed many times before in the physics literature (e.g., in the context of adiabatic quantum waveguides and thin films [1,2]). However, the only work considering constraint manifolds with general geometries in quantum mechanics from this point of view so far is Ref.…”

“…The effective Hamiltonian on L 2 (C,dµ) ⊗ C M is now given by H (2) eff = U ε P ε H ε P ε U * ε and solves all three problems mentioned previously.…”

“…The derivation of effective Hamiltonians for constrained quantum systems has been considered many times in the literature with different motivations and applications in mind [1][2][3][4][5][6][7][8]. Roughly speaking, the available results split into two different categories, which are related to two different energy scales.…”

“…Roughly speaking, the available results split into two different categories, which are related to two different energy scales. In the context of adiabatic quantum waveguides, one considers the situation, where the strong forces that restrict the particle to the waveguide change their form along the direction of propagation [1][2][3][4]. The eigenvalues of the transverse Hamiltonian, thus, also vary along this direction and produce an effective adiabatic potential for the tangential dynamics (i.e., for the propagation).…”

Semiclassical spectral series for the two-component Hartree-type equation

“…The constructed semiclassical spectral series are localized in the vicinity of the zero-dimensional manifolds of the classical Einstein-Ehrenfest system. Generalization of the results obtained to the case of curves and surface localized in the vicinity [11,13] (see also [39,40]) is of considerable interest.…”