Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonadiabatic couplings and gauge-theoretical structure of curved quantum
  waveguides   We investigate the quantum mechanics of a single particle constrained to move
along an arbitrary smooth reference curve by a confinement that is allowed to
vary along the waveguide. The Schr\"odinger equation is evaluated in the
adapted coordinate frame and a transverse mode decomposition is performed,
taking into account both curvature and torsion effects and the possibility of a
cross-section potential that changes along the curve in an arbitrary way. We
discuss the adiabatic structure of the problem, and examine nonadiabatic
couplings that arise due to the curved geometry, the varying transverse profile
and their interplay. The exact multi-mode matrix Hamiltonian is taken as the
natural starting point for few-mode approximations. Such approximate equations
are provided, and it is worked out how these recover known results for twisting
waveguides and can be applied to other types of waveguide designs. The quantum
waveguide Hamiltonian is recast into a form that clearly illustrates how it
generalizes the Born-Oppenheimer Hamiltonian encountered in molecular physics.
In analogy to the latter, we explore the local gauge structure inherent to the
quantum waveguide problem and suggest the usefulness of diabatic states, giving
an explicit construction of the adiabatic-to-diabatic basis transformation.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an