Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering and delay time for 1D asymmetric potentials: the step-linear
  and the step-exponential cases   We analyze the quantum-mechanical behavior of a system described by a
one-dimensional asymmetric potential constituted by a step plus (i) a linear
barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation
by means of the integral representation method, classifying the independent
solutions as equivalence classes of homotopic paths in the complex plane.
  We discuss the structure of the bound states as function of the height U_0 of
the step and we study the propagation of a sharp-peaked wave packet reflected
by the barrier. For both the linear and the exponential barrier we provide an
explicit formula for the delay time \tau(E) as a function of the peak energy E.
We display the resonant behavior of \tau(E) at energies close to U_0. By
analyzing the asymptotic behavior for large energies of the eigenfunctions of
the continuous spectrum we also show that, as expected, \tau(E) approaches the
classical value for E -> \infty, thus diverging for the step-linear case and
vanishing for the step-exponential one.

25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ