Christopher Robert Schleif
cschleif@ucmerced.edu
chrisschleif.com
Office: 308 S&E Building
(209) 228-4527
University of California at Merced
5200 North Lake Rd.
Merced, California USA
95344

Research Interests:
"Quantum Chaos" and the Atom:
  Hydrogenic states of an atomic electron, when influenced by external electric and magnetic fields, provide an ideal setting for the study of the quantum mechanical behavior of classically chaotic systems. We study these systems using both classical and quantum mechanics, and make connections between the two theoretical frameworks through the asymptotic short wave limit of the Schrodinger matter wave equation.
  The classical system describing an atom in fields may be chaotic in two manners: (i) the presence of the external fields introduces nonlinearity in the electron's equations of motion, having a greater effect at relatively large distances from the nucleus (ii) for atoms other than hydrogen, a finite sized core of inner electrons introduces chaotic scattering of electron trajectories at small distances from the nucleus.
  We are interested in quantum mechanical signatures of classical chaos. One manner of observing that a quantum system has a classically chaotic counterpart is in the statistical distribution of the quantum energy levels. When quantum calculations are carried out for chaotic atomic systems, one finds that the statistics of the distribution of the quantum energy levels have a different character than that of the field free hydrogen atom. However a wealth of chaotic properties may be ascribed to a quantum system by appealing to the short wave limit of the Schrodinger equation. Much of our research lies within this semiclassical description of the atom and is driven by the desire to extend our understanding of the properties of quantum systems when their classical counterparts are chaotic.

Refereed Publications:

C.R.Schleif and J.B.Delos "Monodromy and the structure of the energy spectrum of hydrogen in near perpendicular electric and magnetic fields"
Phys. Rev. A 76 013404 (2007)

Errata:

XXXX Phys. Rev. A 76 013404 (2007):

Fig. 4 Caption: The reported n manifold, and n manifolds used in the basis for the quantum calculation are incorrect. They actually are:
n = 20 and the quantum basis included n manifolds 18 - 22


XXXX Phys. Rev. A 77 043422 (2008):

Eq. (5d): The fourth term should be multiplied by 1/2
...+ 1/2 d²H₀/dN² (df₁ / d phi_N)² + ...

Eq. (10b): This collection of commutators have a sign error, this equation should read
{M,M} = epsilon L

Eq. (A2): The right hand side of this equation is actually the definition of the components of R^T
R^T_i,j = rhs

Fig. 3(a): The W axis is inverted (W = mu_1 - mu_2)