73 research outputs found
Introduction to determinantal point processes from a quantum probability viewpoint
Determinantal point processes on a measure space X whose kernels represent
trace class Hermitian operators on L^2(X) are associated to "quasifree" density
operators on the Fock space over L^2(X).Comment: Contributed to the proceedings of the 26th Conference on Quantum
Probability and Infinite Dimensional Analysi
Convergence of continuous-time quantum walks on the line
The position density of a "particle" performing a continuous-time quantum
walk on the integer lattice, viewed on length scales inversely proportional to
the time t, converges (as t tends to infinity) to a probability distribution
that depends on the initial state of the particle. This convergence behavior
has recently been demonstrated for the simplest continuous-time random walk
[see quant-ph/0408140]. In this brief report, we use a different technique to
establish the same convergence for a very large class of continuous-time
quantum walks, and we identify the limit distribution in the general case.Comment: Version to appear in Phys. Rev.
Strongly separated pairs of core electrons in computed ground states of small molecules
We have performed full configuration interaction computations of the ground
states of the molecules Be, BeH_2, Li, LiH, B, and BH and verified that the
core electrons constitute "separated electron pairs." These separated pairs of
core electrons have nontrivial structure; the core pair does not simply occupy
a single spatial orbital.
Our method of establishing the presence of separated electron pairs is direct
and conclusive. We do not fit a separated pair model; we work with the
wavefunctions of interest directly. To establish that a given group of
spin-orbitals contains a quasi-separated pair, we verify by direct computation
that the quantum state of the electrons that occupy those spin-orbitals is
nearly a pure 2-electron state.Comment: To appear in Computational and Theoretical Chemistr
Properties of nonfreeness: an entropy measure of electron correlation
"Nonfreeness" is the (negative of the) difference between the von Neumann
entropies of a given many-fermion state and the free state that has the same
1-particle statistics. It also equals the relative entropy of the two states in
question, i.e., it is the entropy of the given state relative to the
corresponding free state. The nonfreeness of a pure state is the same as its
"particle-hole symmetric correlation entropy", a variant of an established
measure of electron correlation. But nonfreeness is also defined for mixed
states, and this allows one to compare the nonfreeness of subsystems to the
nonfreeness of the whole. Nonfreeness of a part does not exceed that in the
whole; nonfreeness is additive over independent subsystems; and nonfreeness is
superadditive over subsystems that are independent on the 1-particle level.Comment: 20 pages. Submitted to Phys. Rev.
- …