Density of excited particle--hole states

Anatoly V. Ignatyuk, Yu. V. Sokolov

Jacopo De Nardis, Miłosz Panfil

Abstract We review the recently introduced thermodynamic form factors for pairs of particle-hole excitations on finite-entropy states in the Lieb–Liniger model. We focus on the density operator and we show how the form factors can be used for analytic computations of dynamical correlation functions. We derive a new representation for the form factors and we discuss some aspects of their structure. We rigorously show that in the small momentum limit (or equivalently, on hydrodynamic scales) a single particle-hole excitation fully saturates the spectral sum and we also discuss the contribution from two particle-hole pairs. Finally we show that thermodynamic form factors can be also used to study the ground state correlations and to derive the edge exponents.

Anatoly V. Ignatyuk, Yu. V. Sokolov

Anthony Dean Dutoi, L. S. Cederbaum

In our analysis of the dynamic one-electron difference-density matrices arising from time-dependent many-body states, we have observed two very distinct modes for the migration of an excitation through a system. In one case, coherences in the density matrix give rise to single particle and hole states that appear to migrate as independent units. Though interacting, they are independent in the sense that the single-electron state that describes an individual particle or hole is everywhere entangled with the same state of the electrons that have been integrated/traced out. These pseudo-wavefunctions carry nontrivial phase information (nonzero momentum), which is consistent with their observed direction of travel. The other case is dominated by a transition that can be thought of as the closing of a particle--hole pair in one location, entangled with the opening of such a pair in another location. In this case, the spatially-dependent phase of a given particle or hole state lies very near the real axis, reminiscent of time-independent molecular orbitals.

Frederick C. Williams

Everett G. Larson

Abstract A density operator analysis is made of the particle‐ejection (e.g., photoionization) problem in the “generalized sudden approximation” for the case in which the ejected particle is detected but its dynamical properties are not observed. It is shown that the resultant statistical density operator may be derived from that obtained in a particle‐conserving Hamiltonian‐evolution linear‐response model with a random impulse perturbation, and that the physical applicability of the latter model embraces the range of applicability of the former. The initial value of the statistical density operator for the above particle‐ejection problem is shown to be the N – (1)‐particle reduced density operator of the initial state; and the initial value of the statistical density operator for the excitations in the random impulse model is shown to be the N‐particle Hermitian operator whose matrix representation is the G matrix of Garrod and Percus. The significance of the eigenvalue spectrum of these operators to the excitation properties of the system is discussed, especially for the random impulse model, where a large eigenvalue of the G matrix can signal strong preferential excitation to its corresponding particle‐hole collective state, even for a random perturbation. Extensions of these ideas to excitations from states with a large eigenvalue of the two‐particle reduced density operator (e.g., superconducting states) are mentioned. The The applicability of these density matrices to the description of the excitation spectrum due to a well‐defined perturbation is discussed. The relationship of these time‐dependent density operators to the one‐particle propagator and the particle–hole propagator (polarization propagator) is established.