Symplectic Density Matrix

Maurice A. de Gosson

Jakub Herko, Mark A. Caprio

Abstract The symplectic no-core configuration interaction (SpNCCI) framework is an ab initio many-body method for nuclear structure which makes use of the approximate symplectic symmetry of nuclei by appropriate choice of many-body basis states. In this paper we derive recurrence relations allowing for calculation of one-body and two-body density matrix elements between the SpNCCI basis states. Availability of these matrix elements allows for integration of the SpNCCI framework with other modern many-body methods and for calculation of matrix elements of any one-body or two-body operator.

Jessica Graber, George Rosensteel

Adolfo del Campo, Vladimir I. Man’ko, Giuseppe Marmo

The phase space is the natural ground to smoothly extrapolate between local and nonlocal correlation functions. With this objective, we introduce the symplectic tomography of many-body quantum gases in tight waveguides, and concentrate on the reduced single-particle symplectic tomogram (RSPST) whose marginals are the density profile and momentum distribution. We present an operational approach to measure the RSPST from the time evolution of the density profile after shutting off the interactions in a variety of relevant situations: Free expansion, fall under gravity, and oscillations in a harmonic trap. From the RSPST, the one-body density matrix of the trapped state can be reconstructed.

D. J. Simms, L. Castel

Maurice A. de Gosson, Charlyne de Gosson

Polar duality is a well-known concept from convex geometry and analysis. In the present paper we study a symplectically covariant versions of polar duality, having in mind their applications to quantum harmonic analysis. It makes use of the standard symplectic form on phase space and allows a precise study of the covariance matrix of a density operator.