Search results for "Density matrix"
showing 6 items of 106 documents
Time-Dependent Reduced Density Matrix Functional Theory
2012
In this chapter we will give an introduction into one-body reduced density matrix functional theory (RDMFT). This is a rather new method to deal with the quantum many-body problem. Especially the development of a time-dependent version, TDRDMFT , is very recent. Therefore, there are many open questions and the formalism has not crystalized yet into a standard form such as in (TD)DFT. Although RDMFT has similarities with DFT, there are many more differences. This chapter is too short for a full introduction into the wondrous world of RDMFT, but we hope to give an idea what (TD)RDMFT might bring.
Duality of reduced density matrices and their eigenvalues
2014
For states of quantum systems of N particles with harmonic interactions we prove that each reduced density matrix ρ obeys a duality condition. This condition implies duality relations for the eigenvalues λk of ρ and relates a harmonic model with length scales ${{\ell }_{1}},{{\ell }_{2}},\ldots ,{{\ell }_{N}}$ with another one with inverse lengths $1/{{\ell }_{1}},1/{{\ell }_{2}},\ldots ,1/{{\ell }_{N}}$. Entanglement entropies and correlation functions inherit duality from ρ. Self-duality can only occur for noninteracting particles in an isotropic harmonic trap.
Parametrizations of density matrices
2011
This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some r…
OpenMolcas: From Source Code to Insight
2019
In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multico…
Approach to equilibrium of a quarkonium in a quark-gluon plasma
2018
We derive equations of motion for the reduced density matrix of a heavy quarkonium in contact with a quark-gluon plasma in thermal equilibrium. These equations allow in particular a proper treatment of the regime when the temperature of the plasma is comparable to the binding energy of the quarkonium. These equations are used to study how the quarkonium approaches equilibrium with the plasma, and we discuss the corresponding entropy increase, or free energy decrease, depending on the temperature regime. The effect of collisions can be accounted for by the generalization of the imaginary potential introduced in previous studies, and from which collision rates are derived. An important outcom…
Quantum and classical dynamics of heavy quarks in a quark-gluon plasma
2018
We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling between the heavy quarks and the plasma, the fast response of the plasma to the perturbation caused by the heavy quarks. An additional semi-classical approximation is performed. This allows us to recover results previously obtained for the abelian plasma using the influence functional formalism. In the case of QCD, specific features of the color dynamics make the implementation of the semi-classical approximation more involved. We explore two approximate…