Matrix Elements Of Density Operator Research Articles

Direct measurement methods of density matrix of an entangled quantum state

In general, the state of a quantum system represented by the density operator and its determination is a fundamental problem in quantum theory. In this study, two theoretical methods such as using postselected measurement characterized by modular value and sequential measurements of triple products of complementary observables to direct measurement of matrix elements of density operator of a two photon entangled quantum state are introduced. The similarity and possible feasibilities of those two methods are discussed by considering the previous theoretical and experimental works.

Shapes of the proton

A model proton wave function, constructed using Poincare invariance, and constrained by recent electromagnetic form factor data, is used to study the shape of the proton. Spin-dependent quark densities are defined as matrix elements of density operators in proton states of definite spin-polarization, and shown to have an infinite variety of non-spherical shapes. For high momentum quarks with spin parallel to that of the proton, the shape resembles that of a peanut, but for quarks with anti-parallel spin the shape is that of a bagel.

Unification of the Jaynes–Cummings model and Planck’s radiation law

By combining iterative methods with Laplace transformation, we construct the solution of a dissipative Jaynes–Cummings model. The dissipative part of the model is based on the standard Markovian master equation for a harmonic oscillator that is coupled to a heat bath of nonzero temperature. Besides photon loss, we also take into account frequency detuning between atom and field. Before commencing the iteration, we subject the matrix elements of the density operator to a transformation that depends on temperature. As a result, the pole structure of all Laplace transformed matrix elements is improved. It becomes manifest which poles do not contribute to the asymptotic behavior of the density operator. In proving that our iterative process yields convergent results, we assume upper bounds on: the matrix elements of the density operator, the matrix elements of the initial density operator, the damping parameter of the heat bath, and the temperature of the heat bath. All of these bounds are physically acceptable. The photon field may start from a coherent state or a number state. For experiments in a microwave cavity, temperatures of the order of 0.1 [K] are allowed. As an application, the evolution of the atomic density matrix is studied. We propose a limit for which this matrix converges to the state of maximum von Neumann entropy. The time, the cubed initial energy density, and the inverse of the damping parameter must tend to infinity equally fast. The photon field is assumed to be in a number state at time zero, whereas the initial state of the atom can be chosen freely.

Densities in a microscopic multicluster model and the proton-halo problem in 8B

Abstract The microscopic cluster model is extended to the calculation of matrix elements of density operators with an exact treatment of angular-momentum and center-of-mass effects. The 8 B and 8 Li densities are studied with the three-cluster version of the model. The similarity between these densities and an analysis of the quadrupole moment do not support the existence of a proton-halo in 8 B.

Convergence properties of coherent state path integrals from statistical mechanics

Coherent state path integral representations for matrix elements of density operators are compared to various formulations of coordinate space path integrals discussed recently [R. D. Coalson, J. Chem. Phys. 85, 926 (1986)]. The convergence properties of finite-dimensional approximations to these path integrals are tested for the harmonic oscillator. It is found that at low temperatures the coherent state path integrals converge much better than the coordinate space path integrals and thus should be preferred in numerical (e.g., Monte Carlo) calculations of low-temperature properties.