Density matrix operator

Altematively, in the case of incoherent (e.g. statistical) initial conditions, the density matrix operator P(t) I 1>(0) (v(01 at time t can be obtained as the solution of the Liouville-von Neumann equation ... 

Subotnik JE, Hansen T, Ratner MA, Nitzan A (2009) Nonequilibrium steady-state transport via the reduced density-matrix operator. J Chem Phys 130 144105... 

It is worth mentioning that constant term disappears in Eq. (6) because of the suitable choice of the basis in the form (4). In the following, the evolution of the density matrix of the relevant system will be examined by means of the standard projection technique. The matrix elements pa/it) of the reduced density matrix operator are defined as follows... 

Here, the phase factor e k R,x is associated with the wave vector of applied laser field and the center of mass (or the center of charge) position of the molecule. The density matrix operator can be then defined as... 

Fano, U. (1957). Description of states in quantum mechanics by density matrix operator techniques, Rev. Mod. Phys., 29, 74-93. 

Consider the operator H of the crystal-plus-impurity system let us denote by i, ) and its eigenstates and eigenfimctions. The (spinless) density matrix operator for the ground state is... 

Note that the density matrix operator e H is the same as the time evolution operator c Wt// if we assign the imaginary value x = // ( to the time interval... 

The density matrix (the thermal average density matrix operator) is introduced through... 

Equation (38) provides a simple form of the fluctuation-dissipation theorem that relates the fluctuations to dissipation. Here the fluctuation in energy AE is related to the dissipation coefficient E appearing in the exponential decay of P t) exp ( - jt). The same expression (38) was derived by Cohen-Tannoudji et al. from a "coarse-grained" expression of the rate of variation of the density matrix (operator) describing a statistical mixture of states (see D in Chapter IV of Ref. [7]). Because the expression (38) was derived by perturbation, the conditions of validity of perturbation theory must be satisfied. The eigenfunctions associated with Si and Si are... 

We can express this in terms of the Feynman operator M and the relativistic density matrix operator p, where... 

Therefore, performing measurements of observables which are the products of the Pauli matrices, it is possible to determine all the elements of the density matrix operator p, with an arbitrary precision. This process is referred to as Quantum State Tomography, and is a procedure for measuring the quantum state of a system. 

Therefore, the Wigner function is directly related to the density matrix operator, p, which characterizes the quantum system [28] in Hilbert space. 

In PI work on homogeneous and isotropic fluids one utilizes the three basic statistical ensembles canonical, isothermal-isobaric, and grand canonical. In the canonical ensemble the partition function is given by the trace (Tr) of the density matrix operator... 

The Liouville equation. We now derive the differential equation which controls the time development of the density matrix operator p. From equations (15.8) and (15-10) the rate of change of the matrix element p is given by... 

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