Symbolic nuclear magnetic resonance (NMR) product operator calculations provide an analytic, intuitive, yet precise description of the time evolution of the density operator during an NMR experiment. NMR experiments are implemented as pulse sequences consisting of short radiofrequency pulses separated by delay periods during which the spin system evolves under the influence of the static extern...

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-...

Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of 4n-dimen...

1 Single System 5 1.1 Pure and Mixed States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Density Matrices and Operators . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Density Matrices for Pure and Mixed States . . . . . . . . . . . . . . 7 1.2.2 Density Operator in Thermal Equilibrium . . . . . . . . . . . . . . . 8 1.3 Statistical Expectation Values of Operators...

We prove that the integrated density of states (IDS) associated to a random Schrödinger operator is locally uniformly Hölder continuous as a function of the disorder parameter λ. In particular, we obtain convergence of the IDS, as λ → 0, to the IDS for the unperturbed operator at all energies for which the IDS for the unperturbed operator is continuous in energy.