Density Matrices and Their Time Evolution
| Autor: | Erwin Brüning, Francesco Petruccione |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Statistics and Probability
Higher-dimensional gamma matrices Mathematical analysis Time evolution Hilbert space Statistical and Nonlinear Physics Constraint (information theory) Nonlinear system symbols.namesake symbols Differentiable function Special case Representation (mathematics) Mathematical Physics Mathematics |
| Zdroj: | Open Systems & Information Dynamics. 15:109-121 |
| ISSN: | 1793-7191 1230-1612 |
| DOI: | 10.1142/s1230161208000109 |
| Popis: | Already in the case of finite dimensional Hilbert spaces [Formula: see text] the general form of density matrices ρ is not known. The main reason for this lack of knowledge is the nonlinear constraint for these matrices. We propose a representation of density matrices on finite dimensional Hilbert spaces in terms of finitely many independent parameters. For dimensions 2, 3, and 4 we write down this representation explicitly. As a further application of this representation we study the time dependence of density matrices ρ(t) which in our case is implemented through time dependence of the independent parameters. Under obvious differentiability assumptions the explicit form of [Formula: see text] is determined. As a special case we recover, for instance, the Lindblad form. |
| Databáze: | OpenAIRE |
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