Details
| Original language | English |
|---|---|
| Article number | 1740015 |
| Number of pages | 1 |
| Journal | Open Sys. Inf. Dyn. |
| Volume | 24 |
| Issue number | 4 |
| Publication status | Published - 30 Nov 2017 |
Abstract
Keywords
- Dynamical semigroup, unbounded generators, standard form
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Mathematical Physics
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In: Open Sys. Inf. Dyn., Vol. 24, No. 4, 1740015, 30.11.2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Unbounded generators of dynamical semigroups
AU - Siemon, Inken
AU - Holevo, Alexander S.
AU - Werner, Reinhard F.
N1 - Funding information: I.S. and R.F.W. are supported by RTG 1991 and SFB DQ-mat of the DFG.
PY - 2017/11/30
Y1 - 2017/11/30
N2 - Dynamical semigroups have become the key structure for describing open system dynamics in all of physics. Bounded generators are known to be of a standard form, due to Gorini, Kossakowski, Sudarshan and Lindblad. This form is often used also in the unbounded case, but rather little is known about the general form of unbounded generators. In this paper we first give a precise description of the standard form in the unbounded case, emphasizing intuition, and collecting and even proving the basic results around it. We also give a cautionary example showing that the standard form must not be read too naively. Further examples are given of semigroups, which appear to be probability preserving to first order, but are not for finite times. Based on these, we construct examples of generators which are not of standard form.
AB - Dynamical semigroups have become the key structure for describing open system dynamics in all of physics. Bounded generators are known to be of a standard form, due to Gorini, Kossakowski, Sudarshan and Lindblad. This form is often used also in the unbounded case, but rather little is known about the general form of unbounded generators. In this paper we first give a precise description of the standard form in the unbounded case, emphasizing intuition, and collecting and even proving the basic results around it. We also give a cautionary example showing that the standard form must not be read too naively. Further examples are given of semigroups, which appear to be probability preserving to first order, but are not for finite times. Based on these, we construct examples of generators which are not of standard form.
KW - Dynamical semigroup
KW - unbounded generators, standard form
UR - http://www.scopus.com/inward/record.url?scp=85038435655&partnerID=8YFLogxK
U2 - 10.1142/S1230161217400157
DO - 10.1142/S1230161217400157
M3 - Article
VL - 24
JO - Open Sys. Inf. Dyn.
JF - Open Sys. Inf. Dyn.
IS - 4
M1 - 1740015
ER -