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| TIME-DELAY AND SPECTRAL DENSITY FOR STARK HAMILTONIANS(II)--ASYMPTOTICS OF TRACE FORMULAE |
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Citation： |
D. Robert,Wang Xueping.TIME-DELAY AND SPECTRAL DENSITY FOR STARK HAMILTONIANS(II)--ASYMPTOTICS OF TRACE FORMULAE[J].Chinese Annals of Mathematics B,1991,12(3):358~384 |
| Page view： 891
Net amount： 863 |
Authors： |
D. Robert; Wang Xueping |
Foundation： |
Partially supported by Chinese NSF under grant No. 0187401 and by State Education Consmission of China. |
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| Abstract： |
This paper studies the Schrodinger operator with a homogeneous electric field of the form $\[ - \Delta + {x_1} + V(x)\]$ where $\[x = ({x_1}, \cdots ,{x_n}) \in {R^n}\]$. It is proved that in the spectral representation of the ftee Stark Hamiltonian,the time-delay operator in scattering theory can be expressed in trems of scattering matrix and under reasonable assumptions on the decay of the potential $V$, the on-shell time-delay operator is of trace class and its trace is related to the local spectral density via an explicit integral formulas. Some asymptotics for the trace are established when the energy tends to infinity. |
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