Exponential Decay of Quasi-stationary States of Time-periodic Schrodinger Equation with Short Range Potentials
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概要
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A solution $u(t,x)\in C(R_l^1,L^2(R)_x^N))$ to a time dependent Schrodinger equation $i(\partial U/\partial t)=-\Delta u+v(t,x)u$ with time periodic potential $V(t+2\pi ,x)=V(t,x)$ is called quasi-stationary state with quasi-level λ if it satisfies $u(t-2\pi ,x)=V(t,x)=exp(-2\pi i\lambdau(t,x)$. We show, under the condition $(1+\mid x \mid )^(1+\epsilon) V(t,x)\in C^1(R_l^1,L^(\infty )(R_x^N))$, that every non-threshold quasi-stationary state decays exponentially at infinity in the sense that exp $(\alpha \mid x \mid )u(t,x)\in C^1(R_l^1,L^2(R_x^N))$ for $\alpha ^2<1-(\lambda - [\lambda ]),$ if \lambda is its quasilevel, where [\lambda ] is the integral part of \lambda .
- The University of Tokyo,Department of Pure and Applied Sciences, College of Arts and Sciences, University of Tokyoの論文
The University of Tokyo,Department of Pure and Applied Sciences, College of Arts and Sciences, University of Tokyo | 論文
- Exponential Decay of Quasi-stationary States of Time-periodic Schrodinger Equation with Short Range Potentials
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