REGULARITY OF SOLUTIONS TO LINEAR STOCHASTIC SCHR?DINGER EQUATIONS

CARLOS M. MORA; ROLANDO REBOLLEDO

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REGULARITY OF SOLUTIONS TO LINEAR STOCHASTIC SCHR?DINGER EQUATIONS

机译：线性随机Schrüdinger方程解的规则性

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We develop linear stochastic Schr?dinger equations driven by standard cylindrical Brownian motions (LSSs) that unravel quantum master equations in Lindblad form into quantum trajectories. More precisely, this paper establishes the existence and uniqueness of the smooth strong solution Xt to a LSS with regular initial condition. Moreover, we obtain that the mean value of the square norm of Xt is constant. We also treat the approximation of LSSs by ordinary stochastic differential equations. We apply our results to:(i) models of quantum measurements of position and momentum; and(ii) a system formed by fermions.

机译：我们开发了由标准圆柱布朗运动（LSSs）驱动的线性随机Schr？dinger方程，该方程将Lindblad形式的量子主方程分解为量子轨迹。更准确地说，本文建立了具有规则初始条件的LSS的光滑强解Xt的存在性和唯一性。此外，我们获得Xt平方规范的平均值是恒定的。我们还通过普通的随机微分方程来处理LSS的逼近。我们将结果应用于：（i）位置和动量的量子测量模型; （ii）由费米子形成的系统。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2007年第2期|共23页
作者
CARLOS M. MORA; ROLANDO REBOLLEDO;
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正文语种 eng
中图分类物理学;
关键词
Linear stochastic Schrodinger equation; stochastic evolution equation; regular solution; existence and uniqueness;

机译：线性随机Schrodinger方程;随机演化方程;正则解;存在唯一性;

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1. REGULARITY OF SOLUTIONS TO LINEAR STOCHASTIC SCHR?DINGER EQUATIONS [J] . CARLOS M. MORA, ROLANDO REBOLLEDO Infinite dimensional analysis, quantum probability, and related topics . 2007,第2期

机译：线性随机Schrüdinger方程解的规则性
2. The Fu?ík spectrum of Schr?dinger operator and the existence of four solutions of Schr?dinger equations with jumping nonlinearities [J] . Chong Li, Shujie Li Journal of Differential Equations . 2017,第10期

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REGULARITY OF SOLUTIONS TO LINEAR STOCHASTIC SCHR?DINGER EQUATIONS

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