Physics Letters A 305 (2002) 1–6
Continuous measurements and quantum oscillator evolution
M.V. Lomonosov State University, Department of Physics, Moscow 119899, Russia
Received 23 July 2002; received in revised form 8 September 2002; accepted 9 September 2002
Communicated by V.M. Agranovich
The goal of this Letter is to examine linear system evolution under external action during continuous partially selective
measurement of its coordinate. The equation, obtained in the article Phys. Lett. A 297 (2002) 300, generalized for the case of
optimal observable of quantum reading system (QRS) choice, was used for the analysis.
2002 Published by Elsevier Science B.V.
Keywords: Continuous measurement; Quantum oscillator; Partial selection
For the past few decades the theory of continu-
ous measurements has received a great deal of atten-
tion. A number of various approaches to the descrip-
tion of continuous measurements have been put for-
ward [1–7]. In our resent paper  we suggested an-
other approach to describe the state of the object under
continuous measurement. This approach is based on
the modelingof continuousmeasurementby the series
of single instantaneous measurements. The approach
used in  allows to take into account the number of
physical factors presented in real measurements:
1. The approximate character of the quantum read-
ing system (QRS) observable;
2. The arbitrariness of the initial QRS state (there
was considered the case of pure QRS state);
E-mail address: email@example.com (Yu.A. Rembovsky).
3. The time lag of register part of the device that
leads to averaging of outputs.
As the result, the equation that describes the evolu-
tion of object under continuous measurement was ob-
The equation takes intermediate place between the
two equations obtained by restricted path integral
method (RPI) [1,2] that correspond to the case of se-
lective measurement and non-selective measurement.
The equation in  describes the case of partially se-
The goal of this Letter is to examine linear system
evolution under external action during continuous
partially selective measurement of its coordinate. This
Letter consists of the following sections. The basic
properties and consequences of the equation obtained
in  are brieﬂy discussed in Section 2. The method
of linear system analysis is presented in Section 3.
The results of analysis are stated and discussed in
Section 4. The conclusion is formulated in Section 5.
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