EAN: 9783540309918

OPEN QUANTUM SYSTEMS I - STÉPHANE ATTAL ALAIN J...

This is the ?rst in a series of three volumes dedicated to the lecture notes of the Summer
School ¿Open Quantum Systems¿ which took place at the Institut Fourier in Grenoble from June
16th to July 4th 2003. The contributions presented in these volumes are revised and expanded
versions of the notes provided to the students during the School. Closed vs. Open Systems By
de?nition  the time evolution of a closed physical systemS is deterministic. It is usually
described by a differential equation x ? = X(x ) on the manifold M of t t possible
con?gurations of the system. If the initial con?guration x ? M is known 0 then the solution of
the corresponding initial value problem yields the con?guration x at any future time t. This
applies to classical as well as to quantum systems. In the t classical case M is the phase
space of the system and x describes the positions and t velocities of the various components
(or degrees of freedom) ofS at time t. Inthe quantum case  according to the
orthodoxinterpretation of quantum mechanics  M is a Hilbert space and x a unit vector ¿ the
wave function ¿ describing the quantum t state of the system at time t. In both cases the
knowledge of the state x allows t to predict the result of any measurement made onS at time t.

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