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Mathematics Of Open Quantum Systems, The: Dissipative And Non-unitary Representations And Quantum Measurements (Hardcover)
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Mathematics Of Open Quantum Systems, The: Dissipative And Non-unitary Representations And Quantum Measurements (Hardcover)
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This book presents new developments in the open quantum systems
theory with emphasis on applications to the (frequent) measurement
theory.In the first part of the book, the uniqueness theorems for
the solutions to the restricted Weyl commutation relations braiding
unitary groups and semi-groups of contractions are discussed. The
major theme involves an intrinsic characterization of the simplest
symmetric operator solutions to the Heisenberg uncertainty
relations, the problem posed by Jorgensen and Muhly, followed by
the proof of the uniqueness theorems for the simplest solutions to
the restricted Weyl commutation relations. The detailed study of
unitary invariants of the corresponding dissipative and symmetric
operators opens up a look at the classical Stone-von Neumann
uniqueness theorem from a new angle and provides an extended
version of the uniqueness result relating various realizations of a
differentiation operator on the corresponding metric graphs.The
second part of the book is devoted to mathematical problems of the
quantum measurements under continuous monitoring. Among the topics
discussed are the complementarity of the Quantum Zeno effect and
Exponential Decay scenario in frequent quantum measurements, and a
rigorous treatment, within continuous monitoring paradigm, of the
celebrated 'double-slit experiment' where the renowned exclusive
and interference measurement alternatives approach in quantum
theory is presented in a way that is accessible for mathematicians.
One of the striking applications of the generalized (1-stable)
central limit theorem is the mathematical evidence of exponential
decay of unstable states of the quantum pendulum under continuous
monitoring.
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