Quantum Mechanics of Non-Hamiltonian and Dissipative Systems
Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006.
• Requires no preliminary knowledge of graduate and advanced mathematics
• Discusses the fundamental results of last 15 years in this theory
• Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences
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adjoint Banach algebra Banach space basis binary operation bounded operators bounded superoperator C∗-algebra called Cauchy problem classical observables classical system commutative compact completely positive converges deﬁned DEFINITION denote density operator derivation domain dynamical semi-group eigenvalues element evolution exists following conditions four-valued logic gate groupoid Hamiltonian systems involutive isomorphic Jordan algebra kinematical Let us consider Lie algebra Lie—Jordan algebra Lindblad equation linear functional linear operator linear space linear superoperator Liouville space locally Hamiltonian logic gate matrix multiplication non-Hamiltonian systems nonnegative norm obtain one-parameter operator operator algebra operator Hilbert space operator space phase-space Poisson bracket positive superoperator quantum four-valued logic quantum mechanics quantum observables quantum operation quantum system real numbers representation result satisfied scalar product self-adjoint operator space H spectral statement structure subalgebra subset superop superoperator functions THEOREM trace-preserving unitary vector Weyl ordered operator Weyl quantization Wigner