Mathematics Of Open Quantum Systems, The: Dissipative And Non-unitary Representations And Quantum Measurements
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A01=Eduard R Tsekanovskii
A01=Konstantin A Makarov
Aharonov-Bohm Ring
Author_Eduard R Tsekanovskii
Author_Konstantin A Makarov
Bassein of Attraction
Blaschke Product
Bound States
Boundary Conditions
Breight-wigner Shape
Canonical Commutation Relations
Category=PHQ
Cauchy Distribution
Character Automorphic Functions
Characteristic Function
Coinvariant Subspace
Complementarity Principle
Compressed Resolvent
Configuration Space
Continuous Monitoring
Contraction Semigroups
Convergence in Distribution
Decay Rate
Deficiency Indices
Density Matrix
Dilation
Dissipative Operator
Domain
Energy-Time Uncertainty Relation
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
Exclusive And Interference Measurements
Exponential Decay
Extension Theory
Fixed Point Theorems
Flow
Friedrichs Extension
Functional Models
Gauge Transformations
Gaussian Distribution
Generalized Central Limit Theorem
Hamiltonian
Hardy Spaces
Hilbert Space
Incoming and Outgoing Subspaces
Independent Random Variable
Inner Function
Inner Product
Interference
Invariance Principle
Law of Large Numbers
Levy Distribution
Magnetic Hamiltonian
Magnetic Potential
Mathematical Expectation
Metric Graphs
Momentum Operator
Multiplication Theorem
Open Systems
Operator Coupling
Outer Function
Position Operator
Prime Operators
Probability Amplitude
Probability Measure
Quantum Dynamics
Quantum Gate Coefficient
Quantum Measurement
Quantum Oscillator
Rank One Perturbation
Resolvent
Resolvent Set
Riesz Integral
Scattering Matrix
Self-Adjoin Operator
Sobolev Spaces
Spectral Projections
Spectrum
Stable Distributions
Symmetric Operator
Time Scales
Transmission Coefficient
Triples of Operators
Two Slit Experiment
Uncertainty Principle
Unitary Evolution
Unitary Invariant
Unstable States
Variance
Von Neumann's Parameter
Wave Function
Wave-particle Dualism
Weak Law of Large Numbers
Weyl Function
Zeno Effect
Product details
- ISBN 9789811241222
- Publication Date: 11 Feb 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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 Jørgensen 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.
