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"This book discusses issues associated with the quantum mechanical formulation of dissipative systems. It begins with an introductory review of phenomenological damping forces, and the construction of the Lagrangian and Hamiltonian for the damped motion. It is shown, in addition to these methods, that classical dissipative forces can also be derived from solvable many-body problems. A detailed discussion of these derived forces and their dependence on dynamical variables is also presented. The second part of this book investigates the use of classical formulation in the quantization of dynamical systems under the influence of dissipative forces. The results show that, while a satisfactory solution to the problem cannot be found, different formulations represent different approximations to the complete solution of two interacting systems. The third and final part of the book focuses on the problem of dissipation in interacting quantum mechanical systems, as well as the connection of some of these models to their classical counterparts. A number of important applications, such as the theory of heavy-ion scattering and the motion of a radiating electron, are also discussed."

Energy dissipation. --- Quantum theory. --- Mechanics. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Degradation, Energy --- Dissipation (Physics) --- Energy degradation --- Energy losses --- Losses, Energy --- Force and energy

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This volume is devoted to the exciting topic of dissipative solitons, i.e. pulses or spatially localised waves in systems exhibiting gain and loss. Examples are laser systems, nonlinear resonators and optical transmission lines. The physical principles and mathematical concepts are explained in a clear and concise way, suitable for students and young researchers. The similarities and differences in the notion of a soliton between dissipative systems and Hamiltonian and integrable systems are discussed, and many examples are given. The contributions are written by the world's leading experts in the field, making it a unique exposition of this emerging topic.

Physics. --- Quantum optics. --- Engineering. --- Optics, Lasers, Photonics, Optical Devices. --- Quantum Optics. --- Engineering, general. --- Solitons. --- Energy dissipation. --- Solitons --- Dissipation d'énergie --- EPUB-LIV-FT LIVCHIMI SPRINGER-B --- Construction --- Industrial arts --- Technology --- Lasers. --- Photonics. --- Optics --- Photons --- Quantum theory --- New optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators

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Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

Lyapunov stability --- Energy dissipation --- Dynamics --- Large scale systems --- Information Technology --- General and Others --- Lyapunov stability. --- Energy dissipation. --- Dynamics. --- Large scale systems. --- Systems, Large scale --- Dynamical systems --- Kinetics --- Liapunov stability --- Ljapunov stability --- Degradation, Energy --- Dissipation (Physics) --- Energy degradation --- Energy losses --- Losses, Energy --- Engineering systems --- System analysis --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Control theory --- Stability --- Clausius-type inequality. --- KalmanЙakubovichАopov conditions. --- KalmanЙakubovichАopov equations. --- KrasovskiiЌaSalle theorem. --- asymptotic stabilizability. --- combustion processes. --- comparison system. --- compartmental dynamical system theory. --- compartmental dynamical system. --- control Lyapunov function. --- control design. --- control signal. --- control vector Lyapunov function. --- convergence. --- coordination control. --- decentralized affine. --- decentralized control. --- decentralized controller. --- decentralized finite-time stabilizer. --- discrete-time dynamical system. --- dissipativity theory. --- dynamical system. --- ectropy. --- energy conservation. --- energy dissipation. --- energy equipartition. --- energy flow. --- entropy. --- feedback control law. --- feedback interconnection stability. --- feedback stabilizer. --- finite-time stability. --- finite-time stabilization. --- gain margin. --- hybrid closed-loop system. --- hybrid decentralized controller. --- hybrid dynamic controller. --- hybrid finite-time stabilizing controller. --- hybrid vector comparison system. --- hybrid vector dissipation inequality. --- impulsive differential equations. --- impulsive dynamical system. --- interconnected dynamical system. --- large-scale dynamical system. --- law of thermodynamics. --- linear energy exchange. --- maximum entropy control. --- multiagent interconnected system. --- multiagent systems. --- multivehicle coordinated motion control. --- nonconservation of ectropy. --- nonconservation of entropy. --- nonlinear dynamical system. --- optimality. --- plant energy. --- scalar Lyapunov function. --- sector margin. --- semistable dissipation matrix. --- stability analysis. --- stability theory. --- stability. --- state space. --- subsystem decomposition. --- subsystem energy. --- thermoacoustic instabilities. --- thermodynamic modeling. --- time-invariant set. --- time-varying set. --- vector Lyapunov function. --- vector available storage. --- vector comparison system. --- vector dissipation inequality. --- vector dissipative system. --- vector dissipativity theory. --- vector dissipativity. --- vector field. --- vector hybrid supply rate. --- vector lossless system. --- vector required supply. --- vector storage function. --- vector supply rate.