Quantum Dissipative Systems (5版)

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This comprehensive textbook provides the fundamental concepts and methods of dissipative quantum mechanics and related issues in condensed matter physics starting from first principles. It deals with the phenomena and theory of decoherence, relaxation and dissipation in quantum mechanics that arise from the random exchange of energy with the environment. Major theoretical advances in combination with stunning experimental achievements and the arising perspective for quantum computing have brightened the field and brought it to the attention of the general community in natural sciences. Expertise in dissipative quantum mechanics is by now beneficial in a broad sphere. This book — originally published in 1992 and republished as enlarged and updated second, third and fourth edition in 1999, 2008, and 2012 — dives even deeper into the fundamental concepts, methods and applications of quantum dissipation. The fifth edition provides a self-contained and updated account of the quantum mechanics and quantum statistics of open systems. The subject matter of the book has been thoroughly revised to better comply with the needs of newcomers and the demands of the advanced readership. Most of the chapters are rewritten to enhance clarity and topicality. Four new chapters covering recent developments in the field have been added. There are about 600 references. This book is intended for use by advanced undergraduate and graduate students in physics, and for researchers active in the field. They will find the monograph as a rich and stimulating source. Sample Chapter(s) Preface Prefaces to former editions 1: Introduction Request Inspection Copy Contents: Introduction General Theory of Open Quantum Systems: Diverse Limited Approaches: A Brief Survey System-Plus-Reservoir Models Imaginary-Time Approach and Equilibrium Dynamics Real-Time Approach and Nonequilibrium Dynamics Miscellaneous Applications: Damped Linear Quantum Mechanical Oscillator Quantum Brownian Free Motion The Thermodynamic Variational Approach Suppression of Quantum Coherence Quantum Statistical Decay: Introduction Classical Rate Theory: A Brief Overview Quantum Rate Theory: Basic Methods Multidimensional Quantum Rate Theory Crossover from Thermal to Quantum Decay Thermally Activated Decay The Crossover Region Dissipative Quantum Tunneling The Dissipative Two-State System: Introduction Thermodynamics Electron Transfer and Incoherent Tunneling Two-State Dynamics: Basics and Methods Two-State Dynamics: Sundry Topics The Driven Two-State System The Dissipative Multi-State System: Quantum Brownian Particle in a Washboard Potential Multi-State Dynamics Exact Formal Expressions for Current and Current Noise The Ohmic Case Duality Symmetry Full Counting Statistics at Zero Temperature Twisted Partition Function and Nonlinear Mobility Charge Transport in Quantum Impurity Systems Nonlinear Quantum Brownian Duet as Work-to Work Converter Readership: Advanced undergraduate and graduate students; researchers in quantum statistical and condensed matter physics, in quantum/classical mechanics, in quantum information and quantum state engineering, in quantum optics, and in Bose-condensed systems.

Classical and Quantum Dissipative Systems

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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.

Elementary Quantum Mechanics: With Problems and Solutions (1版)

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【簡介】 The impact of quantum mechanics on our day-to-day life is growing at an exponential rate, of which most people are unaware. For example, the toaster is a prime example of a quantum mechanical device. While quantum mechanics arose as a subject in physics, quantum mechanical thinking has had, and continues to have, a broad impact on mathematics. For example, operator theory as we know it today would not exist without von Neumann’s effort to put quantum mechanics on a solid mathematical foundation. This book is defined for undergraduate students of mathematics to obtain an introduction to quantum mechanical ideas, and the associated mathematics, without requiring an extensive background in physics.This book is focused around the following topics. 1) The Mathematical Structure of Quantum Mechanics. We develop the main mathematical structure of quantum theory in the setting of the accepted postulates of quantum mechanics. Dirac’s bra-ket notation for the required linear algebra aspects will be utilized, as well as the mathematical and physical implications arising from the mathematical aspects of self-adjoint linear operators, with emphasis on the finite dimensional setting. 2) Dynamics of a Quantum Particle. We introduce the Schrodinger equation and discuss its physical meaning and mathematical structure. The required partial differential equations theory is elementary, and will be developed from scratch. 3) Measurement, Time Evolution, Uncertainty, and the Harmonic Oscillator. This builds on the previously developed mathematics and culminates with a detailed discussion of the quantum mechanical workhorse example - the harmonic oscillator. 4) Quantum Mechanics of Angular Momentum. Most of the book is developed in the context of the (relatively) simple one dimensional quantum systems. This topic goes into three dimensions and illustrates how very interesting mathematics can yield novel physical explanations that are unobtainable with classical methods. 5) The Postulates of Quantum Mechanics, Measurement, Composite Systems, Tensor Products, and Entanglement. This is the area that most students have heard of - quantum entanglement, ＂action-at-a- distance＂ and Bell’s inequality. The mathematics will be at an elementary level (except possibly for tensor products, which are sadly neglected many linear algebra courses today, but which are literally exploding in a variety of current applications).