The Wigner function in science and technology / David K. Ferry, Mihail Nedjalkov.

By: Ferry, David K [author.]Contributor(s): Nedjalkov, Mihail [author.] | Institute of Physics, IOP - EBA (Great Britain) [publisher.]Material type: TextTextSeries: IOP (Series)Release 5 | IOP expanding physicsPublisher: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2018]Description: 1 online resource (various pagings) : illustrations (some color)Content type: text Media type: electronic Carrier type: online resourceISBN: 9780750316712 ebookSubject(s): Wigner distribution | Mathematical physics | Phase space (Statistical physics) | Quantum theory -- Mathematical models | Quantum physics (quantum mechanics & quantum field theory) | SCIENCE / Physics / Quantum TheoryAdditional physical formats: Print version:: No titleDDC classification: 530.13 LOC classification: QC174.85.P48 F478 2018ebOnline resources: e-book Full-text access Also available in print.
Contents:
1. Introduction -- 1.1. Classical mechanics -- 1.2. Rise of quantum mechanics -- 1.3. Eugene Wigner -- 1.4. Modern devices and simulation -- 1.5. Our approach
2. Approaches to quantum transport -- 2.1. Modes and the Landauer formula -- 2.2. The scattering matrix approach -- 2.3. The density matrix -- 2.4. Green's functions -- 2.5. What are the relative advantages?
3. Wigner functions -- 3.1. Preliminary considerations -- 3.2. The equations of motion -- 3.3. Generalizing the Wigner function -- 3.4. Other phase space approaches -- 3.5. Wigner-Weyl transforms -- 3.6. The hydrodynamic equations
4. Effective potentials -- 4.1. Size of the electron -- 4.2. The Bohm potential -- 4.3. Bohm and the two-slit experiment -- 4.4. The Wigner potential -- 4.5. Feynman and effective potentials
5. Numerical solutions -- 5.1. The initial state -- 5.2. Numerical techniques -- 5.3. The resonant tunneling diode : Wigner function simulations -- 5.4. Other devices
6. Particle methods -- 6.1. The classical Monte Carlo technique -- 6.2. Paths in quantum mechanics -- 6.3. Using particles with the Wigner function
7. Collisions and the Wigner function -- 7.1. The interaction representation -- 7.2. The electron-phonon interaction -- 7.3. The Wigner scattering integrals -- 7.4. Collisions in the Monte Carlo approach
8. Entanglement -- 8.1. An illustration of entanglement -- 8.2. Entanglement in harmonic oscillators -- 8.3. Measures of entanglement -- 8.4. Some illustrative examples
9. Quantum chemistry -- 9.1. Quantum statistics -- 9.2. Reactions and rates -- 9.3. Tunneling -- 9.4. Spectroscopy
10. Signal processing -- 10.1. Signal propagation -- 10.2. Wavelets
11. Quantum optics -- 11.1. Propagation -- 11.2. The Jaynes-Cummings model -- 11.3. Squeezed states -- 11.4. Coherence I -- 11.5. Coherence II -- 11.6. Bell states
12. Quantum physics -- 12.1. The harmonic oscillator -- 12.2. Quantum physics -- 12.3. Superconductivity -- 12.4. Plasmas -- 12.5. Relativistic systems -- 12.6. Quantum cascade laser.
Abstract: This book is designed to give a background on the origins and development of Wigner functions, as well as its mathematical underpinnings. Along the way the authors emphasise the connections, and differences, from the more popular non-equilibrium
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IOP Science eBook - EBA QC174.85.P48 F478 2018eb (Browse shelf (Opens below)) Available IOP_20210047

"Version: 20181101"--Title page verso.

Includes bibliographical references.

1. Introduction -- 1.1. Classical mechanics -- 1.2. Rise of quantum mechanics -- 1.3. Eugene Wigner -- 1.4. Modern devices and simulation -- 1.5. Our approach

2. Approaches to quantum transport -- 2.1. Modes and the Landauer formula -- 2.2. The scattering matrix approach -- 2.3. The density matrix -- 2.4. Green's functions -- 2.5. What are the relative advantages?

3. Wigner functions -- 3.1. Preliminary considerations -- 3.2. The equations of motion -- 3.3. Generalizing the Wigner function -- 3.4. Other phase space approaches -- 3.5. Wigner-Weyl transforms -- 3.6. The hydrodynamic equations

4. Effective potentials -- 4.1. Size of the electron -- 4.2. The Bohm potential -- 4.3. Bohm and the two-slit experiment -- 4.4. The Wigner potential -- 4.5. Feynman and effective potentials

5. Numerical solutions -- 5.1. The initial state -- 5.2. Numerical techniques -- 5.3. The resonant tunneling diode : Wigner function simulations -- 5.4. Other devices

6. Particle methods -- 6.1. The classical Monte Carlo technique -- 6.2. Paths in quantum mechanics -- 6.3. Using particles with the Wigner function

7. Collisions and the Wigner function -- 7.1. The interaction representation -- 7.2. The electron-phonon interaction -- 7.3. The Wigner scattering integrals -- 7.4. Collisions in the Monte Carlo approach

8. Entanglement -- 8.1. An illustration of entanglement -- 8.2. Entanglement in harmonic oscillators -- 8.3. Measures of entanglement -- 8.4. Some illustrative examples

9. Quantum chemistry -- 9.1. Quantum statistics -- 9.2. Reactions and rates -- 9.3. Tunneling -- 9.4. Spectroscopy

10. Signal processing -- 10.1. Signal propagation -- 10.2. Wavelets

11. Quantum optics -- 11.1. Propagation -- 11.2. The Jaynes-Cummings model -- 11.3. Squeezed states -- 11.4. Coherence I -- 11.5. Coherence II -- 11.6. Bell states

12. Quantum physics -- 12.1. The harmonic oscillator -- 12.2. Quantum physics -- 12.3. Superconductivity -- 12.4. Plasmas -- 12.5. Relativistic systems -- 12.6. Quantum cascade laser.

This book is designed to give a background on the origins and development of Wigner functions, as well as its mathematical underpinnings. Along the way the authors emphasise the connections, and differences, from the more popular non-equilibrium

Graduate students and researchers in STEM fields working with quantum phenomena and open quantum systems.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

David Ferry is Regents' Professor Emeritus in the School of Electrical, Computer, and Energy Engineering at Arizona State University. He was also graduate faculty in the Department of Physics and the Materials Science and Engineering program at

Title from PDF title page (viewed on December 14, 2018).