| Description |
1 online resource (xxi, 815 pages) : illustrations |
| Contents |
1. Quantum mechanics : perspectives. 1.1. Wave Mechanics of particles : Schrödinger wave function. 1.2. Generator of position eigenstates. 1.3. Discrete phase space on finite fields. 1.4. Non-hermitian canonical variables. 1.5. Coherent state formulation as a mixed q-p representation -- 2. Quantum mechanics of classical fields. 2.1. Quantization of harmonic oscillator -- 3. The linear chain of atoms coupled by harmonic forces. 3.1. Complex dynamical variables -- 4. Lattice vibrations in crystalline solids : phonons. 4.1. Elementary lattice dynamics : the linear chain. 4.2. Lattice vibrations in three dimensions. 4.3. Normal coordinates in three dimensions. 4.4. Experimental probes : elastic constants. 4.5. Hamiltonian in terms of normal coordinates. 4.6. Phonons in three dimensions -- 5. Quantization of electromagnetic fields. 5.1. Maxwell equations. 5.2. The electromagnetic wave equations. 5.3. Covariant formulation of electrodynamics. 5.4. Complex dynamical variables -- 6. Quantum states of classical fields. 6.1. Wave function for the harmonic oscillator. 6.2. Second quantization of the classical ø and ø*. 6.3. Biorthogonal bases. 6.4. Coherent state bases -- 7. Coherent states formulation of quantum mechanics. 7.1. Non-orthogonality of coherent states. 7.2. Completeness of coherent states. 7.3. Generation of coherent states. 7.4. Displacement operator. 7.5. Linear dependence of coherent states. 7.6. General completeness relation for states generated by the displacement operator. 7.7. Coordinate representation of a coherent state. 7.8. The power of coherent state representation and the virtue of over-completeness -- 8. Density-matrix operator and quasi-probability density. 8.1. Diagonal representation of density-matrix operator. 8.2. Procedures for determining [symbol] -- 9. Operator algebra. 9.1. General operators. 9.2. Boson annihilation and creation operators, ordering. 9.3. Characteristic functions and distribution functions. 9.4. Generalized coherent states and squeezing. 9.5. Algebra and calculus within ordered products -- 10. Discrete quantum mechanics of Bloch electrons. 10.1. Energy-band dynamics of Bloch electrons. 10.2. Application to calculation of magnetic susceptibility -- 11. The effective Hamiltonian. 11.1. Two-body effective Hamiltonian. 11.2. Effective Hamiltonian in second quantization. 11.3. Effective non-hermitian Hamiltonian in a magnetic field -- 12. Path integral formulation. 12.1. Evolution operator and sumover trajectories. 12.2. Path integral in quantum-field theory -- 13. Gauge theory and geometric phase in quantum systems. 13.1. Directional (covariant) derivative on curve spaces. 13.2. Parallel transport in curvilinear space. 13.3. Parallel transport around closed curve. 13.4. Generalization to quantum mechanics. 13.5. Born-Oppenheimer approximation -- 14. Generalizations of geometric phase : fiber bundles. 14.1. The fiber bundle concept. 14.2. Generalizations of Berry's geometric phase in quantum physics. 14.3. Geometric phase in many-body systems -- 15. Geometric phase in quantum field theories : standard model. 15.1. Classical gauge theory. 15.2. The Yang-Mills lagrangian for the gauge field. 15.3. Electrodynamics as a gauge theory. 15.4. Quantization of gauge theories -- 16. String theory. 16.1. Feynman diagrams. 16.2. The birth of string theory. 16.3. Need for extra dimensions in string theory. 16.4. Nanoelectronics and string theory -- 17. Mesoscopic physics. 17.1. Introduction. 17.2. Mesoscopic quantum transport. 17.3. Electrical resistance due to a quantum scattering event. 17.4. The multichannel conductance formula. 17.5. Quantum interference in small-ring structures. 17.6. Generalized four-probe conductance formula -- 18. Model of an inelastic scatterer with complete randomization. 18.1. Conductance formula for a sample containing an inelastic scatterer between two elastic scatterers. 18.2. Quantum coherence in a chain of elastic and inelastic scatterers -- 19. Other applications of Landauer-Büttiker counting argument. 19.1. Integral and fractional quantum hall effect. 19.2. Universal conductance fluctuations. 19.3. Persistent currents in small normal-metal loop. 19.4. Transport in one-channel Luttinger liquid. 19.5. Mesoscopic thermal noise and excess noise. 19.6. High-frequency behavior -- 20. "Gated" Schrödinger waveguide structures and ballistic transport. 20.1. Phenomena associated with the quantization of charge -- 21. Steady-state nonlinear many-body quantum transport. 21.1. Correlation functions. 21.2. Integral equations of mesoscopic physics. 21.3. Tight-binding recursive technique -- 22. Numerical matrix-equation technique in steady-state quantum transport. 22.1. Kinetic equation at low temperatures. 22.2. Kinetic equation at higher temperatures and arbitrary bias. 22.3. Relation with multiple-probe Büttiker current formula -- 23. Alternative derivation of Büttiker multiple-probe current formula -- 24. Nanoelectronics. 24.1. Introduction. 24.2. Nanodevices. 24.3. Vertical vs lateral transport in nanotransistor designs. 24.4. Nanotransistor designs -- 25. Nanodevice physics. 25.1. Introduction. 25.2. Time-dependent nonequilibrium Green's function. 25.3. Intrinsic bistability of RTD. 25.4. Quantum inductance and equivalent circuit model for RTD -- 26. QDF approach and classical picture of quantum tunneling. 26.1. Lattice Wigner function and band structure effects. 26.2. Coherent and incoherent particle tunneling trajectories -- 27. RTD as a two-state memory device, a memdiode or a memristor. 27.1. Binary information storage at zero bias -- 28. RTD as a Tera-Herz source. 28.1. Type I RTD high-frequency operation. 28.2. Type II RTD high-frequency operation. 28.3. Regional block renormalization : Type-I RTD. 28.4. Regional block renormalization : Type-II RTD. 28.5. Two sites Bloch-equation 'Instanton' approach. 28.6. Stability analysis. 28.7. Numerical results. 28.8. Perturbation theory and limit cycle solutions -- 29. General theory of nonequilibrium quantum physics in real time. 29.1. Introduction. 29.2. Quantum dynamics in Liouville space -- 30. Super-Green's functions. 30.1. Connected diagrams : correlation function [symbol]. 30.2. Self-consistent equations for GQDF -- 31. Quantum transport equations of particle systems. 31.1. General quantum transport equations. 31.2. Transport equations and lattice Weyl transformation -- 32. Generalized Bloch equations. 32.1. Generalized Bloch equations in quantum optics. 32.2. The Bloch vector representation. 32.3. Bloch vector equations. 32.4. Atomic energy and dipole moment. 32.5. Rotating wave approximation. 32.6. Transformation to rotating frame. 32.7. Analytical solutions of the Bloch equations -- 33. Generalized coherent-wave theory. 33.1. The tight-binding limit -- 34. Impact ionization and Zener effect. 34.1. Coulomb pair potential [symbol] for impact ionization and Auger recombination. 34.2. Pair potential [symbol] due to Zener effect -- 35. Quantum transport equations in phase space. 35.1. Conservation of particle in Zener tunneling. 35.2. Nanosystem applications -- 36. QSFT of second-quantized classical fields : phonons. 36.1. Liouvillian space phonon dynamics. 36.2. The phonon super-Green's function. 36.3. Transport equation for the phonon super-correlation function. 36.4. Phonon transport equations in phase space. 36.5. The phonon Boltzmann equation -- 37. Operator Hilbert-space methodology in quantum physics. 37.1. The density operator in operator vector space. 37.2. Formulation in terms of translation operators. 37.3. Point projector in terms of line projectors -- 38. The Wigner function construction. 38.1. The quasi-probability distribution and Radon transform. 38.2. Line Eigenstates and line projection operators. 38.3. Translational covariance of the Wigner function. 38.4. Transformation properties of the Radon transform. 38.5. Intersection of line projectors : mutually unbiased basis -- 39. Discrete phase space on finite fields. 39.1. Discrete Wigner function on finite fields. 39.2. Generalized Pauli matrices. 39.3. Discrete Fourier transform and generalized Hadamard matrix -- 40. Discrete quantum mechanics on finite fields. 40.1. Tensor product of operators. 40.2. Quantum control. 40.3. Striations and mutually unbiased bases -- 41. Discrete Wigner distribution function construction. 41.1. Discrete Wigner function for a single qubit. 41.2. Discrete phase space structure for two qubits. 41.3. Line projectors for two qubit systems. 41.4. Discrete Wigner function for two qubits. 41.5. Examples of two-qubit discrete Wigner function. 41.6. Quantum nets : arbitrary assignment to a 'Vacuum' line. 41.7. Potential applications -- 42. Interference and measurement. 42.1. Projective measurements -- 43. Quantum operations on density operators. 43.1. The Kraus representation theorem. 43.2. Examples of quantum operations -- 44. Generalized measurements. 44.1. Distinguishing quantum states. 44.2. Utility of POVM -- 45. Phenomenological density matrix evolution. 45.1. Quantum channels. 45.2. Depolarizing channel. 45.3. Phase damping channel. 45.4. Amplitude-damping channel -- 46. Master equation for the density operator. 46.1. The Lindblad master equation. 46.2. Examples. 46.3. The Pauli master equation. 46.4. Lindblad equation for a damped harmonic oscillator. 46.5. Lindblad equation for phase damped harmonic oscillator. 46.6. Coherent state and decoherence -- 47. Microscopic considerations of a two-level system revisited. 47.1. Quantized radiation field. 47.2. Perturbation expansion of density operator. 47.3. Second order contribution. 47.4. Master equation to second order -- 48. Stochastic meaning of nonequilibrium quantum superfield theory. 48.1. Kubo-Martin-Schwinger condition. 48.2. A two-state system interacting with a heat bath. 48.3. Nonequilibrium quantum superfield theory correlations. 48.4. Lamb shift, dissipation kernel, and noise kernel -- 49. Discrete phase space viewpoint |
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49.1. Quantum teleportation. 49.2. N-state particles. 49.3. Formal derivation of entangled basis states. 49.4. Teleportation using three-particle entanglement and an ancilla. 49.5. Two-qubit teleportation using three-particle entanglement -- 50. Superdense coding. 50.1. General dense coding scheme. 50.2. Reduced density matrices. 50.3. Quantum channel, generalized dense coding -- 51. Quantum algorithm. 51.1. Quantum Fourier transform. 51.2. Quantum search algorithm. 51.3. Discrete logarithms. 51.4. Hidden subgroup problem |
| Summary |
This book presents the first comprehensive treatment of discrete phase-space quantum mechanics and the lattice Weyl-Wigner formulation of energy band dynamics, by the originator of these theoretical techniques. The author's quantum superfield theoretical formulation of nonequilibrium quantum physics is given in real time, without the awkward use of artificial time contour employed in previous formulations. These two main quantum theoretical techniques combine to yield general (including quasiparticle-pairing dynamics) and exact quantum transport equations in phase-space, appropriate for nanodevices. The derivation of transport formulas in mesoscopic physics from the general quantum transport equations is also treated. Pioneering nanodevices are discussed in the light of the quantum-transport physics equations, and an in-depth treatment of the physics of resonant tunneling devices is given. Operator Hilbert-space methods and quantum tomography are discussed. Discrete phase-space quantum mechanics on finite fields is treated for completeness and by virtue of its relevance to quantum computing. The phenomenological treatment of evolution superoperator and measurements is given to help clarify the general quantum transport theory. Quantum computing and information theory is covered to demonstrate the foundational aspects of discrete quantum dynamics, particularly in deriving a complete set of multiparticle entangled basis states |
| Bibliography |
Includes bibliographical references (pages 803-809) and index |
| Notes |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
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Print version record |
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digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL |
| Subject |
Phase space (Statistical physics)
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Mesoscopic phenomena (Physics)
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Transport theory.
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Nanostructured materials -- Transport properties
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Quantum theory.
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Nanoscience.
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Quantum Theory
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SCIENCE -- Physics -- General.
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Mesoscopic phenomena (Physics)
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Nanoscience
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Phase space (Statistical physics)
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Quantum theory
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Transport theory
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| Form |
Electronic book
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| Author |
World Scientific (Firm)
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| ISBN |
9789812835376 |
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9812835377 |
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9786612760495 |
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6612760494 |
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