The Resource Nonequilibrium quantum transport physics in nanosystems : foundation of computational nonequilibrium physics in nanoscience and nanotechnology, Felix A. Buot
Nonequilibrium quantum transport physics in nanosystems : foundation of computational nonequilibrium physics in nanoscience and nanotechnology, Felix A. Buot
 Summary
 This book presents the first comprehensive treatment of discrete phasespace quantum mechanics and the lattice WeylWigner 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 quasiparticlepairing dynamics) and exact quantum transport equations in phasespace, 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 quantumtransport physics equations, and an indepth treatment of the physics of resonant tunneling devices is given. Operator Hilbertspace methods and quantum tomography are discussed. Discrete phasespace 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
 Language
 eng
 Extent
 1 online resource (xxi, 815 pages)
 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. Nonhermitian canonical variables. 1.5. Coherent state formulation as a mixed qp 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. Nonorthogonality 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 overcompleteness  8. Densitymatrix operator and quasiprobability density. 8.1. Diagonal representation of densitymatrix 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. Energyband dynamics of Bloch electrons. 10.2. Application to calculation of magnetic susceptibility  11. The effective Hamiltonian. 11.1. Twobody effective Hamiltonian. 11.2. Effective Hamiltonian in second quantization. 11.3. Effective nonhermitian Hamiltonian in a magnetic field  12. Path integral formulation. 12.1. Evolution operator and sumover trajectories. 12.2. Path integral in quantumfield 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. BornOppenheimer 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 manybody systems  15. Geometric phase in quantum field theories : standard model. 15.1. Classical gauge theory. 15.2. The YangMills 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 smallring structures. 17.6. Generalized fourprobe 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 LandauerBüttiker counting argument. 19.1. Integral and fractional quantum hall effect. 19.2. Universal conductance fluctuations. 19.3. Persistent currents in small normalmetal loop. 19.4. Transport in onechannel Luttinger liquid. 19.5. Mesoscopic thermal noise and excess noise. 19.6. Highfrequency behavior  20. "Gated" Schrödinger waveguide structures and ballistic transport. 20.1. Phenomena associated with the quantization of charge  21. Steadystate nonlinear manybody quantum transport. 21.1. Correlation functions. 21.2. Integral equations of mesoscopic physics. 21.3. Tightbinding recursive technique  22. Numerical matrixequation technique in steadystate quantum transport. 22.1. Kinetic equation at low temperatures. 22.2. Kinetic equation at higher temperatures and arbitrary bias. 22.3. Relation with multipleprobe Büttiker current formula  23. Alternative derivation of Büttiker multipleprobe 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. Timedependent 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 twostate memory device, a memdiode or a memristor. 27.1. Binary information storage at zero bias  28. RTD as a TeraHerz source. 28.1. Type I RTD highfrequency operation. 28.2. Type II RTD highfrequency operation. 28.3. Regional block renormalization : TypeI RTD. 28.4. Regional block renormalization : TypeII RTD. 28.5. Two sites Blochequation '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. SuperGreen's functions. 30.1. Connected diagrams : correlation function [symbol]. 30.2. Selfconsistent 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 coherentwave theory. 33.1. The tightbinding 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 secondquantized classical fields : phonons. 36.1. Liouvillian space phonon dynamics. 36.2. The phonon superGreen's function. 36.3. Transport equation for the phonon supercorrelation function. 36.4. Phonon transport equations in phase space. 36.5. The phonon Boltzmann equation  37. Operator Hilbertspace 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 quasiprobability 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 twoqubit 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. Amplitudedamping 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 twolevel 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. KuboMartinSchwinger condition. 48.2. A twostate 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
 49.1. Quantum teleportation. 49.2. Nstate particles. 49.3. Formal derivation of entangled basis states. 49.4. Teleportation using threeparticle entanglement and an ancilla. 49.5. Twoqubit teleportation using threeparticle 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
 Isbn
 9789812835376
 Label
 Nonequilibrium quantum transport physics in nanosystems : foundation of computational nonequilibrium physics in nanoscience and nanotechnology
 Title
 Nonequilibrium quantum transport physics in nanosystems
 Title remainder
 foundation of computational nonequilibrium physics in nanoscience and nanotechnology
 Statement of responsibility
 Felix A. Buot
 Language
 eng
 Summary
 This book presents the first comprehensive treatment of discrete phasespace quantum mechanics and the lattice WeylWigner 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 quasiparticlepairing dynamics) and exact quantum transport equations in phasespace, 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 quantumtransport physics equations, and an indepth treatment of the physics of resonant tunneling devices is given. Operator Hilbertspace methods and quantum tomography are discussed. Discrete phasespace 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
 Action
 digitized
 Cataloging source
 LLB
 Dewey number
 530.13
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QC174.85.P48
 LC item number
 B68 2009eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Label
 Nonequilibrium quantum transport physics in nanosystems : foundation of computational nonequilibrium physics in nanoscience and nanotechnology, Felix A. Buot
 Bibliography note
 Includes bibliographical references (pages 803809) and index
 http://library.link/vocab/branchCode

 net
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 black and white
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 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. Nonhermitian canonical variables. 1.5. Coherent state formulation as a mixed qp 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. Nonorthogonality 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 overcompleteness  8. Densitymatrix operator and quasiprobability density. 8.1. Diagonal representation of densitymatrix 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. Energyband dynamics of Bloch electrons. 10.2. Application to calculation of magnetic susceptibility  11. The effective Hamiltonian. 11.1. Twobody effective Hamiltonian. 11.2. Effective Hamiltonian in second quantization. 11.3. Effective nonhermitian Hamiltonian in a magnetic field  12. Path integral formulation. 12.1. Evolution operator and sumover trajectories. 12.2. Path integral in quantumfield 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. BornOppenheimer 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 manybody systems  15. Geometric phase in quantum field theories : standard model. 15.1. Classical gauge theory. 15.2. The YangMills 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 smallring structures. 17.6. Generalized fourprobe 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 LandauerBüttiker counting argument. 19.1. Integral and fractional quantum hall effect. 19.2. Universal conductance fluctuations. 19.3. Persistent currents in small normalmetal loop. 19.4. Transport in onechannel Luttinger liquid. 19.5. Mesoscopic thermal noise and excess noise. 19.6. Highfrequency behavior  20. "Gated" Schrödinger waveguide structures and ballistic transport. 20.1. Phenomena associated with the quantization of charge  21. Steadystate nonlinear manybody quantum transport. 21.1. Correlation functions. 21.2. Integral equations of mesoscopic physics. 21.3. Tightbinding recursive technique  22. Numerical matrixequation technique in steadystate quantum transport. 22.1. Kinetic equation at low temperatures. 22.2. Kinetic equation at higher temperatures and arbitrary bias. 22.3. Relation with multipleprobe Büttiker current formula  23. Alternative derivation of Büttiker multipleprobe 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. Timedependent 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 twostate memory device, a memdiode or a memristor. 27.1. Binary information storage at zero bias  28. RTD as a TeraHerz source. 28.1. Type I RTD highfrequency operation. 28.2. Type II RTD highfrequency operation. 28.3. Regional block renormalization : TypeI RTD. 28.4. Regional block renormalization : TypeII RTD. 28.5. Two sites Blochequation '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. SuperGreen's functions. 30.1. Connected diagrams : correlation function [symbol]. 30.2. Selfconsistent 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 coherentwave theory. 33.1. The tightbinding 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 secondquantized classical fields : phonons. 36.1. Liouvillian space phonon dynamics. 36.2. The phonon superGreen's function. 36.3. Transport equation for the phonon supercorrelation function. 36.4. Phonon transport equations in phase space. 36.5. The phonon Boltzmann equation  37. Operator Hilbertspace 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 quasiprobability 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 twoqubit 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. Amplitudedamping 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 twolevel 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. KuboMartinSchwinger condition. 48.2. A twostate 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
 49.1. Quantum teleportation. 49.2. Nstate particles. 49.3. Formal derivation of entangled basis states. 49.4. Teleportation using threeparticle entanglement and an ancilla. 49.5. Twoqubit teleportation using threeparticle 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
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 ocn613414695
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 other
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 1 online resource (xxi, 815 pages)
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 Isbn
 9789812835376
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 c
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