Holdings: Nonequilibrium quantum transport physics in nanosystems

Nonequilibrium quantum transport physics in nanosystems: foundation of computational nonequilibrium physics in nanoscience and nanotechnology

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Bibliographic Details
Main Author:	Buot, Felix A. (Author)
Format:	Book
Language:	English
Published:	New Jersey [u.a.] World Scientific 2009
Subjects:	Nanostruktur Transportprozess
Online Access:	Inhaltsverzeichnis
Physical Description:	XXI, 815 S. Ill., graph. Darst.
ISBN:	9789812566799 9812566791

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adam_text	Contents Preface vii Overview of Quantum Mechanical Techniques 1 1. Quantum Mechanics: Perspectives 3 1.1 Wave Mechanics of Particles: Schrödinger Wave Function ..... 7 1.1.1 Some Algebraic Relations of Q and P ............ 10 1.1.2 Deterministic Schrödinger Wave Equation ......... 11 1.1.3 Isotopie Wavef unction and Many-Body Wavefunction ... 12 1.1.3.1 Decoupling of Isotopie Degrees of Freedom ... 13 1.1.3.2 Phenomenological Decoupling oi Reduction of Many-Body Problems ............... 14 1.2 Generator of Position Eigenstates .................. 14 1.3 Discrete Phase Space on Finite Fields ................ 18 1.4 Non-Hermitian Canonical Variables ................. 18 1.4.1 Left and Right Eigenvectors of Non-Hermitian Operators . 19 1.5 Coherent State Formulation as a Mixed q-p Representation .... 21 2. Quantum Mechanics of Classical Fields 23 2.1 Quantization of Harmonic Oscillator ................. 23 2.1.1 The Complex Canonical Variables .............. 23 2.1.2 Classical Schrödinger-Like Equation for Harmonic Oscillator ........................... 25 2.1.3 Second-quantization of the Schrödinger-Like Equation . . 25 3. The Linear Chain of Atoms Coupled by Harmonic Forces 26 3.1 Complex Dynamical Variables .................... 27 x Nonequilibrium Quantum Transport Physics in N ano systems 3.1.1 Creation and Annihilation Operator for a Coupled Linear Chain of Atoms ........................ 27 4. Lattice Vibrations in Crystalline Solids: Phonons 30 4.1 Elementary Lattice Dynamics: The Linear Chain .......... 30 4.1.1 Quantization of the Vibrational Mode: Phonons ...... 35 4.2 Lattice Vibrations in Three Dimensions ............ 36 4.3 Normal Coordinates in Three Dimensions .............. 37 4.3.1 Acoustic and Optic Modes .................. 42 4.3.2 Frequency Distribution of Normal Modes .......... 44 4.4 Experimental Probes: Elastic Constants ............... 46 4.5 Hamiltonian in Terms of Normal Coordinates ............ 46 4.6 Phonons in Three Dimensions .................... 48 5. Quantization of Electromagnetic Fields 50 5.1 Maxwell Equations ........................... 50 5.2 The Electromagnetic Wave Equations ................ 51 5.2.1 A Single Electromagnetic Wave Equation .......... 52 5.3 Covariant Formulation of Electrodynamics ............. 54 5.4 Complex Dynamical Variables .................... 56 6. Quantum States of Classical Fields 62 6.1 Wave Function for the Harmonic Oscillator ............. 62 6.2 Second Quantization of the Classical φ and φ* ........... 62 6.3 Biorthogonal Bases .......................... 65 6.4 Coherent State Bases ......................... 66 7. Coherent States Formulation of Quantum Mechanics 68 7.1 Non-Orthogonality of Coherent States ................ 72 7.2 Completeness of Coherent States ................... 73 7.3 Generation of Coherent States .................... 73 7.4 Displacement Operator ........................ 75 7.5 Linear Dependence of Coherent States ................ 76 7.6 General Completeness Relation for States Generated by the Dis¬ placement Operator .......................... 77 7.7 Coordinate Representation of a Coherent State ........... 78 7.8 The Power of Coherent State Representation and the Virtue of Over-Completeness ........................... 79 8. Density-Matrix Operator and Quasi-Probability Density 82 8.1 Diagonal Representation of Density-Matrix Operator ........ 83 8.2 Procedures for Determining σ (α) .................. 84 Contents xi 9. Operator Algebra 87 9.1 General Operators........................... 87 9.2 Boson Annihilation and Creation Operators, Ordering ....... 91 9.2.1 Traces of Function of Boson Operators........... 95 9.3 Characteristic Functions and Distribution Functions ........ 98 9.3.1 The Wigner Distribution Function ............. 100 9.3.1.1 Q-function and P-Function ............ 104 9.3.2 The Husimi Distribution Function .............. 105 9.4 Generalized Coherent States and Squeezing ............. 109 9.5 Algebra and Calculus within Ordered Products ........... 113 9.5.1 Algebra within Ordered Products .............. 113 9.5.1.1 Differentiation within Ordered Products ..... 114 9.5.2 Integration within Ordered Products in Quantized Classi¬ cal Field ............................ 114 9.5.3 Evaluation of Integral of Some Important Mapping Operators ........................... 115 9.5.4 Symplectic Transformation and Symplectic Group ..... 116 9.5.4.1 Quadrature States ................. 119 9.5.5 Complex Form of Symplectic Transformation Matrix ... 120 10. Discrete Quantum Mechanics of Bloch Electrons 124 10.1 Energy-Band Dynamics of Bloch Electrons ............. 124 10.1.1 Wannier Function and Bloch Function ........... 124 10.1.2 Lattice Weyl-Wigner Formulation of Energy-Band Dynamics ........................... 125 10.2 Application to Calculation of Magnetic Susceptibility ....... 131 11. The Effective Hamiltonian 135 11.1 Two-Body Effective Hamiltonian ................ 136 11.2 Effective Hamiltonian in Second Quantization ........... 137 11.3 Effective Non-Hermitian Hamiltonian in a Magnetic Field ..... 141 12. Path Integral Formulation 146 12 J Evolution Operator and Sum over Trajectories ........... 146 12.2 Path Integral in Quantum-Field Theory ............... 148 12.2.1 Bose Systems ......................... 148 12.2.2 Path Integral for Fermion Systems ............. 149 13. Gauge Theory and Geometric Phase in Quantum Systems 157 13.1 Directional (Covariant) Derivative on Curve Spaces ........ 158 13.2 Parallel Transport in Curvilinear Space ............... 159 13.3 Parallel Transport Around Closed Curve .............. 160 xii Nonequüibrium Quantum Trans-port Physics in Nanosystems 13.4 Generalization to Quantum Mechanics ................162 13.5 Born-Oppenheimer Approximation ..................166 14. Generalizations of Geometric Phase: Fiber Bundles 170 14.1 The Fiber Bundle Concept ......................170 14.2 Generalizations of Berry s Geometric Phase in Quantum Physics . 173 14.3 Geometric Phase in Many-Body Systems ..............174 14.3.1 Localized Disturbances of the Ground State of 2+1-D Many-Body Systems .....................176 14.3.2 Reconstructing Statistical Quantum Fields in Many-Body Physics .............................179 14.3.2.1 Bosonization ....................181 15. Geometric Phase in Quantum Field Theories: Standard Model 182 15.1 Classical Gauge Theory ........................ 182 15.2 The Yang-Mills Lagrangian for the Gauge Field .......... 186 15.3 Electrodynamics as a Gauge Theory ................. 187 15.4 Quantization of Gauge Theories ................... 187 16. String Theory 189 16.1 Feynman Diagrams .......................... 189 16.2 The Birth of String Theory ...................... 190 16.3 Need for Extra Dimensions in String Theory ............ 191 16.4 Nanoelectronics and String Theory .................. 192 Mesoscopic Physics 195 17. Mesoscopic Physics 197 17.1 Introduction .............................. 197 17.2 Mesoscopic Quantum Transport ................... 198 17.3 Electrical Resistance Due to a Quantum Scattering Event ..... 199 17.4 The Multichannel Conductance Formula ............... 204 17.5 Quantum Interference in Small-Ring Structures ........... 206 17.6 Generalized Four-Probe Conductance Formula ........... 209 17.6.1 Two-Probe Conductance Formula .............. 211 17.6.2 Three-Probe Conductance Formula: Model of Inelastic Scatterers ........................... 212 17.6.3 Wealdy-Coupled Voltage Probes: Barrier Point Contacts . 213 17.6.4 The Landauer Four-Probe Conductance Limit ....... 214 18. Model of an Inelastic Scatterer with Complete Randomization 216 Contents xiii 18.1 Conductance Formula for a Sample Containing an Inelastic Scat- terer between Two Elastic Scatterers ................. 220 18.2 Quantum Coherence in a Chain of Elastic and Inelastic Scatterers ................................ 224 19. Other Applications of Landauer-Btlttiker Counting Argument 228 19.1 Integral and Fractional Quantum Hall Effect ............ 229 19.2 Universal Conductance Fluctuations ................. 230 19.3 Persistent Currents in Small Normal-Metal Loop .......... 230 19.4 Transport in One-Channel Luttinger Liquid ............. 231 19.5 Mesoscopic Thermal Noise and Excess Noise ............ 231 19.6 High-Frequency Behavior ....................... 232 20. Gated Schrödinger Waveguide Structures and Ballistic Transport 233 20.1 Phenomena Associated with the Quantization of Charge ...... 233 21. Steady-State Nonlinear Many-Body Quantum Transport 237 21.1 Correlation Functions ......................... 237 21.2 Integral Equations of Mesoscopic Physics .............. 240 21.3 Tight-Binding Recursive Technique ................. 244 21.3.1 Tight-Binding Expression for the Current ......... 245 21.3.2 Multidimensional Current Expression ............ 250 21.3.3 Mesoscopic Transport Along a Linear Atomic Chain . . . 250 21.3.4 The Four-Probe Landauer Current Formula ........ 254 21.3.5 Current Formula in the Presence of Real Phonon Scatterings ........................... 254 22. Numerical Matrix-Equation Technique in Steady-State Quantum Transport 258 22.1 Kinetic Equation at Low Temperatures ............... 259 22.2 Kinetic Equation at Higher Temperatures and Arbitrary Bias . . . 262 22.3 Relation with Multiple-Probe Büttiker Current Formula ...... 263 23. Alternative Derivation of Büttiker Multiple-Probe Current Formula 268 Heterostructure Quantum Devices: Nanoelectronics 271 24. Nanoelectronics 273 24.1 Introduction ..............................273 24.2 Nanodevices ..............................276 24.3 Vertical vs Lateral Transport in Nanotransistor Designs ......280 xiv Nonequüibrium Quantum Transport Physics in Nn.noityiite.ms 24.4 Nanotransistor Designs ........................ 281 24.4.1 Vertical Transport Designs .................. 281 24.4.2 Lateral Transport Designs .................. 289 24.4.3 GaAs/AlGaAs MODFET-Based Nanotransistors ..... 292 25. Nanodevice Physics 294 25.1 Introduction.............................. 294 25.2 Time-Dependent Nonequilibrium Green s Function .........295 25.2.1 Electron-Electron Interaction via Exchange of Phonons . . 300 25.2.2 Relaxation-Time Approximation ............... 301 25.3 Intrinsic Bistability of RTD ...................... 301 25.4 Quantum Inductance and Equivalent Circuit Model for RTD . . . 305 25.4.1 Transient Switching Behavior and Small-Signal Response of RTD from the QDF Approach ..............311 25.4.2 High-Frequency Behavior and Small Signal Response of RTD using an Equivalent Circuit Model ..........313 25.4.2.1 Linear Response ..................313 25.4.2.2 Nonlinear Response ................316 26. QDF Approach and Classical Picture of Quantum Tunneling 318 26.1 Lattice Wigner Function and Band Structure Effects ........318 26.2 Coherent and Incoherent Particle Tunneling Trajectories .....319 27. RTD as a Two-State Memory Device, a Memdiode or a Memristor 324 27.1 Binary Information Storage at Zero Bias ..............324 27.1.1 Intrinsic Behavior of Double-Barrier Structures ......324 27.1.2 The Physical Picture .....................325 27.1.3 Analysis of a RTD Memory or Memdiode .........326 27.1.4 Two-State I-V and Two Charge States ...........331 28. RTD as a Тега -Herz Source 333 28.1 Type I RTD High-Frequency Operation ...............333 28.2 Type II RTD High-Frequency Operation ..............335 28.3 Regional Block Renormalization: Туре -I RTD ...........338 28.3.1 Estimation of Ą and Jf ................... 339 28.3.2 Elimination of Fast-Relaxing Variable for Туре -I RTD . . 340 28.4 Regional Block Renormalization: Type -П RTD ........... 341 28.5 Two Sites Bloch-Equation Instanton Approach .......... 343 28.5.1 Туре -I RTD .......................... 343 28.5.1.1 Tunneling Matrix Elements ............344 28.5.1.2 Elimination of Off-Diagonal Elements of the Density-Matrix ...................347 Contents xv 28.5.2 Туре-П RTD ......................... 350 28.6 Stability Analysis ........................... 351 28.7 Numerical Results ........................... 352 28.8 Perturbation Theory and Limit Cycle Solutions ........... 353 General Theory of Nonequilibrium Quantum Physics 359 29. General Theory of Nonequilibrium Quantum Physics in Real Time 361 29.1 Introduction .............................. 361 29.2 Quantum Dynamics in Liouville Space ................ 363 30. Super-Green s Functions 372 30.1 Connected Diagrams: Correlation Function /C ............ 379 30.2 Self-Consistent Equations for GQDF ................. 380 30.2.1 Schwinger Equation as Generalization of the Kohn-Sham and Gross-Pitaevskii Equations ............... 381 30.2.2 Closure Problem and Renormalization Procedure ..... 381 30.2.3 Iterative Equations for the Vertex Functions ........ 384 31. Quantum Transport Equations of Particle Systems 387 31.1 General Quantum Transport Equations ............... 390 31.2 Transport Equations and Lattice Weyl Transformation ...... 392 32. Generalized Bloch Equations 396 32.1 Generalized Bloch Equations in Quantum Optics .......... 397 32.2 The Bloch Vector Representation ................... 401 32.3 Bloch Vector Equations ........................ 403 32.4 Atomic Energy and Dipole Moment ................. 403 32.5 Rotating Wave Approximation .................... 406 32.6 Transformation to Rotating Frame .................. 406 32.6.1 State Preparation and Adiabatic Following Phenomenon . 408 32.7 Analytical Solutions of the Bloch Equations ............. 408 32.7.1 The Rabi Problem ...................... 408 32.7.2 Response to Light Pulse ................... 410 32.7.3 Self-Induced Transparency .................. 411 33. Generalized Coherent-Wave Theory 415 33.1 The Tight-Binding Limit ....................... 418 33.1.1 Flat Band Case ........................ 419 34. Impact Ionization and Zener Effect 421 xvi Nonequílibrium Quantum Transport Physics in Nanosystems 34.1 Coulomb Pair Potential Δ for Impact Ionization and Auger Recombination .............................422 34.2 Pair Potential Δ due to Zener Effect .................424 35. Quantum Transport Equations in Phase Space 426 35.1 Conservation of Particle in Zener Tunneling .............429 35.2 Nanosystem Applications .......................429 35.2.1 Resonant Tunneling Diode (RTD) ..............429 36. QSFT of Second-Quantized Classical Fields: Phonons 431 36.1 Liouvillian Space Phonon Dynamics ................. 433 36.2 The Phonon Super-Green s Function ................. 435 36.3 Transport Equation for the Phonon Super-Correlation Function . 438 36.4 Phonon Transport Equations in Phase Space ............ 439 36.5 The Phonon Boltzmann Equation .................. 442 Operator Space Methods and Quantum Tomography 445 37. Operator Hilbert-Space Methodology in Quantum Physics 447 37.1 The Density Operator in Operator Vector Space ..........447 37.2 Formulation in Terms of Translation Operators ...........450 37.2.1 Weyl Transform of GPM Operator ............. 452 37.2.2 Weyl Transform of the GPM Eigenstate Projector ..... 454 37.3 Point Projector in Terms of Line Projectors ............. 456 37.3.1 Δ (ρ, q) in Terms of Intersecting Lines at Point (p, q) ... 456 38. The Wigner Function Construction 460 38.1 The Quasi-Probability Distribution and Radon Transform ................................ 460 38.1.1 The Radon Transform .................... 461 38.2 Line Eigenstates and Line Projection Operators .......... 462 38.2.1 Density Operator in Terms of Line Projectors ....... 465 38.3 Translational Covariance of the Wigner Function .......... 467 38.4 Transformation Properties of the Radon Transform ........ 469 38.5 Intersection of Line Projectors: Mutually Unbiased Basis ..... 471 Discrete Phase Space on Finite Fields 475 39. Discrete Phase Space on Finite Fields 477 39.1 Discrete Wigner Function on Finite Fields ..............477 Contents xvii 39.1.1 Line in Discrete Phase Space: Pure Quantum State .... 478 39.1.2 Commutation Relation Between Q (A) and T (q,p)sym ..479 39.2 Generalized Pauli Matrices ...................... 480 39.2.1 Commutation Relations and Products of Yqivi ....... 481 39.2.2 Expansion of Operators: Hamiltonian in Terms of Generalized Pauli Matrices .................. 483 39.2.3 Pauli Matrices ......................... 484 39.3 Discrete Fourier Transform and Generalized Hadamard Matrix . . 486 39.3.1 Eigenfunctions and Eigenvalues of X , Z , and Уід .... 487 39.3.2 General Quantum State of a Two-Level System: Bloch Sphere ............................. 489 39.3.2.1 Range of the Parameters ............. 491 39.3.2.2 Bloch Sphere . . ..................491 39.3.2.3 Quantum States on Opposite Points of Bloch Sphere ........................ 493 39.3.3 Exponential Map ....................... 493 39.3.3.1 Rotation about an Arbitrary Axis in Real 3-D Space ........................ 497 39.3.3.2 Arbitrary Unitary Operator for a Qubit: Quan¬ tum Control .................... 498 39.3.4 Density Operator for a Two-Level System: Disordered and Pure States .......................... 500 40. Discrete Quantum Mechanics on Finite Fields 501 40.1 Tensor Product of Operators ..................... 501 40.1.1 Entanglement Due to Interactions .............. 505 40.1.2 The No-Cloning Theorem .................. 506 40.1.2.1 Consequences .................... 507 40.2 Quantum Control ........................... 507 40.2.1 Pauli Operators over Power-of-Prime Finite Fields .... 509 40.2.1.1 Phase Space for a Spin-! System or Single Qubit ........................ 511 40.3 Striations and Mutually Unbiased Bases ............... 512 41. Discrete Wigner Distribution Function Construction 517 41.1 Discrete Wigner Function for a Single Qubit ............ 520 41.2 Discrete Phase Space Structure for Two Qubits ........... 528 41.2.1 Striations Construction .................... 529 41.2.2 Binary String Encoding of Points in Discrete Phase Space .............................. 531 41.2.3 Construction of Dual Field Basis for Two Qubits ..... 533 41.2.3.1 Commutation Relation .............. 534 Nonequüibrium Quantum Transport Physics in Nanosystems 41.3 Line Projectors for Two Qubit Systems ............... 535 41.3.1 Product Hilbert Space for a Two Qubit System ...... 535 41.3.2 Eigenvectors of Commuting Translation Operators .... 541 41.3.3 Vertical Striation Ray and Position Basis ......... 541 41.3.4 Horizontal Striation Ray and Momentum Basis ...... 544 41.3.5 Diagonal Striation Ray and ΎΥ Basis ........... 547 41.3.6 Low-Slope-Striation Ray and Belle Basis ......... 550 41.3.7 High-Slope-Striation Ray and Beau Basis ......... 552 41.4 Discrete Wigner Function for Two Qubits .............. 556 41.4.1 The Origin in Phase Space, q = 0,p=0 .......... 556 41.4.2 The Point (1,0) in Phase Space Structure ......... 557 41.4.3 The Point (ω,Ο) ........................ 557 41.4.4 The Point (ώ,Ο) ........................ 557 41.4.5 The Point (0,1)........................ 558 41.4.6 The Point (Ο,ω) ........................ 558 41.4.7 The Point (0,w) ........................ 558 41.4.8 The Point (1,1)........................ 559 41.4.9 The Point (ω, ω) ....................... 559 41.4.10 The Point (ω,ω) ....................... 559 41.4.11 The Point (ω, 1)........................ 560 41.4.12 The Point (ω, 1)........................ 560 41.4.13 The Point (ώ,ω) ....................... 560 41.4.14 The Point (Ι,ω) ........................ 561 41.4.15 The Point (ω,ώ) ....................... 561 41.4.16 The Point (Ι,ώ) ........................ 561 41.5 Examples of Two-Qubit Discrete Wigner Function ......... 562 41.5.1 Example 1........................... 562 41.5.2 Example 2........................... 562 41.5.3 Example 3........................... 563 41.6 Quantum Nets: Arbitrary Assignment to a Vacuum Line ..... 564 41.7 Potential Applications ......................... 565 Phenomenological Superoperator of Open Quantum Systems: Generalized Measurements 567 42. Interference and Measurement 569 42.1 Projective Measurements ....................... 571 42.1.1 Effects of Measurements ................... 573 42.1.2 Effects of Measurements on Entanglement ......... 573 42.1.3 Measurements in Quantum Teleportation .......... 574 43. Quantum Operations on Density Operators 575 Contents xix 43.1 The Kraus Representation Theorem................. 576 43.2 Examples of Quantum Operations .................. 576 43.2.1 Unitary Evolution ....................... 576 43.2.2 Probabilistic Unitary Evolution ............... 576 43.2.3 Von Neumann Measurements ................ 576 43.2.4 POVMs ............................ 577 44. Generalized Measurements 579 44.1 Distinguishing Quantum States .................... 583 44.2 Utility of POVM ............................ 584 45. Phenomenological Density Matrix Evolution 586 45.1 Quantum Channels .......................... 588 45.1.1 Time Evolution ........................ 589 45.1.2 Partial Trace ......................... 589 45.2 Depolarizing Channel ......................... 589 45.2.1 Unitary Representation of the Channel ........... 590 45.2.2 Kraus Representation of the Channel ............ 590 45.2.3 Relative-State Representation ................ 591 45.2.4 Bloch Sphere Picture ..................... 593 45.2.5 Semigroup Property ..................... 593 45.3 Phase Damping Channel ....................... 593 45.3.1 Unitary Representation for the Whole System ....... 594 45.3.2 Kraus Operators ....................... 594 45.4 Amplitude-Damping Channel ..................... 595 45.4.1 POVM and Unchanging Environment ............ 596 46. Master Equation for the Density Operator 598 46.1 The Lindblad Master Equation .................... 599 46.2 Examples ................................ 603 46.2.1 Spontaneous Emission .................... 603 46.2.2 Bloch Equations in Magnetic Resonance for Spin 1/2 . . . 604 46.3 The Pauli Master Equation ...................... 605 46.4 Lindblad Equation for a Damped Harmonic Oscillator ....... 606 46.5 Lindblad Equation for Phase Damped Harmonic Oscillator .... 608 46.6 Coherent State and Decoherence ................... 610 47. Microscopic Considerations of a Two-Level System Revisited 612 47.1 Quantized Radiation Field ...................... 613 47.2 Perturbation Expansion of Density Operator ............ 618 47.2.1 First-order Contribution ................... 620 47.2.2 Resonance Approximation .................. 621 xx Nonequilibrium Quantum Transport Physics in Nanosystems 47.2.3 Bloch Equation ........................ 622 47.3 Second Order Contribution ...................... 624 47.4 Master Equation to Second Order .................. 626 47.4.1 Thermal Reservoir ...................... 629 48. Stochastic Meaning of Nonequilibrium Quantum Superfield Theory 634 48.1 Kubo-Martin-Schwinger Condition ..................636 48.1.1 Mass, Dissipation, and Noise Kernels in Nonequilibrium Quantum Superfield Theory ................. 639 48.2 A Two-State System Interacting with a Heat Bath ......... 641 48.3 Nonequilibrium Quantum Superfield Theory Correlations ..... 644 48.4 Lamb Shift, Dissipation Kernel, and Noise Kernel ......... 650 48.4.1 Comparison with the Master Equation of Sec. 47.4 .... 652 Quantum Computing and Quantum Information: Discrete Phase Space Viewpoint 657 49. Discrete Phase Space Viewpoint 659 49.1 Quantum Teleportation ........................ 659 49.1.1 Unified Teleportation Procedure ............... 664 49.2 N-State Particles ............................ 665 49.3 Formal Derivation of Entangled Basis States ............ 665 49.3.1 Bell Basis ........................... 666 49.3.2 Three-Qubit Entangled Basis ................ 670 49.3.3 A Qubit Teleportation Using Three-Particle Entanglement ......................... 672 49.4 Teleportation Using Three-Particle Entanglement and an Ancilla . 674 49.5 Two-Qubit Teleportation Using Three-Particle Entanglement . . . 676 50. Superdense Coding 680 50.1 General Dense Coding Scheme ....................684 50.2 Reduced Density Matrices .......................684 50.3 Quantum Channel, Generalized Dense Coding ...........685 51. Quantum Algorithm 687 51.1 Quantum Fourier Transform .....................687 51.1.1 Order-Finding Algorithm ................... 693 51.1.2 Phase Estimation Algorithm ................. 695 51.1.3 Connection Between Root Finding and Phase Estimation . 699 51.2 Quantum Search Algorithm ...................... 702 51.2.1 Performance of the Search Algorithm ............ 704 Contents xxi 51.3 Discrete Logarithms .......................... 704 51.3.1 Quantum Solution ...................... 705 51.4 Hidden Subgroup Problem ...................... 706 51.4.1 Quantum Hidden Subgroup Algorithm ........... 708 Appendix A Commutation Relation between Components of π (χ, t) and A (x , t) 711 Appendix В Lattice Weyl Transform of One-Particle Effective Hamiltonian in Magnetic Field 715 Appendix С Second Quantization Operators in Solid-State Band Theory 718 Appendix D Direct Construction of Fermionic Path Integral 724 Appendix E Hot-Electron Green s Function 730 Appendix F Derivation of Generalized Semiconductor Bloch Equations 732 Appendix G Calculation of Nonequilibrium Self-Energies 741 G.I Nonequilibrium Self-Energy due to Electron-Electron Interaction ............................... 741 G.I.I First-Order Contribution to the Electron Self-Energy ... 741 G.I. 2 Four-Point Vertex Function to Second Order ........ 742 Appendix H Radon Transformation of Phase Space Functions 776 Appendix I Introduction to Finite Fields 790 1.1 Constructing Finite Fields ...................... 793 1.1.1 GF(9) ............................. 793 1.1.2 GFCS) ............................. 795 1.2 Constructing Bases of Finite Field .................. 796 1.3 Trace Operation on Elements of Finite Field ............ 798 1.4 Dual Basis ............................... 800 1.4.1 Construction of Dual Basis .................. 800 1.5 Transformation of Coordinates .................... 802 Bibliography 803 Index 811
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author	Buot, Felix A.
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discipline	Physik
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id	DE-604.BV035771663
illustrated	Illustrated
indexdate	2024-07-09T22:04:10Z
institution	BVB
isbn	9789812566799 9812566791
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-018631352
oclc_num	634419946
open_access_boolean
owner	DE-355 DE-BY-UBR DE-83 DE-11 DE-19 DE-BY-UBM
owner_facet	DE-355 DE-BY-UBR DE-83 DE-11 DE-19 DE-BY-UBM
physical	XXI, 815 S. Ill., graph. Darst.
publishDate	2009
publishDateSearch	2009
publishDateSort	2009
publisher	World Scientific
record_format	marc
spelling	Buot, Felix A. Verfasser aut Nonequilibrium quantum transport physics in nanosystems foundation of computational nonequilibrium physics in nanoscience and nanotechnology Felix A. Buot New Jersey [u.a.] World Scientific 2009 XXI, 815 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nanostruktur (DE-588)4204530-7 gnd rswk-swf Transportprozess (DE-588)4185932-7 gnd rswk-swf Transportprozess (DE-588)4185932-7 s Nanostruktur (DE-588)4204530-7 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018631352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Buot, Felix A. Nonequilibrium quantum transport physics in nanosystems foundation of computational nonequilibrium physics in nanoscience and nanotechnology Nanostruktur (DE-588)4204530-7 gnd Transportprozess (DE-588)4185932-7 gnd
subject_GND	(DE-588)4204530-7 (DE-588)4185932-7
title	Nonequilibrium quantum transport physics in nanosystems foundation of computational nonequilibrium physics in nanoscience and nanotechnology
title_auth	Nonequilibrium quantum transport physics in nanosystems foundation of computational nonequilibrium physics in nanoscience and nanotechnology
title_exact_search	Nonequilibrium quantum transport physics in nanosystems foundation of computational nonequilibrium physics in nanoscience and nanotechnology
title_full	Nonequilibrium quantum transport physics in nanosystems foundation of computational nonequilibrium physics in nanoscience and nanotechnology Felix A. Buot
title_fullStr	Nonequilibrium quantum transport physics in nanosystems foundation of computational nonequilibrium physics in nanoscience and nanotechnology Felix A. Buot
title_full_unstemmed	Nonequilibrium quantum transport physics in nanosystems foundation of computational nonequilibrium physics in nanoscience and nanotechnology Felix A. Buot
title_short	Nonequilibrium quantum transport physics in nanosystems
title_sort	nonequilibrium quantum transport physics in nanosystems foundation of computational nonequilibrium physics in nanoscience and nanotechnology
title_sub	foundation of computational nonequilibrium physics in nanoscience and nanotechnology
topic	Nanostruktur (DE-588)4204530-7 gnd Transportprozess (DE-588)4185932-7 gnd
topic_facet	Nanostruktur Transportprozess
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018631352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT buotfelixa nonequilibriumquantumtransportphysicsinnanosystemsfoundationofcomputationalnonequilibriumphysicsinnanoscienceandnanotechnology

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