Nonequilibrium quantum transport physics in nanosystems: foundation of computational nonequilibrium physics in nanoscience and nanotechnology
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| 100 | 1 | |a Buot, Felix A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonequilibrium quantum transport physics in nanosystems |b foundation of computational nonequilibrium physics in nanoscience and nanotechnology |c Felix A. Buot |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2009 | |
| 300 | |a XXI, 815 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Nanostruktur |0 (DE-588)4204530-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Transportprozess |0 (DE-588)4185932-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Transportprozess |0 (DE-588)4185932-7 |D s |
| 689 | 0 | 1 | |a Nanostruktur |0 (DE-588)4204530-7 |D s |
| 689 | 0 | |5 DE-604 | |
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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
|
| any_adam_object | 1 |
| author | Buot, Felix A. |
| author_facet | Buot, Felix A. |
| author_role | aut |
| author_sort | Buot, Felix A. |
| author_variant | f a b fa fab |
| building | Verbundindex |
| bvnumber | BV035771663 |
| classification_rvk | UP 3200 |
| ctrlnum | (OCoLC)634419946 (DE-599)BVBBV035771663 |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV035771663 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:10Z |
| institution | BVB |
| isbn | 9789812566799 9812566791 |
| language | English |
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| oclc_num | 634419946 |
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| 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 |