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Open Quantum Systems Far from Equilibrium [Minkštas viršelis]

  • Formatas: Paperback / softback, 207 pages, aukštis x plotis: 235x155 mm, weight: 3401 g, 10 Illustrations, color; 34 Illustrations, black and white; IX, 207 p. 44 illus., 10 illus. in color., 1 Paperback / softback
  • Serija: Lecture Notes in Physics 881
  • Išleidimo metai: 21-Jan-2014
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319038761
  • ISBN-13: 9783319038766
Kitos knygos pagal šią temą:
Open Quantum Systems Far from EquilibriumDidesnis paveikslėlis
  • Formatas: Paperback / softback, 207 pages, aukštis x plotis: 235x155 mm, weight: 3401 g, 10 Illustrations, color; 34 Illustrations, black and white; IX, 207 p. 44 illus., 10 illus. in color., 1 Paperback / softback
  • Serija: Lecture Notes in Physics 881
  • Išleidimo metai: 21-Jan-2014
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319038761
  • ISBN-13: 9783319038766
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783319038766.html
Raktažodžiai:
Focusing on the link between microscopic models and the resulting open-system dynamics, this book presents a useful, self-contained toolbox for understanding the dynamics of open quantum systems. Each method includes easy-to-follow examples.

This monograph provides graduate students and also professional researchers aiming to understand the dynamics of open quantum systems with a valuable and self-contained toolbox. Special focus is laid on the link between microscopic models and the resulting open-system dynamics. This includes how to derive the celebrated Lindblad master equation without applying the rotating wave approximation. As typical representatives for non-equilibrium configurations it treats systems coupled to multiple reservoirs (including the description of quantum transport), driven systems and feedback-controlled quantum systems. Each method is illustrated with easy-to-follow examples from recent research. Exercises and short summaries at the end of every chapter enable the reader to approach the frontiers of current research quickly and make the book useful for quick reference.
1 Dynamics of Open Quantum Systems
1(26)
1.1 Conventions
2(1)
1.2 Evolution of Closed Systems
2(2)
1.3 Master Equations
4(6)
1.3.1 Definition
4(2)
1.3.2 Examples
6(4)
1.4 Density Matrix Formalism
10(7)
1.4.1 Density Matrix
10(2)
1.4.2 Dynamical Evolution of a Density Matrix
12(3)
1.4.3 Tensor Product
15(1)
1.4.4 The Partial Trace
16(1)
1.5 Lindblad Quantum Master Equation
17(6)
1.5.1 Representations
17(2)
1.5.2 Preservation of Positivity
19(2)
1.5.3 Rate Equation Representation
21(1)
1.5.4 Examples
21(2)
1.6 Superoperator Notation
23(4)
References
26(1)
2 Microscopic Derivation
27(20)
2.1 Tensor Product Representation of Fermionic Tunnel Couplings
28(1)
2.2 A Mapping for Short Times or Weak Couplings
29(6)
2.3 Master Equation in the Weak Coupling Limit
35(8)
2.3.1 Coarse-Graining Master Equation
35(4)
2.3.2 Quantum Optical Master Equation
39(1)
2.3.3 Properties of the Quantum Optical Master Equation
40(3)
2.4 Strong Coupling Limit
43(4)
References
44(3)
3 Exactly Solvable Models
47(14)
3.1 Pure Dephasing Spin-Boson Model
47(5)
3.1.1 Time Evolution Operator
48(1)
3.1.2 Reduced Dynamics
49(2)
3.1.3 Master Equation Approach
51(1)
3.2 Quantum Dot Coupled to Two Fermionic Leads
52(9)
3.2.1 Heisenberg Picture Dynamics
53(1)
3.2.2 Stationary Occupation
54(3)
3.2.3 Stationary Current
57(3)
References
60(1)
4 Technical Tools
61(26)
4.1 Analytic Techniques for Solving Master Equations
61(3)
4.1.1 Laplace Transform
62(1)
4.1.2 Equation of Motion Technique
62(1)
4.1.3 Quantum Regression Theorem
63(1)
4.2 Numerical Techniques for Solving Master Equations
64(7)
4.2.1 Numerical Integration
64(2)
4.2.2 Simulation as a Piecewise Deterministic Process (PDP)
66(5)
4.3 Shannon's Entropy Production
71(5)
4.3.1 Balance Equation Far from Equilibrium
73(2)
4.3.2 Linear Response for Two Terminals
75(1)
4.4 Full Counting Statistics: Phenomenological Introduction
76(11)
4.4.1 Discrete Particle Counting Statistics
76(2)
4.4.2 Continuous Energy Counting Statistics
78(1)
4.4.3 Moments and Cumulants
79(2)
4.4.4 Convenient Calculation of Lower Cumulants
81(1)
4.4.5 Fluctuation Theorems
82(3)
References
85(2)
5 Composite Non-equilibrium Environments
87(64)
5.1 Single Electron Transistor (SET)
88(5)
5.1.1 Model
88(3)
5.1.2 Thermodynamic Interpretation
91(2)
5.2 Serial Double Quantum Dot
93(6)
5.2.1 Model
93(5)
5.2.2 Thermodynamic Interpretation
98(1)
5.3 Interacting Transport Channels: Two Coupled SETs
99(7)
5.3.1 Model
100(2)
5.3.2 Thermodynamic Interpretation
102(1)
5.3.3 Reduced Dynamics
102(3)
5.3.4 Drag Current
105(1)
5.4 SET Monitored by a Low-Transparency QPC
106(10)
5.4.1 Model
107(7)
5.4.2 Detector Limit
114(2)
5.5 Monitored Charge Qubit
116(5)
5.5.1 Model
116(4)
5.5.2 Thermalization and Decoherence
120(1)
5.6 High-Transparency QPC
121(8)
5.6.1 Model
121(6)
5.6.2 Detector Backaction
127(2)
5.7 Phonon-Assisted Tunneling
129(6)
5.7.1 Model
129(3)
5.7.2 Thermodynamic Interpretation
132(2)
5.7.3 Thermoelectric Performance
134(1)
5.8 Beyond Weak Coupling: Phonon-Coupled Single Electron Transistor
135(16)
5.8.1 Model
136(2)
5.8.2 Reservoir Equilibrium in the Polaron Picture
138(1)
5.8.3 Polaron Rate Equation for Discrete Phonon Modes
139(5)
5.8.4 Polaron Rate Equation for Continuum Phonon Modes
144(2)
5.8.5 Thermodynamic Interpretation
146(2)
References
148(3)
6 Piecewise Constant Control
151(8)
6.1 Piecewise Constant Open-Loop Control
152(1)
6.2 Piecewise Constant Feedback Control
152(3)
6.3 Wiseman-Milburn Quantum Feedback
155(2)
6.4 Further Roads to Feedback
157(2)
References
158(1)
7 Controlled Systems
159(46)
7.1 Single Junction
159(10)
7.1.1 Open-Loop Control
162(1)
7.1.2 Closed-Loop Control
163(6)
7.2 Electronic Pump
169(8)
7.2.1 Power-Consuming Pump
170(4)
7.2.2 Open-Loop Control at Zero Power Consumption
174(3)
7.3 Encoding Maxwell's Demon as Feedback Control
177(6)
7.3.1 Feedback Control Loop
178(1)
7.3.2 Current
179(3)
7.3.3 Entropy Production
182(1)
7.4 Self-Controlling Systems: A Complete Description of Maxwell's Demon
183(12)
7.4.1 Derivation of the Rate Equation
184(1)
7.4.2 Counting Statistics and Entropy
185(3)
7.4.3 Global View: A Thermoelectric Device
188(3)
7.4.4 Local View: A Feedback-Controlled Device
191(4)
7.5 Qubit Stabilization
195(10)
7.5.1 Model
195(4)
7.5.2 Feedback Liouvillian
199(1)
7.5.3 Phenomenological Consequences
200(3)
References
203(2)
Index 205