Note: Intro -- Preface -- Acknowledgements -- Contents -- 1 Operator Spaces -- 1.1 Operator Spaces -- 1.1.1 Completely Bounded and Completely Positive Maps -- 1.1.2 Operator Systems -- 1.1.3 Fundamental Factorisation of CB Maps -- 1.2 More on CB and CP Maps -- 1.3 Ruan's Theorem and Its Applications -- 1.3.1 Ruan's Theorem -- 1.3.2 Some Applications and Some Basic Facts -- Analogy with Banach Space Properties -- 1.3.3 min and max Operator Space Structures on a Banach Space -- 1.4 Tensor Products of Operator Spaces -- 1.4.1 Injective Tensor Product -- 1.4.2 Projective Tensor Product -- 1.4.3 General Remarks -- 1.4.4 A Passing Remark on the Haagerup Tensor Product -- 1.5 Tensor Products of C*-Algebras -- 1.5.1 min and max Tensor Products of C*-Algebras -- 1.5.2 Kirchberg's Theorem -- References -- 2 Entanglement in Bipartite Quantum States -- 2.1 Quantum States, Observables and Probabilities -- 2.2 Entanglement -- 2.2.1 Schmidt Decomposition -- 2.2.2 Unitary Bases, EPR States and Dense Coding -- 2.3 Schmidt Rank of Bipartite Entangled States -- 2.3.1 Subspaces of Minimal Schmidt Rank -- 2.4 Schmidt Number of Mixed States -- 2.4.1 Test for Schmidt Number k Using k-Positive Maps -- 2.4.2 Schmidt Number of Generalized Werner States -- References -- 3 Operator Systems -- 3.1 Theorems of Choi -- 3.1.1 Douglas Factorization -- 3.1.2 Choi-Kraus Representation and Choi Rank -- Example: Binary Case Quantum Error Detection/Correction -- 3.2 Quantum Error Correction -- 3.2.1 Applications of Choi's Theorems to Error Correction -- 3.2.2 Shor's Code: An Example -- 3.3 Matrix Ordered Systems and Operator Systems -- 3.3.1 Duals of Matrix Ordered Spaces -- 3.3.2 Choi-Effros Theorem -- 3.4 Tensor Products of Operator Systems -- 3.4.1 Minimal Tensor Product of Operator Systems -- 3.4.2 Maximal Tensor Product of Operator Systems. , An Example of a Nuclear Operator System that is Not a C*-Algebra HP11 -- 3.5 Graph Operator Systems -- 3.5.1 Dual of a Graph Operator System -- 3.6 Three More Operator System Tensor Products -- 3.6.1 The Commuting Tensor Product c. -- 3.6.2 The Tensor Products el and er. -- 3.6.3 Lattice of Operator System Tensor Products -- 3.7 Some Characterizations of Operator System Tensor Products -- 3.7.1 Exact Operator Systems -- 3.7.2 Weak Expectation Property (WEP) -- 3.7.3 Operator System Local Lifting Property (OSLLP) -- 3.7.4 Double Commutant Expectation Property (DCEP) -- 3.8 Operator System Tensor Products and the Conjectures of Kirchberg and Tsirelson -- 3.8.1 Special Operator Sub-systems of the Free Group C*-Algebras -- 3.8.2 Kirchberg's Conjecture -- 3.8.3 Quotient of an Operator System -- References -- 4 Quantum Information Theory -- 4.1 Zero-Error Communication Via Quantum Channels -- 4.1.1 Conditions for Zero-Error Quantum Communication -- 4.1.2 Zero-Error Capacity and Lovasz Function -- 4.2 Strong Subadditivity and Its Equality Case -- 4.2.1 Monotonicity of Relative Entropy: Petz Theorem -- 4.2.2 Structure of States that Saturate Strong Subadditivity -- 4.2.3 An Operator Algebraic Proof of the Koashi-ImotoTheorem -- 4.3 Norms on Quantum States and Channels -- 4.4 Matrix-Valued Random Variables -- 4.4.1 Matrix Tail Bounds -- 4.4.2 Destroying Correlations -- 4.4.3 State Merging -- References -- Further Reading -- Index.

Note: Intro -- Preface -- Contents -- 1 Equiangular Lines -- 1.1 Introduction -- 1.2 Real Lines -- 1.3 Complex Lines -- References -- 2 Optimal Quantum Measurements -- 2.1 Introduction -- 2.2 SIC Representations of Quantum States -- 2.3 Constructing SICs Using Groups -- References -- 3 Geometry and Information Theory for Qubits and Qutrits -- 3.1 Qubits -- 3.2 Qutrits -- 3.3 Coherence -- References -- 4 SICs and Bell Inequalities -- 4.1 Mermin's Three-Qubit Bell Inequality -- 4.2 The Hoggar SIC -- 4.3 Qubit Pairs and Twinned Tetrahedral SICs -- 4.4 Failure of Hidden Variables for Qutrits -- 4.5 Quantum Theory from Nonclassical Probability Meshing -- References -- 5 The Hoggar-Type SICs -- 5.1 Introduction -- 5.2 Simplifying the QBic Equation -- 5.3 Triple Products and Combinatorial Designs -- 5.4 The Twin of the Hoggar SIC -- 5.5 Combinatorial Designs from the Twin Hoggar SIC -- 5.6 Quantum-State Compatibility -- 5.7 From Pauli Operators to Real Equiangular Lines -- 5.8 Concluding Remarks -- References -- 6 Sporadic SICs and the Exceptional Lie Algebras -- 6.1 Root Systems and Lie Algebras -- 6.2 E6 -- 6.3 E8 -- 6.4 E7 -- 6.5 The Regular Icosahedron and Real-Vector-Space Quantum Theory -- 6.6 Open Puzzles Concerning Exceptional Objects -- References -- 7 Exercises -- References -- Appendix Index -- Index.

Note: Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Foreword to the First Edition -- Preface to the Second Edition -- Preface to the First Edition -- Introduction -- 1: Overview of Bohmian Mechanics -- 1.1 Historical Development of Bohmian Mechanics -- 1.1.1 Particles and Waves -- 1.1.2 Origins of the Quantum Theory -- 1.1.3 "Wave or Particle?" vs. "Wave and Particle" -- 1.1.4 Louis de Broglie and the Fifth Solvay Conference -- 1.1.5 Albert Einstein and Locality -- 1.1.6 David Bohm and Why the "Impossibility Proofs" were Wrong? -- 1.1.7 John Bell and Nonlocality -- 1.1.8 Quantum Hydrodynamics -- 1.1.9 Is Bohmian Mechanics a Useful Theory? -- 1.2 Bohmian Mechanics for a Single Particle -- 1.2.1 Preliminary Discussions -- 1.2.2 Creating a Wave Equation for Classical Mechanics -- 1.2.2.1 Newton's second law -- 1.2.2.2 Hamilton's principle -- 1.2.2.3 Lagrange's equation -- 1.2.2.4 Equation for an (infinite) ensemble of trajectories -- 1.2.2.5 Classical Hamilton-Jacobi equation -- 1.2.2.6 Local continuity equation for an (infinite) ensemble of classical particles -- 1.2.2.7 Classical wave equation -- 1.2.3 Trajectories for Quantum Systems -- 1.2.3.1 Schrödinger equation -- 1.2.3.2 Local conservation law for an (infinite) ensemble of quantum trajectories -- 1.2.3.3 Velocity of Bohmian particles -- 1.2.3.4 Quantum Hamilton-Jacobi equation -- 1.2.3.5 A quantum Newton-like equation -- 1.2.4 Similarities and Differences between Classical and Quantum Mechanics -- 1.2.5 Feynman Paths -- 1.2.6 Basic Postulates for a Single-Particle -- 1.3 Bohmian Mechanics for Many-Particle Systems -- 1.3.1 Preliminary Discussions: The Many Body Problem -- 1.3.2 Many-Particle Quantum Trajectories -- 1.3.2.1 Many-particle continuity equation -- 1.3.2.2 Many-particle quantum Hamilton-Jacobi equation. , 1.3.3 Factorizability, Entanglement, and Correlations -- 1.3.4 Spin and Identical Particles -- 1.3.4.1 Single-particle with s = 1/2 -- 1.3.4.2 Many-particle system with s = 1/2 particles -- 1.3.5 Basic Postulates for Many-Particle Systems -- 1.3.6 The Conditional Wave Function: Many-Particle Bohmian Trajectories without the Many-Particle Wave Function -- 1.3.6.1 Single-particle pseudo-Schrödinger equation for many-particle systems -- 1.3.6.2 Example: Application in factorizable many-particle systems -- 1.3.6.3 Example: Application in interacting many-particle systems without exchange interaction -- 1.3.6.4 Example: Application in interacting many-particle systems with exchange interaction -- 1.4 Bohmian Explanation of the Measurement Process -- 1.4.1 The Measurement Problem -- 1.4.1.1 The orthodox measurement process -- 1.4.1.2 The Bohmian measurement process -- 1.4.2 Theory of the Bohmian Measurement Process -- 1.4.2.1 Example: Bohmian measurement of the momentum -- 1.4.2.2 Example: Sequential Bohmian measurement of the transmitted and reflected particles -- 1.4.3 The Evaluation of a Mean Value in Terms of Hermitian Operators -- 1.4.3.1 Why Hermitian operators in Bohmian mechanics? -- 1.4.3.2 Mean value from the list of outcomes and their probabilities -- 1.4.3.3 Mean value from the wave function and the operators -- 1.4.3.4 Mean value from Bohmian mechanics in the position representation -- 1.4.3.5 Mean value from Bohmian trajectories -- 1.4.3.6 On the meaning of local Bohmian operators AB(x) -- 1.5 Concluding Remarks -- 1.6 Problems and Solutions -- A.1 Appendix: Numerical Algorithms for the Computation of Bohmian Mechanics -- A.1.1 Analytical Computation of Bohmian Trajectories -- A.1.1.1 Time-dependent Schrödinger equation for a 1D space (TDSE1D-BT) with an explicit method. , A.1.1.2 Time-independent Schrödinger equation for a 1D space (TISE1D) with an implicit (matrix inversion) method -- A.1.1.3 Time-independent Schrödinger equation for a 1D space (TISE1D) with an explicit method -- A.1.2 Synthetic Computation of Bohmian Trajectories -- A.1.2.1 Time-dependent quantum Hamilton-Jacobi equations (TDQHJE1D) with an implicit (Newton-like fixed Eulerian mesh) method -- A.1.2.2 Time-dependent quantum Hamilton-Jacobi equations (TDQHJE1D) with an explicit (Lagrangian mesh) method -- A.1.3 More Elaborated Algorithms -- 2: Hydrogen Photoionization with Strong Lasers -- 2.1 Introduction -- 2.1.1 A Brief Overview of Photoionization -- 2.1.2 The Computational Problem of Photoionization -- 2.1.3 Photoionization with Bohmian Trajectories -- 2.2 One-Dimensional Photoionization of Hydrogen -- 2.2.1 The Physical Model -- 2.2.2 Harmonic Generation -- 2.2.3 Above Threshold Ionization -- 2.3 Hydrogen Photoionization with Beams Carrying Orbital Angular Momentum -- 2.3.1 Physical System -- 2.3.2 Bohmian Equations in an Electromagnetic Field -- 2.3.3 Selection Rules -- 2.3.4 Numerical Simulations -- 2.3.4.1 Gaussian pulses -- 2.3.4.2 Laguerre-Gaussian pulses -- 2.4 Conclusions -- 3: Atomtronics: Coherent Control of Atomic Flow via Adiabatic Passage -- 3.1 Introduction -- 3.1.1 Atomtronics -- 3.1.2 Three-Level Atom Optics -- 3.1.3 Adiabatic Transport with Trajectories -- 3.2 Physical System: Neutral Atoms in Optical Microtraps -- 3.2.1 One-Dimensional Hamiltonian -- 3.3 Adiabatic Transport of a Single Atom -- 3.3.1 The Matter Wave STIRAP Paradox with Bohmian Trajectories -- 3.3.2 Velocities and Accelerations of Bohmian Trajectories -- 3.4 Adiabatic Transport of a Single Hole -- 3.4.1 Hole Transfer as an Array-Cleaning Technique -- 3.4.2 Adiabatic Transport of a Hole in an Array of Three Traps -- 3.4.2.1 Three-level approximation description. , 3.4.2.2 Numerical simulations -- 3.4.3 Hole Transport Fidelity -- 3.4.4 Bohmian Trajectories for the Hole Transport -- 3.4.5 Atomtronics with Holes -- 3.4.5.1 Single-hole diode -- 3.4.5.2 Single-hole transistor -- 3.5 Adiabatic Transport of a Bose-Einstein Condensate -- 3.5.1 Madelung Hydrodynamic Formulation -- 3.5.2 Numerical Simulations -- 3.6 Conclusions -- 4: Bohmian Pathways into Chemistry: A Brief Overview -- 4.1 Introduction -- 4.2 Approaching Molecular Systems at Different Levels -- 4.2.1 The Born-Oppenheimer Approximation -- 4.2.2 Electronic Configuration -- 4.2.3 Dynamics of "Small" Molecular Systems -- 4.2.4 Statistical Approach to Large (Complex) Molecular Systems -- 4.3 Bohmian Mechanics -- 4.3.1 Fundamentals -- 4.3.2 Nonlocality and Entanglement -- 4.3.3 Weak Values and Equations of Change -- 4.4 Applications -- 4.4.1 Time-Dependent DFT: The Quantum Hydrodynamic Route -- 4.4.2 Bound System Dynamics: Chemical Reactivity -- 4.4.3 Scattering Dynamics: Young's Two-Slit Experiment -- 4.4.4 Effective Dynamical Treatments: Decoherence and Reduced Bohmian Trajectories -- 4.4.5 Pathways to Complex Molecular Systems: Mixed Bohmian-Classical Mechanics -- 4.5 Concluding Remarks -- 5: Adaptive Quantum Monte Carlo Approach States for High-Dimensional Systems -- 5.1 Introduction -- 5.2 Mixture Modeling Approach -- 5.2.1 Motivation for a Trajectory-Based Approach -- 5.2.1.1 Bohmian interpretation -- 5.2.1.2 Quantum hydrodynamic trajectories -- 5.2.1.3 Computational considerations -- 5.2.2 Density Estimation -- 5.2.2.1 The mixture model -- 5.2.2.2 Expectation maximization -- 5.2.3 Computational Results -- 5.2.3.1 Bivariate distribution with multiple nonseparable Gaussian components -- 5.2.4 The Ground State of Methyl Iodide -- 5.3 Quantum Effects in Atomic Clusters at Finite Temperature -- 5.4 Quantum Structures at Zero and Finite Temperature. , 5.4.1 Zero Temperature Theory -- 5.4.2 Finite Temperature Theory -- 5.4.2.1 Computational approach: The mixture model -- 5.4.2.2 Computational approach: Equations of motion for the sample points -- 5.4.3 Computational Studies -- 5.4.3.1 Zero temperature results -- 5.4.3.2 Finite temperature results -- 5.5 Overcoming the Node Problem -- 5.5.1 Supersymmetric Quantum Mechanics -- 5.5.2 Implementation of SUSY QM in an Adaptive Monte Carlo Scheme -- 5.5.3 Test Case: Tunneling in a Double-Well Potential -- 5.5.4 Extension to Higher Dimensions -- 5.5.4.1 Discussion -- 5.6 Summary -- 6: Nanoelectronics: Quantum Electron Transport -- 6.1 Introduction: From Electronics to Nanoelectronics -- 6.2 Evaluation of the Electrical Current and Its Fluctuations -- 6.2.1 Bohmian Measurement of the Current as a Function of the Particle Positions -- 6.2.1.1 Relationship between current in the ammeter Iammeter, g(t) and the current in the device-active region Ig(t) -- 6.2.1.2 Relationship between the current on the device-active region Ig(t) and the Bohmian trajectories {r1,g[t], . . . , rMP,g[t]} -- 6.2.1.3 Reducing the number of degrees of freedom of the whole circuit -- 6.2.2 Practical Computation of DC, AC, and Transient Currents -- 6.2.3 Practical Computation of Current Fluctuations and Higher Moments -- 6.2.3.1 Thermal and shot noise -- 6.2.3.2 Practical computation of current fluctuations -- 6.3 Solving Many-Particle Systems with Bohmian Trajectories -- 6.3.1 Coulomb Interaction Among Electrons -- 6.3.2 Exchange and Coulomb Interaction Among Electrons -- 6.3.2.1 Algorithm for spinless electrons -- 6.3.2.2 Algorithm for electrons with spins in arbitrary directions -- 6.4 Dissipation with Bohmian Mechanics -- 6.4.1 Parabolic Band Structures: Pseudo Schrödinger Equation -- 6.4.2 Linear Band Structures: Pseudo Dirac Equation -- 6.5 The BITLLES Simulator. , 6.5.1 Overall Charge Neutrality and Current Conservation.

Note: Intro -- Abstract -- Contents -- 1 Introduction -- 2 Mathematical Preliminaries -- 2.1 Basic Concepts of Vector Spaces -- 2.1.1 Minkowski Functionals -- 2.1.2 The Hahn-Banach Theorem -- 2.1.3 Locally Compact Spaces -- 2.1.4 Seminorms and Local Convexity -- 2.2 Vector Spaces With Order Unit -- 2.3 Base-norm Spaces -- 2.4 Functional Representation -- 2.5 Archimedeanization and Categories -- 2.6 Tensor Products -- 2.6.1 Tensor Products of Vector Spaces -- 2.6.2 Tensor Products of Order Unit Spaces -- 2.7 C*-algebras -- 2.8 Completely Positive Maps -- 2.9 Convex Polytopes -- 3 Generalized probabilistic theories -- 3.1 Preparation and Measurements -- 3.2 Attributes of GPTs -- 3.3 Examples of GPTs -- 4 Sections and Subsystems -- 4.1 Sections of the Effect Cone -- 4.2 Sections of the State Space -- 4.3 Spekkens' Toy Model -- 5 Two-Sections of Quantum Mechanics -- 5.1 Classification of Two Dimensional Sections -- 5.2 Geometric Evolution of State Spaces -- 6 Conclusion -- Bibliography.

Note: Cover -- Title Page -- Copyright Page -- Dedication -- Preface -- Contents -- Notations & -- Fundamental Constants -- 1 Basic Concepts & -- Formulation -- 1.1 Introduction -- 1.2 Measurements -- 1.3 Basic Postulates -- (i) Postulate 1. State of the System -- (ii) Postulate 2. Superposition of States -- (iii) Postulate 3. Operators for Dynamical Variables -- (iv) Postulate 4. Eigenvalues and Eigenvectors of Operators -- (v) Postulate 5. Hermitian Operator -- (vi) Postulate 6. Basis Vectors and Completeness Condition -- (vii) Expectation Value -- 2 Representation Theory -- 2.1 Elements of Representation Theory -- (i) The Energy Representation, called the E-representatrion -- (ii) Operators as Matrices -- 2.2 Change in Representation and Unitary Transformation -- 2.3 Commuting Observables -- 2.4 Uncertainty Relation -- 3 Position & -- Momentum Operators -- 3.1 Position Operator and its Eigenkets -- 3.2 Spatial Translation and Momentum Operator -- 3.3 Momentum Operator in Position Basis -- 3.4 Momentum Wavefunction -- 3.5 Gaussian as Minimum Uncertainty Wave Packet -- 3.6 Extension to Three Dimension -- 4 Time Evolution of Quantum Systems -- 4.1 Time Evolution Operator -- 4.2 The Schrödinger Equation of Motion -- 4.3 Time Dependence of Expectation Values: Ehrenfest Theorem -- 4.4 The Schrödinger and Heisenberg Pictures -- 4.5 The Heisenberg Equation of Motion -- 4.6 Operator Form of the Hamiltonian: Classical Analogue -- 4.7 Time Dependence of the Base Kets -- 5 Propagators and Feynman Path Integral -- 5.1 Propagators -- 5.2 Feynman's Path -- 6 Application in One Dimension -- 6.1 Free Particle -- 6.2 Rectangular Potential Well -- (i) Bound State Solution -- (ii) Unbound State Solution -- 6.3 Rectangular Potential Barrier -- 6.4 Delta Function Potential -- 6.5 Oscillator Problem by Schrödinger Method. , 6.6 Linear Harmonic Oscillator by Operator Method -- (i) Time Evolution of Oscillator -- (ii) Coherent State -- 6.7 Periodic Potential -- 7 Rotation and Angular Momentum -- 7.1 Introduction -- 7.2 Rotation in Three Dimension -- 7.3 Rotation of System Kets -- 7.4 Eigenvalue and Eigenvectors of Angular Momentum -- 7.5 Matrix Representation of Angular Momentum Operator -- 7.6 Orbital Angular Momentum -- 8 Spin Angular Momentum -- 8.1 The Stern Gerlach Experiment -- 8.2 Matrix Representation of Spin -- 8.3 Finite Rotations in Spin-½ Space -- 8.4 Pauli Two Component Spinor Formalism -- 9 Addition of Angular Momenta -- 9.1 Addition of Two Angular Momenta Ĵ[sub(1)] and Ĵ[sub(2)] -- 9.2 Addition of Orbital Angular Momentum and Spin of a Particle -- 9.3 Addition of Two Spins -- 10 Applications II -- 10.1 Hydrogen Atom -- 10.2 Charged Particle in Magnetic Field -- (i) The Landau Levels -- (ii) The Aharanov Bohm Effect -- 11 Symmetry in Quantum Mechanics -- 11.1 Symmetry Principle and Conservation Laws -- (i) Symmetry and Degeneracy -- 11.2 Space Reflection or Parity Operation -- 11.3 Time Reversal Symmetry -- 12 Approximate Methods -- 12.1 Semiclassical Aprroximation or WKB Method -- 12.2 Rayleigh Schrödinger Perturbation -- (i) Non-Degenerate Case -- (ii) Perturbation Calculations for Degenerate Energy Levels -- 12.3 The Variational Method -- 13 Methods for Time Dependent Problems -- 13.1 Time Dependent Perturbation -- 13.2 Harmonic Perturbation -- (i) Fermi's Golden Rule -- (ii) Ionization of Hydrogen Atom -- 13.3 Adiabatic Approximation -- 13.4 The Sudden Approximation -- 14 Scattering Theory I -- 14.1 Scattering Experiments: Cross Section -- 14.2 Potential Scattering -- 14.3 The Method of Partial Waves -- 14.4 The Optical Theorem -- 15 Scattering Theory II -- 15.1 The Lippmann Schwinger Equation -- 15.2 The Born Approximation. , 15.3 The Higher Order Born Approximation -- 16 Relativistic Wave Equations -- 16.1 Introduction -- 16.2 The Klein Gordon Equation -- 16.3 The Dirac Relativistic Equation -- 16.4 Conclusion -- A: Appendix -- A.1 Expansion in a Series of Orthonormal Functions -- A.2 Fourier Series -- A.3 Fourier Transforms -- A.4 The Dirac Delta Function -- Bibliography -- Index.

Note: Cover -- Half Title -- Title -- Copyright -- Dedication -- About The Authors -- Contents -- List Of Abbreviations -- List Of Symbols -- List Of Figures -- Preface -- Acknowledgments -- Introduction -- Chapter 1 Introduction To Superposition Principle Waves -- 1.1 Waves Superposition -- Chapter 2 The Wave Function, Expectations Values, And Uncertainty -- 2.1 The Foundations Of Quantum Mechanics -- 2.2 The Postulates Of Quantum Mechanics -- 2.3 Uncertainty And Expectation Values -- 2.4 Compatibility Condition Between Observable -- 2.5 Relation Of Indeterminacy -- 2.6 Evolution Operator -- Chapter 3 The Schr¨odinger Equation -- 3.1 Introduction -- 3.2 Symmetry Transformations -- 3.3 Equation Of Motion Of A Free Particle -- 3.4 Temporal Evolution Pictures -- 3.5 Solutions Of The Schr¨odinger Equation -- Chapter 4 Quantum Axiomatics -- 4.1 Introduction -- 4.2 The Postulates -- Chapter 5 Quantum Measurements -- 5.1 Introduction -- 5.2 The Quantum Measurement -- Chapter 6 Path Integral Formulation Of Quantum Mechanics -- 6.1 Calculating The Transition Amplitude -- 6.2 Interpretation Of The Classical Limit -- 6.3 Functional Integrals And Properties -- Chapter 7 Supersymmetry In Quantum Mechanics -- 7.1 Construction Of The Supersymmetric Partners -- 7.2 Algebra Of A Supersymmetric System -- 7.3 Violation Of The Supersymmetry -- 7.4 Successive Factoring Of A Hamiltonian -- Chapter 8 Quantum Persistent Currents -- 8.1 Persistent Currents -- 8.2 Persistent Charge Currents -- 8.3 Persistent Spin Currents -- 8.4 Equilibrium Currents In A Mesoscopic Ring Coupled To A Reservoir -- 8.5 The Decoupled So Active Ring -- 8.6 Decoherence With Spin Orbit Coupling -- 8.7 Persistent Charge Currents -- 8.8 Persistent Spin Currents -- 8.9 Equilibrium Currents In A Mesoscopic Graphene Ring -- 8.10 Ring Hamiltonian And Boundary Conditions. , 8.11 Closing The Wave Function On A Graphene Ring -- 8.12 Spin-orbit Coupling -- 8.13 Charge Persistent Currents -- 8.14 Equilibrium Spin Currents -- 8.15 Velocity Operators For Graphene -- Chapter 9 Cryptography And Quantum Mechanics -- 9.1 Classical Cryptography -- 9.2 Schr¨odinger's Cat -- 9.3 Heisenberg Uncertainty Principle -- 9.4 The Density Operator -- 9.5 Quantum Computation -- Chapter 10 Non-equilibrium Quantum Mechanics -- 10.1 Systems In Equilibrium -- 10.2 Systems Out Of Equilibrium -- Chapter 11 Introductory Spintronics -- 11.1 About Spin -- 11.2 Effects Associated To Spintronics -- 11.3 Giant Magnetic Resistance -- 11.4 Spin Valves -- 11.5 Magnetic Tunnel Junction -- 11.6 Julliere Model For Tmr -- 11.7 Spin Torque Momentum -- 11.8 Semiconductor Spintronics -- Chapter 12 Quantum Dots -- 12.1 Structure Of Quantum Dots -- Chapter 13 Magnetic Resonance -- 13.1 Spin -- 2 Hilbert Space -- 13.2 Complete Description Of A -- 2 Spin Particle -- 13.3 Magnetic Spin Moment -- 13.4 Spatial And Spin Uncorrelated Variables -- 13.5 The Magnetic Resonance -- Chapter 14 Introductory Theory Of Scattering -- 14.1 Amplitude Of Scattering F(k -- -- ) -- 14.2 Born Approximation -- 14.3 The Scattering Operator, The S Matrix -- 14.4 Partial Waves Theory For Central Potentials -- Chapter 15 Introduction To Quantum Hall Effect -- 15.1 Classical Hall Effect -- 15.2 Two-dimensional Electronic Systems -- 15.3 The Quantum Hall Effect-integer Quantum Hall Effect . -- Bibliography -- Index.