Kinetic theory for quantum nanosystems

Statistical mechanics......Page 9
Emerging irreversible processes in nanosystems......Page 12
Quantum measurement as a nonequilibrium process......Page 14
Plan of the thesis......Page 15
Quantum dynamics of isolated systems......Page 17
Quantum statistical ensemble dynamics......Page 18
Liouville space......Page 22
Projected dynamics......Page 24
Generalized master equation......Page 25
Markovian approximation......Page 26
Slippage of initial conditions......Page 27
Positivity-preserving evolution......Page 28
Perturbative expansion of the von Neumann equation......Page 31
Linear response theory......Page 34
Fermi golden rule......Page 38
The derivation of the transition rates......Page 39
Dissipated power......Page 43
Pauli equation......Page 44
The derivation of the Pauli equation......Page 45
Redfield equation......Page 49
The projector......Page 50
The derivation of the Redfield equation......Page 51
Slippage of initial conditions......Page 53
Delta correlated environments......Page 54
Markovian approximation......Page 55
Our new kinetic equation......Page 59
The new projector......Page 60
The derivation of our kinetic equation......Page 61
Markovian approximation......Page 66
Population dynamics......Page 67
Coherence dynamics......Page 69
The infinite-environment limit......Page 70
Application to a two-level subsystem......Page 75
The spin-GORM model......Page 85
The model......Page 86
Spectral analysis......Page 89
Smoothed density of states......Page 91
Eigenvalue diagrams......Page 93
Spacing distribution......Page 95
The shape of the eigenstates (SOE)......Page 97
Asymptotic transition probability kernel (ATPK)......Page 102
Spin dynamics......Page 104
The weak-coupling regime (1)......Page 105
The strong-coupling regime (1)......Page 110
Numerical results......Page 113
Average versus individual realizations......Page 123
Equilibrium distribution of the subsystem......Page 125
Thermalization of the subsystem......Page 126
Thermalization of the total system......Page 131
Quantum diffusion......Page 135
Subsystem......Page 136
Coupling to the environment......Page 137
Bloch theorem......Page 140
Simplifying the problem......Page 142
The eigenvalue problem......Page 143
The diffusive eigenvalue (1)......Page 145
The eigenvalues (2)......Page 148
The eigenvalues (4)......Page 150
Description of the spectrum......Page 153
Theoretical predictions......Page 162
Numerical results......Page 164
Spectrum......Page 168
Temperature dependence of the diffusion coefficient......Page 172
Summary......Page 175
Summary of the main results......Page 179
Emergence of relaxation and decoherence in nanosystems......Page 180
Transport in nanosystems......Page 183
Perspectives......Page 184
Correlation functions of quantum systems......Page 189
Systems with a large heat capacity......Page 195
Redfield equation for two-level subsystems......Page 197
Gaussian orthogonal random matrices......Page 201
Perturbation theory for the spin-GORM model......Page 203