Probability in Classical and Quantum Physics / I: |
Classical probability theory and stochastic processes / 1: |
The probability space / 1.1: |
The [sigma]-algebra of events / 1.1.1: |
Probability measures and Kolmogorov axioms / 1.1.2: |
Conditional probabilities and independence / 1.1.3: |
Random variables / 1.2: |
Definition of random variables / 1.2.1: |
Transformation of random variables / 1.2.2: |
Expectation values and characteristic function / 1.2.3: |
Stochastic processes / 1.3: |
Formal definition of a stochastic process / 1.3.1: |
The hierarchy of joint probability distributions / 1.3.2: |
Markov processes / 1.4: |
The Chapman-Kolmogorov equation / 1.4.1: |
Differential Chapman-Kolmogorov equation / 1.4.2: |
Deterministic processes and Liouville equation / 1.4.3: |
Jump processes and the master equation / 1.4.4: |
Diffusion processes and Fokker-Planck equation / 1.4.5: |
Piecewise deterministic processes / 1.5: |
The Liouville master equation / 1.5.1: |
Waiting time distribution and sample paths / 1.5.2: |
Path integral representation of PDPs / 1.5.3: |
Stochastic calculus for PDPs / 1.5.4: |
Levy processes / 1.6: |
Translation invariant processes / 1.6.1: |
The Levy-Khintchine formula / 1.6.2: |
Stable Levy processes / 1.6.3: |
References |
Quantum probability / 2: |
The statistical interpretation of quantum mechanics / 2.1: |
Self-adjoint operators and the spectral theorem / 2.1.1: |
Observables and random variables / 2.1.2: |
Pure states and statistical mixtures / 2.1.3: |
Joint probabilities in quantum mechanics / 2.1.4: |
Composite quantum systems / 2.2: |
Tensor product / 2.2.1: |
Schmidt decomposition and entanglement / 2.2.2: |
Quantum entropies / 2.3: |
Von Neumann entropy / 2.3.1: |
Relative entropy / 2.3.2: |
Linear entropy / 2.3.3: |
The theory of quantum measurement / 2.4: |
Ideal quantum measurements / 2.4.1: |
Operations and effects / 2.4.2: |
Representation theorem for quantum operations / 2.4.3: |
Quantum measurement and entropy / 2.4.4: |
Approximate measurements / 2.4.5: |
Indirect quantum measurements / 2.4.6: |
Quantum non-demolition measurements / 2.4.7: |
Density Matrix Theory / II: |
Quantum master equations / 3: |
Closed and open quantum systems / 3.1: |
The Liouville-von Neumann equation / 3.1.1: |
Heisenberg and interaction picture / 3.1.2: |
Dynamics of open systems / 3.1.3: |
Quantum Markov processes / 3.2: |
Quantum dynamical semigroups / 3.2.1: |
The Markovian quantum master equation / 3.2.2: |
The adjoint quantum master equation / 3.2.3: |
Multi-time correlation functions / 3.2.4: |
Irreversibility and entropy production / 3.2.5: |
Microscopic derivations / 3.3: |
Weak-coupling limit / 3.3.1: |
Relaxation to equilibrium / 3.3.2: |
Singular-coupling limit / 3.3.3: |
Low-density limit / 3.3.4: |
The quantum optical master equation / 3.4: |
Matter in quantized radiation fields / 3.4.1: |
Decay of a two-level system / 3.4.2: |
Decay into a squeezed field vacuum / 3.4.3: |
More general reservoirs / 3.4.4: |
Resonance fluorescence / 3.4.5: |
The damped harmonic oscillator / 3.4.6: |
Non-selective, continuous measurements / 3.5: |
The quantum Zeno effect / 3.5.1: |
Density matrix equation / 3.5.2: |
Quantum Brownian motion / 3.6: |
The Caldeira-Leggett model / 3.6.1: |
High-temperature master equation / 3.6.2: |
The exact Heisenberg equations of motion / 3.6.3: |
The influence functional / 3.6.4: |
Non-linear quantum master equations / 3.7: |
Quantum Boltzmann equation / 3.7.1: |
Mean field master equations / 3.7.2: |
Mean field laser equations / 3.7.3: |
Non-linear Schrodinger equation / 3.7.4: |
Super-radiance / 3.7.5: |
Decoherence / 4: |
The decoherence function / 4.1: |
An exactly solvable model / 4.2: |
Time evolution of the total system / 4.2.1: |
Decay of coherences and the decoherence factor / 4.2.2: |
Coherent subspaces and system-size dependence / 4.2.3: |
Markovian mechanisms of decoherence / 4.3: |
The decoherence rate / 4.3.1: |
Internal degrees of freedom / 4.3.2: |
Scattering of particles / 4.3.4: |
Vacuum decoherence / 4.4: |
Thermal noise / 4.4.2: |
Electromagnetic field states / 4.5: |
Atoms interacting with a cavity field mode / 4.5.1: |
Schrodinger cat states / 4.5.2: |
Caldeira-Leggett model / 4.6: |
General decoherence formula / 4.6.1: |
Ohmic environments / 4.6.2: |
Decoherence and quantum measurement / 4.7: |
Dynamical selection of a pointer basis / 4.7.1: |
Dynamical model for a quantum measurement / 4.7.2: |
Stochastic Processes in Hilbert Space / III: |
Probability distributions on Hilbert space / 5: |
The state vector as a random variable in Hilbert space / 5.1: |
A new type of quantum mechanical ensemble / 5.1.1: |
Stern-Gerlach experiment / 5.1.2: |
Probability density functionals on Hilbert space / 5.2: |
Probability measures on Hilbert space / 5.2.1: |
Distributions on projective Hilbert space / 5.2.2: |
Expectation values / 5.2.3: |
Ensembles of mixtures / 5.3: |
Probability density functionals on state space / 5.3.1: |
Description of selective quantum measurements / 5.3.2: |
Stochastic dynamics in Hilbert space / 6: |
Dynamical semigroups and PDPs in Hilbert space / 6.1: |
Reduced system dynamics as a PDP / 6.1.1: |
The Hilbert space path integral / 6.1.2: |
Diffusion approximation / 6.1.3: |
Stochastic representation of continuous measurements / 6.1.4: |
Stochastic time evolution of [epsilon subscript P]-ensembles / 6.2.1: |
Short-time behaviour of the propagator / 6.2.2: |
Direct photodetection / 6.3: |
Derivation of the PDP / 6.3.1: |
Path integral solution / 6.3.2: |
Homodyne photodetection / 6.4: |
Derivation of the PDP for homodyne detection / 6.4.1: |
Stochastic Schrodinger equation / 6.4.2: |
Heterodyne photodetection / 6.5: |
Stochastic collapse models / 6.5.1: |
Stochastic density matrix equations / 6.6: |
Photodetection on a field mode / 6.7: |
The photocounting formula / 6.7.1: |
QND measurement of a field mode / 6.7.2: |
The stochastic simulation method / 7: |
Numerical simulation algorithms for PDPs / 7.1: |
Estimation of expectation values / 7.1.1: |
Generation of realizations of the process / 7.1.2: |
Determination of the waiting time / 7.1.3: |
Selection of the jumps / 7.1.4: |
Algorithms for stochastic Schrodinger equations / 7.2: |
General remarks on convergence / 7.2.1: |
The Euler scheme / 7.2.2: |
The Heun scheme / 7.2.3: |
The fourth-order Runge-Kutta scheme / 7.2.4: |
A second-order weak scheme / 7.2.5: |
Examples / 7.3: |
The driven two-level system / 7.3.1: |
A case study on numerical performance / 7.4: |
Numerical efficiency and scaling laws / 7.4.1: |
The damped driven Morse oscillator / 7.4.2: |
Applications to quantum optical systems / 8: |
Continuous measurements in QED / 8.1: |
Constructing the microscopic Hamiltonian / 8.1.1: |
Determination of the QED operation / 8.1.2: |
Stochastic dynamics of multipole radiation / 8.1.3: |
Representation of incomplete measurements / 8.1.4: |
Dark state resonances / 8.2: |
Waiting time distribution and trapping state / 8.2.1: |
Measurement schemes and stochastic evolution / 8.2.2: |
Laser cooling and Levy processes / 8.3: |
Dynamics of the atomic wave function / 8.3.1: |
Coherent population trapping / 8.3.2: |
Waiting times and momentum distributions / 8.3.3: |
Strong field interaction and the Floquet picture / 8.4: |
Floquet theory / 8.4.1: |
Stochastic dynamics in the Floquet picture / 8.4.2: |
Spectral detection and the dressed atom / 8.4.3: |
Non-Markovian Quantum Processes / IV: |
Projection operator techniques / 9: |
The Nakajima-Zwanzig projection operator technique / 9.1: |
Projection operators / 9.1.1: |
The Nakajima-Zwanzig equation / 9.1.2: |
The time-convolutionless projection operator method / 9.2: |
The time-local master equation / 9.2.1: |
Perturbation expansion of the TCL generator / 9.2.2: |
The cumulant expansion / 9.2.3: |
Perturbation expansion of the inhomogeneity / 9.2.4: |
Error analysis / 9.2.5: |
Stochastic unravelling in the doubled Hilbert space / 9.3: |
Non-Markovian dynamics in physical systems / 10: |
Spontaneous decay of a two-level system / 10.1: |
Exact master equation and TCL generator / 10.1.1: |
Jaynes-Cummings model on resonance / 10.1.2: |
Jaynes-Cummings model with detuning / 10.1.3: |
Spontaneous decay into a photonic band gap / 10.1.4: |
The model and frequency renormalization / 10.2: |
Factorizing initial conditions / 10.2.2: |
The stationary state / 10.2.3: |
Non-factorizing initial conditions / 10.2.4: |
Disregarding the inhomogeneity / 10.2.5: |
The spin-boson system / 10.3: |
Microscopic model / 10.3.1: |
Relaxation of an initially factorizing state / 10.3.2: |
Equilibrium correlation functions / 10.3.3: |
Transition from coherent to incoherent motion / 10.3.4: |
Relativistic Quantum Processes / V: |
Measurements in relativistic quantum mechanics / 11: |
The Schwinger-Tomonaga equation / 11.1: |
States as functionals of spacelike hypersurfaces / 11.1.1: |
Foliations of space-time / 11.1.2: |
The measurement of local observables / 11.2: |
The operation for a local measurement / 11.2.1: |
Relativistic state reduction / 11.2.2: |
Multivalued space-time amplitudes / 11.2.3: |
The consistent hierarchy of joint probabilities / 11.2.4: |
EPR correlations / 11.2.5: |
Continuous measurements / 11.2.6: |
Non-local measurements and causality / 11.3: |
Entangled quantum probes / 11.3.1: |
Non-local measurement by EPR probes / 11.3.2: |
Quantum state verification / 11.3.3: |
Non-local operations and the causality principle / 11.3.4: |
Restrictions on the measurability of operators / 11.3.5: |
QND verification of non-local states / 11.3.6: |
Preparation of non-local states / 11.3.7: |
Exchange measurements / 11.3.8: |
Quantum teleportation / 11.4: |
Coherent transfer of quantum states / 11.4.1: |
Teleportation and Bell-state measurement / 11.4.2: |
Experimental realization / 11.4.3: |
Open quantum electrodynamics / 12: |
Density matrix theory for QED / 12.1: |
Field equations and correlation functions / 12.1.1: |
The reduced density matrix / 12.1.2: |
The influence functional of QED / 12.2: |
Elimination of the radiation degrees of freedom / 12.2.1: |
Vacuum-to-vacuum amplitude / 12.2.2: |
Second-order equation of motion / 12.2.3: |
Decoherence by emission of bremsstrahlung / 12.3: |
Introducing the decoherence functional / 12.3.1: |
Physical interpretation / 12.3.2: |
Evaluation of the decoherence functional / 12.3.3: |
Path integral approach / 12.3.4: |
Decoherence of many-particle states / 12.4: |
Index |