Distributed for Karolinum Press, Charles University
Quantum Statistical Physics of Molecular Systems
A text designed for courses in quantum statistical physics, which explains the concept of the density matrix and links it with the quantum theory of relaxation and decoherence and with the most common spectroscopic probes.
This book covers the material for a one-semester introductory course in quantum statistical physics, designed for Master’s students in chemical physics and biophysics preparing to work in the fields of NMR, vibrational spectroscopy, or electronic spectroscopy. The course introduces the density matrix formalism and connects it to students’ existing knowledge of classical statistical physics. It then presents the main results of quantum relaxation theory in terms of population transfer and decoherence, and relates quantum relaxation to its most widely used experimental probes in spectroscopy.
Table of Contents
1 Quantum models in biophysics and chemical physics
1.1 Nuclear spins
1.2 Molecular vibrations
1.3 Electronic states
2 Density matrix
2.1 Statistical ensembles
2.2 Statistical operator
2.3 Pure and mixed states
2.4 Populations and coherences
2.5 Wave function collapse
2.6 Liouville-von Neumann equation
3 Quantum-classical mapping
3.1 Bloch sphere
3.2 Wigner function
3.3 Quasiclassical evolution
3.4 Wigner-Weyl transform
3.5 Bohr-Sommerfeld quantization
4 Quantum statistics at equilibrium
4.1 Canonical density matrices
4.2 Spaces of symmetrized wave functions
4.3 Boson condensation
4.4 Fermi-Dirac & Bose-Einstein distribution
4.5 Gibbs paradox
4.6 Quasiparticles
II Noise and dissipation in quantum dynamics
5 Emergence of relaxation
5.1 Von Neumann entropy
5.2 Unitary evolution
5.3 Reduced density matrix
5.4 Random Hamiltonian
5.5 Decoherence
6 Liouville space
6.1 Superoperators
6.2 Hadamard formula
7 Quantum master equations
7.1 Quantum semigroups
7.2 Lindblad form
7.3 Stochastic Liouville equations
7.4 Open quantum systems
7.5 Secular dynamics
7.6 Thermodynamics of quantum relaxation
III Molecules in optical fields
8 Optical dynamics of two-level chromophore
8.1 Bloch equations
8.2 Absorption
8.3 Line-shape theory
9 Photon counting statistics
9.1 Conditional density matrix
9.2 Photon arrival trajectories
10 And some spectroscopy
10.1 Multilevel Bloch equations
10.2 Transient absorption
10.3 Nonlinear response
10.4 Spontaneous emission
10.5 Two-photon absorption