Dynamics of a quantum system coupled to an environment (bath) — decoherence, dissipation, relaxation, and loss of purity. Master-equation formalism: Redfield (non-secular Born-Markov), Lindblad / GKSL (1976 Gorini-Kossakowski-Sudarshan,…
open-quantum-systems
Environment-induced decoherence: off-diagonals decay exp(−t/T₂)
Zeh 1970 / Zurek 1981-1991 / Joos-Zeh 1985: coupling of a quantum system to a macroscopic environment causes the off-diagonal coherences of…
Born-Markov: weak coupling + memoryless bath → Redfield / Lindblad master equation
The Nakajima-Zwanzig projection-operator formalism yields the exact non-local-in-time integro-differential equation for ρ_S(t); the Born +…
Redfield equation: non-secular Born-Markov master equation
Redfield 1957 nuclear-magnetic-resonance relaxation theory, repurposed for general Born-Markov open dynamics: non-secular…
Lindblad trace preservation: Tr(dρ/dt) = 0 from canonical form
Gorini-Kossakowski-Sudarshan 1976 / Lindblad 1976: the most general generator of a completely-positive trace-preserving (CPTP) quantum…
Markov validity: τ_B ≪ τ_S; error ≈ (τ_B/τ_S)²
Breuer-Petruccione §3 / Rivas-Huelga 2011: the Markov approximation in Born-Markov master-equation theory replaces the non-local-in-time…
Fermi golden rule decoherence: Γ = (2π/ℏ) |⟨f|V|i⟩|² ρ(E_f)
Dirac 1927 / Fermi 1950 golden rule: transition rate from initial eigenstate |i⟩ of H₀ to a continuum / quasi-continuum of final states…