← Mathematical compendium

Published equation contexts

Hf=HS⊗IB+IS⊗HB+HSBH_f = H_S \otimes I_B + I_S \otimes H_B + H_{SB}

Why this formula appears here

Start with the setting the open-quantum-systems literature calls a fine description: a Hilbert space Hf\mathcal H_f = HS\mathcal H_S ⊗\otimes HB\mathcal H_B holding a system S and everything else, B , that a working physicist has decided not to track in detail — a resonant bath, an environment, a set of nuclear spins, whatever “everything else” means for the apparatus at hand. The fine Hamiltonian is Hf=HS⊗IB+IS⊗HB+HSBH_f = H_S \otimes I_B + I_S \otimes H_B + H_{SB}. three Hermitian terms, each in units of energy: the system’s own generator, the bath’s own generator, and an interaction coupling the two. A fine state is a density operator ρ\rho on Hf\mathcal H_f — trace one, positive semidefinite, dimensionless as a probability object.

Read the full article-specific guide →

Read the representative guide

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Learn the mathematics behind it

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

Hf=HS⊗IB+IS⊗HB+HSB,H_f = H_S \otimes I_B + I_S \otimes H_B + H_{SB},

Equation 4 · Evolutionary Physics

The Entry a Relabeling Cannot Write

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Start with the setting the open-quantum-systems literature calls a fine description: a Hilbert space Hf\mathcal H_f = HS\mathcal H_S ⊗\otimes HB\mathcal H_B holding a system S and everything else, B , that a working physicist has decided not to track in detail — a resonant bath, an environment, a set of nuclear spins, whatever “everything else” means for the apparatus at hand. The fine Hamiltonian is Hf=HS⊗IB+IS⊗HB+HSBH_f = H_S \otimes I_B + I_S \otimes H_B + H_{SB}. three Hermitian terms, each in units of energy: the system’s own generator, the bath’s own generator, and an interaction coupling the two. A fine state is a density operator ρ\rho on Hf\mathcal H_f — trace one, positive semidefinite, dimensionless as a probability object.

Meanings in this article

Equation guide → · Article →