Model Index
This index points to the canonical homes for named models used across measurement theory, decoherence, quantum channels, and open quantum systems. It is a routing page, not a place to duplicate derivations.
Use the index when you know the model name but need to find:
- the physical setting it approximates,
- the page that owns the formulas,
- the assumptions that must be checked,
- nearby models that are often confused with it.
Status Key
Section titled “Status Key”| Status | Meaning |
|---|---|
| canonical page | the main explanation is in this volume |
| reference model | the main model card lives in the site-wide reference library |
| nearest home | a standalone model card is planned or not yet present; the link points to the closest existing explanation |
Measurement and Channel Models
Section titled “Measurement and Channel Models”| Model | Status | Use When | Canonical or Nearest Page |
|---|---|---|---|
| von Neumann measurement model | canonical page | You need the unitary system-pointer correlation behind ideal measurement. | von Neumann Measurement Model |
| pure dephasing qubit | canonical page | A qubit loses phase coherence in a specified basis without population relaxation. | Pure Dephasing Master Equation and Dephasing Channel |
| amplitude damping qubit | canonical page | A two-level system relaxes from an excited state toward a lower state. | Amplitude Damping Master Equation and Amplitude-Damping Channel |
| depolarizing benchmark | canonical page | You need an isotropic finite-dimensional noise benchmark, not a microscopic bath model. | Depolarizing Channel |
| generalized measurement instrument | canonical page | Outcome probabilities and conditional state updates must be specified together. | Quantum Instruments |
Bath and Dissipation Models
Section titled “Bath and Dissipation Models”| Model | Status | Use When | Canonical or Nearest Page |
|---|---|---|---|
| spin–boson model | canonical page | A two-level system couples to a bosonic environment through one or more Pauli operators. | Spin–Boson Model |
| Caldeira–Leggett model | canonical page | A coordinate couples linearly to an oscillator bath, giving Brownian damping and force noise. | Caldeira–Leggett Model |
| damped harmonic oscillator | canonical page | A cavity, vibrational mode, or oscillator relaxes toward vacuum or a thermal state. | Thermal Master Equations and Common Master Equations |
| quantum optical master equation | canonical page | Atoms, cavities, or light-matter systems couple to broadband electromagnetic reservoirs. | Quantum Optical Master Equation |
| central spin model | nearest home | One distinguished spin couples to a bath of environmental spins. | System–Bath Hamiltonians |
Light-Matter and Platform Models
Section titled “Light-Matter and Platform Models”| Model | Status | Use When | Canonical or Nearest Page |
|---|---|---|---|
| Jaynes–Cummings model | reference model | One two-level system exchanges excitations coherently with one quantized mode under a rotating-wave approximation. | Jaynes–Cummings Model |
| Jaynes–Cummings model with damping | nearest home | You add cavity loss, spontaneous emission, dephasing, or measurement to the closed Jaynes–Cummings Hamiltonian. | Quantum Optical Master Equation and Circuit QED |
| input–output cavity model | canonical page | A damped cavity or waveguide-coupled system is described through input and output fields. | Input–Output Theory |
| circuit-QED dispersive readout | canonical page | A qubit is measured through a coupled microwave resonator. | Circuit QED |
| quantum-optics trajectory model | canonical page | Photon counts, homodyne currents, or heterodyne records condition an optical state. | Quantum Optics and Stochastic Master Equations |
Non-Markovian and Repeated-Interaction Models
Section titled “Non-Markovian and Repeated-Interaction Models”| Model | Status | Use When | Canonical or Nearest Page |
|---|---|---|---|
| collision model | canonical page | A system interacts sequentially with ancillas, with memory controlled by whether ancillas are fresh or correlated. | Collision Models |
| pseudomode model | canonical page | A structured reservoir can be represented by one or more damped effective modes. | Pseudomode Methods |
| reaction-coordinate model | canonical page | A collective environmental coordinate should be promoted into the system boundary. | Reaction-Coordinate Mapping |
| hierarchical equations model | canonical page | Gaussian bath correlations are expanded into auxiliary density operators. | Hierarchical Equations of Motion |
Choosing Between Nearby Models
Section titled “Choosing Between Nearby Models”Pure dephasing vs amplitude damping. Use pure dephasing when populations in the relevant basis are unchanged. Use amplitude damping when energy or excitation population relaxes.
Spin–boson vs Caldeira–Leggett. The spin–boson model has a two-level system as the retained degree of freedom. The Caldeira–Leggett model has a coordinate or particle coupled to oscillator coordinates.
Jaynes–Cummings vs quantum optical master equation. Jaynes–Cummings is a coherent Hamiltonian model. A quantum optical master equation adds irreversible channels such as cavity loss, spontaneous emission, pumping, or dephasing.
Collision model vs Markov master equation. A fresh-ancilla collision model can generate Markovian dynamics. Reused, correlated, or internally evolving ancillas can create memory and non-Markovian behavior.
Central spin vs spin–boson. Central spin environments are spin baths, often non-Gaussian and finite. Spin–boson baths are bosonic oscillator baths. They can produce superficially similar dephasing but have different microscopic structures.
Self-Checks
Section titled “Self-Checks”- You see a qubit coherence decay but no energy population transfer. Which index entries should you check first?
Solution
Start with pure dephasing: Pure Dephasing Master Equation and Dephasing Channel.
- A cavity mode coherently swaps excitations with a qubit, and photons also leak from the cavity. Which two homes are relevant?
Solution
Use the Jaynes–Cummings Model for the coherent Hamiltonian and the Quantum Optical Master Equation for damping and other irreversible channels.
- A repeated-interaction model reuses the same ancilla after it has interacted with the system. Is that automatically Markovian?
Solution
No. Reusing an ancilla can carry memory back to the system. Fresh, uncorrelated ancillas are the usual route to Markovian repeated-interaction dynamics.
References
Section titled “References”- J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955.
- H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, 2002.
- U. Weiss, Quantum Dissipative Systems, World Scientific, 2012.
- A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Reviews of Modern Physics 59, 1, 1987.
- A. O. Caldeira and A. J. Leggett, “Path integral approach to quantum Brownian motion,” Physica A 121, 587, 1983.
- E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proceedings of the IEEE 51, 89, 1963.
- H. J. Carmichael, Statistical Methods in Quantum Optics 1, Springer, 1999.