Physics 581 Spring 2023

Open Quantum Systems


University of New Mexico

Department of Physics and Astronomy

Instructor: Prof. Ivan H. Deutsch
Lectures: Tuesday and Thursday 9:30am-10:45am, P&A Room 1140
Teaching Assistants: Andrew Forbes & S. Vikas Buchemmavari

Office Hours: TBA


Synopsis: All quantum systems interact with their environment, be it through unwanted interactions with a noisy bath of thermal and quantum fluctuations, or because we want to observed the system through a quantum measurement.  This class will cover the foundations of open quantum systems and its relationship to classical nonequilibrium statistical physics.  New features arise in quantum mechanics  -- entanglement and negative probabilities -- with profound implications.   With a foundation in open quantum systems, we will address fundamental processes in quantum mechanics: dissipation, decoherence, and measurement. 

On this page:


General Information


"Recommended" Texts (none required)


* Problem Sets (5-8 assignments) 75%
* Final Project 25%
  *Problem sets will be available on the web, about every other week. Generally assignments will be due Thursdays in the TA mailbox.




Tentative Syllabus


I. Quantum Mechanical Building Blocks

    - Closed quantum systems: states and evolution
    - Two level systems:  qubits
    - Infinite dimension systems: bosons
    - Multipartite systems: entanglement

II. Foundation theory of open quantum systems

    - Completely positive maps and quantum channels
    - Kraus representation
    - Quantum channels for qubits
    - Measurment model

III. Lindblad Master Equation - formal theory

    - Markov differential maps - Lindblad form
    - Born-Markov approximation and the derivation of the Master Equation
    - Examples for qubits: amplitude damping, dephasing, depolarizating channels
    - Damped simple harmonic oscillator

IV. Langevin equations

    - Stochastics processes
    - Brownian motion
    - Langevin equation
    - Heisenberg-Langevin

V. Fokker-Planck equation

    - Classical statistical physics theory
    - Damped harmonic oscillator
    - Decoherence and the emergence of the classical world

VI. Quantum Trajectories

    - Quantum trajectories — the measurement model
    - Quantum Monte-Carlo wavefunctions
    - Different unravellings of master equation
    - Stochastic Schrödinger equation and continuous measurement




Lecture notes in pdf.   Podcasts for Lectures:  Microsoft Stream

 Jan. 17

Introduction to Open Quantum Systems:
Dissipation, Irreversibility,  Decoherence, Measurement
Lecture #1

Jan. 19

Quantum Foundations: Density operators,
Measurements qubits,  Bloch sphere

Lecture #2

 Jan. 24

Qubit Dynamics: Rabi Oscillations

Lecture #3
Jan. 26

Qubits : Phenomenological Damping - Bloch equations

Lecture #4

Jan. 31

Continuous Variable Quantum Mechanics: 
Simple harmonic oscillator, coherent states,
boson algebra
Lecture #5


Introduction to Phase Space Representations
Lecture #6

 Feb. 7


 Feb. 9

Quasiprobability functions Wigner (W), Husumi (Q), and Glauber (P)

 Feb. 14

Dynamics in Phase Space

Feb. 16

Tensor product structure and entanglement
Schmidt decomposition
Lecture #7

 Feb. 21

Intro to open quantum system dynamics:
 Quantum operations, CP maps, Kraus Representation

Lecture #8
Feb. 23
Quantum Channels for qubits

Feb. 28

Irreversible bipartite system-reservoir interaction.
Markov approximation - Lindblad Master Equation
Lecture #9

Mar. 2

Derivation of the Lindblad Master Equation Born-Markov approximation

Mar. 7

Examples of Master Equation Evolution:

Damped two-level atom

Lecture #10

Mar. 9

Damped Simple Harmonic Oscillator

Mar. 13-17

Spring Break

Mar. 21 No Class

Mar. 23
Damped Simple Harmonic Oscillator in Phase Space
Lecture #11


Mar. 28

Decoherence and the Emergence of the Classical World

Mar. 30


 Apr. 4

Brownian Motion and Heisenberg-Langevin Equation
Lecture #12


Apr. 6

No lecture


Apr. 11



Apr. 13

Classical stochastic processes and the master equation
Lecture #13


Aprl. 18


Wiener processes and
Ito stochastic differential equations

Apr. 20


Apr. 25


Quantum Trajectories I
Measurement model

Lecture #14

Molmer 1
Molmer 2

 Apr. 27

Quantum Trajectories II
Quantum Monte-Carlo Wave Function Algorithm

Lecture #15

Molmer 3
Molmer 4

 May 2

Quantum Trajectories III
Different Unravelings of the Master Equation

Lecture #16

May 4


The Stochastic Schrodinger Equation.

Quantum State Diffusion

Lecture #17

May 9

Continuous Measurement

Lecture #18


Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3

Problem Set #4
Problem Set #5
Final Project