Observables, Density Matrix, Reduced Density Matrix, Entanglement Entropy
Quantum Condensed Matter Physics: Lecture 6
Theoretical physicist Dr Andrew Mitchell presents an advanced undergraduate / introductory Master's level lecture course on Quantum Condensed Matter Physics at University College Dublin. This is a complete and self-contained set of lectures, in which the theory is built up from scratch, and requires only a knowledge of basic quantum mechanics.
In this lecture, I discuss how to calculate physical observables from the solution of a given Hamiltonian. With the eigenstates and energies, we use statistical mechanics to find the thermal expectation value of a quantum mechanical operator. This problem is then formulated in terms of the density matrix. Pure and mixed states are discussed. Finally, we consider measurements on a part of a quantum system, and introduce the concept of the reduced density matrix. The entanglement entropy is calculated and analyzed.
Navigate through the lectures of this course in order using the playlist:
https://www.youtube.com/playlist?list=PLotxEOxVaaoKRXdDN-7lI3Y88PaHqyOZL
Recommended course textbook: "Many-body quantum theory in condensed matter physics" by Bruss and Flensberg
Видео Observables, Density Matrix, Reduced Density Matrix, Entanglement Entropy канала Dr Mitchell's physics channel
Theoretical physicist Dr Andrew Mitchell presents an advanced undergraduate / introductory Master's level lecture course on Quantum Condensed Matter Physics at University College Dublin. This is a complete and self-contained set of lectures, in which the theory is built up from scratch, and requires only a knowledge of basic quantum mechanics.
In this lecture, I discuss how to calculate physical observables from the solution of a given Hamiltonian. With the eigenstates and energies, we use statistical mechanics to find the thermal expectation value of a quantum mechanical operator. This problem is then formulated in terms of the density matrix. Pure and mixed states are discussed. Finally, we consider measurements on a part of a quantum system, and introduce the concept of the reduced density matrix. The entanglement entropy is calculated and analyzed.
Navigate through the lectures of this course in order using the playlist:
https://www.youtube.com/playlist?list=PLotxEOxVaaoKRXdDN-7lI3Y88PaHqyOZL
Recommended course textbook: "Many-body quantum theory in condensed matter physics" by Bruss and Flensberg
Видео Observables, Density Matrix, Reduced Density Matrix, Entanglement Entropy канала Dr Mitchell's physics channel
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4 февраля 2021 г. 3:24:52
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