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:
• Quantum condensed matt...
Recommended course textbook: "Many-body quantum theory in condensed matter physics" by Bruss and Flensberg
Пікірлер: 6
Thanks...superb videos
Thank you!
Hi ,thank you for your videos , I just have a question for you , if I have a density matrix for an ensemble , a square unity matrix (without knowing the order of this matrix ) , how then can I find the entropy ?? Plz help me
@drmitchellsphysicschannel2955
3 жыл бұрын
The von Neumann entropy is S=-Tr[rho*ln(rho)] in terms of the density matrix, rho. To compute the log of a matrix you switch to its eigenbasis.
56:42, why is |gs> = [ + ], |ex> = [ - ], it seems H = |L> = +1|gs>, H|ex> = -1|ex>, so why is not [|L> - |R>] the ground state?
This video is like a car wreck. You cant look away, you just absorb everything.