Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

198 submissions , 156 unreviewed
4,910 questions , 2,086 unanswered
5,311 answers , 22,546 comments
1,470 users with positive rep
805 active unimported users
More ...

  N site Hamiltonians

+ 0 like - 0 dislike
40 views

Hello, I have a question I need to solve in my physics and I have absolutely no Idea how to solve it.

Any chance someone can help me with the solution?

Given a system of three sites arranged in a chain. The standard basis is | x⟩ with x = −1,0,1. In addition, the system is symmetrical for mirroring. Such a system can be described (after calibration) using only two parameters.

1) Write down the matrix that represents a mirroring operation.
2) Continuing from the previous section define a base of self-states for mirroring | 0⟩, | +⟩, | −⟩

3) If Hamiltonian is registered in the standard base - what will be the free parameters?
4) Write down what the Hamiltonian looks like at the base defined in Section 2.
5) Suppose you add an option to jump between the first and last site. In addition suppose there is no magnetic field. How it will affect the Hamiltonian you have listed in sections 3 and 4.


Tip: The result of section 4 can be clarified on the basis of symmetry considerations. The system has a "trivial" self-state whose identity is not affected by the values ​​of the parameters. Who is this situation? The system makes a "trivial" reduction to the problem of only two modes.

asked Jun 9 in Theoretical Physics by Alexander [ no revision ] 1 flag
recategorized Jun 10 by Dilaton

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOver$\varnothing$low
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...