A Numerical implementation of creation and annhilation operators in the SSH model

  • A
  • Thread starter Thread starter JangMilad
  • Start date Start date
JangMilad
Messages
1
Reaction score
0
Hi all,

I'm working on a numerical simulation involving the SSH model and the density matrix formalism. I'm using annihilation and creation operators at the first site, denoted by a_1 and a_1^\dagger, and I'm trying to understand how to construct and compute expressions like:

a_1 \rho a_1^\dagger
a_1^\dagger \rho a_1

where \rho is the density matrix of the system.

My goal is to implement this numerically. I would appreciate any insights on:

How to define the annihilation/creation operators for a lattice model like SSH.

The physical meaning of the above expressions (e.g., in the context of Lindblad dissipators).

Any tips or references for constructing these operators explicitly in matrix form.

Thanks in advance for your help!
 
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
Back
Top