What is Non-hermitian: Definition and 13 Discussions
Non-Hermitian quantum mechanics is the study of quantum-mechanical Hamiltonians that are not Hermitian. Notably, they appear in the study of dissipative systems. Also, non-Hermitian Hamiltonians with unbroken parity-time (PT) symmetry have all real eigenvalues.
I noticed the research on NHQM in the following news release.
New physics rules tested on quantum computer
Published: 19.2.2021
Information for relevant paper is provided as follows.
Quantum simulation of parity–time symmetry breaking with a superconducting quantum processor
Shruti Dogra...
I was wondering if anyone has worked with non-Hermitian wavefunctions, and know of an approach to derive real and trivial values for their observables using numerical calculations?
Cheers
Hi, I have the two operators:
\begin{equation}
Q = i\hbar \frac{d}{dx} - \gamma
\end{equation}\begin{equation}
Q' = -i\hbar \frac{d}{dx} - \gamma
\end{equation}
where ##\gamma## is a constant. Both of these are not self-adjoint, as they do not follow the condition:
\begin{equation}...
Hello, I Have a non-Hermitian Hamiltonian, which is defined as an ill-condition numbered complex matrix, with non-orthogonal elements and linearily independent vectors spanning an open subspace.
However, when accurate initial conditions are given to the ODE of the Hamiltoanian, it appears to...
Hi, I have not been able to learn how a pseudo-Hermitian differs from a Hermitian model. If one has a hermitian model that satisfies all the fundamental prescriptions of quantum mechanics, a non-Hermitian would not, as it yields averages with complex values. How does a pseudo-Hermitian differ...
It is said that no Hermitian operator gives a time evolution where "I observed the spin to be both up and down" is a possible result. If you use non-Hermitian operator.. then it's possible.. and what operator is that where it is possible in principle where "I observed the spin to be both up and...
Homework Statement
Given a non-hermitian hamiltonian with V = (Re)V -i(Im)V. By deriving the conservation of probability, it can be shown that the total probability of finding a system/particle decreases exponentially as e(-2*ImV*t)/ħ
Homework Equations
Schrodinger Eqn, conservation of...
Hey,
I have two quick questions,
Does mathematica automatically find the eigenvectors and values when you find the eigensystem of a non-Hermitian matrix?
I've been searching the net trying to find a way to find these vectors/values but everything I find briefly touches upon...
I'm learning "the transformation optics" and the first document about this method is "Photonic band structures" ( Pendry, J. B. 1993). In this document, the transfer matrix T is non-hermitian, Ri and Li are the right and left eigenvectors respectively.
Pendry defined a unitary matrix...
A valuable math result for quantum mechanics is that if two hermitian operators (physical observables) commute, then a simultaneous basis of eigenvectors exists. Nevertheless, there are cases in which two operators commute without being both hermitians -- a really common one is when one operator...
theres one line that keeps coming up in proofs that I don't get. How do i get from
\int (\hat{p}\Psi1)*\Psi2 + i \int (\hat{x}\Psi1)\Psi2
to
\int ( (\hat{p}-i\hat{x}) \Psi1)*\Psi2
using the fact that p and x are Hermitian.
im sure its painfully simple but i can't see it.
I know that with an Hermitian operator the expectation value can be found by calculating the (relative) probabilities of each eigenvalue: square modulus of the projection of the state-vector along the corresponding eigenvector.
The normalization of these values give the absolute probabilities...