# Which Metrics Are Consistent with a Given Pseudo-Hermitian Matrix?

@inproceedings{Feinberg2021WhichMA, title={Which Metrics Are Consistent with a Given Pseudo-Hermitian Matrix?}, author={Joshua Feinberg and Miloslav Znojil}, year={2021} }

Given a diagonalizable N × N matrix H , whose non-degenerate spectrum consists of p pairs of complex conjugate eigenvalues and additional N − 2p real eigenvalues, we determine all metrics M , of all possible signatures, with respect to which H is pseudo-hermitian. In particular, we show that any compatible M must have p pairs of opposite eigenvalues in its spectrum so that p is the minimal number of both positive and negative eigenvalues of M . We provide explicit parametrization of the space…

## One Citation

### Dynamics of entropy in bipartite quasi-Hermitian systems and their Hermitian counterparts

- Physics, Mathematics
- 2022

A quasi-Hermitian quantum system can be mapped to a multitude of Hermitian systems by the Dyson map. All Hermitian systems thus obtained are globally unitarily equivalent but the unitary may entangle…

## References

SHOWING 1-7 OF 7 REFERENCES

### Level statistics of a pseudo-Hermitian Dicke model.

- Physics, MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

The level statistics of a pseudo-Hermitian Dicke Hamiltonian that undergoes quantum phase transition (QPT) are studied and it is found that the level-spacing distribution of this Hamiltonian near the integrable limit is close to Poisson distribution, while it is Wigner distribution for the ranges of the parameters for which the Hamiltonian is nonintegrable.

### Pseudosymmetric random matrices: Semi-Poisson and sub-Wigner statistics.

- PhysicsPhysical review. E
- 2017

It is conjecture that for these ensembles of a large number N of pseudosymmetric n×n (n large) matrices, the nearest level spacing distributions [NLSDs, p(s)] are sub-Wigner as p_{abc}(s)=ase^{-bs^{c}}(0<c<2) and the distributions of their eigenvalues fit well to D(ε).

### Level density and level-spacing distributions of random, self-adjoint, non-Hermitian matrices.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

We investigate the level density σ(x) and the level-spacing distribution p(s) of random matrices M = AF ≠ M{†}, where F is a (diagonal) inner product and A is a random, real, symmetric or complex,…

### As a simple example, with the indefinite metric m m mCC taken to be the parity operator, see Eq

### associated with the vPHHQP seminar series on PT-symmetry and non-hermitian operators in physics

- Journal of Physics: Conference Series

### Linear Operators in Spces with an Indefinite Metric

- 1989