arXiv subjects

Gaurav Hajong

Publications and source records attributed to Gaurav Hajong.

4 recordsLinked to original sources

arXiv2026

Two flavor neutrino oscillations in presence of non-Hermitian dynamics

We develop a consistent mathematical framework for studying two flavor neutrino oscillations in presence of non-Hermitian dynamics. We consider two approaches : (a) bi-orthonormal inner product defined by a positive-definite metric operator $\mathcal{G}$ and (b) the density matrix prescription by Brody and Graefe [Phys. Rev. Lett. 109, 230405 (2012)]. For the $\mathcal{PT}$-symmetric case, we show that the $\mathcal{G}$ metric approach does not work well (probabilities are not conserved) both in $\mathcal{PT}$-unbroken as well as $\mathcal{PT}$-broken regime. Hence, we adopt the density matrix prescription by Brody and Graefe which is a positive semi-definite map. In the density matrix prescription, we note that probability in the steady state limit is not necessarily $1/2$ thereby indicating non-Markovian behavior.

quant-ph↗

arXiv2026

Emergence of Hermitian topology from non-Hermitian knots

The non-Hermiticity of the system gives rise to a distinct knot topology in the complex eigenvalue spectrum, which has no counterpart in Hermitian systems. In contrast, the singular values of a non-Hermitian (NH) Hamiltonian are always real by definition, meaning that they can also be interpreted as the eigenvalues of some underlying Hermitian Hamiltonian. In this work, we demonstrate that if the singular values of an NH Hamiltonian are treated as eigenvalues of prototype translational invariant Hermitian models that undergo a topological phase transition between two distinct topological phases, the complex eigenvalues of the NH Hamiltonian will also undergo a {\it{first order knot transition}} between different knot structures. Unlike the usual knot transition, this transition is not accompanied by an Exceptional point (EP); in contrast, the real and complex parts of the eigenvalues of the NH Hamiltonian show a discrete jump at the transition point. We emphasize that the choice of an NH Hamiltonian whose singular values match the eigenvalues of a Hermitian model is not unique. However, our study suggests that this connection between the NH and Hermitian models remains robust as long as the periodicity in lattice momentum is the same for both. Furthermore, we provide an example showing that a change in the topology of the Hermitian model implies a transition in the underlying NH knot topology, but a change in knot topology does not necessarily signal a topological transition in the Hermitian system.

quant-ph↗

arXiv2025

Modified Hellmann Feynman Theorem

We review the well-known Hellmann Feynman Theorem (HFT), originally developed for Hermitian systems to facilitate the calculation of forces among the molecules. Our work extends this foundational theorem to the domain of non-Hermitian quantum mechanics, in particular the PT symmetric non-Hermitian quantum physics. We derive a modified form of the HFT (MHFT) which holds good for both PT broken, unbroken phases and even at the exceptional point of the theory as demonstrated with help of a discrete and a continumm model. Since a PT-symmetric Hamiltonian admits biorthonormal set of eigenvectors, a more appropriate inner product known as the G inner product is defined, based on which, the system in the unbroken phase can be shown to satisfy unitary time evolution, while a system in broken phase does not. We show here that the MHFT obtained is valid for both these situations.

quant-ph↗

arXiv2023

Hellmann Feynman Theorem in Non-Hermitian system

We revisit the celebrated Hellmann-Feynman theorem (HFT) in the PT invariant non-Hermitian quantum physics framework. We derive a modified version of HFT by changing the definition of inner product and explicitly show that it holds good for both PT broken, unbroken phases and even at the exceptional point of the theory. The derivation is extremely general and works for even PT non-invariant Hamiltonian. We consider several examples of discrete and continuum systems to test our results. We find that if the eigenvalue goes through a real to complex transition as a function of the Hermiticity breaking parameter, both sides of the modified HFT expression diverge at that point. If that point turns out to be an EP of the PT invariant quantum theory, then one also sees the divergence at EP. Finally, we also derive a generalized Virial theorem for non-Hermitian systems using the modified HFT, which potentially can be tested in experiments.

quant-ph↗