PT -symmetric, non-Hermitian quantum many-body physics—a methodological perspective

In this work, we study the non-PT symmetry phase of the Swanson Hamiltonian in the framework of the Complex Scaling Method.By constructing a bi-orthogonality relation, we apply the formalism of the response function to analyse the time evolution of different initial wave packages. The Wigner Functions, mean value of operators, and the probabilities of survival and persistence for the different wave packages are evaluated as a function of time. We analyse in detail the time evolution in the neighbourhood of Exceptional Points. We derive a continuity equation for the system. We compare the results obtained using the Complex Scaling Method to the ones obtained by working in a Rigged Hilbert Space.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complex scaling method applied to the study of the Swanson Hamiltonian in the broken PT-symmetry phase

Fernández,

Ramírez,

Reboiro

2024

Three perspectives on entropy dynamics in a non-Hermitian two-state system

Felski,

Beygi,

Karapoulitidis

et al. 2024

A comparative study of entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. To begin with, we illustrate the phase portrait of this non-Hermitian model on the Bloch sphere, elucidating the changes in behavior as one moves across the phase transition boundary, as well as the emergent feature of unidirectional state evolution in the spontaneously broken PT-symmetry regime. This is followed by an examination of the purity and entropy dynamics. Here we distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping. In this it is demonstrated that their differences are rooted in the treatment of the environmental coupling mode. For unbroken PT symmetry of the system, a notable characteristic feature of the perspective taken is the presence or absence of purity oscillations, with an associated entropy revival. The description of the system is then continued from its PT-symmetric pseudo-Hermitian phase into the regime of spontaneously broken symmetry, in the latter two approaches through a non-analytic operator-based continuation, yielding a Lindblad master equation based on the PT charge operator C. This phase transition indicates a general connection between the pseudo-Hermitian closed-system and the Lindbladian open-system formalism through a spontaneous breakdown of the underlying physical reflection symmetry.

On Some novel features of a Non-Hermitian multi-boson Hamiltonian : partial P T -symmetry and ghosts

Chakraborty

2024

The eigenvalues and eigenstates of a three-boson Hamiltonian areconsidered. The Hamiltonian is found to be pseudo-Hermitian in relation to itsvarious partial PT -symmetries understood in a Fock space setting. The possibilitiesof symmetry adopting and symmetry breaking states are also discussed. Ghost statesare found in relation to different symmetry induced inner-products. At least two of theghost states show some kind of transition to normal states depending on the values ofcertain parameter.