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Nuclear Physics B

q-deformed catability in coupled Kerr, graphene, and quantum phase transitions

Abdelmalek Bouzenada

Published May 31, 2026• 0 citations
Publisher

Abstract

We develop a unified framework for studying superposed coherent states in coupled nonlinear bosonic systems using a q-deformed Kerr oscillator model. A quantitative measure, termed catability, is introduced to quantify robustness and structural coherence of Schrödinger-cat-like states under nonlinear and deformation effects within the framework. Within the q-deformed bosonic algebra, we analyze the dynamics of two coupled Kerr oscillators to demonstrate that the deformation parameter governs coherence redistribution and nonlinear coupling-induced state transformation. Establish local cat states emerge from the relation between Kerr nonlinearity and q-deformed interactions, coherence transfer between subsystems becomes sensitive to the deformation strength. In this case, construct a phase diagram of catability, revealing distinct regimes of quantum behavior, identifying coupling-driven quantum phase transitions in a deformed algebraic structure system. The generalized analysis extended the covariant formulation and graphene-inspired catability operators generalized curved space-time backgrounds, establishing a connection between nonlinear quantum optics, condensed matter analog systems, relativistic quantum structures framework. In this context, results explain complete description deformationcontrolled quantum coherence and establish new directions for engineered nonclassical states in complex quantum systems.

DOI
10.1016/j.nuclphysb.2026.117534

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Parametrically driven Kerr nonlinear quantum oscillator plays a central role in quantum optics, superconducting circuits, and in engineered light-matter interactions. For the development of future quantum technologies, it is crucial to understand the behavior of this quantum system under realistic dissipative conditions. The objective of this thesis is to investigate the phase-space dynamics of a dissipative Kerr nonlinear oscillator under different driving regimes and corresponding dissipation channels, with a particular focus on the emergence of nonclassical features in phase space. The aim is also to understand how nonlinearity and different driving mechanisms influence quantum properties such as coherence, nonclassicality, and phase-space structure. The analysis was carried out using the Wigner phase-space formalism and numerical simulations of the Lindblad master equation. The results show that in the case of finite nonlinearity the coherence time is prolonged compared to the harmonic case. In the single photon regime, the interplay between the photon drive and nonlinearity can lead to coherence revivals after which the system relaxes into a squeezed steady state. In the two photon and dissipation regime, the system exhibits parity-protected dynamics, leading to very long coherence times.
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