arXiv subjects

Ahmad Hazazi Ahmad Sumadi

Publications and source records attributed to Ahmad Hazazi Ahmad Sumadi.

2 recordsLinked to original sources

arXiv2026

Frequency Detuning and Interference-Induced Bohmian Chaos in a Two-Dimensional Anisotropic Harmonic Oscillator

We investigate the emergence of chaotic Bohmian trajectories in a three-mode superposition of the ground and first excited states of a two-dimensional anisotropic harmonic oscillator. The analysis focuses on the interference-induced phase structure of the wavefunction, which determines the Bohmian velocity field through its phase gradient. We show that the spatial extent of chaotic motion is controlled by the temporal coherence of the interference pattern, set by the detuning between oscillator modes. Near resonance, slow beating generates long-lived phase-gradient structures that repeatedly stretch and fold nearby trajectories, leading to more spatially extended chaotic regions. In contrast, strong detuning produces rapid temporal decorrelation of the phase field and confines chaotic dynamics to localized regions of configuration space. To quantify this behavior, we use a dimensionless coherence parameter comparing the beating time scale with a characteristic transport time. The results identify temporal coherence of the interference-induced phase field as a useful diagnostic for chaotic transport in low-dimensional Bohmian systems.

quant-ph↗

arXiv2025

Qubit Geometry through Holomorphic Quantization

We develop a wave mechanics formalism for qubit geometry using holomorphic functions and Mobius transformations, providing a geometric perspective on quantum computation. This framework extends the standard Hilbert space description, offering a natural interpretation of standard quantum gates on the Riemann sphere that is examined through their Mobius action on holomorphic wavefunction. These wavefunctions emerge via a quantization process, with the Riemann sphere serving as the classical phase space of qubit geometry. We quantize this space using canonical group quantization with holomorphic polarization, yielding holomorphic wavefunctions and spin angular momentum operators that recover the standard $SU(2)$ algebra with interesting geometric properties. Such properties reveal how geometric transformations induce quantum logic gates on the Riemann sphere, providing a novel perspective in quantum information processing. This result provides a new direction for exploring quantum computation through Isham's canonical group quantization and its holomorphic polarization method.

quant-ph↗