arXiv subjects

Chan Kar Tim

Publications and source records attributed to Chan Kar Tim.

3 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↗

arXiv2021

Isomorphism of Analytical Spectrum between Noncommutative Harmonic Oscillator and Landau Problem

The comparison of the Hamiltonians of the noncommutative isotropic harmonic oscillator and Landau problem are analysed to study the specific conditions under which these two models are indistinguishable. The energy eigenvalues and eigenstates of Landau problem in symmetric and two Landau gauges are evaluated analytically. The Hamiltonian of a noncommutative isotropic harmonic oscillator is found by using Bopp's shift in commutative coordinate space. The result shows that the two systems are isomorphic up to the similar values of $n_{r}$ and $m_{l}$ and $qB = eB > 0$ for both gauge choices. However, there is an additional requirement for Landau gauge where the noncommutative oscillator has to lose one spatial degree of freedom. It also needs to be parametrized by a factor $\zeta$ for their Hamiltonians to be consistent with each other. The wavefunctions and probability density functions are then plotted and the behaviour that emerges is explained. Finally, the effects of noncommutativity or magnetic field on the eigenstates and their probability distribution of the isomorphic system are shown.

quant-ph↗

arXiv2012

Jensen-Shannon Divergence and Non-linear Quantum Dynamics

Using the statistical inference method, a non-relativistic, spinless, non-linear quantum dynamical equation is derived with the Fisher information metric substituted by the Jensen-Shannon distance information. Among all possible implications, it is shown that the non-linear Schrödinger equation preserves the symplectic structure of the complex Hilbert space, hence a Hamiltonian dynamics. The canonically projected dynamics is obtained on the corresponding projective Hilbert space of pure state density operators.

math-ph↗