Snake instability, vortex lattices and fractional quantum Hall states in two-dimensional anisotropic bosonic quantum gases

Date

2025-7

Author

Tanyeri, Umut

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This thesis consists of two main works. First, we investigate the snake instability of solitons in 2D Bose-Einstein condensates. By proposing a variational wavefunction and using the Gross–Pitaevskii equation, we analytically and numerically explore stability criteria for dark solitons, which depend on the system's physical constants. In the second part, we consider a rapidly rotating anisotropic Bose gas. Projecting the full Hamiltonian onto the lowest Landau level, we derive a two-parameter model to study the effects of interaction strength, rotation, and anisotropy on the ground state of the system. Through exact diagonalization and density matrix renormalization group techniques, we obtain a phase diagram featuring broken-symmetry phases and topologically ordered quantum Hall states, paving the way for future exploration of anisotropic quantum fluids.

Subject Keywords

Ultracold atomic gases, Gross-Pitaevskii theory, Snake instability, Density matrix renormalization group, Fractional quantum Hall rffect

URI

https://hdl.handle.net/11511/115536

Collections

Graduate School of Natural and Applied Sciences, Thesis