Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction
arXiv:0711.4786 · doi:10.1103/PhysRevA.77.013618
Abstract
The extended Gross-Pitaevskii equation for the Bose-Einstein condensation of gases with attractive 1/r-interaction has a second solution which is born together with the ground state in a tangent bifurcation. At the bifurcation point both states coalesce, i.e., the energies and the wave functions are identical. We investigate the bifurcation point in the context of exceptional points, a phenomenon known for linear non-Hermitian Hamiltonians. We point out that the mean field energy, the chemical potential, and the wave functions show the same behavior as an exceptional point in a linear, non-symmetric system. The analysis of the analytically continued Gross-Pitaevskii equation reveals complex waves at negative scattering lengths below the tangent bifurcation. These solutions are interpreted as a decay of the condensate caused by an absorbing potential.
9 pages, 6 figures
References in corpus (5)
- Exceptional Points in Atomic Spectra
- Coupling of eigenvalues of complex matrices at diabolic and exceptional points
- Projective Hilbert space structures at exceptional points
- Non-Hermitian degeneracy of two unbound states
- Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping
Cited by in corpus (31)
- Non-Hermitian Physics
- The physics of exceptional points
- Topological energy transfer in an optomechanical system with exceptional points
- Non-reciprocal phase transitions
- Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
- Eigenvalue structure of a Bose-Einstein condensate in a PT-symmetric double well
- Exceptional points in the spectra of atoms in external fields
- Floquet exceptional points and chirality in non-Hermitian Hamiltonians
- State Flip at Exceptional Points in Atomic Spectra
- Optical lattices with exceptional points in the continuum
- Bifurcations and exceptional points in dipolar Bose-Einstein condensates
- Dipolar Bose-Einstein condensates in a PT-symmetric double-well potential
- Barrier transmission for the one-dimensional nonlinear Schrödinger equation: resonances and transmission profiles
- Fingerprints of exceptional points in the survival probability of resonances in atomic spectra
- Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. II. Applications
- Spectral singularities in PT-symmetric Bose-Einstein condensates
- Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential
- Pitchfork bifurcations in blood-cell shaped dipolar Bose-Einstein condensates
- Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction
- Bifurcations, order, and chaos in the Bose-Einstein condensation of dipolar gases
- Harmonic inversion analysis of exceptional points in resonance spectra
- Bose-Einstein Condensates with Derivative and Long-Range Interactions as Set-Ups for Analog Black Holes
- Exceptional Points of Resonant States on a Periodic Slab
- Bicomplex Hamiltonian systems in Quantum Mechanics
- Relation between the eigenfrequencies of Bogoliubov excitations of Bose-Einstein condensates and the eigenvalues of the Jacobian in a time-dependent variational approach
- Exceptional points in bichromatic Wannier-Stark systems
- Macroscopic quantum tunneling of Bose-Einstein condensates with long-range interaction
- Spectral Singularities and Zero Energy Bound States
- Population transfer at exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields
- Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates
- Exceptional points in the elliptical three-disk scatterer using semiclassical periodic orbit quantization