Dennis Dast

Eigenvalue structure of a Bose–Einstein condensate in a

We study a Bose–Einstein condensate in a -symmetric double-well potential where particles are coherently injected in one well and removed from the other well. In mean-field approximation the condensate is described by the Gross–Pitaevskii equation thus falling into the category of nonlinear non-Hermitian quantum systems. After extending the concept of symmetry to such systems, we apply an analytic continuation to the Gross–Pitaevskii equation from complex to bicomplex numbers and show a thorough numerical investigation of the four-dimensional bicomplex eigenvalue spectrum. The continuation introduces additional symmetries to the system which are confirmed by the numerical calculations and furthermore allows us to analyse the bifurcation scenarios and exceptional points of the system. We present a linear matrix model and show the excellent agreement with our numerical results. The matrix model includes both exceptional points found in the double-well potential, namely an EP2 at the tangent bifurcation and an EP3 at the pitchfork bifurcation. When the two bifurcation points coincide the matrix model possesses four degenerate eigenvectors. Close to that point we observe the characteristic features of four interacting modes in both the matrix model and the numerical calculations, which provides clear evidence for the existence of an EP4.

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Non-Hermitian systems with

-symmetric double well

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Relation between PT -symmetry breaking and topologically nontrivial phases in the Su-Schrieffer-Heeger and Kitaev models

symmetry can possess purely real eigenvalue spectra. In this work two one-dimensional systems with two different topological phases, the topological nontrivial Phase (TNP) and the topological trivial phase (TTP) combined with

Nonlinear quantum dynamics in a PT-symmetric double well

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Dipolar Bose-Einstein condensates in aPT-symmetric double-well potential

-symmetric non-Hermitian potentials are investigated. The models of choice are the Su-Schrieffer-Heeger (SSH) model and the Kitaev chain. The interplay of a spontaneous

Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates

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Quantum master equation with balanced gain and loss

-symmetry breaking due to gain and loss with the topological phase is different for the two models. The SSH model undergoes a

Purity oscillations in Bose-Einstein condensates with balanced gain and loss

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Stationary and Dynamical Solutions of the Gross-Pitaevskii Equation for a Bose-Einstein Condensate in a PT symmetric Double Well

-symmetry breaking transition in the TNP immediately with the presence of a non-vanishing gain and loss strength