Homoclinic chaos in the discrete self-trapping trimer

Abstract

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Chaotic behavior, collective modes, and self-trapping in the dynamics of three coupled Bose-Einstein condensates

“…Substituting q i with q i = −(x r q r + x s q s )/x i , where r, s = i (and the choice of i depends in general on the condition x i = 0) finally gives h(q ; 6U, T, µ) ≡ Let us start by analyzing the Hessian eigenvalues of Hamiltonian p sector namely of Eq. (20). These eigenvalues are given by Eq.…”

“…Hence the diagonalization of the (local) quadratic form associated to H 3 can be performed in a separate way on (19) and (20). Further simplifications come from the fact that matrix M p is proven to always have a vanishing eigenvalue (see Appendix C), while, due to the conserved quantity N = Σ i |z i | 2 = const, the induced local constraint q 1 x 1 + q 2 x 2 + q 3 x 3 = 0 makes h(q ; 2U, T, µ) dependent only on two variables q i (see Appendix D).…”

“…Concerning the instability of trimer dynamics, we wish to recall that the presence of homoclinic chaos has been revealed for the asymmetric trimer in Ref. [20], while, at the quantum level, the survival of breather configurations has been investigated in Ref. [21].…”

Chaos, metastability and ergodicity in Bose-Hubbard superfluid circuits

“…We start by introducing the model and the traditional theory for the stability of the superflow. The first configuration we consider is the smallest possible ring, with M = 3 sites [17][18][19][20][21][22][23][24] Fig.1(a). We observe the existence of a novel type of superflow state, which is supported by a chaotic pond in phase-space.…”

Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit

“…A close relative is the linear BoseHubbard trimer. The trimer phase-space has been partially studied in several papers [31][32][33][34][35][36][37][38][39][40][41][42][43], and has been Representative eigen-energies Eα of a rotating ring system are classified by the current I they carry in the rotating frame of reference. The filled and hollow blue circles represent stable and unstable vortex-states for which I/N is quantized.…”