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Durham University

Institute of Advanced Study

Past Events

IAS Fellow's Seminar - Suppression of the quantum-mechanical collapse by repulsive interactions

5th March 2018, 13:00 to 14:00, Seminar Room, Institute of Advanced Study, Professor Boris Malomed (Tel Aviv University)


Abstract


The quantum-mechanical collapse (alias "fall onto the center" of particles attracted by potential ~ -V/r^2, with V > 0) is a well-known issue in the quantum theory.

This work demonstrates that, in a rarefied gas of quantum particles attracted by the above-mentioned potential, the repulsive nonlinearity induced by collisions between the particles prevents the collapse, recreating the missing ground state, in the framework of the mean-field approximation [1].

Further, a phase transition in the ground state is found at a critical value of V.

The setting may be realized in the 3D gas of dipolar bosons attracted by a central charge, including the case of the binary gas [2]. The addition of the harmonic-oscillator trapping potential gives rise to a tristability, in the case when the Schroedinger equation still does not lead to the collapse. In the 2D setting, the cubic nonlinearity is not strong enough to prevent the collapse; however, the quintic term does it. The analysis was also extended to the 3D anisotropic setting, with the dipoles polarized by an external uniform field [3].

Finally, an exact numerical analysis of the same model in the framework of the multi-bodyquantum theory [4] demonstrates that, although the complete suppression of the quantum collapse does not occur, the ground state predicted by the mean-field approximation corresponds to a metastable state which emerges in the framework of the multi-body system.

[1] H. Sakaguchi and B. A. Malomed, Suppression of the quantum-mechanical collapse by repulsive interactions in a quantum gas, Phys. Rev. A 83, 013907 (2011).

[2] H. Sakaguchi and B. A. Malomed, Suppression of the quantum collapse in binary bosonic gases, Phys. Rev. A 88, 043638 (2013).

[3] H. Sakaguchi and B. A. Malomed, Suppression of the quantum collapse in an

anisotropic gas of dipolar bosons, Phys. Rev. A 84, 033616 (2011).

[4] G. E. Astrakharchik and B. A. Malomed, Quantum versus mean-field collapse in a many-body system, Phys. Rev. A 92, 043632 (2015).

Places are limited and so any academic colleagues interested in attending a seminar should register online in advance to reserve a place. Places will be confirmed within 48 hours of receipt (subject to availability).

Contact enquiries.ias@durham.ac.uk for more information about this event.