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# How an interacting many-body system tunnels through a potential barrier to open space

Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Heidelberg, Germany.

Proceedings of the National Academy of Sciences (Impact Factor: 9.67). 08/2012; 109(34):13521-5. DOI: 10.1073/pnas.1201345109 Source: PubMed

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Alexej I. Streltsov, Available from: Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

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**ABSTRACT:**The many-body Schr\"odinger dynamics of a one-dimensional bosonic Josephson junction is investigated for up to ten thousand bosons and long times. The initial states are fully condensed and the interaction strength is weak. We report on a universal fragmentation dynamics on the many-body level: systems consisting of different numbers of particles fragment to the same value at constant mean-field interaction strength. The phenomenon manifests itself in observables such as the correlation functions of the system. We explain this universal fragmentation dynamics analytically based on the Bose-Hubbard model. We thereby show that the extent to which many-body effects become important at later times depends crucially on the initial state. Even for arbitrarily large particle numbers and arbitrarily weak interaction strength the dynamics is many-body in nature and the fragmentation universal. There is no weakly interacting limit where the Gross-Piatevskii mean-field is valid for long times.Physical Review A 07/2012; 89(2). DOI:10.1103/PhysRevA.89.023602 · 2.81 Impact Factor -
##### Article: Two trapped particles interacting by a finite-range two-body potential in two spatial dimensions

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**ABSTRACT:**We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-ranged Gaussian-shaped potential in two spatial dimensions. We derive an approximative transcendental equation for the energy and study the resulting spectrum as a function of the interparticle interaction strength. Both the attractive and repulsive systems are analyzed. We study the impact of the potential's range on the ground-state energy. Complementary, we also explicitly verify by a variational treatment that in the zero-range limit the positive delta potential in two dimensions only reproduces the non-interacting results, if the Hilbert space in not truncated. Finally, we establish and discuss the connection between our finite-range treatment and regularized zero-range results from the literature.Physical Review A 10/2012; 87(3). DOI:10.1103/PhysRevA.87.033631 · 2.81 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the full-fledged microscopic dynamics of two interacting, ultracold bosons in a one- dimensional double-well potential, through the numerically exact diagonalization of the many-body Hamiltonian. With the particles initially prepared in the left well, we increase the width of the right well in subsequent trap realizations and witness how the tunneling oscillations evolve into particle loss. In this closed system, we analyze the spectral signatures of single- and two-particle tunneling for the entire range of repulsive interactions. We conclude that for comparable widths of the two wells, pair-wise tunneling of the bosons may be realized for specific system parameters. In contrast, the decay process (corresponding to a broad right well) is dominated by uncorrelated single-particle decay.Physical Review A 02/2013; 87(4). DOI:10.1103/PhysRevA.87.043626 · 2.81 Impact Factor