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We reply to Jacek Dziarmaga, Piotr Deuar, and Krzysztof Sachas comment, arXiv:1001.1045, supporting the authors simulations but differentiating between near-mean-field and strongly quantum regimes. We clarify that we have three lines of evidence on decay of dark solitons and connect our work to Liebs Type-II excitations and the true meaning of a quantum dark soliton.
Critical behavior developed near a quantum phase transition, interesting in its own right, offers exciting opportunities to explore the universality of strongly-correlated systems near the ground state. Cold atoms in optical lattices, in particular,
As the temperature of a many-body system approaches absolute zero, thermal fluctuations of observables cease and quantum fluctuations dominate. Competition between different energies, such as kinetic energy, interactions or thermodynamic potentials,
Scalable, coherent many-body systems can enable the realization of previously unexplored quantum phases and have the potential to exponentially speed up information processing. Thermal fluctuations are negligible and quantum effects govern the behavi
This is the reply to the comment arXiv:0801.4620 by Vidal, Dusuel, and Schmidt.
Over the last years the exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of thos