TY - CONF AU - Robert Seiringer ED - Weder, Richardo ED - Exner, Pavel ED - Grébert, Benoit ID - 2339 TI - Symmetry breaking in a model of a rotating Bose gas VL - 307 ER - TY - JOUR AB - We study the Gross-Pitaevskii functional for a rotating two-dimensional Bose gas in a trap. We prove that there is a breaking of the rotational symmetry in the ground state; more precisely, for any value of the angular velocity and for large enough values of the interaction strength, the ground state of the functional is not an eigenfunction of the angular momentum. This has interesting consequences on the Bose gas with spin; in particular, the ground state energy depends non-trivially on the number of spin components, and the different components do not have the same wave function. For the special case of a harmonic trap potential, we give explicit upper and lower bounds on the critical coupling constant for symmetry breaking. AU - Robert Seiringer ID - 2351 IS - 3 JF - Communications in Mathematical Physics TI - Gross-Pitaevskii theory of the rotating Bose gas VL - 229 ER - TY - JOUR AB - The Bose-Einstein condensation (BEC) of the ground state of bosonic atoms in a trap was discussed. The BEC was proved for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schrodinger equation. The BEC was 100% into the state which minimized the Gross-Pitaevskii energy functional. The analysis also included rigorous proof of BEC in a physically realistic, continuum model. AU - Lieb, Élliott H AU - Robert Seiringer ID - 2349 IS - 17 JF - Physical Review Letters TI - Proof of Bose-Einstein condensation for dilute trapped gases VL - 88 ER - TY - JOUR AB - We present a generalization of the Fefferman-de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions V on ℝn going to zero at infinity. This generalized decomposition can be used to extend previous results on N-body quantum systems with Coulomb interaction to a more general class of interactions. As an example of such an application, we derive the high density asymptotics of the ground state energy of jellium with Yukawa interaction in the thermodynamic limit, using a correlation estimate by Graf and Solovej. AU - Hainzl, Christian AU - Robert Seiringer ID - 2352 IS - 1 JF - Letters in Mathematical Physics TI - General decomposition of radial functions on ℝn and applications to N-body quantum systems VL - 61 ER - TY - JOUR AB - Synapses exhibit different short-term plasticity patterns and this behaviour influences information processing in neuronal networks. We tested how the short-term plasticity of excitatory postsynaptic currents (EPSCs) depends on the postsynaptic cell type, identified by axonal arborizations and molecular markers in the hippocampal CA1 area. Three distinct types of short-term synaptic behaviour (facilitating, depressing and combined facilitating-depressing) were defined by fitting a dynamic neurotransmission model to the data. Approximately 75 % of the oriens-lacunosum-moleculare (O-LM) interneurones received facilitating EPSCs, but in three of 12 O-LM cells EPSCs also showed significant depression. Over 90 % of the O-LM cells were immunopositive for somatostatin and mGluR1α and all tested cells were decorated by strongly mGluR7a positive axon terminals. Responses in eight of 12 basket cells were described well with a model involving only depression, but the other cells displayed combined facilitating-depressing EPSCs. No apparent difference was found between the plasticity of EPSCs in cholecystokinin- or parvalbumin-containing basket cells. In oriens-bistratified cells (O-Bi), two of nine cells showed facilitating EPSCs, another two depressing, and the remaining five cells combined facilitating-depressing EPSCs. Seven of 10 cells tested for somatostatin were immunopositive, but mGluR1α was detectable only in two of 11 tested cells. Furthermore, most O-Bi cells projected to the CA3 area and the subiculum, as well as outside the hippocampal formation. Postsynaptic responses to action potentials recorded in vivo from a CA1 place cell were modelled, and revealed great differences between and within cell types. Our results demonstrate that the short-term plasticity of EPSCs is cell type dependent, but with significant heterogeneity within all three interneurone populations. AU - Losonczy, Attila AU - Zhang, Limei AU - Ryuichi Shigemoto AU - Somogyi, Péter AU - Nusser, Zoltán ID - 2617 IS - 1 JF - Journal of Physiology TI - Cell type dependence and variability in the short-term plasticity of EPSCs in identified mouse hippocampal interneurones VL - 542 ER -