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Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-fiel...
We study the evolution of an N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper Grillakis, Machedon, and Margetis (2010) [13], in which we derived a second-o...
SECOND ORDER CORRECTIONS TO MEAN FIELD EVOLUTION FOR WEAKLY INTERACTING BOSONS, I     SECOND ORDER  equation       font style='font-size:12px;'> 2015/10/15
Inspired by the works of Rodnianski and Schlein [31] and Wu [34, 35], we derive a new nonlinear Schr¨odinger equation that describes a second-order correction to the usual tensor product (mean-ʂ...
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I [13], in which we derived a second-order correction to a mean-field e...
In our previous work [20],[21] we introduced a correction to the mean eld approximation of interacting Bosons. This correction describes the evolution of pairs of particles that leave the condensat...
We study the decay of two repulsively interacting bosons tunneling through a delta potentialm barrier by direct numerical solution of the time-dependent Schr¨odinger equation. The solutions are analyz...
In systems with a spontaneously broken continuous symmetry, the perturbative loop expansion is plagued with infrared divergences due to the coupling between transverse and longitudinal fluctuations.A...
We calculate the rst order perturbation correction to the ground state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the in nite repulsion Tonks-G...
Experimental observation of superfluidity in a microscopic cluster, M : (4He)x, of a molecule (M) and x number of 4He atoms (with x ranging from 1 to many) is qualitatively analyzed. It concludes th...
Physical reality of the existence of electron bubble in liquid 4He (or 3He) renders a clear experimental evidence for a quantum particle (in an interacting environment as seen by electron in liquid ...
We calculate the first order perturbation correction to the ground state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the infinite repulsion Tonks...
The correct form of the Schmidt decomposition of the stationary wave functions for a system of two interacting particles trapped in a two-dimensional harmonic potential is given
We report on frequency comparison of two optical lattice clocks based on fermionic 87Sr trapped in 1D optical lattice and bosonic 88Sr in 3D one. We discuss that these two lattice clock configurations...

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