We provide further evidence to support the fact that a four-dimensional effective field theory description with de Sitter isometries in IIB string theory, overcoming the no-go and the swampland criteria, can only exist if de Sitter space is realized as a Glauber-Sudarshan state. We show here that this result is independent of the choice of de Sitter slicings. The Glauber-Sudarshan state, constructed by shifting the interacting vacuum in the M-theory uplift of the scenario, differs from a standard coherent state in QFT in the sense that the shape and size of the state changes with respect to time, implying changes in the graviton and the flux quanta. Despite this, the expectation values of the graviton and flux operators in such a state reproduce the exact de Sitter background, as long as we are within the temporal bound set by the onset of the strong coupling in the dual type IIA side, and satisfy the corresponding Schwinger-Dyson's equations in the presence of hierarchically controlled perturbative and non-perturbative quantum corrections. Additionally, we provide a detailed study of the fluxes supporting the Glauber-Sudarshan state in the M-theory uplift of the IIB scenario. We show explicitly how the Bianchi identities, anomaly cancellation and flux quantization conditions, along-with the constraints from the Schwinger-Dyson's equations, conspire together to provide the necessary temporal dependences to support such a state in full M-theory. We also discuss how our analysis points towards a surprising connection to the four-dimensional null energy condition, for a Friedman-Lemaitre-Robertson-Walker state in the IIB side, as a consistency condition for the existence of an effective field theory description in M-theory. Lord Carnarvon: Can you see anything? Howard Carter: Yes ..... wonderful things! − Reply that Howard Carter gave to Lord Carnarvon just before entering the main annexe of the tomb of Tut.Ankh.Amen on Sunday, November 26, 1922 around 4:00 pm. Taken from [1].
A trial wave function for two-dimensional quantum dot helium in an arbitrary perpendicular magnetic field (a system of two interacting electrons in a two-dimensional parabolic confinement potential) is introduced. A key ingredient of this trial wave function is a Jastrow pair correlation factor that has a displaced Gaussian form. The above choice of the pair correlation factor is instrumental on assuring the overall quality of the wave function at all values of the magnetic field. Exact numerical diagonalization results are used to gauge the quality of the proposed trial wave function. We find out that this trial wave function is an excellent representation of the true ground state at all values of the magnetic field including weak (or zero) and strong magnetic fields.
We apply the exact numerical diagonalization technique to study two interacting electrons
in a one-dimensional parabolic quantum dot. We consider a modified Coulomb interaction
potential between the electrons with a truncation parameter that serves to regularize the
behaviour of the bare Coulomb potential in one dimension. We report the dependence of
ground and excited state energies for several values of the truncation parameter as the
strength of electronic correlations is varied relative to the confinement energy. The
similarity of this quantum dot system to the ammonia molecule is pointed out.
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