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A mathematical analysis of the GW0 method for computing electronic excited state energies of molecules 
Posted on 20150612
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This paper analyses the GW method for finite electronic systems. In a first step, we provide a mathematical framework for the usual onebody operators that appear naturally in manybody perturbation theory. We then discuss the GW equations which construct an approximation of the onebody Green's function, and give a rigorous mathematical formulation of these equations. Finally, we study the wellposedness of the GW0 equations, proving the existence of a unique solution to these equations in a perturbative regime. . . . . 






Babel of Units. The Evolution of Units Systems in Classical Electromagnetism 
Posted on 20150611
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We recount the history of development of units systems in electrodynamics, and fully derive how each system is constructed. Done for Electromagnetic (emu), Electrostatic (esu), Gaussian, a variantGaussian, HeavisideLorentz, and SI systems. The article fills in large gaps in standard textbook treatments of units. . . . . 






Lectures on singular stochastic PDEs 
Posted on 20150530
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These are the notes for a course at the 18th Brazilian School of Probability held from August 3rd to 9th, 2014 in Mambucaba. The aim of the course is to introduce the basic problems of nonlinear PDEs with stochastic and irregular terms. We explain how it is possible to handle them using two main techniques: the notion of energy solutions and that of paracontrolled distributions. In order to maintain a link with physical intuitions, we motivate such singular SPDEs via a homogenisation result for a diffusion in a random potential. . . . . 






Quantum Hamiltonian Complexity 
Posted on 20150529
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We survey the growing field of Quantum Hamiltonian Complexity, which includes the study of Quantum Constraint Satisfaction. In particular, our aim is to provide a computer scienceoriented introduction to the subject in order to help bridge the language barrier between computer scientists and physicists in the field. As such, we include the following in this paper: (1) The motivations and history of the field, (2) a glossary of condensed matter physics terms explained in computerscience friendly language, (3) overviews of central ideas from co . . . . 






Metric and Topological Spaces 
Posted on 20150510
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The syllabus for the course is defined by the Faculty Board Schedules
(which are minimal for lecturing and maximal for examining). What is presented here
contains some results which it would not, in my opinion, be fair to set as bookwork
although they could well appear as problems. In addition, I have included a small amount
of material which appears in other 1B courses. I should very much appreciate being told
of any corrections or possible improvements and might even part with a small reward to
the first finder of particular errors. . . . . 






Manybody physics with ultracold gases 
Posted on 20150509
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This paper reviews recent experimental and theoretical progress concerning manybody phenomena
in dilute, ultracold gases. It focuses on effects beyond standard weakcoupling descriptions, such as the
MottHubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or
lowestLandaulevel physics in quasitwodimensional gases in fast rotation. Strong correlations in
fermionic gases are discussed in optical lattices or nearFeshbach resonances in the BCSBEC
crossover. . . . . 






