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## Quantum simulation of dark energy candidates

Additional scalar fields from scalar-tensor, modified gravity or higher dimensional theories beyond general relativity may account for dark energy and the accelerating expansion of the Universe. These theories have led to proposed models of screening mechanisms, such as chameleon and symmetron fields, to account for the tight experimental bounds on fifth-force searches. Cold atom systems have been very successfully used to constrain the parameters of these screening models, and may in the future eliminate the interesting parameter space of some models entirely. In this paper, we show how to manipulate a Bose-Einstein condensate to simulate the effect of any scalar field model coupled conformally to the metric. We give explicit expressions for the simulation of various common models. This result may be useful for investigating the computationally challenging evolution of particles on a screened scalar field background, as well as for testing the metrology scheme of an upcoming detector proposal.

We theoretically analyze exciton-photon oscillatory dynamics within a homogenous polariton condensate in presence of energy detuning between the cavity and quantum well modes. Whereas pure Rabi oscillations consist of the particle exchange between the photon and exciton components in the polariton system without any oscillations of their quantum phases, we demonstrate that any non-zero detuning results in oscillations of the relative phase of the photon and exciton macroscopic wave functions. Different initial conditions reveal a variety of behaviors of the relative phase between the two condensates, and a crossover from Rabi-like to Josephson-like oscillations is predicted

My goal is to conceive how the reality would look like for hypothetical creatures that supposedly perceive on time scales much faster or much slower that of us humans. To attain the goal, I propose modelling in two steps. At step we have to single out a uni“ed parameter that sets time scale of perception. Changing substantially the value of the parameter would mean changing scale. argue that the required parameter is duration of discrete perceptive frames, snapshots, whose sequencing constitutes perceptive process. I show that different standard durations of perceptive frames is the ground for differences in perceptive time scales of various animals. Abnormally changed duration of perceptive frames is the cause of the effect of distorted subjective time observed by humans under some conditions. Now comes step two of the modelling. By inserting some arbitrary duration of a perceptive frame, we set a hypothetical scale and thus emulate viewpoint for virtual observation of the reality in a wider or narrower angle embracing events in time. Like changing lenses of a microscope, viewing reality different temporal scales makes certain features of reality manifested, others veiled. These are, in particular, features of life. If we observe an object in an inappropriate interval, we may not notice the very essence of a process it is undergoing.

I develop the idea that there exists a special dimension of depth, or of scale. The depth dimension is physically real and extends from the bottom micro-level to the ultimate macro-level of the Universe. The depth dimension, or the scales axis, complements the standard three spatial dimensions. I discuss the tentative qualities of the depth dimension and the universal arrangement of matter along this dimension. I suggest that all matter in the Universe, at least in the present cosmological epoch, is in joint downward motion along the depth dimension. The joint downward motion manifests itself in the universal contraction of matter. The opposite direction of motion, upward the dimension, would cause the expansion of matter. The contraction of matter is a primary factor, whereas the shrinking of space in the vicinity of matter is a derivative phenomenon. The observed expansion of the Universe is explained by the fact that celestial bodies become smaller due to matter contraction, while the overall space remains predominantly intact. Thus, relative to the contracting material bodies, the total span of cosmic space appears to be becoming vaster. I attempt to explain how the contraction of matter engenders the effect of universal gravity. I use over thirty animated and graphical color visualizations in the text to make the explanation of the proposed ideas more lucid.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.