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1. Effect of electron–electron interaction on magnitude of quantum oscillations of dissipative resistance in magnetic fields

   https://doi.org/10.1063/5.0127286  

   Abedi, Sara; Vitkalov, Sergey; Bykov, A. A.; Bakarov, A. K. (December 2022, Journal of Applied Physics)

   Magneto-intersubband resistance oscillations (MISOs) of highly mobile 2D electrons in symmetric GaAs quantum wells with two populated subbands are studied in magnetic fields [Formula: see text] tilted from the normal to the 2D electron layer at different temperatures [Formula: see text]. The in-plane component ([Formula: see text]) of the field [Formula: see text] induces magnetic entanglement between subbands, leading to beating in oscillating density of states (DOS) and to MISO suppression. Model of the MISO suppression is proposed. Within the model, a comparison of MISO amplitude in the entangled and disentangled ([Formula: see text]) 2D systems yields both difference frequency of DOS oscillations, [Formula: see text], and strength of the electron–electron interaction, described by parameter [Formula: see text], in the 2D system. These properties are analyzed using two methods, yielding consistent but not identical results for both [Formula: see text] and [Formula: see text]. The analysis reveals an additional angular dependent factor of MISO suppression. The factor is related to spin splitting of quantum levels in magnetic fields. 

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2. 2019/20 lessons from τ(Ωc0) and τ(Ξc0) and CP asymmetry in charm decays

   https://doi.org/10.1142/S0217751X20300136  

   Bianco, S.; Bigi, I. I. (August 2020, International Journal of Modern Physics A)

   null (Ed.)

   Our 2003 “Cicerone” had discussed charm dynamics with different directions and levels. 1 Here we focus on two items, where the “landscape” has changed sizably. (a) The lifetimes and semileptonic decays of charm hadrons show the impact of nonperturbative QCD and to which degree one can apply heavy quark expansion (HQE) for charm hadrons. It is more complex as we have learnt from 2019/20 data. (b) CP asymmetry has been established in 2019: 2 [Formula: see text] is quite an achievement by the LHCb collaboration! Our community is at the beginning of a long travel for fundamental dynamics. Can the SM account for these? We discuss the assumptions that were made up to 2018 data and new conclusions from 2019/20 ones. We need more data; however, one has to discuss correlations between different transitions. We give an Appendix, what we have learnt for large CP asymmetry in [Formula: see text]. 

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3. Continuous dependence on the initial data in the Kadison transitivity theorem and GNS construction

   https://doi.org/10.1142/S0129055X22500313  

   Spiegel, Daniel; Moreno, Juan; Qi, Marvin; Hermele, Michael; Beaudry, Agnès; Pflaum, Markus J. (October 2022, Reviews in Mathematical Physics)

   We consider how the outputs of the Kadison transitivity theorem and Gelfand–Naimark–Segal (GNS) construction may be obtained in families when the initial data are varied. More precisely, for the Kadison transitivity theorem, we prove that for any nonzero irreducible representation [Formula: see text] of a [Formula: see text]-algebra [Formula: see text] and [Formula: see text], there exists a continuous function [Formula: see text] such that [Formula: see text] for all [Formula: see text], where [Formula: see text] is the set of pairs of [Formula: see text]-tuples [Formula: see text] such that the components of [Formula: see text] are linearly independent. Versions of this result where [Formula: see text] maps into the self-adjoint or unitary elements of [Formula: see text] are also presented. Regarding the GNS construction, we prove that given a topological [Formula: see text]-algebra fiber bundle [Formula: see text], one may construct a topological fiber bundle [Formula: see text] whose fiber over [Formula: see text] is the space of pure states of [Formula: see text] (with the norm topology), as well as bundles [Formula: see text] and [Formula: see text] whose fibers [Formula: see text] and [Formula: see text] over [Formula: see text] are the GNS Hilbert space and closed left ideal, respectively, corresponding to [Formula: see text]. When [Formula: see text] is a smooth fiber bundle, we show that [Formula: see text] and [Formula: see text] are also smooth fiber bundles; this involves proving that the group of ∗-automorphisms of a [Formula: see text]-algebra is a Banach Lie group. In service of these results, we review the topology and geometry of the pure state space. A simple non-interacting quantum spin system is provided as an example illustrating the physical meaning of some of these results. 

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4. Some remarks on the Erdős Distinct subset sums problem

   https://doi.org/10.1142/S1793042123500860  

   Steinerberger, Stefan (September 2023, International Journal of Number Theory)

   Let [Formula: see text] be a set of positive integers, [Formula: see text] denoting the largest element, so that for any two of the [Formula: see text] subsets the sum of all elements is distinct. Erdős asked whether this implies [Formula: see text] for some universal [Formula: see text]. We prove, slightly extending a result of Elkies, that for any [Formula: see text], [Formula: see text] with equality if and only if all subset sums are [Formula: see text]-separated. This leads to a new proof of the currently best lower bound [Formula: see text]. The main new insight is that having distinct subset sums and [Formula: see text] small requires the random variable [Formula: see text] to be close to Gaussian in a precise sense. 

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5. Bounds on the superconducting transition temperature

   https://doi.org/10.1142/S0217984924300047  

   Randeria, Mohit (December 2024, Modern Physics Letters B)

   I summarize recent progress on obtaining rigorous upper bounds on superconducting transition temperature [Formula: see text] in two dimensions independent of pairing mechanism or interaction strength. These results are derived by finding a general upper bound for the superfluid stiffness for a multi-band system with arbitrary interactions, with the only assumption that the external vector potential couples to the kinetic energy and not to the interactions. This bound is then combined with the universal relation between the superfluid stiffness and the Berezinskii–Kosterlitz–Thouless [Formula: see text] in 2D. For parabolic dispersion, one obtains the simple result that [Formula: see text], which has been tested in recent experiments. More generally, the bounds are expressed in terms of the optical spectral weight and lead to stringent constraints for the [Formula: see text] of low-density, strongly correlated superconductors. Results for [Formula: see text] bounds for models of flat-band superconductors, where the kinetic energy vanishes and the vector potential must couple to interactions, are briefly summarized. Upper bounds on [Formula: see text] in 3D remains an open problem, and I describe how questions of universality underlie the challenges in 3D. 

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