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Fusion of irreducible modules in the periodic Temperley–Lieb algebra

We propose a new family \mathsf{Y}_{k,\ell,x,y,[z,w]}𝖸k,ℓ,x,y,[z,w] of modules over the enlarged periodic Temperley–Lieb algebra \mathsf{\mathcal EPTL}_N(\beta)ℰ𝖯𝖳𝖫N(β). These modules are built from link states with two marked points, similarly to the modules \mathsf{X}_{k,\ell,x,y,z}𝖷k,ℓ,x,y,z that we constructed in a previous paper. They however differ in the way that defects connect pairwise. We analyse the decomposition of \mathsf{Y}_{k,\ell,x,y,[z,w]}𝖸k,ℓ,x,y,[z,w] over the irreducible standard modules \mathsf{W}_{k,x}𝖶k,x for generic values of the parameters zz and ww, and use it to deduce the fusion rules for the fusion \mathsf{W} × \mathsf{W}𝖶×𝖶 of standard modules. These turn out to be more symmetric than those obtained previously using the modules \mathsf{X}_{k,\ell,x,y,z}𝖷k,ℓ,x,y,z. From the work of Graham and Lehrer, it is known that, for \beta = -q-q^{-1}β=−q−q−1 where qq is not a root of unity, there exists a set of non-generic values of the twist yy for which the standard module \mathsf{W}_{\ell,y}𝖶ℓ,y is indecomposable yet reducible with two composition factors: a radical submodule \mathsf{R}_{\ell,y}𝖱ℓ,y and a quotient module \mathsf{Q}_{\ell,y}𝖰ℓ,y. Here, we construct the fusion products \mathsf{W}×\mathsf{R}𝖶×𝖱, \mathsf{W}×\mathsf{Q}𝖶×𝖰 and \mathsf{Q} × \mathsf{Q}𝖰×𝖰, and analyse their decomposition over indecomposable modules. For the fusions involving the quotient modules \mathsf{Q}𝖰, we find very simple results reminiscent of \mathfrak{sl}(2)𝔰𝔩(2) fusion rules. This construction with modules \mathsf{Y}_{k,\ell,x,y,[z,w]}𝖸k,ℓ,x,y,[z,w] is a good lattice regularization of the operator product expansion in the underlying logarithmic bulk conformal field theory. Indeed, it fits with the correspondence between standard modules and connectivity operators, and is useful for the calculation of their correlation functions. Remarkably, we show that the fusion rules \mathsf{W}×\mathsf{Q}𝖶×𝖰 and \mathsf{Q}×\mathsf{Q}𝖰×𝖰 are consistent with the known fusion rules of degenerate primary fields.

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Evidence of the Quantum Optical Nature of High-Harmonic Generation

High-harmonic generation is a light up-conversion process occurring in a strong laser field, leading to coherent bursts of extreme ultrashort broadband radiation [Lewenstein , Phys. Rev. A , 2117 (1994)]. As a new perspective, we propose that ultrafast strong-field electronic or photonic processes such as high-harmonic generation can potentially generate nonclassical states of light well before the decoherence of the system occurs [Gorlach , Nat. Commun. , 4598 (2020); Stammer ., Phys. Rev. Lett. , 123603 (2022)]. This could address fundamental challenges in quantum technology such as scalability, decoherence, or the generation of massively entangled states [Lewenstein , Luca Argenti Michael Chini, 27 (2024)]. Here, we report experimental evidence of the nonclassical nature of the harmonic emission in several semiconductors excited by a femtosecond infrared laser. By investigating single- and double-beam intensity cross-correlation [Loudon, Rep. Prog. Phys. , 913 (1980)], we measure characteristic nonclassical features in the single-photon statistics. We observe two-mode squeezing in the generated harmonic radiation, which depends on the laser intensity that governs the transition from super-Poissonian to Poissonian photon statistics. The measured violation of the Cauchy-Schwarz inequality realizes a direct test of multipartite entanglement in high-harmonic generation [Wasak, Phys. Rev. A , 033616 (2014)]. This result is supported by the theory of multimodal detection and the Hamiltonian from which the effective squeezing modes of the harmonics can be derived [Gonoskov , Phys. Rev. B , 125110 (2024); Christ New J. Phys. , 033027 (2011)]. With this work, we show experimentally that high-harmonic generation is a new quantum bosonic platform that intrinsically produces nonclassical states of light with unique features such as multipartite broadband entanglement or multimode squeezing. The source operates at room temperature, using standard semiconductors and a standard commercial fiber laser, opening up new routes for the quantum industry, such as optical quantum computing, communication, and imaging. Published by the American Physical Society 2024

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The Common Denominators of Parkinson's Disease Pathogenesis and Methamphetamine Abuse.

The pervasiveness and mortality associated with methamphetamine abuse have doubled during the past decade, suggesting a possible worldwide substance use crisis. Epitomizing the pathophysiology and toxicology of methamphetamine abuse proclaims severe signs and symptoms of neurotoxic and neurobehavioral manifestations in both humans and animals. Most importantly, chronic use of this drug enhances the probability of developing neurodegenerative diseases manifolds. Parkinson's disease is one such neurological disorder, which significantly and evidently not only shares a number of toxic pathogenic mechanisms induced by methamphetamine exposure but is also interlinked both structurally and genetically. Methamphetamine-induced neurodegeneration involves altered dopamine homeostasis that promotes the aggregation of α-synuclein protofibrils in the dopaminergic neurons and drives these neurons to make them more vulnerable to degeneration, as recognized in Parkinson's disease. Moreover, the pathologic mechanisms such as mitochondrial dysfunction, oxidative stress, neuroinflammation and decreased neurogenesis detected in methamphetamine abusers dramatically resemble to what is observed in Parkinson's disease cases. Therefore, the present review comprehensively cumulates a holistic illustration of various genetic and molecular mechanisms putting across the notion of how methamphetamine administration and intoxication might lead to Parkinson's disease-like pathology and Parkinsonism.

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