Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant

Comparison of laparoscopic ureterolithotomy and retrograde lithotripsy in the treatment of proximal ureteral stones

The current approach in the surgical treatment of ureteral calculi involves the use of endourological procedures such as retrograde ureteroscopy with lithotripsy or percutaneous antegrade lithotripsy in the proximal ureter. Ureterolithotomy as a treatment method is of an auxiliary nature and is used when endourological intervention is impossible or in case of intraoperative collisions during access conversion. However, there are several comparative studies on lithotripsy and lithotomy.The aim. Comparative analysis of the outcomes of laparoscopic lithotomy and retrograde lithotripsy in the surgical treatment of proximal ureteral calculi, as well as the search for predictors of prolonged disability.Materials and methods. A prospective randomized multicenter study included 53 patients with an established diagnosis of ureterolithiasis who were treated in the period 2018–2021 in urological hospitals in Irkutsk. All patients were divided into two comparison groups: Lithotomy group (group 1; n = 30) and Lithotripsy group (group 2; n = 23).Results. When analyzing the results of the study, it was found that the level of complications of class II–III according to Clavien – Dindo was statistically comparable in both groups (p > 0.05). However, in absolute and relative terms, the prevalence of this indicator was noted during retrograde ureterolithotripsy. According to hard endpoints (reoperation, presence of residual stones or migration during the operation), 29 (96.6 %) patients of group 1 and 17 (73.4 %) patients of group 2 (p = 0.514) were successfully operated on.Conclusion. Laparoscopic ureterolithotomy may be offered to patients with large proximal ureteral stones as an alternative treatment option with better residual stone freedom but generally similar overall outcomes and complication rates

Analytic definition of spin structure

We work on a parallelizable time-orientable Lorentzian 4-manifold and prove that in this case the notion of spin structure can be equivalently defined in a purely analytic fashion. Our analytic definition relies on the use of the concept of a non-degenerate two-by-two formally self-adjoint first order linear differential operator and gauge transformations of such operators. We also give an analytic definition of spin structure for the 3-dimensional Riemannian case

Spintronics: Fundamentals and applications

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.Comment: invited review, 36 figures, 900+ references; minor stylistic changes from the published versio