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Journal of Physics A: Mathematical and Theoretical - latest papers

Latest articles for Journal of Physics A: Mathematical and Theoretical

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  • Hammerstein equations for sparse random matrices
    Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not been previously applied to sparse matrix problems. We close this gap in the literature by showing how one can employ numerical solutions of Hammerstein equations to accurately recover the spectra of adjacency matrices and Laplacians of random graphs. While our treatment focuses on random graphs for concreteness, the methodology has broad applications to more general sparse random matrices.

  • Freezing imaginarity measures with real operations
    Imaginarity plays an essential role in many quantum information processing tasks. Usually, real operations do not increase imaginarity measures. In present work, we aim to discuss freezing of imaginarity measures with real operations. It is proved that a real operation Φ freezes all imaginarity measures of a state ρ if and only if it freezes the relative entropy measure of imaginarity of the state ρ. In the qubit case, real operations that freeze imaginarity measures based on trace distance and relative entropy are characterized, respectively. Moreover, the freezing of imaginarity measure based on trace distance is not necessarily dilated into multipartite systems, while that based on the Tsallis relative entropy can be dilated into multipartite systems. Finally, we characterize real local operations that freeze the imaginarity measure based on trace distance of a special type of X-states in a multi-qubit system.

  • Equilibrium of charges and differential equations solved by polynomials II
    We continue study of equilibrium of two species of 2d coulomb charges (or point vortices in 2d ideal fluid) started in (Loutsenko 2004 J. Phys. A: Math. Gen.37 1309). Although for two species of vortices with circulation ratio −1 the relationship between the equilibria and the factorization/Darboux transformation of the Schrodinger operator was established a long ago, the question about similar relationship for the ratio −2 remained unanswered. Here we present the answer: one has to consider Darboux-type transformations of third order differential operators rather than second order Schrodinger operators. Furthermore, we show that such transformations can also generate equilibrium configurations where an additional charge of a third specie is present. Relationship with integrable hierarchies is briefly discussed.

  • Localization in quantum field theory for inertial and accelerated observers
    We study the problem of localization in quantum field theory (QFT) from the point of view of inertial and accelerated experimenters. We consider the Newton–Wigner, the algebraic QFT (AQFT) and the modal localization schemes, which are, respectively, based on the orthogonality condition for states localized in disjoint regions of space, on the algebraic approach to QFT and on the representation of single particles as positive frequency solution of the field equation. We show that only the AQFT scheme obeys causality and physical invariance under diffeomorphisms. Then, we consider the nonrelativistic limit of quantum fields in the Rindler frame. We demonstrate the convergence between the AQFT and the modal scheme and we show the emergence of the Born notion of localization of states and observables. Also, we study the scenario in which an experimenter prepares states over a background vacuum by means of nonrelativistic local operators and another experimenter carries out nonrelativistic local measurements in a different region. We find that the independence between preparation of states and measurements is not guaranteed when both experimenters are accelerated and the background state is different from Rindler vacuum, or when one of the two experimenters is inertial.

  • Existence results of non-local integro-differential problem with singularity under a new fractional Musielak–Sobolev space *
    In this article, we construct a new fractional Musielak–Sobolev space designed to address the non-locality associated with the corresponding integro-differential operators. The completeness, reflexivity, and uniform convexity of this new space, along with an associated embedding theorem are established. As a practical application, we investigate the solvability of a class of non-local problems with singular nonlinearities under the new fractional Musielak–Sobolev space. Based on appropriate assumptions, we derive an existence result for two weak solutions utilizing the fibering method in form of the Nehari manifold. Furthermore, we provide two concrete operator examples within the framework of the fractional Musielak–Sobolev space as examples.