Article
Physics, Multidisciplinary
Lucas Sa, Pedro Ribeiro, Tomas Prosen
Summary: In this study, we systematically classify many-body Lindblad superoperators describing open quantum systems based on their behavior under antiunitary symmetries and unitary involutions. We find that the preservation of certain properties reduces the number of symmetry classes, and the presence of additional symmetries can lead to different sets of classes. The classification is applicable to both Markovian and non-Markovian dynamics.
Article
Physics, Mathematical
Yuqiao Li
Summary: This paper investigates the evolution of the square of the first eigenvalue of the Dirac operator under metric flow and Ricci flow. It proves the non-decreasing property of this eigenvalue under certain conditions.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Serhan Eker
Summary: In this paper, we generalized E.C. Kim's estimates by considering the trace of the divergence-free symmetric nonzero tensor. We have also shown that E.C. Kim's estimates are still valid when the trace of the divergence-free symmetric tensor is identically zero. In the equality case, we characterized the eta-Killing spinor with Killing pair over Sasakian spin manifolds.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
P. D'Ancona, L. Fanelli, D. Krejcirik, N. M. Schiavone
Summary: This note highlights new results on the absence and localization of eigenvalues for the Dirac and Klein-Gordon operators, utilizing known resolvent estimates and the Birman-Schwinger principle established in the literature.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics
Xuejun Guo, Xin Li, Zhengyu Tao, Tao Wei
Summary: In this paper, we prove several conjectures raised by Zhi-Wei Sun on determinants and permanents using the eigenvectors-eigenvalues identity recently highlighted by Denton, Parke, Tao, and Zhang.
LINEAR & MULTILINEAR ALGEBRA
(2023)
Article
Materials Science, Multidisciplinary
Anjishnu Bose, Manodip Routh, Sreekar Voleti, Sudip Kumar Saha, Manoranjan Kumar, Tanusri Saha-Dasgupta, Arun Paramekanti
Summary: Recent theoretical and experimental research suggests that honeycomb cobaltates can be described by a pseudospin-1/2 easy-plane spin Hamiltonian with frustrated nearest-neighbor ferromagnetic exchange and weaker compass anisotropies. The model exhibits different phases, including ferromagnetic order, zigzag order, and an intermediate phase, which shows spin-liquid-like correlations. The optimal orders and the intermediate phase are found to be closely related to a parent Dirac spin liquid.
Article
Mathematics, Applied
David Hartman, Milan Hladik, David Riha
Summary: The study introduces an algorithm for computing the spectral decomposition of interval matrices and applies it to computing powers of interval matrices. By tight outer estimations of eigenvalues and eigenvectors, the algorithm achieves a total time complexity of O(n(4), discussing general interval matrices and symmetric interval matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Evgeny Korotyaev, Dmitrii Mokeev
Summary: This paper discusses the properties of the Dirac operator with a periodic potential on the half-line, including its spectrum and the response of the levels to the translation of the potential. Formulas for recovering potentials of special forms are derived.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics
Serhan Eker
Summary: We generalize the lower bound estimates for eigenvalues of the twisted Dirac operator on compact Riemannian Spinc-submanifold obtained by Roger Nakad and Julien Roth in 2015.
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
(2022)
Article
Mathematics
Pierluigi Benevieri, Alessandro Calamai, Massimo Furi, Maria Patrizia Pera
Summary: The study examines the persistence of eigenvalues and eigenvectors in perturbed eigenvalue problems in Hilbert spaces, assuming the unperturbed problem has a nontrivial kernel of odd dimension. A Rabinowitz-type global continuation result is proven using a topological approach based on a notion of degree for oriented Fredholm maps of index zero between real differentiable Banach manifolds.
Article
Multidisciplinary Sciences
Tatiana Martynova, Galina Muratova, Pavel Oganesyan, Olga Shtein
Summary: The generalized eigenvalue problem for a symmetric definite matrix pencil obtained from finite-element modeling of electroelastic materials is numerically solved using the Lanczos algorithm. In the considered problem, the mass matrix is singular, and hence the semi-inner product defined by this matrix is used in the process. The shift-and-invert Lanczos algorithm is employed to find multiple eigenvalues closest to a given shift and their corresponding eigenvectors. The results of numerical experiments are presented.
Article
Engineering, Multidisciplinary
S. M. Helal, A. Elmekawy
Summary: A new form of two-point nonlocal boundary conditions is introduced in this paper. This condition generalizes a Dirichlet condition at one boundary and a mixed condition at the other one. The focus of this study is not on the numerical solution of the problem, but rather on the effect of the proposed nonlocal boundary condition on the difference eigenvalue problem for an elliptic partial differential equation in one and two dimensions.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Multidisciplinary
Johannes Kalliauer, Herbert A. Mang
Summary: During proportional loading of structures, the re-arrangement of stresses can lead to a transition from softening to stiffening structures. However, there is currently limited research on the conditions for minimum stiffness in proportionally loaded structures. This publication presents a condition based on a linear eigenvalue problem and complex eigenvalues, which can determine the load-level of minimum stiffness. The proposed condition is verified numerically and compared with an alternative condition based on a mechanically objective arc length. The results demonstrate good agreement between the two conditions.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Physics, Multidisciplinary
H-T Ding, S-T Li, Swagato Mukherjee, A. Tomiya, X-D Wang, Y. Zhang
Summary: Novel relations between Dirac eigenvalue spectrum derivatives with respect to quark mass and correlations among eigenvalues were introduced, with lattice QCD results showing the impact of light quark mass on the eigenvalue spectrum and manifestation of axial anomaly in meson correlation functions.
PHYSICAL REVIEW LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Lucas B. Rezende, Jose Eduardo O. Pessanha
Summary: The paper proposes a block-Krylov algorithm based on the augmented block Householder Arnoldi method for computing eigenvalues in small-signal stability problems with CME matrices. Through numerical experiments, it is found that the algorithm performs better in terms of efficiency and robustness for CME matrices compared to conventional methods.
INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS
(2021)
Article
Astronomy & Astrophysics
Rajiv V. Gavai, Sayantan Sharma
Article
Physics, Multidisciplinary
Rajiv V. Gavai
PRAMANA-JOURNAL OF PHYSICS
(2015)
Article
Physics, Multidisciplinary
Rajiv V. Gavai
CONTEMPORARY PHYSICS
(2016)
Article
Physics, Multidisciplinary
Rajiv V. Gavai
ACTA PHYSICA POLONICA B
(2012)
Article
Physics, Particles & Fields
P. Castorina, R. V. Gavai, H. Satz
EUROPEAN PHYSICAL JOURNAL C
(2010)
Article
Physics, Nuclear
Rajiv V. Gavai
Article
Physics, Nuclear
Saumen Datta, Rajiv V. Gavai, Sourendu Gupta
Article
Astronomy & Astrophysics
R. V. Gavai, Sayantan Sharma
Article
Astronomy & Astrophysics
Debasish Banerjee, Rajiv V. Gavai, Sourendu Gupta
Article
Astronomy & Astrophysics
R. V. Gavai, Sayantan Sharma
Article
Astronomy & Astrophysics
Debasish Banerjee, Saumen Datta, Rajiv Gavai, Pushan Majumdar
Article
Astronomy & Astrophysics
Rajiv V. Gavai
Article
Astronomy & Astrophysics
R. V. Gavai, Sourendu Gupta
Article
Astronomy & Astrophysics
Rajiv V. Gavai, Sayantan Sharma
Proceedings Paper
Physics, Particles & Fields
Rajiv V. Gavai, Sayantan Sharma
EXTREME QCD 2012 (XQCD)
(2013)