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Evans function and Fredholm determinants [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015 We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first-order linear differential operators on the real line. The applications we have in mind include linear stability problems associated with travelling wave solutions to nonlinear partial differential equations, for example ...
Simon Malham
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Central European Journal of Mathematics, 2011 The Fredholm alternative is one of the cornerstones of Functional Analysis. In his classical paper ``Sur une classe d'équations fonctionnelles'' [Acta Math. 27, 365--390 (1903; JFM 34.0422.02)], \textit{I.~Fredholm} obtained it by means of his theory of determinants, which nowadays has somewhat gone into oblivion, being replaced by the Riesz-Schauder ...
Henry P McKean
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On finite-temperature Fredholm determinants
Physica D: Nonlinear PhenomenaWe consider finite-temperature deformation of the sine kernel Fredholm determinants acting on the closed contours. These types of expressions usually appear as static two-point correlation functions in the models of free fermions and can be equivalently presented in terms of Toeplitz determinants.
Oleksandr Gamayun
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Infinite-Dimensional Quantum Entropy: The Unified Entropy Case [PDF]
EntropyInfinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models.
Roman Gielerak +2 more
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Quantum Gravity Microstates from Fredholm Determinants [PDF]
Physical Review Letters, 2021 A large class of two dimensional quantum gravity theories of Jackiw-Teitelboim form have a description in terms of random matrix models. Such models, treated fully non-perturbatively, can give an explicit and tractable description of the underlying ``microstate'' degrees of freedom.
Clifford Johnson
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An extension of the theory of Fredholm determinants [PDF]
Publications Mathematiques De L'Institut Des Hautes Etudes Scientifiques, 1990 It is the aim of Fredholm's determinant theory to write the resolvent of an operator K as the quotient of an operator-valued entire function N(z) and a scalar-valued entire function d(z). This means that \[ (I-zK)^{- 1}=N(z)/d(z) \] for all z in the resolvent set. For certain integral operators occuring in the theory of dynamical systems, the author is
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Quasi-Rational and Rational Solutions to the Defocusing Nonlinear Schrödinger Equation
Journal of Mathematical Sciences and Modelling, 2022 Quasi-rational solutions to the defocusing nonlinear Schrödinger equation (dNLS) in terms of wronskians and Fredholm determinants of order $2N$ depending on $2N-2$ real parameters are given.
Pierre Gaillard
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Multi-Parametric Families of Real and Non Singular Solutions of the Kadomtsev-Petviasvili I Equation
Universal Journal of Mathematics and Applications, 2021 Multi-parametric solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants are constructed in function of exponentials. A representation of these solutions as a quotient of wronskians of order $2N$ in terms of trigonometric
Pierre Gaillard
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Statistical properties of general Markov dynamical sources: applications to information theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2004 In Dynamical sources in information theory: fundamental intervals and word prefixes, B. Vallée studies statistical properties of words generated by dynamical sources. This is done using generalized Ruelle operators.
Frédéric Chazal +1 more
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Effective free-fermionic form factors and the XY spin chain
SciPost Physics, 2021 We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors.
O. Gamayun, N. Iorgov, Yu. Zhuravlev
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