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About 6,546 papers for “Heat kernel”
I. G. Avramidi, R. Schimming, I. G. Avramidi et al. · 1995
We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in more detail. * Alexander von Humboldt Fellow. On leave of absence from Research Institute for
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Ivan G. Avramidi · 2015
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Martin T. Barlow · Cambridge University Press eBooks · 2017
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M. W. Wong · 2022
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Viatcheslav Mukhanov, Sergei Winitzki · Cambridge University Press eBooks · 2007
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A. V. Ivanov · arXiv (Cornell University) · 2023
The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and concepts as uniqueness, a symmetry of the Seeley-DeWitt coefficients, extension on the whole manifold, a family of special functions, and the late-time asymptotics with the use of the path integral formulation.
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Stephen Dokroug Kolog, Jun Wang · SSRN Electronic Journal · 2024
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Artiom Kovnatsky, Michael M. Bronstein, Alexander M. Bronstein et al. · Lecture notes in computer science · 2012
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T. Kulczycki, B. Siudeja · 2016
Abstract. We prove that the diagonal of the transition probabilities for the d–dimensional Bessel processes on (0, 1], reflected at 1, which we denote by pNR (t, r, r), is an increasing function of r for d> 2 and that this is false for d = 2. 1.
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L. L. Salcedo · EPJ direct · 2001
Cited by 4Open access
Krzysztof Burdzy · Lecture notes in mathematics · 2014
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2011
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zeusindomitable-max · Zenodo (CERN European Organization for Nuclear Research) · 2025
Initial release of the Heat-Kernel Regularization framework. Features Implementation of Heat-Kernel Regularization on Riemannian manifolds S² manifold geometry with metric tensor and geodesic distance Seeley-DeWitt asymptotic expansion for regularization Comprehensive mathematical foundation documentation Full test suite with CI/CD automation Mathematical Foundation This package implements the theoretical framework from: Seeley-DeWitt heat kernel expansion Variational regularization on parameter manifolds Geometric deep learning principles Usage from heat_kernel import SphereManifold, HeatKernelRegularizer manifold = SphereManifold() regularizer = HeatKernelRegularizer(manifold)
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Contemporary mathematics - American Mathematical Society · 2006
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J. J. Duistermaat · Birkhäuser Boston eBooks · 2011
The goal of the heat kernel method is to express (2.40) as an integral over the fixed point set M γ in M of the transformation γ. Here M γ = M if γ is the identity. The method is based on the following observations about arbitrary elliptic differential operators D, acting on sections of a smooth vector bundle F over a compact manifold M, which admits a a direct sum decomposition F = F + ⊕ F − . In our case, F = E ⊗ L, with the splitting F ± = E ± ⊗ L, and D is the spin-c Dirac operator. For the required facts about trace class operators, see for instance Hörmander [42, Sec. 19.1], or Duistermaat [19].
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J. J. Duistermaat · Birkhäuser Boston eBooks · 2011
Our operator Q = D 2 , the square of the spin-c Dirac operator, has scalar principal symbol. So for the discussion of the asymptotic expansion of its heat kernel, we may restrict ourselves to the case that Q is a second order differential operator, acting on sections of a complex vector bundle F over a d-dimensional Riemannian manifold (M, β), with principal symbol given by 8.1 $$\sigma _{\it{Q}} (\xi)\,=\,\beta ^{-1}\,(\xi,\,\xi)\, \cdot \,1,\,\,\,\,\xi\,\in\,\rm{T}^{*}\,\it{M}.$$
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Gopakumar, Rajesh, Gupta, Rajesh Kumar, Lal, Shailesh · arXiv (Cornell University) · 2011
We explicitly evaluate the heat kernel for the Laplacian of arbitrary spin tensor fields on the thermal quotient of (Euclidean) $AdS_N$ for $N\geq 3$ using the group theoretic techniques employed for $AdS_3$ in arXiv:0911.5085. Our approach is general and can be used, in principle, for other quotients as well as other symmetric spaces.
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Moss, Ian G, Naylor, Wade · arXiv (Cornell University) · 2001
A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as covariant perturbation theory. The new technique gives an expansion for the heat kernel at coincident points. It can also be used to obtain the derivative of the heat kernel and this is useful for evaluating the expectation values of the stress-energy tensor.
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J.D. Curry · Zenodo (CERN European Organization for Nuclear Research) · 2025
Heat-Kernel-Attention
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Guardati, Emanuele · AMS Degree Thesis (University of Bologna) · 2017
L’integrale funzionale fu introdotto per la prima volta da Feynman nel 1948. Esso costituisce un differente approccio alla meccanica quantistica non relativistica, equivalente \nalle precedenti formulazioni. Contrariamente all'approccio prettamente matematico della \nquantizzazione canonica, Feynman predilige un’interpretazione più intuitiva, basando il \nsuo lavoro su una generalizzazione dell’esperimento delle due fenditure. Oltre ad una \ncomprensione più profonda dei ben noti risultati della meccanica quantistica non relativistica, l’utilizzo dell’integrale funzionale ha altresì il vantaggio di esemplificare calcoli \nperturbativi. Oltre a mostrare l’equivalenza con la formulazione di Schödinger, discutiamo il limite classico, e diamo degli esempi di calcoli espliciti, determinando i propagatori \ndella particella libera e dell’oscillatore armonico quantistici. Infine, mediante l’integrale \nfunzionale, studiamo una soluzione perturbativa dell’equazione del calore.
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