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Journal articles on the topic 'Heat kernel asymptotics'

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Author: Grafiati

Published: 14 March 2023

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1

BÄR, CHRISTIAN, and SERGIU MOROIANU. "HEAT KERNEL ASYMPTOTICS FOR ROOTS OF GENERALIZED LAPLACIANS." International Journal of Mathematics 14, no. 04 (June 2003): 397–412. http://dx.doi.org/10.1142/s0129167x03001788.

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We describe the heat kernel asymptotics for roots of a Laplace type operator Δ on a closed manifold. A previously known relation between the Wodzicki residue of Δ and heat trace asymptotics is shown to hold pointwise for the corresponding densities.

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2

Baudoin, Fabrice. "Stochastic Taylor expansions and heat kernel asymptotics." ESAIM: Probability and Statistics 16 (2012): 453–78. http://dx.doi.org/10.1051/ps/2011107.

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3

McAvity, D. M. "Heat kernel asymptotics for mixed boundary conditions." Classical and Quantum Gravity 9, no. 8 (August 1, 1992): 1983–97. http://dx.doi.org/10.1088/0264-9381/9/8/017.

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4

Bolte, Jens, and Stefan Keppeler. "Heat kernel asymptotics for magnetic Schrödinger operators." Journal of Mathematical Physics 54, no. 11 (November 2013): 112104. http://dx.doi.org/10.1063/1.4829061.

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5

Branson, Thomas P., Peter B. Gilkey, Klaus Kirsten, and Dmitri V. Vassilevich. "Heat kernel asymptotics with mixed boundary conditions." Nuclear Physics B 563, no. 3 (December 1999): 603–26. http://dx.doi.org/10.1016/s0550-3213(99)00590-8.

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6

Kirsten, Klaus. "Heat kernel asymptotics: more special case calculations." Nuclear Physics B - Proceedings Supplements 104, no. 1-3 (January 2002): 119–26. http://dx.doi.org/10.1016/s0920-5632(01)01598-5.

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7

Revelle, David. "Heat Kernel Asymptotics on the Lamplighter Group." Electronic Communications in Probability 8 (2003): 142–54. http://dx.doi.org/10.1214/ecp.v8-1092.

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8

AVRAMIDI, IVAN G., and THOMAS BRANSON. "HEAT KERNEL ASYMPTOTICS OF OPERATORS WITH NON-LAPLACE PRINCIPAL PART." Reviews in Mathematical Physics 13, no. 07 (July 2001): 847–90. http://dx.doi.org/10.1142/s0129055x01000892.

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We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part -∇μ∇μ. Our objective is to obtain information on the asymptotic expansions of the corresponding resolvent and the heat kernel. The heat kernel and the Green's function are constructed explicitly in the leading order. The first two coefficients of the heat kernel asymptotic expansion are computed explicitly. A new semi-classical ansatz as well as the complete recursion system for the heat kernel of non-Laplace type operators is constructed. Some particular cases are studied in more detail.

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9

Avramidi, Ivan G. "Heat Kernel Asymptotics of Zaremba Boundary Value Problem." Mathematical Physics, Analysis and Geometry 7, no. 1 (2004): 9–46. http://dx.doi.org/10.1023/b:mpag.0000022837.63824.4c.

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10

Mooers, Edith A. "Heat kernel asymptotics on manifolds with conic singularities." Journal d'Analyse Mathématique 78, no. 1 (December 1999): 1–36. http://dx.doi.org/10.1007/bf02791127.

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11

Collet, Pierre, Mauricio Duarte, Servet Martínez, Arturo Prat-Waldron, and Jaime San Martín. "Asymptotics for the heat kernel in multicone domains." Journal of Functional Analysis 270, no. 4 (February 2016): 1269–98. http://dx.doi.org/10.1016/j.jfa.2015.10.021.

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12

Gusynin, V. P., and E. V. Gorbar. "Local heat kernel asymptotics for nonminimal differential operators." Physics Letters B 270, no. 1 (November 1991): 29–36. http://dx.doi.org/10.1016/0370-2693(91)91534-3.

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13

Ge, Zhong. "Collapsing Riemannian Metrics to Carnot-Caratheodory Metrics and Laplacians to Sub-Laplacians." Canadian Journal of Mathematics 45, no. 3 (June 1, 1993): 537–53. http://dx.doi.org/10.4153/cjm-1993-028-6.

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AbstractWe study the asymptotic behavior of the Laplacian on functions when the underlying Riemannian metric is collapsed to a Carnot-Carathéodory metric. We obtain a uniform short time asymptotics for the trace of the heat kernel in the case when the limit Carnot-Carathéodory metric is almost Heisenberg, the limit of which is the result of Beal-Greiner-Stanton, and Stanton-Tartakoff.

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14

BEGUÉ, MATTHEW, LEVI DEVALVE, DAVID MILLER, and BENJAMIN STEINHURST. "SPECTRUM AND HEAT KERNEL ASYMPTOTICS ON GENERAL LAAKSO SPACES." Fractals 20, no. 02 (June 2012): 149–62. http://dx.doi.org/10.1142/s0218348x12500144.

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We introduce a method of constructing a general Laakso space while calculating the spectrum and multiplicities of the Laplacian operator. Using this information, we find the leading term of the trace of the heat kernel and the spectral dimension on an arbitrary Laakso space.

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15

Ludewig, Matthias. "Heat kernel asymptotics, path integrals and infinite-dimensional determinants." Journal of Geometry and Physics 131 (September 2018): 66–88. http://dx.doi.org/10.1016/j.geomphys.2018.04.012.

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16

Avramidi, Ivan G., and Guglielmo Fucci. "Non-Perturbative Heat Kernel Asymptotics on Homogeneous Abelian Bundles." Communications in Mathematical Physics 291, no. 2 (April 7, 2009): 543–77. http://dx.doi.org/10.1007/s00220-009-0804-6.

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17

Gusynin, V. P. "Asymptotics of the heat kernel for nonminimal differential operators." Ukrainian Mathematical Journal 43, no. 11 (November 1991): 1432–41. http://dx.doi.org/10.1007/bf01067283.

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18

Bruno, Tommaso, and Mattia Calzi. "Asymptotics for the heat kernel on H-type groups." Annali di Matematica Pura ed Applicata (1923 -) 197, no. 4 (November 18, 2017): 1017–49. http://dx.doi.org/10.1007/s10231-017-0713-9.

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19

STRELCHENKO, ALEXEI. "HEAT KERNEL OF NONMINIMAL GAUGE FIELD KINETIC OPERATORS ON MOYAL PLANE." International Journal of Modern Physics A 22, no. 01 (January 10, 2007): 181–202. http://dx.doi.org/10.1142/s0217751x07034921.

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We generalize the Endo formula1 originally developed for the computation of the heat kernel asymptotic expansion for nonminimal operators in commutative gauge theories to the noncommutative case. In this way, the first three nonzero heat trace coefficients of the nonminimal U (N) gauge field kinetic operator on the Moyal plane taken in an arbitrary background are calculated. We show that the nonplanar part of the heat trace asymptotics is determined by U (1) sector of the gauge model. The nonplanar or mixed heat kernel coefficients are shown to be gauge-fixing dependent in any dimension of space–time. In the case of the degenerate deformation parameter the lowest mixed coefficients in the heat expansion produce nonlocal gauge-fixing dependent singularities of the one-loop effective action that destroy the renormalizability of the U (N) model at one-loop level. Such phenomenon was observed at first in Ref. 2 for spacelike noncommutative ϕ4 scalar and U (1) gauge theories. The twisted-gauge transformation approach is discussed.

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20

Garbin, Daniel, and Jay Jorgenson. "Heat kernel asymptotics on sequences of elliptically degenerating Riemann surfaces." Kodai Mathematical Journal 43, no. 1 (March 2020): 84–128. http://dx.doi.org/10.2996/kmj/1584345689.

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21

Fahrenwaldt, M. A. "Heat kernel asymptotics of the subordinator and subordinate Brownian motion." Journal of Evolution Equations 19, no. 1 (September 5, 2018): 33–70. http://dx.doi.org/10.1007/s00028-018-0468-9.

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22

Barilari, D. "Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry." Journal of Mathematical Sciences 195, no. 3 (October 27, 2013): 391–411. http://dx.doi.org/10.1007/s10958-013-1585-1.

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23

Barvinsky, A. O., and D. V. Nesterov. "Infrared Asymptotics of the Heat Kernel and Nonlocal Effective Action." Theoretical and Mathematical Physics 143, no. 3 (June 2005): 760–81. http://dx.doi.org/10.1007/s11232-005-0104-z.

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24

Hambly, B. M. "Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet." Canadian Journal of Mathematics 63, no. 1 (February 1, 2011): 153–80. http://dx.doi.org/10.4153/cjm-2010-079-7.

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Abstract We establish the asymptotic behaviour of the partition function, the heat content, the integrated eigenvalue counting function, and, for certain points, the on-diagonal heat kernel of generalized Sierpinski carpets. For all these functions the leading term is of the form xγΦ (log x) for a suitable exponent γ and Φ a periodic function. We also discuss similar results for the heat content of affine nested fractals.

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25

Bytsenko, A. A., and F. L. Williams. "Asymptotics of the heat kernel on rank-1 locally symmetric spaces." Journal of Physics A: Mathematical and General 32, no. 31 (July 26, 1999): 5773–79. http://dx.doi.org/10.1088/0305-4470/32/31/303.

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26

Stepin, S. A. "Parametrix, heat kernel asymptotics, and regularized trace of the diffusion semigroup." Proceedings of the Steklov Institute of Mathematics 271, no. 1 (December 2010): 228–45. http://dx.doi.org/10.1134/s0081543810040176.

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27

Belani, Kanishka, Payal Kaura, and Aalok Misra. "Supersymmetry of noncompact MQCD-like membrane instantons and heat kernel asymptotics." Journal of High Energy Physics 2006, no. 10 (October 9, 2006): 023. http://dx.doi.org/10.1088/1126-6708/2006/10/023.

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28

Ishige, Kazuhiro, Tatsuki Kawakami, and Kanako Kobayashi. "Asymptotics for a nonlinear integral equation with a generalized heat kernel." Journal of Evolution Equations 14, no. 4-5 (June 8, 2014): 749–77. http://dx.doi.org/10.1007/s00028-014-0237-3.

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29

Norris, James R. "Heat kernel asymptotics and the distance function in Lipschitz Riemannian manifolds." Acta Mathematica 179, no. 1 (1997): 79–103. http://dx.doi.org/10.1007/bf02392720.

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30

Barilari, Davide, Ugo Boscain, and Robert W. Neel. "Small-time heat kernel asymptotics at the sub-Riemannian cut locus." Journal of Differential Geometry 92, no. 3 (November 2012): 373–416. http://dx.doi.org/10.4310/jdg/1354110195.

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31

Hsu, Pei. "Short-Time Asymptotics of the Heat Kernel on a Concave Bboundary." SIAM Journal on Mathematical Analysis 20, no. 5 (September 1989): 1109–27. http://dx.doi.org/10.1137/0520074.

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32

Kvitsinsky, A. A. "Zeta Functions, Heat Kernel Expansions, and Asymptotics for q-Bessel Functions." Journal of Mathematical Analysis and Applications 196, no. 3 (December 1995): 947–64. http://dx.doi.org/10.1006/jmaa.1995.1453.

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33

Ludewig, Matthias. "Strong short-time asymptotics and convolution approximation of the heat kernel." Annals of Global Analysis and Geometry 55, no. 2 (September 22, 2018): 371–94. http://dx.doi.org/10.1007/s10455-018-9630-4.

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34

Wang, Yong. "Volterra calculus and the variation formulas for the equivariant Ray–Singer metric." International Journal of Geometric Methods in Modern Physics 12, no. 07 (July 10, 2015): 1550066. http://dx.doi.org/10.1142/s0219887815500668.

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In this paper, using the Greiner's approach to heat kernel asymptotics, we give new proofs of the equivariant Gauss–Bonnet–Chern formula and the variation formulas for the equivariant Ray–Singer metric, which are originally due to Bismut and Zhang.

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35

Chinta, Gautam, Jay Jorgenson, and Anders Karlsson. "Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori." Nagoya Mathematical Journal 198 (June 2010): 121–72. http://dx.doi.org/10.1215/00277630-2009-009.

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AbstractBy a discrete torus we mean the Cayley graph associated to a finite product of finite cycle groups with the generating set given by choosing a generator for each cyclic factor. In this article we examine the spectral theory of the combinatorial Laplacian for sequences of discrete tori when the orders of the cyclic factors tend to infinity at comparable rates. First, we show that the sequence of heat kernels corresponding to the degenerating family converges, after rescaling, to the heat kernel on an associated real torus. We then establish an asymptotic expansion, in the degeneration parameter, of the determinant of the combinatorial Laplacian. The zeta-regularized determinant of the Laplacian of the limiting real torus appears as the constant term in this expansion. On the other hand, using a classical theorem by Kirchhoff, the determinant of the combinatorial Laplacian of a finite graph divided by the number of vertices equals the number of spanning trees, called the complexity, of the graph. As a result, we establish a precise connection between the complexity of the Cayley graphs of finite abelian groups and heights of real tori. It is also known that spectral determinants on discrete tori can be expressed using trigonometric functions and that spectral determinants on real tori can be expressed using modular forms on general linear groups. Another interpretation of our analysis is thus to establish a link between limiting values of certain products of trigonometric functions and modular forms. The heat kernel analysis which we employ uses a careful study of I-Bessel functions. Our methods extend to prove the asymptotic behavior of other spectral invariants through degeneration, such as special values of spectral zeta functions and Epstein-Hurwitz–type zeta functions.

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36

Chinta, Gautam, Jay Jorgenson, and Anders Karlsson. "Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori." Nagoya Mathematical Journal 198 (June 2010): 121–72. http://dx.doi.org/10.1017/s0027763000009958.

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AbstractBy a discrete torus we mean the Cayley graph associated to a finite product of finite cycle groups with the generating set given by choosing a generator for each cyclic factor. In this article we examine the spectral theory of the combinatorial Laplacian for sequences of discrete tori when the orders of the cyclic factors tend to infinity at comparable rates. First, we show that the sequence of heat kernels corresponding to the degenerating family converges, after rescaling, to the heat kernel on an associated real torus. We then establish an asymptotic expansion, in the degeneration parameter, of the determinant of the combinatorial Laplacian. The zeta-regularized determinant of the Laplacian of the limiting real torus appears as the constant term in this expansion. On the other hand, using a classical theorem by Kirchhoff, the determinant of the combinatorial Laplacian of a finite graph divided by the number of vertices equals the number of spanning trees, called thecomplexity, of the graph. As a result, we establish a precise connection between the complexity of the Cayley graphs of finite abelian groups and heights of real tori. It is also known that spectral determinants on discrete tori can be expressed using trigonometric functions and that spectral determinants on real tori can be expressed using modular forms on general linear groups. Another interpretation of our analysis is thus to establish a link between limiting values of certain products of trigonometric functions and modular forms. The heat kernel analysis which we employ uses a careful study ofI-Bessel functions. Our methods extend to prove the asymptotic behavior of other spectral invariants through degeneration, such as special values of spectral zeta functions and Epstein-Hurwitz–type zeta functions.

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37

Kotani, Motoko, and Toshikazu Sunada. "Albanese Maps and Off Diagonal Long Time Asymptotics for the Heat Kernel." Communications in Mathematical Physics 209, no. 3 (February 1, 2000): 633–70. http://dx.doi.org/10.1007/s002200050033.

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38

Neel, Robert. "The small-time asymptotics of the heat kernel at the cut locus." Communications in Analysis and Geometry 15, no. 4 (2007): 845–90. http://dx.doi.org/10.4310/cag.2007.v15.n4.a7.

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39

Kajino, Naotaka. "Heat Kernel Asymptotics for the Measurable Riemannian Structure on the Sierpinski Gasket." Potential Analysis 36, no. 1 (February 17, 2011): 67–115. http://dx.doi.org/10.1007/s11118-011-9221-5.

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40

Baudoin, Fabrice, and Michel Bonnefont. "The subelliptic heat kernel on SU(2): representations, asymptotics and gradient bounds." Mathematische Zeitschrift 263, no. 3 (October 22, 2008): 647–72. http://dx.doi.org/10.1007/s00209-008-0436-0.

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41

Barilari, Davide, and Jacek Jendrej. "Small time heat kernel asymptotics at the cut locus on surfaces of revolution." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 31, no. 2 (March 2014): 281–95. http://dx.doi.org/10.1016/j.anihpc.2013.03.003.

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42

MUNTEANU, Ovidiu. "Some results on the heat kernel asymptotics of the Laplace operator on Finsler spaces." Hokkaido Mathematical Journal 34, no. 3 (October 2005): 513–31. http://dx.doi.org/10.14492/hokmj/1285766284.

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43

Bytsenko, Andrei A. "Heat-kernel asymptotics of locally symmetric spaces of rank one and Chern-Simons invariants." Nuclear Physics B - Proceedings Supplements 104, no. 1-3 (January 2002): 127–34. http://dx.doi.org/10.1016/s0920-5632(01)01599-7.

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44

Braga, Gastão A., Jussara M. Moreira, and Camila F. Souza. "Asymptotics for nonlinear integral equations with a generalized heat kernel using renormalization group technique." Journal of Mathematical Physics 60, no. 1 (January 2019): 013507. http://dx.doi.org/10.1063/1.5059552.

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45

Wang, Yong. "The Noncommutative Infinitesimal Equivariant Index Formula." Journal of K-Theory 14, no. 1 (July 3, 2014): 73–102. http://dx.doi.org/10.1017/is014006002jkt268.

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AbstractIn this paper, we establish an infinitesimal equivariant index formula in the noncommutative geometry framework using Greiner's approach to heat kernel asymptotics. An infinitesimal equivariant index formula for odd dimensional manifolds is also given. We define infinitesimal equivariant eta cochains, prove their regularity and give an explicit formula for them. We also establish an infinitesimal equivariant family index formula and introduce the infinitesimal equivariant eta forms as well as compare them with the equivariant eta forms.

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46

Odencrantz, K. "The effects of a magnetic field on asymptotics of the trace of the heat kernel." Journal of Functional Analysis 79, no. 2 (August 1988): 398–422. http://dx.doi.org/10.1016/0022-1236(88)90019-5.

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47

Aramaki, Junichi. "On the asymptotics of the trace of the heat kernel for the magnetic Schrödinger operator." Pacific Journal of Mathematics 198, no. 1 (March 1, 2001): 1–14. http://dx.doi.org/10.2140/pjm.2001.198.1.

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48

Pivarski, Melanie. "Heat Kernel Asymptotics of Local Dirichlet Spaces as Co-Compact Covers of Finitely Generated Groups." Potential Analysis 36, no. 3 (May 31, 2011): 429–53. http://dx.doi.org/10.1007/s11118-011-9236-y.

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49

Fahrenwaldt, M. A. "Off-Diagonal Heat Kernel Asymptotics of Pseudodifferential Operators on Closed Manifolds and Subordinate Brownian Motion." Integral Equations and Operator Theory 87, no. 3 (February 4, 2017): 327–47. http://dx.doi.org/10.1007/s00020-017-2344-3.

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50

Cheng, Jin-Hsin, Chin-Yu Hsiao, and I.-Hsun Tsai. "Heat kernel asymptotics, local index theorem and trace integrals for Cauchy-Riemann manifolds with S1 action." Mémoires de la Société mathématique de France 162 (2019): 1–140. http://dx.doi.org/10.24033/msmf.470.

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