The trace formula for quantum graphs with general self adjoint boundary conditions

We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing spectral properties of Laplacians, we prove several versions of trace formulae, relating Laplace spectra to sums over periodic orbi

8

2

y

a

M

2

]

h

p

-h

ta

m

[

1

v

1

1

1

3

.

5

8

:0v

i

X

r

aThetraceformulaforquantumgraphswithgeneralselfadjointboundaryconditionsJensBolte1DepartmentofMathematicsRoyalHolloway,UniversityofLondonEgham,TW200EX,UnitedKingdomSebastianEndres2Institutf¨urTheoretischePhysikUniversit¨atUlm,Albert-Einstein-Allee11D-89069Ulm,GermanyAbstractWeconsidercompactmetricgraphswithanarbitraryselfadjointrealisationofthe

di erentialLaplacian.AfterdiscussingspectralpropertiesofLaplacians,weproveseveralversionsoftraceformulae,relatingLaplacespectratosumsoverperiodicorbitsonthegraph.Thisincludestraceformulaewith,respectively,absolutelyandconditionallyconvergentperiodicorbitsums;theconvergencedependingonproper-tiesofthetestfunctionsused.Wealsoproveatraceformulafortheheatkernelandprovidesmall-tasymptoticsforthetraceoftheheatkernel.

搜索“diyifanwen.net”或“第一范文网”即可找到本站免费阅读全部范文。收藏本站方便下次阅读，第一范文网，提供最新高中教育The trace formula for quantum graphs with general self adjoint boundary conditions全文阅读和word下载服务。