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W W "Schrödinger Operators and Related Topics"

174wK@wXyNg_Z~i[

F2019 N 11 23 iyj 15:00 -- 17:30
ꏊF wK@w@42K 205Z~i[

1. 15:00--16:00
u: @G iÉEj

TitleFDivergence of non-random fluctuation in First-passage percolation

Abstract: First-passage percolation was first introduced by Hammersley and Welsh in 1965 as a dynamical model of percolation. There are two types of fluctuations in First-passage percolation: the random fluctuation and the non-random fluctuation. They are both important and well studied. Although there has been a significant progress of the upper bound due to the development of concentration inequalities, it is hard to get a non-trivial lower bound because of the lack of techniques. In this talk, we discuss the divergence of the non-random fluctuation and related research.

16:00--16:30 tea time

2. 16:30--17:30
u: J@^ꎁ iw_j

Title: KdV̉ƃV[fBK[pf̃XyNg@

AbstractF]ĂKdV͏lꍇIȏꍇłDʂKdV̉Ԃ~߂ċԕϐɂĂ̊֐Ƃ݂ȂC̊֐PV[fBK[pf̃|eV݂ȂƁC̃V[fBK[pf͎ԂقȂĂunitarylł邱ƂmĂDꍇC܂͎Iȏꍇ|eVɎV[fBK[pf̖{IXyNg͐ΘAłDāC]KdV̓V[fBK[pf̃XyNg̊ϓ_͖{IɐΘAȏꍇ݈̂ĂƂɂȂDCŋ߁Cu҂͔񌸐EIȍL͈͂̏lɑ΂KdV̉\邱ƂɐDOɂƁCΘAXyNgKdVɂCكXyNg̏ꍇKdV̉̐ȂǂRȖƂčlDuł͂̕ӂ̎ɂċߔNlĂ邱ƂqׂD

Wu

F2019 N 11 19 i΁j 15:00 -- 17:00 : P
2019 N 11 21 i؁j 14:00 -- 16:00 : QiύX܂j
2019 N 11 22 ij 15:00 -- 17:00 : R
Ԃ͎኱ύX̉\܂BȂC20ij͂܂D

ꏊF wK@w@42K 205Z~i[

u : J^ꎁiw_j

Title: GS[hߒlɎKdVɂā@

Abstract : KdV1967ÑV[fBK[pfƂ̊֘A炩ɂȂĈȗ̊ϓ_猤ĂĂCłɌꂽƂ̊. CߔNC܂ŌĂȂ񌸐CIȃNX̏lɑ΂KdVC̐𒲂ׂƂɋ悤ɂȂ. ułKdV̉̍\CLc-_͓Iȗꂩ猩Ƃɂ. ɂL͈͂̔񌸐CIȏlɑ΂KdV̉̍\\ɂȂDGS[h_̊ϓ_̖̏ɂĂqׂD

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173wK@wXyNg_Z~i[

F2019 N 11 9 iyj 16:30 -- 17:30
ꏊF wK@w@42K 205Z~i[

u : Pavel Exner (Doppler Institute for Mathematical Physics and Applied Mathematics, Prague

Title: Spectral properties of leaky quantum structures@

Abstract : The subject of the talk are Schrödinger operators with an attractive singular potential', supported by a manifold or a geometric complex $$\Gamma$$ of codimension one, formally written as $$- \Delta - \alpha \delta(x - \Gamma)$$. We discuss the ways in which spectral properties of such systems are influenced by the geometry of the interaction support with the main attention paid to situations when the coupling constant is large or the geometric perturbation is weak, and asymptotic expansion can be derived. We also show how these can be approximated by regular potentials or by arrays of point interactions, and discuss effects arising from the presence of a magnetic field, in particular, the influence of an Aharonov-Bohm flux on the so-called Welsh eigenvalues.

172wK@wXyNg_Z~i[

F2019 N 7 6 iyj 15:00 -- 17:30
ꏊF wK@w@42K 205Z~i[

1. 15:00--16:00
u: @đ iEj

TitleF$$L^2$$ boundedness of pseudodifferential operators on manifolds with end

Abstract: We introduce pseudodifferential operators acting on functions or half-densities on a manifold with end. In the asymtotically hyperbolic case, we have not yet obtained the decay of integral kernel of our pseudodifferential operators in off-diagonal because of the exponential increasing of the coefficients of the metric tensor in the polar coordinate near infinity. In spite of this difficulty, we can prove $$L^2$$ boundedness of the pseudodifferential operators with bounded symbols by the same method as that of usual pseudodifferential operators on Euclidean spaces. As an application, we construct the parametrices of differential operators on manifolds with end and estimate the error term in the $$L^2$$ operator norm.

16:00--16:30 tea time

2. 16:30--17:30
u: @Vp iEj

Title: On a continuum limit of discrete Schrödinger operators on square lattice@

AbstractF {uł́Aiq̗UV[fBK[pf̘AɌɂēꂽʂ񍐂B̓Iɂ́Aiq߂ĂɌŗUV[fBK[pfAԏ̃V[fBK[pfɃm]xg邱ƂAUԂƘAԂ̊Ԃ̓K؂ȑΉ^邱ƂŏؖB̌ʂ̉pƂāAV[fBK[pf̗UŗLlyтɕtŗL֐̑QߋUV[fBK[pf瓾A̎x̏ォ̕]B{͒@iwK@wjƂ̋łB

171wK@wXyNg_Z~i[

F2019 N 6 22 iyj 15:00 -- 17:30
ꏊF wK@w@42K 205Z~i[

1. 15:00--16:00
u: T@Y iEj

TitleFSemiclassical shape resonances for Stark Hamiltonian

Abstract: We discuss semiclassical resonances for the Stark Hamiltonian. The main results are the Weyl law and the resonance expansion of the propagator in the shape resonance model. We introduce the complex distortion outside a cone to define and study Stark resonances for non-globally analytic potentials without energy range restriction. To prove the resonance expansion, we also discuss the functional pseudodifferential calculus for the Stark Hamiltonian.

16:00--16:30 tea time

2. 16:30--17:30
u: O@k iwj

Title: Semiclassical methods and observability estimate for Schrödinger operators with homogeneous potentials of order zero@

AbstractF {uł͂OĎȃ|eVVfBK[pf̕Ǐۂ |x| ł̑Qߋl@BǏۂ͂OĎȃ|eVVfBK[pfтɑΉn~ǧۂƂĒmĂB{uł͂܂̊m̕ǏۂɂĐGꂽAÓTx̕ǏɂďqׂBpƂĂOĎȃ|eVVfBK[pf̏ꍇɊϑs藧߂̕KvɂĂqׂB

170wK@wXyNg_Z~i[

F2019 N 6 8 iyj 15:00 -- 17:30
ꏊF wK@w@42K 205Z~i[

1. 15:00--16:00
u: J@Ǝ iEj

TitleFA remark on wave operators on the scale of Sobolev spaces

Abstract: VfBK[̎U_ɂāAgpf݂̑ƑQߊS͉̑Qߋ肷 dvȐłBU_ł͔gpf $$L^2$$ Œ邱ƂقƂǂł邪A Uɉpۂɂ̓\{tԂł̍l@RƕKvɂȂB̍uł́A ́iCjgpf\{tԏ̋ɌƂđ݂đQߊSł邽߂̏\ ̃|eVUւ̉pɂďЉBႦ1K̃\{tԂ̏ꍇA ̏͗ՊEȓِZ^A炩Ȓ^A1f^^_ݍpȂ L͈͂̃|eVɓKpłBԂΐĎ\{tԂ̏ꍇЉB

16:00--16:30 tea time

2. 16:30--17:30
u: @m i}g喼_j

Title: Continuum limit of scattering solutions for periodic lattices@

AbstractFConsider the Helmholtz equation on periodic lattices. By the scattering solution, we mean the one associated with the continuous spectrum satisfying the radiation condition. For a class of lattices including the square, triangular and hexagonal lattices, we show that, as the mesh size tends to 0, the scattering solution converges to that for the continuous model. This is a joint work with Arne Jensen in Aalborg.

169wK@wXyNg_Z~i[

F2019 N 5 18 iyj 15:00 -- 17:30
ꏊF wK@w@42K 205Z~i[

1. 15:00--16:00
u: 㓡@䂫ݎ iwK@Ej

TitleFBinding of Atoms in Mueller theory

16:00--16:30 tea time

2. 16:30--17:30
u: bc@ iwK@Ej

Title: dq̃n~gjǍŗLl̉E]@

AbstractF̓dqƌqjꍇ̃V[fBK[ɑ΂ẮA܂qjŒ肵ēdq̌ŗLllƂ@܂B̌ŗLl͌ɂ͉Ȃ߁AŗLl̕]@l܂BSdq̃n~gjA͉LEłAŗLl̏E]ɂmin-maxɊÂ@܂BŁAŗLl̉E]Grosse-Hertel-Thirring̕@ɂ΁A1dqn~gjǍŗLlɋA܂BǍŗLlɂ͉AŗLl̉E]͓ɂȂ܂B{uł́A1dqn~gjǍŗLl̉E]^̕@񍐂܂B

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• hisashi.okamotoiƁjgakushuin.ac.jp ({@vj
• shu.nakamuraiƁjgakushuin.ac.jp i@)
• fumihikoiƁjmath.gakushuin.ac.jpijFj