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Last Update : 2023/02/08

ANZX

2023 N 2 21 i΁j 15:30 -- 17:00

F kw@A 8K 801

u : |c@D i֐wj

Title: fBN̍ċAƃV[fBK[̗ՊEɂā@

Abstract : V[fBK[̗ՊEfBN̍ċAƂ̑ΉŒBՊEIȃV[fBK[̍\@ƂāAՊEIȃV[fBK[ɂNX̐̃|eV邱Ƃō\@ƍċNIȃfBNh-ϊō\@ЉAQԖڂ̍\@nIɍœK$$L^2$$-n[fB[^̕s邱ƂɂďqׂB

2023 N 1 27 ij 15:30 -- 17:00

F online

u : Qinghui Liu iBeijing Institute of Technologyj

Title: The Hausdorff dimension of spectrum of a class of substitutional Hamiltonians@

Abstract : We introduce some results on spectrum of 1-dim Schrodinger operator with potentials generated by periodic doubling substitution and generalized Thue-Morse substitutions.

2023 N 1 13 ij 15:30 -- 18:00

Fonline

u : 썇 C , C ᩉ , q m , ۈ J^ , ێR I , ێR S ikww@wȁj

Title: Cm_̓eɂĂ̔\@

Abstract :

2022 N 12 9 ij 17:00 -- 18:30

F online

u : Martin VögeliStrasbourgj

Title: Spectral statistics of noisy non-selfadjoint operators @

Abstract : The spectrum of non-selfadjoint operators can be highly unstable even under very small perturbations. This phenomenon is nowadays referred to as "pseudospectral effect". Traditionally this pseudosepctral effect was considered a drawback since it can be the source of immense numerical errors, as shown for instance in the works of L. N. Trefethen. However, this pseudospectral effect can also be the source of many new insights. A line of works by Hager, Bordeaux-Montrieux, Sjöstrand, Christiansen and Zworski exploits the pseudospectral effect to show that the (discrete) spectrum of a large class of non-selfadjoint pseudo-differential operators subject to a small random perturbation follows a Weyl law with probability close to one. In this talk we will give an overview over recent results on the macroscopic and microscopic distribution of eigenvalues of various non-selfadjoint operators subject to small random perturbations in the pseudospectrum.

2022 N 11 25 ij 15:00 -- 18:15

F kw@A 8K 801

1. 15:00 -- 16:30

u : Y@_ i}gwj

Title: Discrete approximation of reflected Brownian motions by Markov chains on partitions of domains@

Abstract : {uł́A[NbhԂ̗̈̔˕ǃuE^ɑ΂闣UߎɂčlB sł́Ä̊iq_̒P_EH[NpUߎsĂB X̌ł́Asψꐫ⃉_̈̕lA ̏ŁAAԃ_EH[NBׂƂA Ή郉_EH[N̕z̗񂪔˕ǃuE^̕zɎ邽߂ \^B{úA쐳PiswjA^ؐVƂ̋ɊÂB

2. 16:45 -- 18:15

u : yc@ ihqwj

Title: gfBNԂɂ閄ߍݒ藝Ƒ΍@

Abstract : {uł́ALNX̑Ώ̃}Rtߒɑ΂ gfBNԂ炠鐫NX xɊւϕȊ֐Ԃւ̖ߍ݂ RpNgɂȂ錋ʂЉA̎Ɖ@IĊ֐ ̑΍Ƃ̊֘AɂďqׂB (Z.-Q. Chen (Univ. Washington)Ƃ̋)

2022 N 11 11 ij 15:00 -- 17:00

F kw@A 8K 801

1. 15:00 -- 16:30

u : 㓇@F iNational Center for Theoretical Sciences, Taiwanj

Title: Mean-field behavior for the quantum Ising model@

Abstract : The quantum Ising model is a kind of model of ferromagnetic materials. In this model, we consider spin configurations regarded as operators but not scalars. Due to this, spins are fluctuated by a quantum effect $$q\geq 0$$. When $$q=0$$, the model is particularly called the classical Ising model. In the case of the classical one for the nearest-neighbor setting, it is known that the (magnetic) susceptibility $$\chi(\beta, 0)$$ diverges at the critical inverse temperature $$\beta_{c}$$ and exhibits the power-law behavior on $$\mathbb{Z}^d$$. In particular, its critical exponent $$\gamma$$ takes the mean-field value $$1$$ in $$d \geq 4$$. In this talk, I show some attempts to prove that the critical behavior for the susceptibility does not change even when the quantum effect is imposed. Physicists believe this conjecture, but we want to give mathematically rigorous proof. So far, we have obtained the differential inequalities for $$\chi(\beta, q)$$ with respect to $$\beta$$ . They support that $$\gamma=1$$ with an assumption. Also, I mention attempts to derive the lace expansion, which implies the assumption for the differential inequalities. This talk is based on joint work with Akira Sakai (Hokkaido University, Japan).

2. 16:45 -- 18:15

u : V@T itȑwj

Title: KPZŒ_ɊւVȓWJ@

Abstract : KPZՐ͊EʐɂĊς镁ՓIłCݍpqnƊ֘A鐫ł邱ƂmĂD MatetskiCQuastelCRemeniki2021jKPZՃNXtƂ镪z֐̈QKPZŒ_ƂēD sɂẮCfɂKPZŒ_ĂȂD ̂߁CߔNRSKΉp邱ƂŁC̃fɑ΂ēKpłKPZŒ_߂邽߂̎@̊J݂ĂD CL̕@łKPZŒ_𓾂邱ƂłCȖƂĎcĂD {uł́C̏𖞂SĂTASEPfɑ΂ēKpłKPZŒ_߂邽߂̎@ꂽƂЉD ܂CL̎@VɐݏoƂŔTASEPKPZXP[ǑW̐wIӖ\wIɂďqׂD

2022 N 11 4 ij 15:30 -- 17:00

F kw@A 8K 801

u : @A icmwj

Title: ڐG̓_ߒɂ郂f@

Abstract : T^IȂP̂ƏWc̑̐Ƃ̃_ȐڐǦn񂪃|A\_ߒȂƉ肵Aɂ̌̂N_ƂāA҂ւ̊Ƒ҂Ƃ̐ڐGpxƂƂɕωAƂflB̃fɊÂĎĐŸӖlB܂A҂}ߒɏ]đƉ肷ƁAsɂ銴Ґ̎w֐IxƊ{ĐYƂ̊֌WAmz̃[g֐ʂė^Ƃ悭mꂽB

2022 N 10 28 ij 10:00 -- 11:30

F online

u : Rodrigo Matos iTexas A & M Universityj

Title: Localization and Eigenvalue Statistics for the Disordered Hubbard model within Hartree-Fock Theory.@

Abstract : Localization in the disordered Hubbard model within Hartree-Fock theory was previously established in joint work with J. Schenker, in the regime of large disorder in arbitrary dimension and at any disorder in dimension one, provided the interaction strength is sufficiently small. After introducing these results and other relevant background, I will present recent progress on the eigenvalue statistics for this model. Under weak interactions and for energies in the localization regime which are also Lebesgue points of the density of states, it is shown that a suitable local eigenvalue process converges in distribution to a Poisson process with intensity given by the density of states times Lebesgue measure. If time allows, proof ideas and further research directions will be discussed, including a Minami estimate and its applications.

2022 N 10 21 ij 16:30 -- 18:00ipZ~i[ƋÁj

F kw@A 8K 801@

u : Julian Tugaut iUniversit'e Jean Monnetj

Title: From the system of interacting particles to the granular media equation: long-time behavior and exit-time.@

Abstract : We start from the mean-field system of interacting particles. By propagation of chaos, we derive the McKean-Vlasov diffusion then the associated PDE that is to say the granular media equation. The two questions that we are interested in are the long-time behavior (existence and uniqueness of invariant probability measures and convergence towards this steady state) and the first exit-time from some open domain. The two questions are strongly related without interaction and we will see that the same occurs with the nonlinear diffusion and the nonlinear PDE. First, we will study the existence and uniqueness (or thirdness) of the steady state(s). Proofs will be given about the thirdness of the invariant probability measures. Then, we will give the main results concerning the convergence and the exit-time in the nonconvex landscapes case. Finally, we will discuss some intuition about the basins of attraction in the small-noise limit.

2022 N 10 7 ij 15:30 -- 17:00

F kw@A 8K 801

u : @\G ikwj

Title: t2_EH[N2random interlacements̃JbvO@

Abstract : 2Ug[X̒P_EH[N(SRW)핢Ԃ̒萔{܂ő点ƂCSRW܂K₵ĂȂ_(late point)̓NX^[邱ƂmĂ(Dembo-Peres-Rosen-Zeitouni '06, c '19) Dlate point܂̗lq𒲂ׂ1̕@ƂāC2random interlacementsƌĂ΂mf ꂽ(Comets-Popov-Vachkovskaia '16) D̃f́C_ɓBȂ悤ɏÂꂽ2iqSRW̋OՂpč\DComets͎, late point2random interlacementŝ֌WD{uł́CCometšʂ苭, ҂̃JbvO\ł邱Ƃ񍐂Dؖ̌ƂȂ̂soft local time̕@(Popov-Teixeira '15)ł. Ԃ΂̃JbvOplate poinťɊւĂ]邱Ƃ񍐂D

2022 N 9 21 ij 11:00 -- 12:30@iAIMRƋJÁj

F IC@

u : Dumi Culcer iUniversity of New South Wales, Australiaj

Title: Semiclassical equations of motion for disordered conductors: extrinsic velocity and corrected collision integral@

Abstract : The semiclassical equations of motion are widely used to describe carrier transport in conducting materials. Nevertheless, the substantial challenge of incorporating disorder systematically into the semiclassical model persists, leading to quantitative inaccuracies and occasionally erroneous predictions for the expectation values of physical observables. In the present work we provide a general prescription for reformulating the semiclassical equations of motion for carriers in disordered conductors by taking the quantum mechanical density matrix as the starting point. We focus on external electric fields, without magnetic fields, and spin-independent disorder. The density matrix approach allows averaging over impurity configurations, and the trace of the velocity operator with the disorder-averaged density matrix can be reinterpreted as the semiclassical velocity weighted by the Boltzmann distribution function. Through this rationale the well-known intrinsic group and anomalous velocities are trivially recovered, while we demonstrate the existence of an extrinsic interband velocity, namely a disorder correction to the semiclassical velocity of Bloch electrons, mediated by the interband matrix elements of the Berry connection. A similar correction is present in the non-equilibrium expectation value of the spin operator, contributing to spin-orbit torques. To obtain agreement with diagrammatic approaches the scattering term in the Boltzmann equation is corrected to first order in the electric field, and the Boltzmann equation is solved up to sub-leading order in the disorder potential. Our prescription ensures all vertex corrections present in diagrammatic treatments are taken into account, and to illustrate this we discuss model cases in topological insulators, including the anomalous Hall effect as well as spin-orbit torques.

2022 N 7 29 ij 16:00 -- 17:30

F IC

u : Mostafa Sabri (Cairo University)

Title: Quantum ergodicity on large graphs

Abstract : Quantum ergodicity is a result of delocalization. It says that in a weak sense, the eigenvectors of Schrödinger operator are uniformly distributed on the underlying space. After explaining this notion on graphs, I will discuss theorems ensuring that if a sequence of finite graphs converges" to an infinite tree, and if the Schrödinger operator on the limiting tree has absolutely continuous spectrum in an interval, then the eigenfunctions of the finite graphs are quantum ergodic in this interval. This applies in particular to the Anderson model on regular graphs. I will then move to the situation in which the limiting object is not a tree, and give both positive and negative results of quantum ergodicity for graphs which are periodic with respect to a sub-basis of $${\bf R}^d$$. Based on several works with Nalini Anantharaman (Strasbourg) and an ongoing work with Theo Mckenzie (Harvard).

2022 N 7 8 ij 15:30 -- 17:00

F kw@A 8K 801

u : @Y iswj

Title: MuX_ߒɊւ郉_VfBK[pf̏Ԗx@

Abstract : _ɔzuꂽe_̎ɃVOTCg|eVuč|eV悤ȃVfBK[pflD̃VfBK[pf̗ݐϏԖx֐(IDS)̓XyNg̉[Ŏw֐IɌ邱ƂmĂC_mɑݍp(|A\_ߒ)ꍇɂ͌̎v͌肳ĂD{uł́C_mɑݍp(MuX_ߒ)ꍇIDŠlC|A\_ߒ̏ꍇ̌ƔrD

2022 N 6 17 ij 15:30 -- 17:00

F kw@A 8K 801

u : 㓡@䂫 iBwj

Title: Born-Oppenheimer Potential Energy Surfaces for Kohn-Sham Models in the Local Density Approximation@

Abstract : ̓dCIɒizqƓdqȂjȌqnlBʎq͊w̋ȏɂ́A van der Waals ͂ƌĂ΂钷͂ŋ R -6 ixʂ-7jňƏĂALieb Thirring ɂĔ񑊑Θ_IVfBK[_ɂĂ͌ɏؖĂ(Phys. Rev. A 1986)BAȏꏊƌqm߂ÂƁA͂Ȃ͂łB{uł́AxsĊ֐@ɂǏxߎƌĂ΂ɂߎŁA̔͂ R -7 xł邱ƂB͂ƂƂ̃VfBK[_ɂĂ藧 Solovej ɂė\zĂ(Molecular Physics 2016)BؖɂĂ͌qa̕]{IłA̕IȈӖƏؖ̎@ɂĎɐB

2022 N 6 3 ij 15:30 -- 17:00

F kw@A 8K 801

u : ]@ ikCwj

Title: TCY̑傫ȃ_sƂ̎召šŗLlzQߖ@@

Abstract : _sƂ͐mϐŗ^ŝƂłD _s񗝘_ɂȌΏۂ͊mIɒ܂ŗLlCȂ킿ŗLlzłD ƂΓT^Iȃ_šnɊւẴTCY傫ĂƂCmzɌŗLlzŜƂďWĂ悤ȌۂD Ŗ{uł͂ƂɃj^pŕzsςƂȂ郉_G~[gšnɂāC̎召šŗLlzǂ̂悤Ɍ肳邩D uł́C܂lĂɂďڂqׂ邽߁CŗLlzinterlacingƂ{IȐCĖ̓LqMarkov-KreinΉɂďЉDɎ匋ʂ̊TvqׂCۂ̏ؖ̒ŌɂȂWeingarten ƎRm_IȌvZ@D Ȃ{u͒JLikCwjƂ̋ɊÂĂD

2022 N 5 27 ij 15:30 -- 17:00

F kw@A 8K 801

u : Max Lein ikwAIMRj

Title: On the bulk classification of non-selfadjoint topological insulators modeled by spectral operators@

Abstract : The topological classification of selfadjoint operators is solely determined by the presence or absence of certain discrete symmetries. Non-selfadjoint systems not only admit more types of discrete symmetries, their spectrum is a subset of the complex plane. A seminal result by Kawabata et al. classifies periodic tight-binding operators. However, as topological phenomena are expected to be robust under random perturbations, the derivation by Kawabata et al., which rests on sophisticated mathematical tools, no longer applies. Instead, I give an alternative derivation, based on the idea of physically relevant states. Moreover, I give evidence that it is likely not all non-selfadjoint operators, but only so-called spectral operators have a topological classification. An operator on a Banach space is spectral if it admits a generalized Jordan block decomposition; periodic tight-binding operators are spectral, but random operators on the discrete or the continuum need not be.

kbƏWu : 2022N5 16 -- 20

ut : c@厁iRwj

kb F2022 N 5 16 ij 16:00 -- 17:00

Title: m̐ĺ@

Wu F2022 N 5 17 i΁j--20ij 15:00 -- 18:00

Title: m̐ĺ@

AuXgNg

2022 N 4 15 ij 15:30 -- 17:00

F kw@A 8K 801

u : ac iwj

Title: @Ċ֐̕zɂā@

Abstract : {uł́AΏ̈ߒƂ̊炩ȑxɒ߂ VfBK[`ɂāA_܂łɓĂ X̌ʂɂāA܂͘ՂB̓Iɂ
Et@C}JbcQ̎ԑx
EXyNg֐̑Qߕ]
E@Ċ֐̑΍
̂R_̑݊֌W𐮗B𓥂܂ȂA lƂāA@Ċ֐̕zE̓Iɂ́A @Ċ֐̑΍萸邱ƂɂĐGB

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