05915nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168072001700184084002200201245017500223260008200398300003400480336002600514337002600540338003600566347002400602490005400626505308400680506006603764520133803830650004805168650003505216650002405251650004005275700003305315700003105348700002605379856003205405856006805437218-170419CH-001817-320170419234501.0a fot ||| 0|cr nn mmmmamaa170419e20170505sz fot ||| 0|eng d a978303719675570a10.4171/1752doi ach0018173 7aPHT2bicssc 7aPBKJ2bicssc a81-xxa35-xx2msc10aFunctional Analysis and Operator Theory for Quantum Physicsh[electronic resource] :bThe Pavel Exner Anniversary Volume /cJaroslav Dittrich, Hynek Kovařík, Ari Laptev3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (595 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tRelative partition function of Coulomb plus delta interaction /rSergio Albeverio, Claudio Cacciapuoti, Mauro Spreafico --tInequivalence of quantum Dirac fields of different masses and the underlying general structures involved /rAsao Arai --tOn a class of Schrödinger operators exhibiting spectral transition /rDiana Barseghyan, Olga Rossi --tOn the quantum mechanical three-body problem with zero-range interactions /rGiulia Basti, Alessandro Teta --tOn the index of meromorphic operator-valued functions and some applications /rJussi Behrndt, Fritz Gesztesy, Helge Holden, Roger Nichols --tTrace formulae for Schrödinger operators with singular interactions /rJussi Behrndt, Matthias Langer, Vladimir Lotoreichik --tAn improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in $\mathbb H^n$ /rRafael D. Benguria, Soledad Benguria --tTwisted waveguide with a Neumann window /rPhilippe Briet, Hiba Hammedi --tExample of a periodic Neumann waveguide with a gap in its spectrum /rGiuseppe Cardone, Andrii Khrabustovskyi --tTwo-dimensional time-dependent point interactions /rRaffaele Carlone, Michele Correggi, Rodolfo Figari --tOn resonant spectral gaps in quantum graphs /rNgoc T. Do, Peter Kuchment, Beng Ong --tAdiabatic theorem for a class of stochastic differential equations on a Hilbert space /rMartin Fraas --tEigenvalues of Schrödinger operators with complex surface potentials /rRupert L. Frank --tA lower bound to the spectral threshold in curved quantum layers /rPedro Freitas, David Krejčiřík --tTo the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions /rYaroslav Granovskyi, Mark M. Malamud, Hagen Neidhardt, Andrea Posilicano --tSpectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman–Schwinger analysis of the Dirichlet-to-Neumann operator /rAndré Hänel, Timo Weidl --tDirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality /rBernard Helffer, Rola Kiwan --tA mathematical modeling of electron–phonon interaction for small wave numbers close to zero /rMasao Hirokawa --tThe modified unitary Trotter–Kato and Zeno product formulas revisited /rTakashi Ichinose --tSpectral asymptotics induced by approaching and diverging planar circles /rSylwia Kondej --tSpectral estimates for the Heisenberg Laplacian on cylinders /rHynek Kovařík, Bartosch Ruszkowski, Timo Weidl --tVariational proof of the existence of eigenvalues for star graphs /rKonstantin Pankrashkin --tOn the boundedness and compactness of weighted Green operators of second-order elliptic operators /rYehuda Pinchover --tAbstract graph-like spaces and vector-valued metric graphs /rOlaf Post --tA Cayley–Hamiltonian theorem for periodic finite band matrices /rBarry Simon --tPath topology dependence of adiabatic time evolution /rAtushi Tanaka, Taksu Cheon --tOn quantum graph filters with flat passbands /rOndřej Turek --tComments on the Chernoff $\sqrt n$-lemma /rValentin Zagrebnov.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume is dedicated to Pavel Exner on the occasion of his 70th anniversary. It collects contributions by numerous scientists with expertise in mathematical physics and in particular in problems arising from quantum mechanics. The questions addressed in the contributions cover a large range of topics. A lot of attention was paid to differential operators with zero range interactions, which are often used as models in quantum mechanics. Several authors considered problems related to systems with mixed-dimensions such as quantum waveguides, quantum layers and quantum graphs. Eigenvalues and eigenfunctions of Laplace and Schrödinger operators are discussed too, as well as systems with adiabatic time evolution. Although most of the problems treated in the book have a quantum mechanical background, some contributions deal with issues which go well beyond this framework; for example the Cayley–Hamilton theorem, approximation formulae for contraction semigroups or factorization of analytic operator-valued Fredholm functions. As for the mathematical tools involved, the book provides a wide variety of techniques from functional analysis and operator theory.
Altogether the volume presents a collection of research papers which will be of interest to any active scientist working in one of the above mentioned fields.07aQuantum physics (quantum mechanics)2bicssc07aDifferential equations2bicssc07aQuantum theory2msc07aPartial differential equations2msc1 aDittrich, Jaroslav,eeditor.1 aKovařík, Hynek,eeditor.1 aLaptev, Ari,eeditor.40uhttps://doi.org/10.4171/175423cover imageuhttps://www.ems-ph.org/img/books/dittrich_mini.jpg