Functional Analysis and Operator Theory for Quantum Physics Pavel Exner Anniversary Volume / [electronic resource] :
Jaroslav Dittrich, Hynek Kovařík, Ari Laptev
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2017
- 1 online resource (597 pages)
- EMS Series of Congress Reports (ECR) .
Relative partition function of Coulomb plus delta interaction / Inequivalence of quantum Dirac fields of different masses and the underlying general structures involved / On a class of Schrödinger operators exhibiting spectral transition / On the quantum mechanical three-body problem with zero-range interactions / On the index of meromorphic operator-valued functions and some applications / Trace formulae for Schrödinger operators with singular interactions / An improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in $\mathbb H^n$ / Twisted waveguide with a Neumann window / Example of a periodic Neumann waveguide with a gap in its spectrum / Two-dimensional time-dependent point interactions / On resonant spectral gaps in quantum graphs / Adiabatic theorem for a class of stochastic differential equations on a Hilbert space / Eigenvalues of Schrödinger operators with complex surface potentials / A lower bound to the spectral threshold in curved quantum layers / To the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions / Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman–Schwinger analysis of the Dirichlet-to-Neumann operator / Dirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality / A mathematical modeling of electron–phonon interaction for small wave numbers close to zero / The modified unitary Trotter–Kato and Zeno product formulas revisited / Spectral asymptotics induced by approaching and diverging planar circles / Spectral estimates for the Heisenberg Laplacian on cylinders / Variational proof of the existence of eigenvalues for star graphs / On the boundedness and compactness of weighted Green operators of second-order elliptic operators / Abstract graph-like spaces and vector-valued metric graphs / A Cayley–Hamiltonian theorem for periodic finite band matrices / Path topology dependence of adiabatic time evolution / On quantum graph filters with flat passbands / Comments on the Chernoff $\sqrt n$-lemma / Sergio Albeverio, Claudio Cacciapuoti, Mauro Spreafico -- Asao Arai -- Diana Barseghyan, Olga Rossi -- Giulia Basti, Alessandro Teta -- Jussi Behrndt, Fritz Gesztesy, Helge Holden, Roger Nichols -- Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik -- Rafael D. Benguria, Soledad Benguria -- Philippe Briet, Hiba Hammedi -- Giuseppe Cardone, Andrii Khrabustovskyi -- Raffaele Carlone, Michele Correggi, Rodolfo Figari -- Ngoc T. Do, Peter Kuchment, Beng Ong -- Martin Fraas -- Rupert L. Frank -- Pedro Freitas, David Krejčiřík -- Yaroslav Granovskyi, Mark M. Malamud, Hagen Neidhardt, Andrea Posilicano -- André Hänel, Timo Weidl -- Bernard Helffer, Rola Kiwan -- Masao Hirokawa -- Takashi Ichinose -- Sylwia Kondej -- Hynek Kovařík, Bartosch Ruszkowski, Timo Weidl -- Konstantin Pankrashkin -- Yehuda Pinchover -- Olaf Post -- Barry Simon -- Atushi Tanaka, Taksu Cheon -- Ondřej Turek -- Valentin Zagrebnov.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
This 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.
9783037196755
10.4171/175 doi
Quantum physics (quantum mechanics)
Differential equations
Quantum theory
Partial differential equations
Relative partition function of Coulomb plus delta interaction / Inequivalence of quantum Dirac fields of different masses and the underlying general structures involved / On a class of Schrödinger operators exhibiting spectral transition / On the quantum mechanical three-body problem with zero-range interactions / On the index of meromorphic operator-valued functions and some applications / Trace formulae for Schrödinger operators with singular interactions / An improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in $\mathbb H^n$ / Twisted waveguide with a Neumann window / Example of a periodic Neumann waveguide with a gap in its spectrum / Two-dimensional time-dependent point interactions / On resonant spectral gaps in quantum graphs / Adiabatic theorem for a class of stochastic differential equations on a Hilbert space / Eigenvalues of Schrödinger operators with complex surface potentials / A lower bound to the spectral threshold in curved quantum layers / To the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions / Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman–Schwinger analysis of the Dirichlet-to-Neumann operator / Dirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality / A mathematical modeling of electron–phonon interaction for small wave numbers close to zero / The modified unitary Trotter–Kato and Zeno product formulas revisited / Spectral asymptotics induced by approaching and diverging planar circles / Spectral estimates for the Heisenberg Laplacian on cylinders / Variational proof of the existence of eigenvalues for star graphs / On the boundedness and compactness of weighted Green operators of second-order elliptic operators / Abstract graph-like spaces and vector-valued metric graphs / A Cayley–Hamiltonian theorem for periodic finite band matrices / Path topology dependence of adiabatic time evolution / On quantum graph filters with flat passbands / Comments on the Chernoff $\sqrt n$-lemma / Sergio Albeverio, Claudio Cacciapuoti, Mauro Spreafico -- Asao Arai -- Diana Barseghyan, Olga Rossi -- Giulia Basti, Alessandro Teta -- Jussi Behrndt, Fritz Gesztesy, Helge Holden, Roger Nichols -- Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik -- Rafael D. Benguria, Soledad Benguria -- Philippe Briet, Hiba Hammedi -- Giuseppe Cardone, Andrii Khrabustovskyi -- Raffaele Carlone, Michele Correggi, Rodolfo Figari -- Ngoc T. Do, Peter Kuchment, Beng Ong -- Martin Fraas -- Rupert L. Frank -- Pedro Freitas, David Krejčiřík -- Yaroslav Granovskyi, Mark M. Malamud, Hagen Neidhardt, Andrea Posilicano -- André Hänel, Timo Weidl -- Bernard Helffer, Rola Kiwan -- Masao Hirokawa -- Takashi Ichinose -- Sylwia Kondej -- Hynek Kovařík, Bartosch Ruszkowski, Timo Weidl -- Konstantin Pankrashkin -- Yehuda Pinchover -- Olaf Post -- Barry Simon -- Atushi Tanaka, Taksu Cheon -- Ondřej Turek -- Valentin Zagrebnov.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
This 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.
9783037196755
10.4171/175 doi
Quantum physics (quantum mechanics)
Differential equations
Quantum theory
Partial differential equations