Effective Hamiltonians for Constrained Quantum Systems

DOI10.1090/memo/1083zbMath1300.81046arXiv0907.0351OpenAlexW4234967708MaRDI QIDQ2925667

Jakob Wachsmuth, Stefan Teufel

Publication date: 17 October 2014

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.0351

zbMATH Keywords

constraintsadiabatic limiteffective dynamicsSchrödinger equation on manifolds

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Molecular physics (81V55) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Perturbations of PDEs on manifolds; asymptotics (58J37) Time-dependent Schrödinger equations and Dirac equations (35Q41) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Quantum dots, waveguides, ratchets, etc. (81Q37) Quantum waveguides, quantum wires (82D77)

Related Items (max. 100)

Soft quantum waveguides in three dimensions ⋮ REDUCTION OF DIMENSION AS A CONSEQUENCE OF NORM‐RESOLVENT CONVERGENCE AND APPLICATIONS ⋮ Quantum dynamics of a particle constrained to lie on a surface ⋮ The Hölder continuity of spectral measures of an extended CMV matrix ⋮ Generalised quantum waveguides ⋮ Spectral analysis on ruled surfaces with combined Dirichlet and Neumann boundary conditions ⋮ Derivation of the 2d Gross-Pitaevskii equation for strongly confined 3d bosons ⋮ Quantum singular operator limits of thin Dirichlet tubes via \(\Gamma\)-convergence ⋮ Magnetic effects in curved quantum waveguides ⋮ Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ Spontaneous decay of resonant energy levels for molecules with moving nuclei ⋮ Convergence of nodal sets in the adiabatic limit ⋮ Weyl formulae for the Robin Laplacian in the semiclassical limit ⋮ The NLS limit for Bosons in a quantum waveguide ⋮ Quantum waveguides with magnetic fields ⋮ Soft quantum waveguides with an explicit cut-locus ⋮ The magnetic Laplacian in shrinking tubular neighborhoods of hypersurfaces

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