Weakly coupled bound states in quantum waveguides
From MaRDI portal
Publication:4336611
DOI10.1090/S0002-9939-97-03726-XzbMath0868.35080OpenAlexW1820791797MaRDI QIDQ4336611
W. Bulla, W. Renger, Barry Simon, Friedrich Gesztesy
Publication date: 13 May 1997
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9939-97-03726-x
Estimates of eigenvalues in context of PDEs (35P15) Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)
Related Items (76)
Soft quantum waveguides in three dimensions ⋮ Asymptotics for a resonance-counting function for potential scattering on cylinders ⋮ On local perturbations of waveguides ⋮ Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics ⋮ Local perturbations of quantum waveguides ⋮ Asymptotic behavior of the eigenvalues of the Schrödinger operator with transversal potential in a weakly curved infinite cylinder ⋮ Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window ⋮ A quantum waveguide with Aharonov–Bohm magnetic field ⋮ Stability of the Magnetic Schrödinger Operator in a Waveguide ⋮ Trapped modes in piezoelectric and elastic waveguides ⋮ The Y-junction of quantum waveguides ⋮ Asymptotics of bound states and bands for laterally coupled waveguides and layers ⋮ Bound states in straight quantum waveguides with combined boundary conditions ⋮ Geometric coupling thresholds in a two-dimensional strip ⋮ Bound states in coupled guides. I. Two dimensions ⋮ Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide ⋮ Band gap of the spectrum in periodically curved quantum waveguides ⋮ Asymptotics of the frequency of a surface wave trapped by a slightly inclined barrier in a liquid layer ⋮ Various manifestations of wood anomalies in locally distorted quantum waveguides ⋮ Weakly coupled bound state of 2-D Schrödinger operator with potential-measure ⋮ Spectral analysis on ruled surfaces with combined Dirichlet and Neumann boundary conditions ⋮ On a waveguide with an infinite number of small windows ⋮ On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition ⋮ Asymptotics of eigenfrequencies that arise in gaps caused by a perturbation of a periodic waveguide ⋮ Perturbation of threshold of essential spectrum for waveguides with windows. II: Asymptotics ⋮ Asymptotics of an eigenvalue on the continuous spectrum of two quantum waveguides coupled through narrow windows ⋮ A Hardy inequality in a twisted Dirichlet–Neumann waveguide ⋮ Almost standing waves in a periodic waveguide with resonator, and near-threshold eigenvalues ⋮ BOUND STATES IN WEAKLY DEFORMED WAVEGUIDES: NUMERICAL VERSUS ANALYTICAL RESULTS ⋮ Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation ⋮ Asymptotics of the reflection coefficient at critical frequencies in a narrowing waveguide ⋮ Unnamed Item ⋮ Trapped Modes for an Elastic Plate with a Perturbation of Young's Modulus ⋮ A Hardy inequality in twisted waveguides ⋮ Estimates on trapped modes in deformed quantum layers ⋮ Asymptotics of bound state for laterally coupled waveguides. ⋮ On occurrence of resonances from multiple eigenvalues of the Schrödinger operator in a cylinder with distant perturbations ⋮ The geometric potential of a double-frequency corrugated surface ⋮ Eigenvalue inequalities and absence of threshold resonances for waveguide junctions ⋮ Transmission conditions in one-dimensional model of a rectangular lattice of thin quantum waveguides ⋮ Resonance scattering in a waveguide with identical thick perforated barriers ⋮ Schrödinger operator with a strong varying interaction on a curve in $\mathbb {R}^2$R2 ⋮ Asymptotic behavior of eigenvalues of the Laplace operator in infinite cylinders perturbed by transverse extensions ⋮ Asymptotic behaviour of the spectrum of a waveguide with distant perturbations ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ Asymptotic formula for an eigenvalue of the Dirichlet problem in a cranked waveguide ⋮ On the discrete spectrum of a spatial quantum waveguide with a disc window ⋮ Vibration of a membrane strip with a segment of higher density: analysis of trapped modes ⋮ Open quantum dots: Resonances from perturbed symmetry and bound states in strong magnetic fields ⋮ Lieb-Thirring inequalities for geometrically induced bound states ⋮ Eigenvalues of the Laplace operator with the Neumann conditions at regular perturbed walls of a waveguide ⋮ Asymptotics of bound states and bands for waveguides coupled through small windows. ⋮ Avoided crossings in mesoscopic systems: Electron propagation on a nonuniform magnetic cylinder ⋮ Forward and inverse scattering on manifolds with asymptotically cylindrical ends ⋮ Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows ⋮ A remark on helical waveguides ⋮ WAVEGUIDES COUPLED THROUGH A SEMITRANSPARENT BARRIER: A BIRMAN–SCHWINGER ANALYSIS ⋮ Resonances near thresholds in slightly twisted waveguides ⋮ Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions ⋮ Asymptotics of bound states and bands for laterally coupled three-dimensional waveguides ⋮ Violation of symmetry in the system of three laterally coupled quantum waveguides, and resonance asymptotics ⋮ Asymptotics of resonances and bound states for laterally coupled curved quantum waveguides ⋮ Asymptotic behavior of the eigenvalues of the Schrödinger operator in thin closed tubes ⋮ The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides ⋮ Asymptotics of eigenvalues in spectral gaps of periodic waveguides with small singular perturbations ⋮ Asymptotic behavior of eigenvalues of the Laplace operator in thin infinite tubes ⋮ Wave scattering by a periodic perturbation: embedded Rayleigh-Bloch modes and resonances ⋮ Trapped modes in an elastic plate with a hole ⋮ Dirac operator spectrum in tubes and layers with a zigzag-type boundary ⋮ Planar waveguide with “twisted” boundary conditions: Discrete spectrum ⋮ On the number of particles that a curved quantum waveguide can bind ⋮ On the spectrum of curved planar waveguides ⋮ Manifolds with cylindrical ends having a finite and positive number of embedded eigenvalues ⋮ Spectral properties of soft quantum waveguides ⋮ Perturbation of threshold of essential spectrum for waveguides with windows. I: Decreasing resonance solutions ⋮ Stark resonances in 2-dimensional curved quantum waveguides
Cites Work
- Unnamed Item
- Unnamed Item
- On the bound state of Schrödinger operators in one dimension
- Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case
- The bound state of weakly coupled Schrödinger operators in one and two dimensions
- Existence of bound states in quantum waveguides under weak conditions
- Bound states in curved quantum waveguides
- Existence theorems for trapped modes
- Bound states in quantum waveguides of a slowly decaying curvature
- CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
This page was built for publication: Weakly coupled bound states in quantum waveguides