Journal of the American Mathematical Society, ISSN 0894-0347, 10/2008, Volume 21, Issue 4, pp. 925 - 950

Unit ball | Eigenvalues | Critical values | Mathematical constants | Ground state | Mathematical inequalities | Mathematical functions | Mathematical vectors | Magnetic fields | Decreasing functions | Lieb-Thirring inequalities | Hardy inequality | Stability of matter | Diamagnetic inequality | Relativistic Schrödinger operator | Sobolev inequalities | MATHEMATICS | RELATIVISTIC MATTER | UNCERTAINTY PRINCIPLE | SHARP CONSTANTS | STABILITY | SOBOLEV

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2017, Volume 272, Issue 4, pp. 1625 - 1660

We consider magnetic Schrödinger operators with periodic magnetic and electric potentials on periodic discrete graphs...

Flat bands | Periodic graph | Discrete magnetic Schrödinger operator | Spectral bands | MATHEMATICS | LAPLACIANS | ELECTRONS | FIELD | Discrete magnetic Schrodinger operator | SPECTRUM | Magnetic fields | Analysis

Flat bands | Periodic graph | Discrete magnetic Schrödinger operator | Spectral bands | MATHEMATICS | LAPLACIANS | ELECTRONS | FIELD | Discrete magnetic Schrodinger operator | SPECTRUM | Magnetic fields | Analysis

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 7/2018, Volume 361, Issue 2, pp. 525 - 582

We study inverse boundary problems for magnetic Schrödinger operators on a compact Riemannian manifold with boundary of dimension ≥ 3...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MANIFOLDS | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | EQUATION | UNIQUENESS | Magnetic fields | Anisotropy

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MANIFOLDS | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | EQUATION | UNIQUENESS | Magnetic fields | Anisotropy

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 11/2018, Volume 275, Issue 9, pp. 2453 - 2472

... Schrödinger operator possesses no point spectrum. The settings of complex-valued electric potentials and singular magnetic potentials of Aharonov...

Absence of eigenvalues | Magnetic Schroedinger operators | Complex potential | Multipliers method | MATHEMATICS | DIRICHLET FORMS | Magnetic fields

Absence of eigenvalues | Magnetic Schroedinger operators | Complex potential | Multipliers method | MATHEMATICS | DIRICHLET FORMS | Magnetic fields

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 12/2013, Volume 265, Issue 11, pp. 2830 - 2854

In this paper we define (local) Dirac operators and magnetic Schrödinger Hamiltonians on fractals and prove their (essential) self-adjointness...

Dirichlet | Fractal | Magnetic | Laplacian | PHASE-TRANSITIONS | SELF-SIMILAR FRACTALS | SIMILAR SETS | GASKET TYPE FRACTALS | SPECTRAL PROPERTIES | KIRCHHOFFS RULE | MATHEMATICS | ENERGY MEASURES | DIRICHLET FORMS | SIERPINSKI GASKET | QUANTUM GRAPHS

Dirichlet | Fractal | Magnetic | Laplacian | PHASE-TRANSITIONS | SELF-SIMILAR FRACTALS | SIMILAR SETS | GASKET TYPE FRACTALS | SPECTRAL PROPERTIES | KIRCHHOFFS RULE | MATHEMATICS | ENERGY MEASURES | DIRICHLET FORMS | SIERPINSKI GASKET | QUANTUM GRAPHS

Journal Article

Inverse Problems, ISSN 0266-5611, 07/2017, Volume 33, Issue 9, p. 95001

In this paper we prove identifiability and stability estimates for a local-data inverse boundary value problem for a magnetic Schrodinger operator in dimension n >= 3...

Carleman estimates | DirichletNeumann map | complex geometric optics solutions | RiemannLebesgue lemma | fourier transform | Magnetic Schrödinger operator | MATHEMATICS, APPLIED | Riemann-Lebesgue lemma | INVERSE PROBLEM | Dirichlet-Neumann map | Magnetic Schrodinger operator | PHYSICS, MATHEMATICAL | EQUATION | UNIQUENESS

Carleman estimates | DirichletNeumann map | complex geometric optics solutions | RiemannLebesgue lemma | fourier transform | Magnetic Schrödinger operator | MATHEMATICS, APPLIED | Riemann-Lebesgue lemma | INVERSE PROBLEM | Dirichlet-Neumann map | Magnetic Schrodinger operator | PHYSICS, MATHEMATICAL | EQUATION | UNIQUENESS

Journal Article

Annals of Physics, ISSN 0003-4916, 05/2019, Volume 404, pp. 47 - 56

... Schrödinger operator in terms of the mass-jump are considered. It is shown that corresponding boundary conditions can be realized for the Hamiltonian with the position...

Self-adjointness | Localized quantum magnetic flux | Mass-jump | Symmetries | Mass-bump | PHYSICS, MULTIDISCIPLINARY | HAMILTONIANS | ENERGY-SPECTRA | POTENTIALS

Self-adjointness | Localized quantum magnetic flux | Mass-jump | Symmetries | Mass-bump | PHYSICS, MULTIDISCIPLINARY | HAMILTONIANS | ENERGY-SPECTRA | POTENTIALS

Journal Article

Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 2017, Volume 53, Issue 1, pp. 79 - 117

Kato's inequality is shown for the magnetic relativistic Schrodinger operator H-A,H-m defined as the operator-theoretical square root of the self-adjoint...

Kato’s inequality | Magnetic relativistic Schrödinger operator | Relativistic Schrödinger operator | MATHEMATICS | SEMIGROUPS | PARTICLE | Kato's inequality | magnetic relativistic Schrodinger operator | FIELD | relativistic Schrodinger operator | HAMILTONIANS

Kato’s inequality | Magnetic relativistic Schrödinger operator | Relativistic Schrödinger operator | MATHEMATICS | SEMIGROUPS | PARTICLE | Kato's inequality | magnetic relativistic Schrodinger operator | FIELD | relativistic Schrodinger operator | HAMILTONIANS

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 5/2014, Volume 327, Issue 3, pp. 993 - 1009

... ≥ 3 , for the magnetic Schrödinger operator with L ∞ magnetic and electric potentials, determines the magnetic field and electric potential inside the set uniquely...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | GLOBAL UNIQUENESS | CONDUCTIVITY PROBLEM | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | EQUATION | Magnetic fields

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | GLOBAL UNIQUENESS | CONDUCTIVITY PROBLEM | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | EQUATION | Magnetic fields

Journal Article

INVERSE PROBLEMS AND IMAGING, ISSN 1930-8337, 12/2018, Volume 12, Issue 6, pp. 1309 - 1342

In this paper we study local stability estimates for a magnetic Schrodinger operator with partial data on an open bounded set in dimension n >= 3...

MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | INVERSE PROBLEM | magnetic Schrodinger operator | Dirichlet-Neumann map | Carleman estimates | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | complex geometric optic solutions | Inverse problems | Radon transform | PARTIAL CAUCHY DATA | EQUATION

MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | INVERSE PROBLEM | magnetic Schrodinger operator | Dirichlet-Neumann map | Carleman estimates | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | complex geometric optic solutions | Inverse problems | Radon transform | PARTIAL CAUCHY DATA | EQUATION

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 9/2017, Volume 221, Issue 2, pp. 779 - 802

We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below...

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | FORMS | MATHEMATICS | EQUATIONS | MAGNETIC-FIELD | SPECTRUM | BOUNDS | Fuzzy sets | Eigenfunctions | Set theory | Schrodinger equation | Research | Mathematical research | Spectral Theory

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | FORMS | MATHEMATICS | EQUATIONS | MAGNETIC-FIELD | SPECTRUM | BOUNDS | Fuzzy sets | Eigenfunctions | Set theory | Schrodinger equation | Research | Mathematical research | Spectral Theory

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2018, Volume 370, Issue 10, pp. 7293 - 7333

This paper deals with global dispersive properties of Schrodinger equations with real-valued potentials exhibiting critical singularities, where our class of potentials is more general than inverse...

Resolvent estimates | Strichartz estimates | Critical singularities | Schrödinger operator | MAGNETIC POTENTIALS | INEQUALITIES | PERTURBATIONS | critical singularities | CRITICAL DECAY | resolvent estimates | L-P | MATHEMATICS | DIMENSIONS | WEAKLY CONJUGATE OPERATOR | ENERGY ASYMPTOTICS | TIME-DECAY | Schrodinger operator | WAVE-EQUATION

Resolvent estimates | Strichartz estimates | Critical singularities | Schrödinger operator | MAGNETIC POTENTIALS | INEQUALITIES | PERTURBATIONS | critical singularities | CRITICAL DECAY | resolvent estimates | L-P | MATHEMATICS | DIMENSIONS | WEAKLY CONJUGATE OPERATOR | ENERGY ASYMPTOTICS | TIME-DECAY | Schrodinger operator | WAVE-EQUATION

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 03/2018, Volume 264, Issue 5, pp. 3336 - 3368

In this paper we focus our attention on the following nonlinear fractional Schrödinger equation with magnetic fieldε2s(−Δ)A/εsu+V(x)u=f(|u|2)u in RN, where ε>0 is a parameter, s∈(0,1), N≥3, (−Δ...

Fractional magnetic operators | Ljusternick–Schnirelmann Theory | Nehari manifold | MATHEMATICS | POSITIVE SOLUTIONS | LIMIT | Ljusternick-Schnirelmann Theory | GROUND-STATES | Magnetic fields

Fractional magnetic operators | Ljusternick–Schnirelmann Theory | Nehari manifold | MATHEMATICS | POSITIVE SOLUTIONS | LIMIT | Ljusternick-Schnirelmann Theory | GROUND-STATES | Magnetic fields

Journal Article

Physica B: Physics of Condensed Matter, ISSN 0921-4526, 09/2015, Volume 472, pp. 78 - 83

... Schrödinger operator of free spinless particle. Despite its model and rather abstract character this question is worth of investigation due to application for one-dimensional nanostructures...

Self-adjointness | Localized quantum magnetic flux | Mass-jump | Symmetries | PHYSICS, CONDENSED MATTER | DISCONTINUOUS TEST FUNCTIONS | HAMILTONIANS | Operators | Superconductors | Condensed matter | Superconductor junctions | Boundary conditions | Schroedinger equation | Nanostructure | Derivatives | Density

Self-adjointness | Localized quantum magnetic flux | Mass-jump | Symmetries | PHYSICS, CONDENSED MATTER | DISCONTINUOUS TEST FUNCTIONS | HAMILTONIANS | Operators | Superconductors | Condensed matter | Superconductor junctions | Boundary conditions | Schroedinger equation | Nanostructure | Derivatives | Density

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2018, Volume 75, Issue 5, pp. 1778 - 1794

In this paper, we consider the fractional Schrödinger–Kirchhoff equations with electromagnetic fields and critical nonlinearity ε2sM([u]s,Aε2)(−Δ)Aεsu+V(x)u=|u|2s∗−2u+h(x,|u|2)u,x∈RN,u(x)→0,as|x|→∞,where (−Δ)Aε...

Fractional Schrödinger–Kirchhoff equation | Variational methods | Fractional magnetic operator | Critical nonlinearity | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLICITY | Fractional Schrodinger-Kirchhoff equation | GROUND-STATES

Fractional Schrödinger–Kirchhoff equation | Variational methods | Fractional magnetic operator | Critical nonlinearity | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLICITY | Fractional Schrodinger-Kirchhoff equation | GROUND-STATES

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2007, Volume 250, Issue 1, pp. 42 - 67

We study generalized magnetic Schrödinger operators of the form H h ( A , V ) = h ( Π A ) + V , where h is an elliptic symbol...

Twisted crossed-product | Pseudodifferential operators | Dynamical system | Essential spectrum | Magnetic field | Schrödinger operators | INFINITY | MATHEMATICS | magnetic field | pseudodifferential operators | spectrum | Schrodinger operators | SYSTEMS | twisted crossed-product | SCATTERING-THEORY | dynamical system | essential | TWISTED CROSSED-PRODUCTS

Twisted crossed-product | Pseudodifferential operators | Dynamical system | Essential spectrum | Magnetic field | Schrödinger operators | INFINITY | MATHEMATICS | magnetic field | pseudodifferential operators | spectrum | Schrodinger operators | SYSTEMS | twisted crossed-product | SCATTERING-THEORY | dynamical system | essential | TWISTED CROSSED-PRODUCTS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 04/2014, Volume 266, Issue 8, pp. 5016 - 5044

Let H:=H0+V and H⊥:=H0,⊥+V be respectively perturbations of the unperturbed Schrödinger operators H0 on L2(R3) and H0,⊥ on L2(R2...

Lieb–Thirring type inequalities | Magnetic Schrödinger operators | Non-self-adjoint relatively compact perturbations | Lieb-Thirring type inequalities | Magnetic schrödinger operators | MATHEMATICS | FIELDS | EIGENVALUE ASYMPTOTICS | Magnetic Schrodinger operators | Magnetic fields | Analysis

Lieb–Thirring type inequalities | Magnetic Schrödinger operators | Non-self-adjoint relatively compact perturbations | Lieb-Thirring type inequalities | Magnetic schrödinger operators | MATHEMATICS | FIELDS | EIGENVALUE ASYMPTOTICS | Magnetic Schrodinger operators | Magnetic fields | Analysis

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2016, Volume 48, Issue 4, pp. 2962 - 2993

We consider the Dirichlet realization of the operator -h(2) Delta + iV in the semiclassical limit h...

Non-self-adjant | Semiclassical | Schrödinger | MATHEMATICS, APPLIED | Schrodinger | NORMAL-STATE | SUPERCONDUCTIVITY | non-self-adjant | semiclassical | PERPENDICULAR ELECTRIC-CURRENT | HALF-PLANE | INDUCED MAGNETIC-FIELD

Non-self-adjant | Semiclassical | Schrödinger | MATHEMATICS, APPLIED | Schrodinger | NORMAL-STATE | SUPERCONDUCTIVITY | non-self-adjant | semiclassical | PERPENDICULAR ELECTRIC-CURRENT | HALF-PLANE | INDUCED MAGNETIC-FIELD

Journal Article

Acta Applicandae Mathematicae, ISSN 0167-8019, 8/2019, Volume 162, Issue 1, pp. 105 - 120

.... We then study the localization properties of the Landau eigenstates by applying an abstract version of the Balian-Low Theorem to the operators corresponding to the coordinates of the centre...

Computational Mathematics and Numerical Analysis | Calculus of Variations and Optimal Control; Optimization | Weyl relations | Balian-Low Theorem | Magnetic translations | Probability Theory and Stochastic Processes | Mathematics | Applications of Mathematics | Partial Differential Equations | Segal-Bargmann space | EXISTENCE | MATHEMATICS, APPLIED | STATES | ELECTRONS | DYNAMICS | PROOF | HILBERT-SPACE | BLOCH | Analysis | Quantum theory | Operators (mathematics) | Electron states | Theorems | Quantum mechanics | Eigenvectors | Representations | Localization | Cyclotrons | Symmetry

Computational Mathematics and Numerical Analysis | Calculus of Variations and Optimal Control; Optimization | Weyl relations | Balian-Low Theorem | Magnetic translations | Probability Theory and Stochastic Processes | Mathematics | Applications of Mathematics | Partial Differential Equations | Segal-Bargmann space | EXISTENCE | MATHEMATICS, APPLIED | STATES | ELECTRONS | DYNAMICS | PROOF | HILBERT-SPACE | BLOCH | Analysis | Quantum theory | Operators (mathematics) | Electron states | Theorems | Quantum mechanics | Eigenvectors | Representations | Localization | Cyclotrons | Symmetry

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 388, Issue 1, pp. 480 - 489

... Schrödinger operators to arbitrary complete Riemannian manifolds. This improves some earlier results of Shubin, Milatovic and others.

Riemannian manifold | Essential selfadjointness | Magnetic Schrödinger operator | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY PROPERTIES | Magnetic Schrodinger operator | POTENTIALS | ESSENTIAL SELF-ADJOINTNESS

Riemannian manifold | Essential selfadjointness | Magnetic Schrödinger operator | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY PROPERTIES | Magnetic Schrodinger operator | POTENTIALS | ESSENTIAL SELF-ADJOINTNESS

Journal Article

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