Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 261, Issue 7, pp. 2053 - 2081

Let H 0 and H be self-adjoint operators in a Hilbert space. We consider the spectral projections of H 0 and H corresponding to a semi-infinite interval of the...

Birman–Schwinger principle | Spectral projections | Essential spectrum | Scattering matrix | Birman-Schwinger principle | FLOW | SIGMA(H) | MATHEMATICS | H-LAMBDA-W | OPERATOR | BOUNDS | EIGENVALUE BRANCHES | GAP | SHIFT FUNCTION

Birman–Schwinger principle | Spectral projections | Essential spectrum | Scattering matrix | Birman-Schwinger principle | FLOW | SIGMA(H) | MATHEMATICS | H-LAMBDA-W | OPERATOR | BOUNDS | EIGENVALUE BRANCHES | GAP | SHIFT FUNCTION

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 2019, Volume 109, Issue 7, pp. 1473 - 1485

We prove the absence of eigenvalues of the three-dimensional Dirac operator with non-Hermitian potentials in unbounded regions of the complex plane under...

Absence of eigenvalues | Pseudo-Friedrichs extension | Birman–Schwinger principle | Dirac operator | Complex potential | Non-self-adjoint perturbation | Birman-Schwinger principle | PHYSICS, MATHEMATICAL

Absence of eigenvalues | Pseudo-Friedrichs extension | Birman–Schwinger principle | Dirac operator | Complex potential | Non-self-adjoint perturbation | Birman-Schwinger principle | PHYSICS, MATHEMATICAL

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 7/2018, Volume 108, Issue 7, pp. 1757 - 1778

We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials....

34L40 | Non-self-adjoint Dirac operator | Lieb–Thirring inequalities | Complex potential | Armchair graphene nanoribbons | Theoretical, Mathematical and Computational Physics | Complex Systems | 34L15 | Physics | Geometry | 35P15 | 81Q12 | Birman–Schwinger principle | Damped wave equation | Group Theory and Generalizations | BOUNDS | Lieb-Thirring inequalities | Birman-Schwinger principle | JACOBI MATRICES | PHYSICS, MATHEMATICAL | RESONANCES | SCHRODINGER-OPERATORS | Graphene | Graphite | Mathematics - Spectral Theory

34L40 | Non-self-adjoint Dirac operator | Lieb–Thirring inequalities | Complex potential | Armchair graphene nanoribbons | Theoretical, Mathematical and Computational Physics | Complex Systems | 34L15 | Physics | Geometry | 35P15 | 81Q12 | Birman–Schwinger principle | Damped wave equation | Group Theory and Generalizations | BOUNDS | Lieb-Thirring inequalities | Birman-Schwinger principle | JACOBI MATRICES | PHYSICS, MATHEMATICAL | RESONANCES | SCHRODINGER-OPERATORS | Graphene | Graphite | Mathematics - Spectral Theory

Journal Article

Applicable Analysis, ISSN 0003-6811, 06/2019, Volume 98, Issue 8, pp. 1451 - 1460

We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrödinger operator with an attractive -interaction...

Robin Laplacian on planes with slits | Primary: 35P15 | lowest eigenvalue | spectral isoperimetric inequality | Secondary: 58J50 | Birman-Schwinger principle | interaction on an open arc | Birman–Schwinger principle | (Formula presented.)-interaction on an open arc | MATHEMATICS, APPLIED | delta-interaction on an open arc | STRONG-COUPLING ASYMPTOTICS | SCHRODINGER-OPERATORS | Operators (mathematics) | Eigenvalues | Spectra | Line spectra | Optimization | Eigen values

Robin Laplacian on planes with slits | Primary: 35P15 | lowest eigenvalue | spectral isoperimetric inequality | Secondary: 58J50 | Birman-Schwinger principle | interaction on an open arc | Birman–Schwinger principle | (Formula presented.)-interaction on an open arc | MATHEMATICS, APPLIED | delta-interaction on an open arc | STRONG-COUPLING ASYMPTOTICS | SCHRODINGER-OPERATORS | Operators (mathematics) | Eigenvalues | Spectra | Line spectra | Optimization | Eigen values

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 2/2016, Volume 186, Issue 2, pp. 231 - 250

We consider a Hamiltonian of a two-boson system on a two-dimensional lattice Z2. The Schrödinger operator H(k 1, k 2) of the system for k 1 = k 2 = π, where k...

perturbation theory | Theoretical, Mathematical and Computational Physics | Schrödinger operator | Birman–Schwinger principle | Applications of Mathematics | Hamiltonian | Physics | bound state | total quasimomentum | eigenvalue | PHYSICS, MULTIDISCIPLINARY | Schrodinger operator | Birman-Schwinger principle | PHYSICS, MATHEMATICAL | SCHRODINGER OPERATORS | RESONANCES

perturbation theory | Theoretical, Mathematical and Computational Physics | Schrödinger operator | Birman–Schwinger principle | Applications of Mathematics | Hamiltonian | Physics | bound state | total quasimomentum | eigenvalue | PHYSICS, MULTIDISCIPLINARY | Schrodinger operator | Birman-Schwinger principle | PHYSICS, MATHEMATICAL | SCHRODINGER OPERATORS | RESONANCES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 371, Issue 1, pp. 282 - 299

This paper is based on our previous results (Haroske and Skrzypczak (2008) [23], Haroske and Skrzypczak (in press) [25]) on compact embeddings of Muckenhoupt...

Birman–Schwinger principle | Distribution of eigenvalues | Degenerate pseudodifferential operators | Muckenhoupt weighted function spaces | Negative spectrum | Compact embeddings | Birman-Schwinger principle | MATHEMATICS, APPLIED | INEQUALITIES | EIGENVALUE DISTRIBUTIONS | LIPSCHITZ | MOLECULAR DECOMPOSITIONS | MATHEMATICS | BOUND-STATES | MUCKENHOUPT WEIGHTS | WEIGHTED BESOV-SPACES | EMBEDDINGS | ENTROPY NUMBERS | TRIEBEL-LIZORKIN SPACES

Birman–Schwinger principle | Distribution of eigenvalues | Degenerate pseudodifferential operators | Muckenhoupt weighted function spaces | Negative spectrum | Compact embeddings | Birman-Schwinger principle | MATHEMATICS, APPLIED | INEQUALITIES | EIGENVALUE DISTRIBUTIONS | LIPSCHITZ | MOLECULAR DECOMPOSITIONS | MATHEMATICS | BOUND-STATES | MUCKENHOUPT WEIGHTS | WEIGHTED BESOV-SPACES | EMBEDDINGS | ENTROPY NUMBERS | TRIEBEL-LIZORKIN SPACES

Journal Article

Asymptotic Analysis, ISSN 0921-7134, 02/2016, Volume 96, Issue 3-4, pp. 251 - 281

We consider the Laplacian in a tubular neighbourhood of a hyperplane subjected to non-self-adjoint PT-symmetric Robin boundary conditions. Its spectrum is...

essential spectrum | reality of the spectrum | weak coupling | spectral analysis | Birman-Schwinger principle | non-self-adjointness | Robin boundary conditions | waveguide | MATHEMATICS, APPLIED | HILBERT-SPACE | SCHRODINGER-OPERATORS

essential spectrum | reality of the spectrum | weak coupling | spectral analysis | Birman-Schwinger principle | non-self-adjointness | Robin boundary conditions | waveguide | MATHEMATICS, APPLIED | HILBERT-SPACE | SCHRODINGER-OPERATORS

Journal Article

Journal of Spectral Theory, ISSN 1664-039X, 2018, Volume 8, Issue 2, pp. 575 - 604

We prove that the spectrum of Schrodinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials...

Absence of eigenvalues | Spectral stability | Technique of multipliers | Birman-Schwinger principle | Non-self-adjoint Schrödinger operator | Subordinate complex potential | MATHEMATICS, APPLIED | INEQUALITIES | spectral stability | Non-self-adjoint Schrodinger operator | MATHEMATICS | WAVE | technique of multipliers | VALUED POTENTIALS | absence of eigenvalues | ABSENCE | subordinate complex potential | EIGENVALUE BOUNDS

Absence of eigenvalues | Spectral stability | Technique of multipliers | Birman-Schwinger principle | Non-self-adjoint Schrödinger operator | Subordinate complex potential | MATHEMATICS, APPLIED | INEQUALITIES | spectral stability | Non-self-adjoint Schrodinger operator | MATHEMATICS | WAVE | technique of multipliers | VALUED POTENTIALS | absence of eigenvalues | ABSENCE | subordinate complex potential | EIGENVALUE BOUNDS

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 6/2008, Volume 84, Issue 2, pp. 99 - 107

We prove that the critical temperature for the BCS gap equation is given by $${T_c = \mu \left( \frac 8\pi {\rm e}^{\gamma -2} + o(1) \right) {\rm...

Geometry | 46N50 | Mathematical and Computational Physics | Birman–Schwinger principle | 82D50 | Group Theory and Generalizations | BCS equation | 81Q10 | superfluidity | Physics | Statistical Physics | scattering length | Scattering length | Birman-Schwinger principle | Superfluidity | WEAK | SUPERCONDUCTIVITY | GAS | STATE | PHYSICS, MATHEMATICAL | Football (College)

Geometry | 46N50 | Mathematical and Computational Physics | Birman–Schwinger principle | 82D50 | Group Theory and Generalizations | BCS equation | 81Q10 | superfluidity | Physics | Statistical Physics | scattering length | Scattering length | Birman-Schwinger principle | Superfluidity | WEAK | SUPERCONDUCTIVITY | GAS | STATE | PHYSICS, MATHEMATICAL | Football (College)

Journal Article

Journal of Spectral Theory, ISSN 1664-039X, 2017, Volume 70, Issue 3, pp. 659 - 697

We study spectral properties of the Schrodinger operator with an imaginary sign potential on the real line. By constructing the resolvent kernel, we show that...

Non-self-adjointness | Birman-Schwinger principle | Discontinuous potential | Pseudospectra | Weak coupling | Schrödinger operators | MATHEMATICS | MATHEMATICS, APPLIED | BOUND-STATES | weak coupling | Schrodinger operators | non-self-adjointness | discontinuous potential

Non-self-adjointness | Birman-Schwinger principle | Discontinuous potential | Pseudospectra | Weak coupling | Schrödinger operators | MATHEMATICS | MATHEMATICS, APPLIED | BOUND-STATES | weak coupling | Schrodinger operators | non-self-adjointness | discontinuous potential

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 5/2015, Volume 82, Issue 1, pp. 61 - 94

We study several natural multiplicity questions that arise in the context of the Birman–Schwinger principle applied to non-self-adjoint operators. In...

Secondary 47B10 | Factorization of operator-valued analytic functions | 47G10 | Analysis | Primary 47A10 | multiplicity of eigenvalues | Mathematics | 47A75 | 47A53 | index computations for finitely meromorphic operator-valued functions | MATHEMATICS | BOUND-STATES | SPECTRUM | PROJECTIONS | RESONANCES | FREDHOLM DETERMINANTS | BIRMAN-SCHWINGER PRINCIPLE

Secondary 47B10 | Factorization of operator-valued analytic functions | 47G10 | Analysis | Primary 47A10 | multiplicity of eigenvalues | Mathematics | 47A75 | 47A53 | index computations for finitely meromorphic operator-valued functions | MATHEMATICS | BOUND-STATES | SPECTRUM | PROJECTIONS | RESONANCES | FREDHOLM DETERMINANTS | BIRMAN-SCHWINGER PRINCIPLE

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 12/2019, Volume 91, Issue 6, pp. 1 - 15

We study location of eigenvalues of one-dimensional discrete Schrödinger operators with complex $$\ell ^{p}$$ ℓp -potentials for $$1\le p\le \infty $$ 1≤p≤∞ ....

47B36 | Analysis | Birman–Schwinger principle | Point spectrum | 34L15 | Mathematics | 47A75 | Discrete Schrödinger operator | Jacobi matrix | LOCATION | MATHEMATICS | Discrete Schrodinger operator | Birman-Schwinger principle | EIGENVALUE BOUNDS | DIRAC

47B36 | Analysis | Birman–Schwinger principle | Point spectrum | 34L15 | Mathematics | 47A75 | Discrete Schrödinger operator | Jacobi matrix | LOCATION | MATHEMATICS | Discrete Schrodinger operator | Birman-Schwinger principle | EIGENVALUE BOUNDS | DIRAC

Journal Article

Opuscula Mathematica, ISSN 1232-9274, 2015, Volume 35, Issue 3, pp. 371 - 395

Journal Article

14.
Full Text
Translation-invariant quasi-free states for fermionic systems and the BCS approximation

Reviews in Mathematical Physics, ISSN 0129-055X, 08/2014, Volume 26, Issue 7, p. 1450012

We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the...

critical temperature | BCS functional | Birman-Schwinger principle | quasi-free states | Superconductivity | WEAK | MODEL | FOCK-BOGOLIUBOV THEORY | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL | Football (College)

critical temperature | BCS functional | Birman-Schwinger principle | quasi-free states | Superconductivity | WEAK | MODEL | FOCK-BOGOLIUBOV THEORY | CRITICAL-TEMPERATURE | PHYSICS, MATHEMATICAL | Football (College)

Journal Article

Communications in Mathematical Analysis, 2014, Volume 17, Issue 1, pp. 1 - 22

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2018, Volume 146, Issue 9, pp. 3935 - 3942

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 4/2007, Volume 127, Issue 2, pp. 191 - 220

A model operator H associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles,...

Mathematical and Computational Physics | Quantum Physics | model operator | conservation of number of particles | infinitely many eigenvalues | Friedrichs model | Physics | conditionally negative definite function | essential spectrum | Physical Chemistry | Efimov effect | Hilbert-Schmidt operator | Birman-Schwinger principle | Statistical Physics | Infinitely many eigenvalues | Model operator | Conservation of number of particles | Essential spectrum | Conditionally negative definite function | 3-PARTICLE SYSTEMS | GENERATOR | PARTICLES | MODEL | PHYSICS, MATHEMATICAL | PERTURBATION-THEORY | BOUND-STATES | LATTICE | RESONANCES | SCATTERING | SCHRODINGER-OPERATORS

Mathematical and Computational Physics | Quantum Physics | model operator | conservation of number of particles | infinitely many eigenvalues | Friedrichs model | Physics | conditionally negative definite function | essential spectrum | Physical Chemistry | Efimov effect | Hilbert-Schmidt operator | Birman-Schwinger principle | Statistical Physics | Infinitely many eigenvalues | Model operator | Conservation of number of particles | Essential spectrum | Conditionally negative definite function | 3-PARTICLE SYSTEMS | GENERATOR | PARTICLES | MODEL | PHYSICS, MATHEMATICAL | PERTURBATION-THEORY | BOUND-STATES | LATTICE | RESONANCES | SCATTERING | SCHRODINGER-OPERATORS

Journal Article

Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, 01/2010, Volume 5, Issue 4, pp. 448 - 469

We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues...

NLS equation | Birman-Schwinger principle | spectral stability | Feshbach map | EXISTENCE | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | BIFURCATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITARY WAVES | MATHEMATICAL & COMPUTATIONAL BIOLOGY | ASYMPTOTIC STABILITY | SPECTRA | GROUND-STATES

NLS equation | Birman-Schwinger principle | spectral stability | Feshbach map | EXISTENCE | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | BIFURCATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITARY WAVES | MATHEMATICAL & COMPUTATIONAL BIOLOGY | ASYMPTOTIC STABILITY | SPECTRA | GROUND-STATES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2018, Volume 146, Issue 9, pp. 3935 - 3942

The spectrum of the singular indefinite Sturm-Liouville operator \displaystyle A=\operatorname {sgn}(\cdot )\bigl (-\tfrac...

MATHEMATICS | MATHEMATICS, APPLIED | indefinite Sturm-Liouville operator | NON-REAL EIGENVALUES | Krein space | Birman-Schwinger principle | ORDINARY DIFFERENTIAL-OPERATORS | Non-real eigenvalue

MATHEMATICS | MATHEMATICS, APPLIED | indefinite Sturm-Liouville operator | NON-REAL EIGENVALUES | Krein space | Birman-Schwinger principle | ORDINARY DIFFERENTIAL-OPERATORS | Non-real eigenvalue

Journal Article

Operator Theory: Advances and Applications, ISSN 0255-0156, 2018, Volume 263, pp. 321 - 334

Journal Article

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