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Interaction problems for \(n\)-dimensional Dirac operators with singular potentials. (English) Zbl 07919561

Duduchava, Roland (ed.) et al., Tbilisi analysis and PDE seminar. Extended abstracts of the 2020–2023. Seminar talks. Cham: Birkhäuser. Trends Math., Res. Perspect. Ghent Anal. PDE Cent. 7, 183-189 (2024).

MSC: 81Q10 81V05 35P15 58C40

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Frymark, Dale; Holzmann, Markus; Lotoreichik, Vladimir

Spectral analysis of the Dirac operator with a singular interaction on a broken line. (English) Zbl 07906087

J. Math. Phys. 65, No. 8, Article ID 083514, 24 p. (2024).

MSC: 81Q10 35P05 35Q40 47B25 35P15

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Behrndt, Jussi; Frymark, Dale; Holzmann, Markus; Stelzer-Landauer, Christian

Nonrelativistic limit of generalized MIT bag models and spectral inequalities. (English) Zbl 07894653

Math. Phys. Anal. Geom. 27, No. 3, Paper No. 12, 30 p. (2024).

MSC: 81Q10 58J50 35Q40

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Heriban, Lukáš; Tušek, Matěj

Non-local relativistic \(\delta\)-shell interactions. (English) Zbl 07880226

Lett. Math. Phys. 114, No. 3, Paper No. 79, 18 p. (2024).

MSC: 81Q10 81Q80

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Behrndt, Jussi; Holzmann, Markus; Stelzer-Landauer, Christian; Stenzel, Georg

Boundary triples and Weyl functions for Dirac operators with singular interactions. (English) Zbl 1536.81052

Rev. Math. Phys. 36, No. 2, Article ID 2350036, 65 p. (2024).

MSC: 81Q10 47B25 34L05 35P05 35Q40 46E35 47E05 47F05

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Michelangeli, Alessandro

On creating new essential spectrum by self-adjoint extension of gapped operators. (English) Zbl 1539.47010

Ann. Funct. Anal. 15, No. 2, Paper No. 18, 24 p. (2024).

Reviewer: Mohammed El Aïdi (Bogotá)

MSC: 47A10 47B25 47N20 47N50

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Cassano, Biagio; Lotoreichik, Vladimir

Self-adjointness for the MIT bag model on an unbounded cone. (English) Zbl 07820031

Math. Nachr. 297, No. 3, 1006-1041 (2024).

MSC: 47F05 35P15 81Q10

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Bonin, C. A.; Lunardi, José T.; Manzoni, Luiz A.

The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics. (English) Zbl 07814456

J. Phys. A, Math. Theor. 57, No. 9, Article ID 095204, 26 p. (2024).

MSC: 81P05 81Q05 83C45 22E43 70H05 22E70

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Benhellal, Badreddine; Pankrashkin, Konstantin

Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions. (English) Zbl 1534.35342

Pure Appl. Anal. 6, No. 1, 237-252 (2024).

MSC: 35Q40 35Q41 47A10 58J40 53A05 81Q05 78A30

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Posilicano, Andrea; Reginato, Linda

\(\mathsf{D}^2=\mathsf{H}+\frac{1}{4}\) with point interactions. (English) Zbl 07812176

Oper. Matrices 17, No. 4, 1167-1190 (2023).

MSC: 47B25 34L40

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Rabinovich, Vladimir S.

Fredholm property of interaction problems on unbounded \(C^2-\) hypersurfaces in \(\mathbb{R}^n\) for Dirac operators. (English) Zbl 1540.81052

J. Math. Sci., New York 271, No. 2, Series A, 136-161 (2023).

MSC: 81Q10 34L40 30J15 78A30 47B25 35P15 58C40

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Rabinovich, V. S.

Method of potential operators for interaction problems on unbounded hypersurfaces in \(\mathbb{R}^n\) for Dirac operators. (English) Zbl 1531.35276

Russ. J. Math. Phys. 30, No. 4, 674-690 (2023).

MSC: 35Q41 35Q40 81Q10 35S05

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Behrndt, Jussi; Holzmann, Markus; Stenzel, Georg

Schrödinger operators with oblique transmission conditions in \(\mathbb{R}^2\). (English) Zbl 1529.81063

Commun. Math. Phys. 401, No. 3, 3149-3167 (2023).

MSC: 81Q10 14H15 26A24 47A10 35P15 81R25 35J05

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Cassano, Biagio; Lotoreichik, Vladimir; Mas, Albert; Tušek, Matěj

General \(\delta\)-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation. (English) Zbl 1528.81132

Rev. Mat. Iberoam. 39, No. 4, 1443-1492 (2023).

MSC: 81Q10 81Q37 47N20 47N50 47B25 52B22 31A25 30C20

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Fucci, Guglielmo; Romaniega, César

Casimir energy for spinor fields with \(\delta\)-shell potentials. (English) Zbl 1523.81100

J. Phys. A, Math. Theor. 56, No. 26, Article ID 265201, 35 p. (2023).

MSC: 81R25 81T55 11R59 57R67

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Arrizabalaga, Naiara; Mas, Albert; Sanz-Perela, Tomás; Vega, Luis

Eigenvalue curves for generalized MIT bag models. (English) Zbl 1521.81060

Commun. Math. Phys. 397, No. 1, 337-392 (2023).

MSC: 81Q05 35G15 78A25 35P15 35P20

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Behrndt, Jussi; Holzmann, Markus; Tušek, Matěj

Two-dimensional Dirac operators with general \(\delta\)-shell interactions supported on a straight line. (English) Zbl 1519.81326

J. Phys. A, Math. Theor. 56, No. 4, Article ID 045201, 29 p. (2023).

MSC: 81R25 81T40 81Q10 35P05 35P15 82D30

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Frymark, Dale; Lotoreichik, Vladimir

Self-adjointness of the 2D Dirac operator with singular interactions supported on star graphs. (English) Zbl 1513.81053

Ann. Henri Poincaré 24, No. 1, 179-221 (2023).

MSC: 81Q10 35P05 35Q40 47B25

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Rabinovich, Vladimir

Interaction problems on periodic hypersurfaces for Dirac operators on \(\mathbb{R}^n \). (English) Zbl 1537.81124

J. Math. Sci., New York 266, No. 1, Series A, 133-147 (2022).

MSC: 81R25 81Q10 81V05 35P15 58C40 81V19 47A10 78A30 70P05 81Q35 14M25 47B25 37C75 37C86

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Barrera-Figueroa, Víctor; Rabinovich, Vladimir S.; Loredo-Ramírez, Samantha Ana Cristina

On the calculation of the discrete spectra of one-dimensional Dirac operators. (English) Zbl 1538.34343

Math. Methods Appl. Sci. 45, No. 16, 10218-10246 (2022).

MSC: 34L40 47B25 34L16 81U30 81Q05

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Cassano, Biagio; Gallone, Matteo; Pizzichillo, Fabio

Dirac-Coulomb operators with infinite mass boundary conditions in sectors. (English) Zbl 1521.81074

J. Math. Phys. 63, No. 7, Article ID 071503, 16 p. (2022).

MSC: 81Q10 47A55 47B25 32F18 78A25 47A10

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Benhellal, Badreddine

Spectral analysis of Dirac operators with delta interactions supported on the boundaries of rough domains. (English) Zbl 1507.81087

J. Math. Phys. 63, No. 1, Article ID 011507, 33 p. (2022).

MSC: 81Q10 35Q40 47B25 35P05 81Q05

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Behrndt, Jussi; Holzmann, Markus; Tušek, Matěj

Spectral transition for Dirac operators with electrostatic \(\delta\)-shell potentials supported on the straight line. (English) Zbl 1497.81056

Integral Equations Oper. Theory 94, No. 3, Paper No. 33, 13 p. (2022).

MSC: 81Q10 35Q40 81R25 31A20 47A10 81V10

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Benhellal, Badreddine

Spectral properties of the Dirac operator coupled with \(\delta\)-shell interactions. (English) Zbl 1490.81073

Lett. Math. Phys. 112, No. 3, Paper No. 52, 52 p. (2022).

MSC: 81Q10 81V05 35P15 58C40

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Rabinovich, Vladimir

Fredholm property and essential spectrum of 3-D Dirac operators with regular and singular potentials. (English) Zbl 1491.35150

Complex Var. Elliptic Equ. 67, No. 4, 938-961 (2022).

Reviewer: David Kapanadze (Tbilisi)

MSC: 35J10 47A10 47A53 81Q10

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Rabinovich, Vladimir

Dirac operators with delta-interactions on smooth hypersurfaces in \(\mathbb{R}^n\). (English) Zbl 1485.35147

J. Fourier Anal. Appl. 28, No. 2, Paper No. 20, 26 p. (2022).

MSC: 35J10 35Q41

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Budyka, Viktoriya S.; Malamud, Mark M.

Deficiency indices and discreteness property of block Jacobi matrices and Dirac operators with point interactions. (English) Zbl 1493.47041

J. Math. Anal. Appl. 506, No. 1, Article ID 125582, 50 p. (2022).

MSC: 47B36 34L40

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Cintio, Andrea; Michelangeli, Alessandro

Self-adjointness in quantum mechanics: a pedagogical path. (English) Zbl 07899168

Quantum Stud. Math. Found. 8, No. 3, 271-306 (2021).

MSC: 81-XX

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Rabinovich, V. S.

Dirac operators with singular potentials supported on unbounded surfaces in \(\mathbb{R}^3 \). (English. Russian original) Zbl 1486.81101

Funct. Anal. Appl. 55, No. 3, 245-249 (2021); translation from Funkts. Anal. Prilozh. 55, No. 3, 85-90 (2021).

MSC: 81Q05 81R25 81R20 26A30 47B25 47A10 78A30 46F10

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Rabinovich, V.

Two-dimensional Dirac operators with interactions on unbounded smooth curves. (English) Zbl 1483.81064

Russ. J. Math. Phys. 28, No. 4, 524-542 (2021).

MSC: 81Q05 81R25 47B25 35P05 81V10 14H20

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Holzmann, Markus

A note on the three dimensional Dirac operator with zigzag type boundary conditions. (English) Zbl 1465.81026

Complex Anal. Oper. Theory 15, No. 3, Paper No. 47, 15 p. (2021).

MSC: 81Q10 35Q40 35F15 35P05

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Cassano, Biagio; Lotoreichik, Vladimir

Self-adjoint extensions of the two-valley Dirac operator with discontinuous infinite mass boundary conditions. (English) Zbl 1462.35212

Oper. Matrices 14, No. 3, 667-678 (2020).

MSC: 35P05 35Q40 81Q10

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Holzmann, Markus; Unger, Gerhard

Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods. (English) Zbl 1464.35274

Oper. Matrices 14, No. 3, 555-599 (2020).

MSC: 35Q40 47J10 47F10 65N38 65N25

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Exner, Pavel

Leaky quantum structures. (English. Russian original) Zbl 1457.81041

Proc. Steklov Inst. Math. 311, 114-128 (2020); translation from Tr. Mat. Inst. Steklova 311, 123-139 (2020).

MSC: 81Q10 46F10 81Q35 47A58 14B07 81Q70 35P05

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Rabinovich, Vladimir

Dirac operators on \(\mathbb{R}\) with general point interactions. (English) Zbl 1540.47065

Bauer, Wolfram (ed.) et al., Operator algebras, Toeplitz operators and related topics. Selected papers based on the presentations at the international workshop, Boca del Rio, Veracruz, Mexico, November 13–19, 2018. In honor of Nikolai Vasilevskin on the occasion of his 70th birthday. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 279, 351-381 (2020).

MSC: 47E05 34L40 81Q10 47A53

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Behrndt, Jussi; Holzmann, Markus; Mas, Albert

Self-adjoint Dirac operators on domains in \(\mathbb{R}^3\). (English) Zbl 1454.81079

Ann. Henri Poincaré 21, No. 8, 2681-2735 (2020).

Reviewer: Miyeon Kwon (Platteville)

MSC: 81Q10 35Q40 81R20 81V35 81V05 81Q05 35F15 35B40 35P05

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Behrndt, Jussi; Holzmann, Markus; Ourmières-Bonafos, Thomas; Pankrashkin, Konstantin

Two-dimensional Dirac operators with singular interactions supported on closed curves. (English) Zbl 1446.35155

J. Funct. Anal. 279, No. 8, Article ID 108700, 46 p. (2020).

MSC: 35Q41 81Q10 35S05 78A35

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Behrndt, Jussi; Holzmann, Markus; Mantile, Andrea; Posilicano, Andrea

Limiting absorption principle and scattering matrix for Dirac operators with \(\delta\)-shell interactions. (English) Zbl 1439.81037

J. Math. Phys. 61, No. 3, 033504, 16 p. (2020).

MSC: 81Q05 81R20 46F10 81U20

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Found 38 Documents (Results 1–38)

Interaction problems for \(n\)-dimensional Dirac operators with singular potentials. (English) Zbl 07919561

Spectral analysis of the Dirac operator with a singular interaction on a broken line. (English) Zbl 07906087

Nonrelativistic limit of generalized MIT bag models and spectral inequalities. (English) Zbl 07894653

Non-local relativistic \(\delta\)-shell interactions. (English) Zbl 07880226

Boundary triples and Weyl functions for Dirac operators with singular interactions. (English) Zbl 1536.81052

On creating new essential spectrum by self-adjoint extension of gapped operators. (English) Zbl 1539.47010

Self-adjointness for the MIT bag model on an unbounded cone. (English) Zbl 07820031

The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics. (English) Zbl 07814456

Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions. (English) Zbl 1534.35342

\(\mathsf{D}^2=\mathsf{H}+\frac{1}{4}\) with point interactions. (English) Zbl 07812176

Fredholm property of interaction problems on unbounded \(C^2-\) hypersurfaces in \(\mathbb{R}^n\) for Dirac operators. (English) Zbl 1540.81052

Method of potential operators for interaction problems on unbounded hypersurfaces in \(\mathbb{R}^n\) for Dirac operators. (English) Zbl 1531.35276

Schrödinger operators with oblique transmission conditions in \(\mathbb{R}^2\). (English) Zbl 1529.81063

General \(\delta\)-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation. (English) Zbl 1528.81132

Casimir energy for spinor fields with \(\delta\)-shell potentials. (English) Zbl 1523.81100

Eigenvalue curves for generalized MIT bag models. (English) Zbl 1521.81060

Two-dimensional Dirac operators with general \(\delta\)-shell interactions supported on a straight line. (English) Zbl 1519.81326

Self-adjointness of the 2D Dirac operator with singular interactions supported on star graphs. (English) Zbl 1513.81053

Interaction problems on periodic hypersurfaces for Dirac operators on \(\mathbb{R}^n \). (English) Zbl 1537.81124

On the calculation of the discrete spectra of one-dimensional Dirac operators. (English) Zbl 1538.34343

Dirac-Coulomb operators with infinite mass boundary conditions in sectors. (English) Zbl 1521.81074

Spectral analysis of Dirac operators with delta interactions supported on the boundaries of rough domains. (English) Zbl 1507.81087

Spectral transition for Dirac operators with electrostatic \(\delta\)-shell potentials supported on the straight line. (English) Zbl 1497.81056

Spectral properties of the Dirac operator coupled with \(\delta\)-shell interactions. (English) Zbl 1490.81073

Fredholm property and essential spectrum of 3-D Dirac operators with regular and singular potentials. (English) Zbl 1491.35150

Dirac operators with delta-interactions on smooth hypersurfaces in \(\mathbb{R}^n\). (English) Zbl 1485.35147

Deficiency indices and discreteness property of block Jacobi matrices and Dirac operators with point interactions. (English) Zbl 1493.47041

Self-adjointness in quantum mechanics: a pedagogical path. (English) Zbl 07899168

Dirac operators with singular potentials supported on unbounded surfaces in \(\mathbb{R}^3 \). (English. Russian original) Zbl 1486.81101

Two-dimensional Dirac operators with interactions on unbounded smooth curves. (English) Zbl 1483.81064

A note on the three dimensional Dirac operator with zigzag type boundary conditions. (English) Zbl 1465.81026

Self-adjoint extensions of the two-valley Dirac operator with discontinuous infinite mass boundary conditions. (English) Zbl 1462.35212

Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods. (English) Zbl 1464.35274

Leaky quantum structures. (English. Russian original) Zbl 1457.81041

Dirac operators on \(\mathbb{R}\) with general point interactions. (English) Zbl 1540.47065

Self-adjoint Dirac operators on domains in \(\mathbb{R}^3\). (English) Zbl 1454.81079

Two-dimensional Dirac operators with singular interactions supported on closed curves. (English) Zbl 1446.35155

Limiting absorption principle and scattering matrix for Dirac operators with \(\delta\)-shell interactions. (English) Zbl 1439.81037

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