Abstract
The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of ${\cal PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These ${\cal PT}$ symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories.
Keywords
Hamiltonian (control theory)Hermitian matrixPhysicsBounded functionEigenvalues and eigenvectorsMathematical physicsSpectral lineQuantum mechanicsMathematicsMathematical analysis
Affiliated Institutions
Related Publications
Model of supersymmetric quantum field theory with broken parity symmetry
Recently, it was observed that self-interacting scalar quantum field theories having a non-Hermitian interaction term of the form $g(i\phi)^{2+\delta}$, where $\delta$ is a real...
Calculated effective Hamiltonian for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Cu<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and solution in the impurity Anderson approximation
We report local-density-functional calculations of hybridization matrix elements and effective electron-electron interactions in ${\mathrm{La}}_{2}$Cu${\mathrm{O}}_{4}$ defining...
Symmetry and Topology in Non-Hermitian Physics
We develop a complete theory of symmetry and topology in non-Hermitian\nphysics. We demonstrate that non-Hermiticity ramifies the celebrated\nAltland-Zirnbauer symmetry classifi...
Topological Band Theory for Non-Hermitian Hamiltonians
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped b...
Spectroscopic Evidence for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>5</mml:mn><mml:mi>f</mml:mi></mml:math>Coulomb Interaction in U<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and U<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Pt</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
The $5f$ spectral weight in the heavy-fermion materials U${\mathrm{Al}}_{2}$ and U${\mathrm{Pt}}_{3}$ has been measured by electron spectroscopy, and compared to that in density...
Publication Info
- Year
- 1998
- Type
- article
- Volume
- 80
- Issue
- 24
- Pages
- 5243-5246
- Citations
- 6254
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
6254
OpenAlex
Cite This
Carl M. Bender,
Stefan Boettcher
(1998).
Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry.
Physical Review Letters
, 80
(24)
, 5243-5246.
https://doi.org/10.1103/physrevlett.80.5243
Identifiers
- DOI
- 10.1103/physrevlett.80.5243