A PSEUDO-UNITARY ENSEMBLE OF RANDOM MATRICES, PT-SYMMETRY AND THE RIEMANN HYPOTHESIS
From MaRDI portal
Publication:5291425
DOI10.1142/S0217732306018792zbMath1138.11038arXivquant-ph/0407167OpenAlexW2075130300MaRDI QIDQ5291425
Publication date: 10 May 2006
Published in: Modern Physics Letters A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/quant-ph/0407167
Quantum measurement theory, state operations, state preparations (81P15) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)
Related Items
Random matrix theories and exactly solvable models ⋮ On the Riemann hypothesis, complex scalings and logarithmic time reversal
Cites Work
- Unnamed Item
- Wigner's function and tunneling
- Quasi-Hermitian operators in quantum mechanics and the variational principle
- Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
- Thermodynamic limit in number theory: Riemann-Beurling gases
- An ensemble of non-Hermitian Gaussian-random \(2\times 2\) matrices admitting the Wigner surmise
- P-, T-, PT-, and CPT-invariance of Hermitian Hamiltonians
- Methods of matrix algebra
- Negative metric and the unitarity of the S-matrix
- Complex Extension of Quantum Mechanics
- Quantum Mechanical Systems with Indefinite Metric. I
- The Riemann Zeros and Eigenvalue Asymptotics
- Gaussian ensemble of 2 2 pseudo-Hermitian random matrices
- Pseudo-reality and pseudo-adjointness of Hamiltonians
- 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
- Systematic search for 𝒫𝒯-symmetric potentials with real energy spectra
- Lorentz-invariant Hamiltonian and Riemann hypothesis
- Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries
- Weak pseudo-Hermiticity and antilinear commutant
- Linear vector spaces with indefinite metric
- Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential
- Energy band structure due to a complex, periodic, PT-invariant potential
- Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: real spectrum of complex potentials
