Publications
286 results found
Bender CM, Mannheim PD, 2011, <i>PT</i> symmetry in relativistic quantum mechanics, PHYSICAL REVIEW D, Vol: 84, ISSN: 1550-7998
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- Citations: 16
Bender CM, Hook DW, 2011, Quantum tunneling as a classical anomaly, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 44, ISSN: 1751-8113
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- Citations: 17
Anderson AG, Bender CM, Morone UI, 2011, Periodic orbits for classical particles having complex energy, PHYSICS LETTERS A, Vol: 375, Pages: 3399-3404, ISSN: 0375-9601
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- Citations: 12
Bender CM, Jones HF, 2011, Bound states of <i>PT</i>-symmetric separable potentials, PHYSICAL REVIEW A, Vol: 84, ISSN: 1050-2947
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- Citations: 1
Bender CM, Klevansky SP, 2011, <i>PT</i>-symmetric representations of fermionic algebras, PHYSICAL REVIEW A, Vol: 84, ISSN: 1050-2947
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- Citations: 18
Bender CM, Kalveks RJ, 2011, Extending PT Symmetry from Heisenberg Algebra to E2 Algebra, International Conference on Pseudo-Hermitian Hamiltonians in Quantum Physics, Publisher: SPRINGER/PLENUM PUBLISHERS, Pages: 955-962, ISSN: 0020-7748
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- Citations: 11
Bender CM, Jones HF, 2011, Quantum counterpart of spontaneously broken classical PT symmetry, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 44, ISSN: 1751-8113
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- Citations: 2
Bender CM, 2011, PT-Symmetric Quantum Field Theory, International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Publisher: AMER INST PHYSICS, ISSN: 0094-243X
Bender CM, Hook DW, Kooner K, 2011, Complex Elliptic Pendulum, Asymptotics in Dynamics, Geometry and PDEs; Generalised Borel Summation vol. 1, Editors: Costin, Fauvet, Menous, Sauzin, Publisher: Edizioni della normale, Pages: 1-18, ISBN: 9788876423741
This paper briefly summarizes previous work on complex classical mechanicsand its relation to quantum mechanics. It then introduces a previouslyunstudied area of research involving the complex particle trajectoriesassociated with elliptic potentials.
Hook DW, Bender CM, Meisinger PN, et al., 2010, Probability density in the complex plane., ANN PHYS-NEW YORK, Vol: 325, Pages: 2332-2362, ISSN: 0003-4916
Bender CM, Klevansky SP, 2010, Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory, PHYSICAL REVIEW LETTERS, Vol: 105, ISSN: 0031-9007
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- Citations: 20
Bender CM, Hook DW, Kooner KS, 2010, Classical particle in a complex elliptic potential, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, ISSN: 1751-8113
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- Citations: 16
Bender CM, Mannheim PD, 2010, <i>PT</i> symmetry and necessary and sufficient conditions for the reality of energy eigenvalues, PHYSICS LETTERS A, Vol: 374, Pages: 1616-1620, ISSN: 0375-9601
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- Citations: 65
Bender CM, Hook DW, Meisinger PN, et al., 2010, Complex Correspondence Principle, PHYSICAL REVIEW LETTERS, Vol: 104, ISSN: 0031-9007
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- Citations: 57
Bender CM, BRODY D, 2010, Optimal time evolution for Hermitian and non-Hermitian Hamiltonians, Time in Quantum Mechanics, Editors: Muga, Ruschhaupt, Campo, Publisher: Springer Verlag, ISBN: 9783642031731
Bender CM, Benincasa G, Jones HF, 2009, Comment on "New ansatz for metric operator calculation in pseudo-Hermitian field theory", PHYSICAL REVIEW D, Vol: 80, ISSN: 1550-7998
Bender CM, Besseghir K, Jones HF, et al., 2009, Small-ε behavior of the non-Hermitian PT-symmetric Hamiltonian <i>H</i> = <i>p</i><SUP>2</SUP> + <i>x</i><SUP>2</SUP>(i<i>x</i>)<SUP>ε</SUP>, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 42, ISSN: 1751-8113
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- Citations: 8
Bender CM, Feinberg J, Hook DW, et al., 2009, Chaotic systems in complex phase space., PRAMANA-J PHYS, Vol: 73, Pages: 453-470, ISSN: 0304-4289
This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.
Bender CM, Cooper F, Khare A, et al., 2009, Compactons in <i>PT</i>-symmetric generalized Korteweg-de Vries equations, 8th Conference on Non-Hermitian Hamiltonians in Quantum Physics, Publisher: INDIAN ACAD SCIENCES, Pages: 375-385, ISSN: 0304-4289
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- Citations: 20
Arpornthip T, Bender CM, 2009, Conduction bands in classical periodic potentials, 8th Conference on Non-Hermitian Hamiltonians in Quantum Physics, Publisher: INDIAN ACAD SCIENCES, Pages: 259-267, ISSN: 0304-4289
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- Citations: 13
Bender CM, Klevansky SP, 2009, Nonunique C operator in PT quantum mechanics, PHYSICS LETTERS A, Vol: 373, Pages: 2670-2674, ISSN: 0375-9601
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- Citations: 16
Bender CM, Ben-Naim E, 2008, Nonlinear-Integral-Equation Construction of Orthogonal Polynomials, 17th Nonlinear Evolution Equations and Dynamical Systems Workshop, Publisher: TAYLOR & FRANCIS LTD, Pages: 73-80, ISSN: 1402-9251
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- Citations: 3
Bender CM, Hook DW, Mead LR, 2008, Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra, Journal of Physics A: Mathematical and Theoretical, Vol: 41
The spectrum of the Hermitian Hamiltonian H = p2 + V(x) is real and discrete if the potential V(x) → ∞ as x → ±∞. However, if V(x) is complex and -symmetric, it is conjectured that, except in rare special cases, V(x) must be analytic in order to have a real spectrum. This conjecture is demonstrated by using the potential V(x) = (ix)a|x|b, where a, b are real.
Bender CM, Mannheim PD, 2008, Giving up the ghost, 5th International Symposium on Quantum Theory and Symmetries, Publisher: IOP PUBLISHING LTD, ISSN: 1751-8113
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- Citations: 44
Bender CM, Mannheim PD, 2008, Giving up the ghost - art. no. 304018, 5th International Symposium on Quantum Theory and Symmetries, Pages: 4018-4018
The Pais-Uhlenbeck model is a quantum theory described by a higher-derivative field equation. It has been believed for many years that this model possesses ghost states (quantum states of negative norm) and therefore that this model is a physically unacceptable quantum theory. The existence of such ghost states was believed to be attributable to the field equation having more than two derivatives. This paper shows that the Pais-Uhlenbeck model does not possess any ghost states at all and that it is a perfectly acceptable quantum theory. The supposed ghost states in this model arise if the Hamiltonian of the model is (incorrectly) treated as being Dirac Hermitian (invariant under combined matrix transposition and complex conjugation). However, the Hamiltonian is not Dirac Hermitian, but rather it is PT symmetric. When it is quantized correctly according to the rules of PT quantum mechanics, the energy spectrum is real and bounded below and all of the quantum states have positive norm.
Bender CM, Brody DC, Hook DW, 2008, Quantum effects in classical systems having complex energy, Journal of Physics A: Mathematical and Theoretical, Vol: 41, ISSN: 0305-4470
Bender CM, Mannheim PD, 2008, Exactly solvable <i>PT</i>-symmetric Hamiltonian having no Hermitian counterpart, PHYSICAL REVIEW D, Vol: 78, ISSN: 1550-7998
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- Citations: 109
Bender CM, Hook DW, 2008, Exact isospectral pairs of PT-symmetric Hamiltonians, Journal of Physics A - Mathematical and Theoretical, Vol: 41
A technique for constructing an infinite tower of pairs of PT symmetric Hamiltonians, (H) over cap (n) and (K) over cap (n) (n = 2, 3, 4, ...), that have exactly the same eigenvalues is described and illustrated by means of three examples (n = 2, 3, 4). The eigenvalue problem for the first Hamiltonian (H) over cap (n) of the pair must be posed in the complex domain, so its eigenfunctions satisfy a complex differential equation and fulfill homogeneous boundary conditions in Stokes' wedges in the complex plane. The eigenfunctions of the second Hamiltonian (K) over cap (n) of the pair obey a real differential equation and satisfy boundary conditions on the real axis. This equivalence constitutes a proof that the eigenvalues of both Hamiltonians are real. Although the eigenvalue differential equation associated with (K) over cap (n) is real, the Hamiltonian (K) over cap (n) exhibits quantum anomalies (terms proportional to powers of h). These anomalies are remnants of the complex nature of the equivalent Hamiltonian (H) over cap (n). For the cases n = 2, 3, 4 in the classical limit in which the anomaly terms in (K) over cap (n) are discarded, the pair of Hamiltonians H-n,H-classical and K-n,K-classical have closed classical orbits whose periods are identical...
Bender CM, Jones HF, 2008, Interactions of Hermitian and non-Hermitian Hamiltonians, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 41, ISSN: 1751-8113
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- Citations: 35
Bender CM, Feinberg J, 2008, Does the complex deformation of the Riemann equation exhibit shocks?, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 41, ISSN: 1751-8113
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- Citations: 18
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