Professor Bender

Bender CM, Brody DC, 2019, Operator-valued zeta functions and Fourier analysis, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 52, ISSN: 1751-8113

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• Citations: 2

Bender CM, Komijani J, Wang Q-H, 2019, Nonlinear eigenvalue problems for generalized Painleve equations, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 52, ISSN: 1751-8113

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• Citations: 5

Beygi A, Klevansky SP, Bender CM, 2019, Relativistic <i>PT</i>-symmetric fermionic theories in 1+1 and 3+1 dimensions, PHYSICAL REVIEW A, Vol: 99, ISSN: 2469-9926

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• Citations: 19

Bender CM, Dorey P, Dunning TC, Tateo R, Fring A, Jones HF, Kuzhel S, Lévai G, Hook Det al., 2019, PT Symmetry In Quantum and Classical Physics, Publisher: World Scientific Publishing Europe Limited, ISBN: 9781786346681

Carl Bender&#39;s work has influenced major advances in physics and generations of students. This book is an accessible entry point to PT symmetry, ideal for students and scientists looking to begin their own research projects in this field.

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Bender CM, Hassanpour N, Klevansky SP, Sarkar Set al., 2018, <i>PT</i>-symmetric quantum field theory in <i>D</i> dimensions, PHYSICAL REVIEW D, Vol: 98, ISSN: 2470-0010

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• Citations: 21

Bender CM, Gianfreda M, 2018, Scattering off <i>PT</i>-symmetric upside-down potentials, PHYSICAL REVIEW A, Vol: 98, ISSN: 2469-9926

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• Citations: 2

Bender CM, Sarkar S, 2018, Asymptotic analysis of the local potential approximation to the Wetterich equation, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 51, ISSN: 1751-8113

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• Citations: 4

Bender CM, Brody DC, 2018, Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 51, ISSN: 1751-8113

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• Citations: 4

Beygi A, Klevansky SP, Bender CM, 2018, Two-and four-dimensional representations of the <i>PT</i>- and <i>CPT</i>-symmetricfermionic algebras, PHYSICAL REVIEW A, Vol: 97, ISSN: 2469-9926

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• Citations: 6

Ford C, Bender C, Hassanpour N, Xia Bet al., 2018, Series solutions of PT -symmetric Schrödinger equations, Journal of Physics Communications, Vol: 2, ISSN: 2399-6528

A simple and accurate numerical technique for finding eigenvalues, node structure, and expectation values of ${ \mathcal P }{ \mathcal T }$-symmetric potentials is devised. The approach involves expanding the solution to the Schrödinger equation in series involving powers of both the coordinate and the energy. The technique is designed to allow one to impose boundary conditions in ${ \mathcal P }{ \mathcal T }$-symmetric pairs of Stokes sectors. The method is illustrated by using many examples of ${ \mathcal P }{ \mathcal T }$-symmetric potentials in both the unbroken- and broken-${ \mathcal P }{ \mathcal T }$-symmetric regions.

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Schindler ST, Bender CM, 2018, Winding in non-Hermitian systems, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 51, ISSN: 1751-8113

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• Citations: 4

Bender CM, Rodriguez-Fortuno FJ, Sarkar S, Zayats AVet al., 2017, Two-Dimensional Pulse Propagation without Anomalous Dispersion, PHYSICAL REVIEW LETTERS, Vol: 119, ISSN: 0031-9007

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• Citations: 5

Bender CM, Hassanpour N, Hook DW, Klevansky SP, Snderhauf C, Wen Zet al., 2017, Behavior of eigenvalues in a region of broken PT symmetry, Physical Review A, Vol: 95, ISSN: 1050-2947

PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix)ɛ. When ɛ≥0, the eigenvalues of this non-Hermitian Hamiltonian are discrete, real, and positive. This portion of parameter space is known as the region of unbroken PT symmetry. In the region of broken PT symmetry, ɛ<0, only a finite number of eigenvalues are real and the remaining eigenvalues appear as complex-conjugate pairs. The region of unbroken PT symmetry has been studied but the region of broken PT symmetry has thus far been unexplored. This paper presents a detailed numerical and analytical examination of the behavior of the eigenvalues for −4<ɛ<0. In particular, it reports the discovery of an infinite-order exceptional point at ɛ=−1, a transition from a discrete spectrum to a partially continuous spectrum at ɛ=−2, a transition at the Coulomb value ɛ=−3, and the behavior of the eigenvalues as ɛ approaches the conformal limit ɛ=−4.

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Bender CM, Brody DC, Mueller MP, 2017, Hamiltonian for the Zeros of the Riemann Zeta Function, PHYSICAL REVIEW LETTERS, Vol: 118, ISSN: 0031-9007

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• Citations: 55

Bender CM, Ghatak A, Gianfreda M, 2017, <i>PT</i>-symmetric model of immune response, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 50, ISSN: 1751-8113

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• Citations: 1

Bender CM, Felski A, Hassanpour N, Klevansky SP, Beygi Aet al., 2017, Analytic structure of eigenvalues of coupled quantum systems, PHYSICA SCRIPTA, Vol: 92, ISSN: 0031-8949

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• Citations: 6

Bender CM, 2017, Nonlinear eigenvalue problems and <i>PT</i>-symmetric quantum mechanics, 5th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE), Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588

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• Citations: 8

Alexandre J, Bender CM, Millington P, 2017, Light neutrino masses from a non-Hermitian Yukawa theory, 5th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE), Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588

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• Citations: 20

Bender CM, Hook DW, Mavromatos NE, Sarkar Set al., 2016, PT-symmetric interpretation of unstable effective potentials, Journal of Physics A: Mathematical and Theoretical, Vol: 49, ISSN: 1751-8113

The conventional interpretation of the one-loop effective potentials of theHiggs field in the Standard Model and the gravitino condensate in dynamicallybroken supergravity is that these theories are unstable at large field values.A PT-symmetric reinterpretation of these models at a quantum-mechanical leveleliminates these instabilities and suggests that these instabilities may alsobe tamed at the quantum-field-theory level.

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Bender CM, 2016, Rigorous backbone of <i>PT</i>-symmetric quantum mechanics, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 49, ISSN: 1751-8113

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• Citations: 11

Cuevas-Maraver J, Kevrekidis PG, Saxena A, Cooper F, Khare A, Comech A, Bender CMet al., 2016, Solitary Waves of a PT-Symmetric Nonlinear Dirac Equation, IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, Vol: 22, ISSN: 1077-260X

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• Citations: 10

Bender CM, Gianfreda M, Hassanpour N, Jones HFet al., 2016, Comment on "On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator" [J. Math. Phys. 48, 032701 (2007)], Journal of Mathematical Physics, Vol: 57, ISSN: 1089-7658

In a remarkable paper Chandrasekar et al. showed that the (second-order constant-coefficient) classical equation of motion for a damped harmonic oscillator can be derived from a Hamiltonian having one degree of freedom. This paper gives a simple derivation of their result and generalizes it to the case of an nth-order constant-coefficient differential equation.

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Bender CM, Brody DC, Hughston LP, Meister BKet al., 2016, Geometric Aspects of Space-Time Reflection Symmetry in Quantum Mechanics, 15th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP), Publisher: SPRINGER-VERLAG BERLIN, Pages: 185-199, ISSN: 0930-8989

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• Citations: 1

Bender CM, Komijani J, 2015, Painleve transcendents and <i>PT</i>-symmetric Hamiltonians, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 48, ISSN: 1751-8113

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• Citations: 14

Alexandre J, Bender CM, Millington P, 2015, Non-Hermitian extension of gauge theories and implications for neutrino physics, Journal of High Energy Physics, Vol: 2015, ISSN: 1126-6708

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Bender CM, Gianfreda M, 2015, <i>PT</i>-symmetric interpretation of the electromagnetic self-force, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 48, ISSN: 1751-8113

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• Citations: 7

Beygi A, Klevansky SP, Bender CM, 2015, Coupled oscillator systems having partial <i>PT</i> symmetry, PHYSICAL REVIEW A, Vol: 91, ISSN: 1050-2947

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• Citations: 35

Alexandre J, Bender CM, 2015, Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 48, ISSN: 1751-8113

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• Citations: 21

Bender CM, 2015, <i>PT</i>-symmetric quantum theory, 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE), Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588

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• Citations: 50

Bender CM, Hook DW, Mavromatos NE, Sarkar Set al., 2014, Infinite Class of PT-Symmetric Theories from One Timelike Liouville Lagrangian, Physical Review Letters, Vol: 113, ISSN: 1079-7114

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