Complex magnetic monopoles, geometric phases and quantum evolution in the vicinity of diabolic and exceptional points

Nesterov, Alexander I.; Cruz, F. Aceves de la

doi:10.1088/1751-8113/41/48/485304

Cited by 31 publications

(33 citation statements)

References 67 publications

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“…Similar works have been done in many systems [39,40,41,42,43], and this conclusion can also be obtained by an exact solution of Schrödinger equation…”

Section: Summary and Discussionsupporting

confidence: 79%

Non-Hermitian heat engine with all-quantum-adiabatic-process cycle

Sun¹,

Song²

2016

J. Phys. A: Math. Theor.

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Abstract. As a quantum device, a quantum heat engine (QHE) is described by a Hermitian Hamiltonian. However, since it is an open system, reservoirs have to be imposed phenomenologically without any description in the context of quantum mechanics. A nonHermitian system is expected to describe an open system which exchanges energy and particles with external reservoirs. Correspondingly, such an exchange can be adiabatic in the context of quantum mechanics. We first propose a non-Hermitian QHE by a concrete simple two-level system, which is an S = 1/2 spin in a complex external magnetic field. The non-Hermitian PTsymmetric Hamiltonian, as a self-contained one, describes both working medium and reservoirs. A heat-engine cycle is composed of completely quantum adiabatic processes. Surprisingly, the heat efficiency is obtained to be the same as that of Hermitian quantum Otto cycle. A classical analogue of this scheme is also presented. Our finding paves the way for revealing what the role of a non-Hermitian Hamiltonian plays in physics.

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“…Similar works have been done in many systems [39,40,41,42,43], and this conclusion can also be obtained by an exact solution of Schrödinger equation…”

Section: Summary and Discussionsupporting

confidence: 79%

Non-Hermitian heat engine with all-quantum-adiabatic-process cycle

Sun¹,

Song²

2016

J. Phys. A: Math. Theor.

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“…In the context of Berry phase, the diabolic point is associated with the 'fictitious magnetic monopole' located at the diabolic point [27,28]. In turn, the exceptional points are associated with the 'fictitious complex magnetic monopoles' [29].…”

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confidence: 99%

Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution

Nesterov¹

2009

SIGMA

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Abstract. Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian PT -symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state |ψ i into a specific final state |ψ f can be made arbitrarily small. Additionally, it has been shown that finding the shortest possible time requires only the solution of the two-dimensional problem for the quantum system governed by the effective Hamiltonian acting in the subspace spanned by |ψ i and |ψ f . In this paper, we study a similar problem for the generic non-Hermitian Hamiltonian, focusing our attention on the geometric aspects of the problem.

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“…To provide a complete description and proof, we start by considering a two-band, non-Hermitian -symmetric model which can be used to describe an array of subwavelength photonic resonators coated with gain media. The -symmetric eigenvalue problem is written in the generic form as2735…”

Section: Two-band -Symmetric Modelmentioning

confidence: 99%

Anomalous Light Scattering by Topological PT-symmetric Particle Arrays

Ling

Choi

Mok

et al. 2016

Sci Rep

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Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological edge modes in a non-Hermitian -symmetric system can give rise to an anomalous sideway scattering when they are simultaneously excited by a plane wave. We propose a realization of such scattering state in a linear array of subwavelength resonators coated with gain media. The prediction is based on an analytical two-band model and verified by rigorous numerical simulation using multiple-multipole scattering theory. The result suggests an extreme situation where leakage of classical information is unnoticeable to the transmitter and the receiver when such a -symmetric unit is inserted into the communication channel.

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Complex magnetic monopoles, geometric phases and quantum evolution in the vicinity of diabolic and exceptional points

Cited by 31 publications

References 67 publications

Non-Hermitian heat engine with all-quantum-adiabatic-process cycle

Non-Hermitian heat engine with all-quantum-adiabatic-process cycle

Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution

Anomalous Light Scattering by Topological PT-symmetric Particle Arrays

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