Piecewise adiabatic following: General analysis and exactly solvable models

Gong, Jiangbin; Wang, Qinghai

doi:10.1103/physreva.99.012107

Cited by 11 publications

(6 citation statements)

References 34 publications

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“…While in Fig. 3(b), a NAT appears and leads to a sudden state switch [43]. That is, the adiabatic following dynamics is piecewise.…”

Section: Chiral State Conversion In Dynamical Encirclementmentioning

confidence: 94%

Chiral state conversion in a levitated micromechanical oscillator with in situ control of parameter loops

Yin,

Luo,

Zhang

et al. 2020

Preprint

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Physical systems with gain and loss can be described by a non-Hermitian Hamiltonian, which is degenerated at the exceptional points (EPs). Many new and unexpected features have been explored in the non-Hermitian systems with a great deal of recent interest. One of the most fascinating features is that, chiral state conversion appears when one EP is encircled dynamically. Here, we propose an easy-controllable levitated microparticle system that carries a pair of EPs and realize slow evolution of the Hamiltonian along loops in the parameter plane. Utilizing the controllable rotation angle, gain and loss coefficients, we can control the structure, size and location of the loops in situ. We demonstrate that, under the joint action of topological structure of energy surfaces and nonadiabatic transitions (NATs), the chiral behavior emerges both along a loop encircling an EP and even along a straight path away from the EP. This work broadens the range of parameter space for the chiral state conversion, and proposes a useful platform to explore the interesting properties of exceptional points physics.I.

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“…While in Fig. 3(b), a NAT appears and leads to a sudden state switch [43]. That is, the adiabatic following dynamics is piecewise.…”

Section: Chiral State Conversion In Dynamical Encirclementmentioning

confidence: 94%

Chiral state conversion in a levitated micromechanical oscillator with in situ control of parameter loops

Yin,

Luo,

Zhang

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…3(b), an NAT appears and leads to a sudden state switch. [43] That is, the adiabatic following dynamics is piecewise. With the combined action of the topological structure around the EP (the adiabatic evolution around the EP) and the appearance of an NAT (a sudden state switch), the final state goes back to the initial state 𝑟 − (0).…”

Section: -2mentioning

confidence: 99%

Chiral State Conversion in a Levitated Micromechanical Oscillator with In Situ Control of Parameter Loops*

Yin¹,

Luo²,

Zhang³

et al. 2020

Chinese Phys. Lett.

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Physical systems with gain and loss can be described by a non-Hermitian Hamiltonian, which is degenerated at the exceptional points (EPs). Many new and unexpected features have been explored in the non-Hermitian systems with a great deal of recent interest. One of the most fascinating features is that chiral state conversion appears when one EP is encircled dynamically. Here, we propose an easy-controllable levitated microparticle system that carries a pair of EPs and realize slow evolution of the Hamiltonian along loops in the parameter plane. Utilizing the controllable rotation angle, gain and loss coefficients, we can control the structure, size and location of the loops in situ. We demonstrate that, under the joint action of topological structure of energy surfaces and nonadiabatic transitions, the chiral behavior emerges both along a loop encircling an EP and even along a straight path away from the EP. This work broadens the range of parameter space for the chiral state conversion, and proposes a useful platform to explore the interesting properties of exceptional points physics.

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“…All these efforts have been devoted to study time-independent non-Hermitian systems. Whereas the treatment for systems with time-dependent non-Hermitian Hamiltonians with time-independent or time-dependent an metric operators have been extensively studied [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60]. Nevertheless, the existence of invariants (constants of the motion or first integral) introduced by Lewis-Riesenfeld [61] is a factor of central importance in the study of time-dependent systems.…”

Section: Introductionmentioning

confidence: 99%

Pseudo-Invariant Approach for a Particle in a Complex Time-Dependent Linear Potential

Koussa

Maamache

2020

Int J Theor Phys

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The Lewis and Riesenfeld method has been investigated, by Ramos et al in Ref.[1], for quantum systems governed by time-dependent PT symmetric Hamiltonians and particularly where the quantum system is a particle submitted to action of a complex time-dependent linear potential. We discuss the method they used and propose an alternative one which leads to physically acceptable uncertainty product and to complex x and p expectation values but describe the classical motion. We used, for this situation, a linear pseudo hermitian invariant operator which allow us to solve analytically the time-dependent Schrödinger equation for this problem and to construct a Gaussian wave packet solution. The normalization condition for the invariant eigenfunctions with the Dirac delta function is correctly obtained, contrary to what is stated in Ref. [1].

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Piecewise adiabatic following: General analysis and exactly solvable models

Cited by 11 publications

References 34 publications

Chiral state conversion in a levitated micromechanical oscillator with in situ control of parameter loops

Chiral state conversion in a levitated micromechanical oscillator with in situ control of parameter loops

Chiral State Conversion in a Levitated Micromechanical Oscillator with In Situ Control of Parameter Loops*

Pseudo-Invariant Approach for a Particle in a Complex Time-Dependent Linear Potential

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