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Correspondence between Berry's Phase and Lewis's Phase

Tong Yong, Pla Uni

The existence of a special invariant for some time-dependent Hamiltonians is displayed and the Lewiss phase related to such an invariant becoming Berrys phase in the adiabatic limit is observed and the correspondence between Berrys phase and Lewiss phase is revealed in this paper.

Journal of PLA University of Science and TechnologyJan 1, 20010 citations

Connection between the Berry phase and the Lewis phase

J. Y. Zeng, Yian Lei

Physics Letters AJun 1, 19963 citations

Lewis and berry phases for a gravitational wave interacting with a quantum harmonic oscillator

Soham Sen, Manjari Dutta, Sunandan Gangopadhyay

Abstract In this work, we compute the Lewis and Berry phases for a gravitational wave interacting with a two dimensional quantum harmonic oscillator in the transverse-traceless gauge. We have considered a gravitational wave consisting of the plus polarization term only. Considering the cross polarization term to be absent makes the Hamiltonian separable in terms of the first and the second spatial coordinates. We then compute the Lewis phase by assuming a suitable form of the Lewis invariant considering only quadratic order contributions from both position and momentum variables. Next, we obtain two Lewis invariants corresponding to each separable part of the full Hamiltonian of the system. Using both Lewis invariants, one can obtain two Ermakov-Pinney equations, from which we finally obtain the corresponding Lewis phase. Then making an adiabatic approximation enables us to isolate the Berry phase for the full system. After this we obtain some explicit expressions of the Berry phase for a plane polarized gravitational wave with different choices of the harmonic oscillator frequency. Finally, we consider a gravitational wave with cross polarization only interacting with an isotropic two dimensional harmonic oscillator. For this we obtain the Lewis phase and the total Berry phase of the system, which is found to be dependent upon the cross polarization part of the gravitational wave.Abstract In this work, we compute the Lewis and Berry phases for a gravitational wave interacting with a two dimensional quantum harmonic oscillator in the transverse-traceless gauge. We have considered a gravitational wave consisting of the plus polarization term only. Considering the cross polarization term to be absent makes the Hamiltonian separable in terms of the first and the second spatial coordinates. We then compute the Lewis phase by assuming a suitable form of the Lewis invariant considering only quadratic order contributions from both position and momentum variables. Next, we obtain two Lewis invariants corresponding to each separable part of the full Hamiltonian of the system. Using both Lewis invariants, one can obtain two Ermakov-Pinney equations, from which we finally obtain the corresponding Lewis phase. Then making an adiabatic approximation enables us to isolate the Berry phase for the full system. After this we obtain some explicit expressions of the Berry phase for a plane polarized gravitational wave with different choices of the harmonic oscillator frequency. Finally, we consider a gravitational wave with cross polarization only interacting with an isotropic two dimensional harmonic oscillator. For this we obtain the Lewis phase and the total Berry phase of the system, which is found to be dependent upon the cross polarization part of the gravitational wave.

arXiv:2307.00901Physica ScriptaDec 4, 20234 citations

Berry phase in quantum mechanics

Yuriy Mokrousov

Jan 1, 20170 citations

Berry-Hannay relation in nonlinear optomechanics

Ludovico Latmiral, Federico Armata

We address the quantum-classical comparison of phase measurements in optomechanics in the general framework of Berry phases for composite systems. While the relation between Berry phase and Hannay angle has been proven for a large set of quadratic Hamiltonians, such correspondence has not been shown so far in the case of non-linear interactions (e.g. when three or more operators are involved). Remarkably, considering the full optomechanical interaction we recover the aforementioned mathematical relation with the Hannay angle obtained from classical equations of motion. Our results link at a fundamental level previous proposals to measure decoherence, such as the one expressed by Marshall et al., with the no-go theorem shown by Armata et al., which provides boundaries to understand the quantum-to-classical transition in optomechanics.We address the quantum-classical comparison of phase measurements in optomechanics in the general framework of Berry phases for composite systems. While the relation between Berry phase and Hannay angle has been proven for a large set of quadratic Hamiltonians, such correspondence has not been shown so far in the case of non-linear interactions (e.g. when three or more operators are involved). Remarkably, considering the full optomechanical interaction we recover the aforementioned mathematical relation with the Hannay angle obtained from classical equations of motion. Our results link at a fundamental level previous proposals to measure decoherence, such as the one expressed by Marshall et al., with the no-go theorem shown by Armata et al., which provides boundaries to understand the quantum-to-classical transition in optomechanics.

Scientific ReportsFeb 10, 20204 citations

A note on the diagonalization of quadratic boson and fermion hamiltonians

J. Leo van Hemmen

Zeitschrift für Physik B Condensed MatterSep 1, 198042 citations

Correspondence between Berry's phase and Lewis's phase for quadratic Hamiltonians

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Correspondence between Berry's phase and Lewis's phase for quadratic Hamiltonians

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