Chaos in the quantum Duffing oscillator in the semiclassical regime under parametrized dissipation

Maris, Andrew; Pokharel, Bibek; Seshachallam, Sharan Ganjam; Misplon, Moses; Pattanayak, Arjendu K.

doi:10.1103/physreve.104.024206

Cited by 2 publications

(1 citation statement)

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“…These assumptions do not lead to distinct equations. Concerning some important issues of contemporary interest, such as the classical quantum correspondence principle and quantum friction [37][38][39][40], the results coming from the present approach would not be distinct from those derived from the Schrödinger equation, the quantum Liouville equation and the Lindblad equation.…”

Section: Discussionmentioning

confidence: 70%

Classical stochastic approach to quantum mechanics and quantum thermodynamics

Oliveira

2024

J. Stat. Mech.

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We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component φ j of the wave vector is understood as a stochastic complex variable whose real and imaginary parts are proportional to the coordinate and momentum associated with a degree of freedom of the underlying classical system. From the classical stochastic equations of motion, we derive a general equation for the covariance matrix of the wave vector, which turns out to be of the Lindblad type. When the noise changes only the phase of φ j , the Schrödinger and the quantum Liouville equations are obtained. The component ψ j of the wave vector obeying the Schrödinger equation is related to the stochastic wave vector by | ψ j | 2 = ⟨ | ϕ j | 2 ⟩ .

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Section: Discussionmentioning

confidence: 70%