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Extracting Lyapunov exponents from the echo dynamics of Bose-Einstein condensates on a lattice
- Publication Year :
- 2017
- Publisher :
- arXiv, 2017.
-
Abstract
- We propose theoretically an experimentally realizable method to demonstrate the Lyapunov instability and to extract the value of the largest Lyapunov exponent for a chaotic many-particle interacting system. The proposal focuses specifically on a lattice of coupled Bose-Einstein condensates in the classical regime describable by the discrete Gross-Pitaevskii equation. We suggest to use imperfect time reversal of the system's dynamics known as the Loschmidt echo, which can be realized experimentally by reversing the sign of the Hamiltonian of the system. The routine involves tracking and then subtracting the noise of virtually any observable quantity before and after the time reversal. We support the theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent can indeed be extracted from the Loschmidt echo routine. We also discuss possible values of experimental parameters required for implementing this proposal.
- Subjects :
- Lyapunov function
Chaotic
FOS: Physical sciences
Lyapunov exponent
01 natural sciences
Instability
010305 fluids & plasmas
law.invention
symbols.namesake
law
Lattice (order)
0103 physical sciences
010306 general physics
Physics
Quantum Physics
Observable
Nonlinear Sciences - Chaotic Dynamics
Nonlinear Sciences::Chaotic Dynamics
Classical mechanics
Quantum Gases (cond-mat.quant-gas)
symbols
Chaotic Dynamics (nlin.CD)
Condensed Matter - Quantum Gases
Hamiltonian (quantum mechanics)
Quantum Physics (quant-ph)
Bose–Einstein condensate
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....a892d75ed967f14513f9341f3bc458fc
- Full Text :
- https://doi.org/10.48550/arxiv.1705.08176