Chaotic Instantons and Exponential Widening of the Ground Quasienergy Doublet in Kicked Double Well Potential

Kuvshinov, V. A.; Kuzmin, A. V.; Piatrou, V. A.

doi:10.1007/978-90-481-3120-4_18

Cited by 1 publication

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References 14 publications

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“…In Fig. (13) and Fig. ( 14), we find exponential growth of OTOCs around the hilltop of the potential for σ = 0.15 and 10, respectively as verified previously.…”

Section: Model(ii)supporting

confidence: 88%

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Groundwater Quality Assessment for Drinking and Industrial Purpose of Rourkela, Sundergarh District, Odisha, India

Das

Goswami

2016

AJW

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In classical mechanics, spontaneous symmetry breaking of the Hamiltonian can embroil the dynamics of some regular systems into chaos. The classical and quantum pictures are not entirely different in these broken symmetric regions. There exists a correspondence between them, but for a brief time window. However, our numerical observations show that quantum mechanics can emulate the opposite role and forge exponential fluctuations in classically non-chaotic systems within an early-time window by introducing a symmetry-breaking term to the Hamiltonian. In this work, we have taken four one-dimensional quantum mechanical models: two Inverted Harmonic Oscillators(IHOs), a triple Well and IHO with a plateau. Then we spontaneously break the already existing symmetry in their Hamiltonian with varying perturbation strength to bring anomaly into the system. Then, we use numerical diagnostic tools such as OTOC, Loschmidt echo and spectral form factor(SFF) to detect the anomalies that may sweep into the system with the introduction of the asymmetry. Our primary focus is on the behaviour of OTOC as it reduces to the Lyapunov exponent in the classical limit, and we observe exponential growth, as expected. However, these exponential growths of OTOC are not widespread over the entire potential well but are limited only to the eigenstates in the neighbourhood of the broken symmetry. These results suggest that the exponential growth of OTOC, backed by Loschmidt echo and SFF, is due to asymmetry. In other words, OTOC detects the effect of symmetry-breaking, which is often synonymous with the butterfly effect.

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“…In Fig. (13) and Fig. ( 14), we find exponential growth of OTOCs around the hilltop of the potential for σ = 0.15 and 10, respectively as verified previously.…”

Section: Model(ii)supporting

confidence: 88%

“…splitting between levels remains close to σ for all doublets lying below the barrier top. The initial inspiration for devising the model is taken from [13][14][15][16].…”

Section: Odel(i)mentioning

confidence: 99%

Groundwater Quality Assessment for Drinking and Industrial Purpose of Rourkela, Sundergarh District, Odisha, India

Das

Goswami

2016

AJW

View full text Add to dashboard Cite

show abstract

Chaotic Instantons and Exponential Widening of the Ground Quasienergy Doublet in Kicked Double Well Potential

Cited by 1 publication

References 14 publications

Groundwater Quality Assessment for Drinking and Industrial Purpose of Rourkela, Sundergarh District, Odisha, India

Groundwater Quality Assessment for Drinking and Industrial Purpose of Rourkela, Sundergarh District, Odisha, India

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