Recurrence network analysis in a model tripartite quantum system

Laha, Pradip; Lakshmibala, S.; Balakrishnan, V.

doi:10.1209/0295-5075/125/60005

Cited by 7 publications

(9 citation statements)

References 42 publications

(56 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For any given value of |α| 2 , there is a unique special value κ with the properties described in the foregoing. For instance, when |α| 2 = 30, we find that κ = 0.0024 [20]. As before, the MLE has a minimum at κ (the blue curve in Fig.…”

Section: Time-series Analysis and Network Propertiessupporting

confidence: 68%

“…1 of Ref. [20]). The corresponding photon annihilation and creation operators are a i and a † i , (i = 1, 2).…”

Section: The Tripartite Modelmentioning

confidence: 88%

“…For ready reference, it is helpful to start with a quick summary of the pertinent features of the system at hand that have been established in earlier work [18,20]. The observable we focus on is the mean photon number of either field.…”

Section: Bifurcation Cascade and Network Analysismentioning

confidence: 99%

“…For different values of κ, -recurrence networks have been constructed [20] from the corresponding time series of N 1 , setting |α| 2 = 25 and χ/λ = 5. In each case, standard network measures such as the average path length, the link density, the clustering coefficients, the transitivity, the assortativity and the degree distributions have been examined.…”

Section: Bifurcation Cascade and Network Analysismentioning

confidence: 99%

“…Recently [20], an -recurrence network has been constructed for the time series of N i (t) . It has been shown that the signatures of the bifurcation cascade are also captured in the manner in which the clustering coefficient and the transitivity of the network vary with κ.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bifurcations, time-series analysis of observables, and network properties in a tripartite quantum system

Laha,

Lakshmibala,

Balakrishnan

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We consider a tripartite quantum system comprising a Λ-atom interacting with two radiation fields in the presence of field nonlinearities and an intensity-dependent field-atom coupling. In earlier work, a bifurcation cascade was shown to occur in the short-time dynamics of the mean photon number Ni(t) (i = 1, 2) corresponding to either field. A special value κ of the intensity parameter κ was identified, that separates collapse to a constant value and oscillatory behavior of Ni(t) as well as the entanglement of the atomic subsystem. In this paper, we carry out a detailed time-series analysis and establish an interesting correlation in the behavior of both the short-time and long-time dynamics of Ni(t) . In particular, we study the manner in which the Lyapunov exponents, return maps, recurrence plots and recurrence statistics vary with κ. The variation of the maximum Lyapunov exponent with κ exhibits a minimum at κ. The return maps, recurrence plots and first-return-time distributions also carry signatures of this special value, as do the clustering coefficient and the transitivity of networks constructed from the time series. These signatures are present independent of the manner in which the networks are constructed from the time series. The novelty in our results lies in the unanticipated correlation between a special feature of the bifurcation cascade in the short-time dynamics of the system, on the one hand, and network behavior and diverse system properties deduced through the time-series analysis, on the other. Our work also brings out the usefulness of applying techniques from nonlinear dynamics to analyze the behavior of expectation values of observables in multipartite quantum mechanical systems.

show abstract

Section: Time-series Analysis and Network Propertiessupporting

confidence: 68%

“…1 of Ref. [20]). The corresponding photon annihilation and creation operators are a i and a † i , (i = 1, 2).…”

Section: The Tripartite Modelmentioning

confidence: 88%

Section: Bifurcation Cascade and Network Analysismentioning

confidence: 99%

Section: Bifurcation Cascade and Network Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%