Arbitrary waveform generator biologically inspired

Vázquez-Medina, Rubén; Jiménez-Ramírez, Omar; Quiroz-Juárez, Mario A.; Aragón, J. L.

doi:10.1016/j.chaos.2013.03.006

Cited by 7 publications

(3 citation statements)

References 30 publications

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“…Although these types of networks are commonly used to perform linear operations, a large number of active components can also implement nonlinear operations, such as logarithms, antilogarithms, and products between variables. A drawback of nonlinear configurations is their high temperature dependence which can lead to functional problems [68]. A possible solution to implement nonlinear functions consists in employing integrated analog multipliers.…”

Section: Discussionmentioning

confidence: 99%

Experimental realization of the classical Dicke model

Quiroz-Juárez

Chávez-Carlos

Aragón

et al. 2020

Phys. Rev. Research

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We report the experimental implementation of the classical description of the Dicke model whose quantum version describes a large number of two-level atoms interacting with a single-mode electromagnetic field in a perfectly reflecting cavity. This is performed by employing two nonlinearly coupled active, synthetic LC circuits, implemented by means of analog electrical components. The simplicity and versatility of our platform allows us not only to experimentally explore the coexistence of regular and chaotic trajectories in the classical Dicke model, but also to directly observe the so-called ground-state and excited-state "quantum" phase transitions. In this analysis, the trajectories in phase space, Lyapunov exponents, and the finite-time Lyapunov exponent are used to identify the different operating regimes of our electronic device. Moreover, with this technology, we measure the classic analog of the fidelity-out-of-time-order-correlator (FOTOC). Exhaustive numerical simulations are performed to show the quantitative and qualitative agreement between theory and experiment.

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Section: Discussionmentioning

confidence: 99%

Experimental realization of the classical Dicke model

Quiroz-Juárez

Chávez-Carlos

Aragón

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…Although these type of networks are commonly used to perform linear operations, a large number of active components can also implement nonlinear operations, such as logarithms, antilogarithms and products between variables. A drawback of nonlinear configurations is their high temperature-dependence which can lead to functional problems [64]. A possible solution to implement nonlinear function consists of employing integrated analog multipliers.…”

Section: Discussionmentioning

confidence: 99%

Experimental realization of the classical Dicke model

Quiroz-Juárez,

Chávez-Carlos,

Aragón

et al. 2020

Preprint

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We report the experimental implementation of the Dicke model in the semiclassical approximation, which describes a large number of two-level atoms interacting with a single-mode electromagnetic field in a perfectly reflecting cavity. This is managed by making use of two non-linearly coupled active, synthetic LC circuits, implemented by means of analog electrical components. The simplicity and versatility of our platform allows us not only to experimentally explore the coexistence of regular and chaotic trajectories in the Dicke model but also to directly observe the so-called ground-state and excited-state "quantum" phase transitions. In this analysis, the trajectories in phase space, Lyapunov exponents and the recently introduced Out-of-Time-Order-Correlator (OTOC) are used to identify the different operating regimes of our electronic device. Exhaustive numerical simulations are performed to show the quantitative and qualitative agreement between theory and experiment.

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“…This has enabled the implementation of experimental systems that offer certain advantages over the original physical systems [13][14][15][16][17] . Especially, analog computers are suited to simulate dynamical systems [18][19][20][21][22][23] , and even, stochastic dynamical systems 24,25 . A potential advantage of analog computers is the simulation of continuous physical quantities by performing real-time simultaneous operations.…”

Section: Chaotic and Periodic Regimesmentioning

confidence: 99%

Classical harmonic three-body system: an experimental electronic realization

Escobar-Ruiz

Quiroz-Juárez

Río-Correa

et al. 2022

Sci Rep

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The classical three-body harmonic system in $${\mathbb {R}}^d$$ R d ($$d>1$$ d > 1 ) with finite rest lengths and zero total angular momentum $$L=0$$ L = 0 is considered. This model describes the dynamics of the $$L=0$$ L = 0 near-equilibrium configurations of three point masses $$(m_1,m_2,m_3)$$ ( m 1 , m 2 , m 3 ) with arbitrary pairwise potential $$V(r_{ij})$$ V ( r ij ) that solely depends on the relative distances between bodies. It exhibits an interesting mixed regular and chaotic dynamics as a function of the energy and the system parameters. The corresponding harmonic quantum system plays a fundamental role in atomic and molecular physics. In this work we report on a novel electronic experimental realization of the model as a complementary tool to analyze the rich dynamics of the classical system. Our setup allows us to experimentally explore different regions of behavior due to the fact that the intrinsic parameters and initial states of the system are independently set by voltage inputs. Chaotic and periodic motions are characterized employing time series, phase planes, and the largest Lyapunov exponents as a function of the energy and system parameters. The results show an excellent qualitative as well as quantitative agreement between theory and experiment.

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Arbitrary waveform generator biologically inspired

Cited by 7 publications

References 30 publications

Experimental realization of the classical Dicke model

Experimental realization of the classical Dicke model

Experimental realization of the classical Dicke model

Classical harmonic three-body system: an experimental electronic realization

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