Turing instability in quantum activator–inhibitor systems

Kato, Yuzuru; Nakao, Hiroya

doi:10.1038/s41598-022-19010-0

Cited by 9 publications

(5 citation statements)

References 97 publications

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“…The idea had been noted early on in quantum optics [114,115]. Its use is now prevalent in physics (often without reference to P-bifurcations), such as in defining limit cycles near a Hopf bifurcation [61,62], relaxation oscillations [116], amplitude and oscillation death [117][118][119][120], and Turing instabilities [121].…”

Section: Preliminaries and The T = 0 Casementioning

confidence: 99%

Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

Chia,

Mok,

Noh

et al. 2023

SciPost Phys.

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It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise-an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system without a classical limit. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When multiplicative environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle also exhibits other genuinely nonclassical traits, such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise.

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Section: Preliminaries and The T = 0 Casementioning

confidence: 99%

Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

Chia,

Mok,

Noh

et al. 2023

SciPost Phys.

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“…The same explanation applies to S 2 and T 2 . Using Equations ( 16), (19), and (20) and the definitions of N mn given by Equation ( 16), we obtain…”

Section: Nonlinearity Effect On the Growth In Amplitudementioning

confidence: 99%

“…Existing studies on diffusion-induced instability have focused primarily on soft matter, including biological [7][8][9][10][11] and chemical [7,[12][13][14][15] systems, in which the typical periodicity in length ranges from cm to mm or slightly less. Conversely, Turing patterns that emerge in "hard" matter show far smaller length scales [16][17][18][19]. A well-known example of such Turing patterns in hard matter is the dislocation patterning that occurs inside plastically deformed metal [20,21].…”

Section: Introductionmentioning

confidence: 99%

Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue

2023

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Spontaneous pattern formation by a large number of dislocations is commonly observed during the initial stages of metal fatigue under cyclic straining. It was experimentally found that the geometry of the dislocation pattern undergoes a crossover from a 2D spot-scattered pattern to a 1D ladder-shaped pattern as the amplitude of external shear strain increases. However, the physical mechanism that causes the crossover between different dislocation patterns remains unclear. In this study, we theorized a bifurcation diagram that explains the crossover between the two dislocation patterns. The proposed theory is based on a weakly nonlinear stability analysis that considers the mutual interaction of dislocations as a nonlinearity. It was found that the selection rule among the two dislocation patterns, “spotted” and “ladder-shaped”, can be described by inequalities with respect to nonlinearity parameters contained in the governing equations.

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“…Consequently, SEM technique is more optimal for the analysis of cooperatively driven ferroelectric fibers then AFM. It is quite obvious that oscillations observed in such systems are oscillations in distributed systems, and the corresponding models of the dynamics of reaction-diffusion processes in such systems should be interpreted as the models of 3D (4D) processes in distributed systems with spatiotemporal reactions under the electron beam, which is a control agent for the wave or pulse propagation with different charges and polarities (as Turing activators and inhibitors in the classical approaches [110][111][112][113][114][115][116][117][118][119][120][121] ).…”

Section: Article Infomentioning

confidence: 99%

Reaction-diffusion effects and spatiotemporal oscillations under SEM, STM and AFM-assisted charging in fiber-like and wire-like systems: From molecular and quantum wires to cooperative ferroelectric nanofibers and microfibers

Adamovich,

Buryanskaya,

Gradova

et al. 2023

Mater. Tech. Rep.

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This review addresses the problem of reaction-diffusion effects and spatiotemporal oscillations in fiber-like and wire-like systems under the electron beam in SEM and in the presence of electric field in some special AFM techniques, such as current sensing atomic force microscopy (CS-AFM)/conductive atomic force microscopy (C-AFM), electrostatic force microscopy (EFM) and Kelvin probe force microscopy (KPFM) also known as surface potential microscopy. Some similar reaction-diffusion effects also can be observed in scanning capacitance microscopy (SCM), scanning gate microscopy (SGM), scanning voltage microscopy (SVM) and piezoresponse force microscopy (PFM). At the end of this paper the authors provide analysis of their own results and approaches. In particular, the possibility of achieving the ion transfer controlled growth of cells along the ion concentration gradients in reaction-diffusion fibers and actuators is indicated. This fundamental idea is discussed within the framework of the implantable fiber “bioiontronics” and “neuroiontronics” controlled by acoustic and electrical signals that regulate the reaction-diffusion or chemical oscillation activity of such fiber structures as reaction-diffusion actuators and sensors. The literature review includes more than 130 references.

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Turing instability in quantum activator–inhibitor systems

Cited by 9 publications

References 97 publications

Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue

Reaction-diffusion effects and spatiotemporal oscillations under SEM, STM and AFM-assisted charging in fiber-like and wire-like systems: From molecular and quantum wires to cooperative ferroelectric nanofibers and microfibers

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