Diffusing up the Hill: Dynamics and Equipartition in Highly Unstable Systems

Šiler, Martin; Ornigotti, Luca; Brzobohatý, Oto; Jákl, Petr; Ryabov, Artem; Holubec, Viktor; Zemánek, Pavel; Filip, Radim

doi:10.1103/physrevlett.121.230601

Cited by 51 publications

(65 citation statements)

References 53 publications

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“…With increasing ω, the boundary shifts away from maximums ofP 1 andP a . Due to the trajectories trapped in the absorbing state [71,73], the maximum ofP a is slightly farther away from the absorbing boundary than the maximum ofP 1 , and thus, with increasing ω, the tail ofP a with small derivative (small j Da ) reaches the boundary at x = −R before the tail ofP 1 . Hence, for large enough barrier height with respect to the noise strength, the inequality between the rates turns over to κ B (∞) ≥ κ M (∞).…”

Section: Methodsmentioning

confidence: 99%

Brownian molecules formed by delayed harmonic interactions

2019

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A time-delayed response of individual living organisms to information exchange within flocks or swarms leads to the formation of complex collective behaviors. A recent experimental setup by Khadka et al., Nat. Commun. 9, 3864 (2018), employing synthetic microswimmers, allows to realize and study such behavior in a controlled way, in the lab. Motivated by these experiments, we study a system of N Brownian particles interacting via a retarded harmonic interaction. For N ≤ 3, we characterize its collective behavior analytically via linear stochastic delay-differential equations, and for N > 3 by Brownian dynamics simulations. The particles form nonequilibrium molecule-like structures which become unstable with increasing number of particles, delay time, and interaction strength. We evaluate the entropy fluxes in the system and develop an approximate time-dependent transition-state theory to characterize transitions between different isomers of the molecules. For completeness, we include a comprehensive discussion of the analytical solution procedure for systems of linear stochastic delay differential equations in finite dimension, and new results for covariance and time-correlation matrices.

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Section: Methodsmentioning

confidence: 99%

Brownian molecules formed by delayed harmonic interactions

2019

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“…These statistical quantities are calculated from an ensemble of 20 reconstructions, each having 10 6 measurement results per reconstructed quadrature. reach this regime [91][92][93] and have also demonstrated the capacity for applying nonlinear external potentials to a mechanical oscillator [58].…”

Section: Nonlinear Squeezingmentioning

confidence: 87%

“…The setting presented here is very general for opto-and electromechanics but we would like to emphasise the applicability of our scheme to levitated systems [91][92][93], given the large range of decoherence parameters over which the scheme is viable. As mentioned, levitated systems are able to employ nonlinear potentials for the dynamics of the levitated particle [58], thus enabling the preparation of nonlinear states, and have already approached the regimes in which the rethermalisation time threshold can be met. The major challenge for the future is to achieve QND couplings with the levitated system and incorporate nonlinear state preparation into a single setup.…”

Section: Discussionmentioning

confidence: 99%

Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator

2019

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Processing quantum information on continuous variables requires a highly nonlinear element in order to attain universality. Noise reduction in processing such quantum information involves the use of a nonlinear phase state as a non-Gaussian ancilla. A necessary condition for a nonlinear phase state to implement a nonlinear phase gate is that noise in a selected nonlinear quadrature should decrease below the level of classical states. A reduction of the variance in this nonlinear quadrature below the ground state of the ancilla, a type of nonlinear squeezing, is the resource embedded in these non-Gaussian states and a figure of merit for nonlinear quantum processes. Quantum optomechanics with levitating nanoparticles trapped in nonlinear optical potentials is a promising candidate to achieve such resources in a flexible way. We provide a scheme for reconstructing this figure of merit, which we call nonlinear squeezing, in standard linear quantum optomechanics, analysing the effects of mechanical decoherence processes on the reconstruction and show that all mechanical states which exhibit reduced noise in this nonlinear quadrature are nonclassical.

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“…Its characteristic feature is fast divergence of trajectories that have left a meta-stable state. The divergence restricts precision and duration of experiments [1,2], and limits applicability of the standard statistical analysis based on the averages, because the latter rapidly diverge with time [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Living on the edge of instability

Ryabov¹,

Holubec²,

Berestneva³

2019

J. Stat. Mech.

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Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave metastable regions of the potential landscape and never return. Using ideas from theory of Q-processes and quasi-stationary distributions, we analyze position statistics of nondiverging trajectories. We discuss two limit distributions which can be considered as (formal) generalizations of the Gibbs canonical distribution to highly unstable systems. Even though the associated effective potentials differ only slightly, properties of the two distributions are fundamentally different for all highly unstable system. The distribution for trajectories conditioned to diverge in an infinitely distant future is localized and light-tailed. The other distribution, describing trajectories surviving in the meta-stable region at the instant of conditioning, is heavy-tailed. The exponent of the corresponding power-law tail is determined by the leading divergent term of the unstable potential. We discuss different equivalent forms of the two distributions and derive properties of the effective statistical force arising in the ensemble of nondiverging trajectories after the Doob h-transform. The obtained explicit results generically apply to non-linear dynamical models with meta-stable states and fast kinetic transitions.

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Diffusing up the Hill: Dynamics and Equipartition in Highly Unstable Systems

Cited by 51 publications

References 53 publications

Brownian molecules formed by delayed harmonic interactions

Brownian molecules formed by delayed harmonic interactions

Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator

Living on the edge of instability

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