Showing papers by "Hiroya Nakao published in 2019"
TL;DR: In this paper, a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators is developed, where the dynamics of quantum dissipative systems exhibiting limitcycle oscillations are reduced to a simple, one-dimensional classical stochastic differential equation.
Abstract: We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a simple, one-dimensional classical stochastic differential equation approximately describing the phase dynamics of the system under the semiclassical approximation. The density matrix and power spectrum of the original quantum system can be approximately reconstructed from the reduced phase equation. The developed framework enables us to analyze synchronization dynamics of quantum limit-cycle oscillators using the standard methods for classical limit-cycle oscillators in a quantitative way. As an example, we analyze synchronization of a quantum van der Pol oscillator under harmonic driving and squeezing, including the case that the squeezing is strong and the oscillation is asymmetric. The developed framework provides insights into the relation between quantum and classical synchronization and will facilitate systematic analysis and control of quantum nonlinear oscillators.
26 citations
TL;DR: In this paper, an overview is given on two representative methods of dynamical reduction known as centre-manifold reduction and phase reduction, which are presented in a somewhat more unified fashion.
Abstract: An overview is given on two representative methods of dynamical reduction known as centre-manifold reduction and phase reduction. These theories are presented in a somewhat more unified fashion tha...
25 citations
08 Oct 2019
TL;DR: In this article, a theoretical framework to describe the dynamics of quantum linear oscillators in the semiclassical regime is proposed, which is a step towards a more systematic and detailed analysis and control of synchronization in these systems.
Abstract: This paper proposes a theoretical framework to describe the dynamics of quantum linear oscillators in the semiclassical regime. This is a step towards a more systematic and detailed analysis and control of synchronization in these systems
24 citations
TL;DR: An overview is given on two representative methods of dynamical reduction known as centre-manifold reduction and phase reduction, and a new formulation of perturbative expansion is presented for discrete populations of oscillators.
Abstract: An overview is given on two representative methods of dynamical reduction known as center-manifold reduction and phase reduction. These theories are presented in a somewhat more unified fashion than the theories in the past. The target systems of reduction are coupled limit-cycle oscillators. Particular emphasis is placed on the remarkable structural similarity existing between these theories. While the two basic principles, i.e. (i) reduction of dynamical degrees of freedom and (ii) transformation of reduced evolution equation to a canonical form, are shared commonly by reduction methods in general, it is shown how these principles are incorporated into the above two reduction theories in a coherent manner. Regarding the phase reduction, a new formulation of perturbative expansion is presented for discrete populations of oscillators. The style of description is intended to be so informal that one may digest, without being bothered with technicalities, what has been done after all under the word reduction.
16 citations
TL;DR: Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase-reduction theory and considers optimization of mutual coupling signals to maximize the linear stability of the synchronized state.
Abstract: Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase-reduction theory. By generalizing our previous study [S. Shirasaka, N. Watanabe, Y. Kawamura, and H. Nakao, Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling, Phys. Rev. E 96, 012223 (2017)2470-004510.1103/PhysRevE.96.012223] on the optimization of cross-diffusion coupling matrices between the oscillators, we consider optimization of mutual coupling signals to maximize the linear stability of the synchronized state, which are functionals of the past time sequences of the oscillator states. For the case of linear coupling, optimization of the delay time and linear filtering of coupling signals are considered. For the case of nonlinear coupling, general drive-response coupling is considered and the optimal response and driving functions are derived. The theoretical results are illustrated by numerical simulations.
12 citations
TL;DR: In this paper, the suppression of macroscopic synchronized oscillations in mixed populations of active and inactive oscillators with local diffusive coupling, described by a lattice complex Ginzburg-Landa.
Abstract: We consider suppression of macroscopic synchronized oscillations in mixed populations of active and inactive oscillators with local diffusive coupling, described by a lattice complex Ginzburg–Landa...
3 citations
01 Dec 2019
TL;DR: It is argued that the optimization of waveforms provides better performance when the phase sensitivity function of the limit cycle has stronger high-harmonic components.
Abstract: We consider entrainment of a quantum nonlinear dissipative oscillator to a periodically modulated harmonic driving in the semiclassical regime. We derive the optimal waveform of the periodic amplitude modulation by extending a classical optimization scheme to the semiclassical phase equation approximately describing the quantum oscillatory dynamics. Specifically, we consider optimization of the waveform for fast entrainment of quantum nonlinear oscillators and show that the optimal waveform yields faster entrainment to the driving signal than the simple sinusoidal waveform. We argue that the optimization of waveforms provides better performance when the phase sensitivity function of the limit cycle has stronger high-harmonic components. The theoretical results are verified by using the quantum van der Pol model, which is a typical model of the quantum nonlinear dissipative oscillator.
TL;DR: In this article, a coupled-oscillator model of the cochlea with feed-forward coupling was used to study the effect of suppressor signals on the response to probe signals.
Abstract: Mechanism of two-tone suppression is studied using a coupled-oscillator model of the cochlea with feed-forward coupling. Local amplification of sound signals is modeled by using Stuart-Landau oscillators near the Hopf bifurcation, and transmission of sound signals is described as feed-forward coupling between the oscillators. Effect of suppressor signals on the response to probe signals is analyzed by numerical simulations. It is found that the effect of suppression is qualitatively different depending on relative frequency between probe and suppressor signals. By analyzing a simplified two-oscillator model, we explain the mechanism of the suppression, where configuration of the oscillators plays an essential role.