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We study the non-equilibrium dissipative dynamics of the center of mass of a particle coupled to a field via its internal degrees of freedom. We model the internal and external degrees of freedom of the particle as quantum harmonic…
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different…
Coherent Ising Machine (CIM) is a network of optical parametric oscillators that can solve large-scale combinatorial optimisation problems by finding the ground state of an Ising Hamiltonian. As a practical application of CIM, Aonishi et…
The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
We show that the nonlinear stochastic dynamics of a measurement-feedback-based coherent Ising machine (MFB-CIM) in the presence of quantum noise can be exploited to sample degenerate ground and low-energy spin configurations of the Ising…
Assuming that a constant potential energy function has meaning for a dissipated harmonic oscillator, then an important issue is the time dependence of the turning points. Turning point studies demonstrate that the common model of external…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of non-interacting oscillators. We follow a non-perturbative approach, proposed earlier by us for the free Brownian particle. The…
Mechanical spectroscopy, i.e. cyclic deformations at varying frequencies, is used theoretically and numerically to measure dissipation in model glasses. From a normal mode analysis, we show that in the high-frequency THz regime where…
We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffective. We characterize the limiting behaviour in a different…
This paper focuses on a fundamental inquiry in a coupled oscillator model framework. It specifically addresses the direction of net information flow in mutually coupled non-identical chaotic oscillators. Adopting a specific form of…
Ising machines (IM) have recently been proposed as unconventional hardware-based computation accelerators for solving NP-hard problems. In this work, we present a model for a time-multiplexed IM based on the nonlinear oscillations in a…
We introduce a functional perturbative method for treating weakly nonlinear systems coupled with a quantum field bath. We demonstrate using this method to obtain the covariance matrix elements and the correlation functions of a quantum…
The ergodic properties of two uncoupled oscillators, a horizontal and vertical one, residing in a class of non rectangular star-shaped polygons with only vertical and horizontal boundaries and impacting elastically from its boundaries are…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation…
A scenario has recently been reported in which in order to stabilize complete synchronization of an oscillator network---a symmetric state---the symmetry of the system itself has to be broken by making the oscillators nonidentical. But how…
We investigate the geometric properties displayed by the magnetic patterns developing on a two-dimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout…
In this work, we present a method of generating a class of nonlinear ordinary differential equations (ODEs), representing the dynamics of appropriate nonlinear oscillators, that have the characteristics of either amplitude independent…