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The $q$-state Potts model is a fundamental model in statistical physics that generalizes the Ising model and plays a key role in the study of phase transitions, critical phenomena, complex systems, and combinatorial optimization. Sampling…
We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the…
This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's…
The dynamical response of an Ising ferromagnet to a plane polarised standing magnetic field wave is modelled and studied here by Monte Carlo simulation in two dimensions. The amplitude of standing magnetic wave is modulated along the…
We study the stability of filaments in equilibrium between gravity and internal as well as external pressure using the grid based AMR-code RAMSES. A homogeneous, straight cylinder below a critical line mass is marginally stable. However, if…
For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the…
Recently, the coherent Ising machine (CIM) as a degenerate optical parametric oscillator (DOPO) network has been researched to solve Ising combinatorial optimization problems. We formulate a theoretical model for the CIM with discrete-time…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
The operator fidelity is a measure of the information-theoretic distinguishability between perturbed and unperturbed evolutions. The response of this measure to the perturbation may be formulated in terms of the operator fidelity…
Industrial coating processes create thin liquid films with tight thickness tolerances, and thus models that predict the response to inevitable disturbances are essential. The mathematical modeling complexities are reduced through…
We introduce an extension to the standard reduction of oscillatory systems to a single phase variable. The standard reduction is often insufficient, particularly when the oscillations have variable amplitude and the magnitude of each…
The paper surveys recent progresses in understanding the dynamics and loss landscape of the gradient flow equations associated to deep linear neural networks, i.e., the gradient descent training dynamics (in the limit when the step size…
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
The in-in formalism and its influence functional generalization are widely used to describe the out-of-equilibrium dynamics of unitary and open quantum systems, respectively. In this paper, we build on these techniques to develop an…
The motions of a passive scalar $\hat{a}$ in a general high-frequency oscillating flow are studied. Our aim is threefold: (i) to obtain different classes of general solutions; (ii) to identify, classify, and develop related asymptotic…
The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example,…
We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the fast variables and have a computational cost determined by…
Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational…
The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between…
We study large networks of parametric oscillators as heuristic solvers of random Ising models. In these networks, known as coherent Ising machines, the model to be solved is encoded in the coupling between the oscillators, and a solution is…