Related papers: Quantum limit-cycles and the Rayleigh and van der …
Advances in controlling and measuring systems of ultra-cold atoms provided strong motivation to theoretical investigations of quantum dynamics in closed many-body systems. Fundamental questions on quantum dynamics and statistical mechanics…
Stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear…
I present a quantum-tunnelling oscillator model as a universal dynamical engine for two paradigmatic problems in quantum cognition theory -- optical illusion perception and group decision making -- where individuals are treated as…
We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In…
Self-oscillation is a phenomenon studied across many scientific disciplines, including the engineering of efficient heat engines and electric generators. We investigate the single electron shuttle, a model nano-scale system that exhibits a…
Open quantum systems with nearly degenerate energy levels have been shown to exhibit long-lived metastable states in the approach to equilibrium, even when modelled with certain Lindblad-form quantum master equations. This is a result of…
In this paper, we investigate the quantum dynamics of underlying two one-dimensional quadratic Li'enard type nonlinear oscillators which are classified under the category of maximal (eight parameter) Lie point symmetry group (J. Math.…
A model of an electrical point contact coupled to a mechanical system (oscillator) is studied to simulate the dephasing effect of measurement on a quantum system. The problem is solved at zero temperature under conditions of strong…
The classical and quantum dynamics of the noncanonically coupled oscillators is considered. It is shown that though the classical dynamics is well--defined for both harmonic and anharmonic oscillators, the quantum one is well--defined in…
Synchronization is a major concept in nonlinear physics. In a large number of systems, it is observed at long times for a sinusoidal excitation. In this paper, we design a transiently non-sinusoidal driving to reach the synchronization…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
The equation of the Van der Pol oscillator, being characterized by a dissipative term, is non-Lagrangian. Appending an additional degree of freedom we bring the equation in the frame of action principle and thus introduce a one-way coupled…
We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…
We construct the classical dynamical system which has a quantum-like behavior. We have shown that the energy-time uncertainty relation takes place for the system and it has purely classical nature. We investigate the behavior of the system…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
Since years a classical oscillator is known representing fundamental properties of quantum mechanical systems without the use of the demanding mathematics of quantum theory. This allows to develop an intuitive notion in introductory quantum…
The aim of this tutorial is to analyze the equilibrium properties of some simple but widely used quantum systems. The canonical ensemble is used to evaluate the required properties here.
Driven-dissipative quantum many-body systems have been the subject of many studies in recent years. They possess unique, novel classes of dissipation-stabilized quantum many-body phases including the limit cycle. For a long time it has been…
A pure quantum state of large number N of oscillators, interacting via harmonic coupling, evolves such that any small subsystem n<<N of the global state approaches equilibrium. This provides a novel example where equilibration emerges as a…
We study the energy flow between a one dimensional oscillator and a chaotic system with two degrees of freedom in the weak coupling limit. The oscillator's observables are averaged over an initially microcanonical ensemble of trajectories…