Related papers: A perturbative approach for the crystal chains wit…
We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to $N$ dissipative baths by using a new approach to large-deviation theory inspired by phase-space quantum optics.…
We study energy transport in a chain of quantum harmonic and anharmonic oscillators where the anharmonicity is induced by interaction between local vibrational states of the chain. Using adiabatic elimination and numerical simulations with…
We study feedback control of coupled nonlinear stochastic oscillators in a force field. We first consider the problem of asymptotically driving the system to a desired {\em steady state} corresponding to reduced thermal noise. Among the…
In this work we consider a new class of oscillatory instabilities that pertain to thermocapillary destabilization of a liquid film heated by a solid substrate. We assume the substrate thickness and substrate-film thermal conductivity ratio…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…
Crystals and glasses exhibit fundamentally different heat conduction mechanisms: the periodicity of crystals allows for the excitation of propagating vibrational waves that carry heat, as first discussed by Peierls; in glasses, the lack of…
We study the problem of a potential interaction of a finite-dimensional Lagrangian system (an oscillator) with a linear infinite-dimensional one (a thermostat). In spite of the energy preservation and the Lagrangian (Hamiltonian) nature of…
We study the stationary state of a chain of harmonic oscillators driven by two active reservoirs at the two ends. These reservoirs exert correlated stochastic forces on the boundary oscillators which eventually leads to a nonequilibrium…
We develop an approach based on stochastic quantum trajectories for an incoherently pumped system of interacting bosons relaxing their energy in a thermal reservoir. Our approach enables the study of the versatile coherence properties of…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
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…
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…
We study the behavior of a subsystem (harmonic oscillator) in contact with a thermal reservoir (finite set of uncoupled harmonic oscillators). We exactly solve the eigenvalue problem and obtain the temporal evolution of the dynamical…
We study prethermal time-crystalline order in periodically driven quantum Ising models on disorder-free decorated lattices. Using a tensor network ansatz for the state which reflects the geometry of a unit cell of the lattice, we show…
We study the transport of heat along a chain of particles interacting through a harmonic potential and subject to heat reservoirs at its ends. Each particle has two degrees of freedom and is subject to a stochastic noise that produces…
We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of…
We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asympotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved…
Cooperative effects in oscillator networks are often associated with enhanced stability of phase-locked solutions, which increases with system size. We show that the stabilization of persistent currents in annular atomic superfluids with…
Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…