Related papers: Markovian evolution of strongly coupled harmonic o…
We discuss Hamiltonian model of oscillator lattice with local coupling. Model describes spatial modes of nonlinear Schr\"{o}dinger equation with periodic tilted potential. The Hamiltonian system manifests reversibility of Topaj - Pikovsky…
Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum…
The standard weak-coupling approximations associated to open quantum systems have been extensively used in the description of a two-level quantum system, qubit, subjected to relatively weak dissipation compared with the qubit frequency.…
We consider the quantum dynamics of a pair of coupled quantum oscillators coupled to a common correlated dissipative environment. The resulting equations of motion for both the operator moments and covariances can be integrated analytically…
We employ the Lindblad master equation method to study the nonequilibrium dynamics following a parametric quench in the Hamiltonian of an open, two-dimensional superconducting system coupled to an external bath. Within our approach we show…
Models of coupled oscillators are useful in describing a wide variety of phenomena in physics, biology and economics. These models typically rest on the premise that the oscillators are weakly coupled, meaning that amplitudes can be assumed…
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…
Recently, an effective Lindblad master equation for quantum systems whose dynamics are coupled to dissipative bosonic modes has been introduced [Phys. Rev. Lett. 129, 063601 (2022)]. In this approach, the bosonic modes are adiabatically…
The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally-local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the…
We consider a harmonic oscillator under periodic driving and coupled to two harmonic-oscillator heat baths at different temperatures. We use the thermofield transformation with chain mapping for this setup, which allows us to study the…
We derive and solve analytically the non-Markovian master equation for harmonic quantum Brownian motion proving that, for weak system-reservoir couplings and high temperatures, it can be recast in the form of the master equation for a…
The stationary multipartite entanglement between three interacting harmonic oscillators subjected to decoherence is analyzed in the largely unexplored non-equilibrium strong dissipation regime. We compute the exact asymptotic Gaussian state…
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…
There is presently considerable interest in accurately simulating the evolution of open systems for which Markovian master equations fail. Examples are systems that are time-dependent and/or strongly damped. A number of elegant methods have…
Spin chains with open boundaries, such as the transverse field Ising model, can display coherence times for edge spins that diverge with the system size as a consequence of almost conserved operators, the so-called strong zero modes. Here,…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a…
For adiabatically and periodically manipulated dissipative quantum systems we derive, using Floquet theory, a simple Markovian master equation. Contrary to some previous works we explicitly take into account the time dependence of the…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…
We derive a semiclassical approximation for the evolution generated by the Lindblad equation as a generalization of complex WKB theory. Linear coupling to the environment is assumed, but the Hamiltonian can be a general function of…