Related papers: Exact time evolution and master equations for the …
The dynamics of a wide range of technologically important quantum systems are dominated by their interaction with just a few environmental modes. Such highly structured environments give rise to long-lived bath correlations that induce…
We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems, based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null…
We introduce a new model of the logarithmic type of wave-like equation with a nonlocal logarithmic damping mechanism, which is rather weakly effective as compared with frequently studied fractional damping cases. We consider the Cauchy…
We point out that the quantum dynamical map of an open quantum system can be generated by an effective Liouville operator. The effective Liouville shows the dynamical breaking of time reversibility. This breaking of reversibility is…
Using a matched filter technique, we derive the minimum variance, unbiased estimator for the equilibrium displacement of a damped harmonic oscillator in thermal equilibrium when interactions with the thermal bath are the leading source of…
We consider a quantum linear oscillator coupled to a bath in equilibrium at an arbitrary temperature and then exposed to an external field arbitrary in form and strength. We then derive the reduced density operator in closed form of the…
Describing open quantum systems far from equilibrium is challenging, in particular when the environment is mesoscopic, when it develops nonequilibrium features during the evolution, or when the memory effects cannot be disregarded. Here, we…
The purpose of this paper is to further exemplify an approach to evolutionary problems originally developed in earlier works for a special case and later extended to more general evolutionary problems. We are here concerned with the $(1+1)$…
This paper has two primary objectives. The first one is to demonstrate that the solutions of master equation \begin{equation*} (\partial_t-\Delta)^s u(x,t) =f(u(x, t)), \,\,(x, t)\in B_1(0)\times \mathbb{R}, \end{equation*} subject to the…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…
Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler approach, the driving enters the…
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…
This paper addresses an optimal control problem governed by a rate independent evolution involving an integral operator. Its particular feature is that the dissipation potential depends on the history of the state. Because of the non-smooth…
We reanalyse the quantum damped harmonic oscillator, introducing three less than common features. These are (i) the use of a continuum model of the reservoir rather than an ensemble of discrete oscillators, (ii) an exact diagonalisation of…
We investigate the thermal responses of a harmonic oscillator chain coupled at its boundaries to heat baths held at different temperatures. This setup sustains a steady energy flux, continuously dissipating heat into both reservoirs. By…
Here, we develop the exact dynamics of the central spin model, modeling a finite-bath open quantum system. Particularly, two different types of interactions are investigated between the system and the bath: Heisenberg interaction with…
Estimates for the spectrum of the Cauchy operator and logarithms of solutions of non-autonomous differential equations in the space, expressed in an arbitrary matrix norm, are found. For equations with periodic coefficients, the lower bound…
In this paper, using the Lewis-Riesenfeld method, we determine the explicit form of the wavefunctions of one- and three-dimensional harmonic oscillators with time-dependent mass and frequency within the framework of the Dunkl derivative,…
This paper considers the ill-posed data assimilation problem associated with hyperbolic/parabolic systems describing 2D coupled sound and heat flow. Given hypothetical data at time T > 0, that may not correspond to an actual solution of the…
We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…