Related papers: Reconstruction of Liouvillian Superoperators
We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum…
In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral…
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the…
We introduce an encoder-only approach to learn the evolution operators of large-scale non-linear dynamical systems, such as those describing complex natural phenomena. Evolution operators are particularly well-suited for analyzing systems…
We develop an approach for understanding the dynamics of open quantum systems by analyzing individual quantum trajectories in the eigenbasis of the Liouvillian superoperator. From trajectory-eigenstate overlaps, we construct a…
Semigroups describing the time evolution of open quantum systems in finite-dimensional spaces have generators of a special form, known as Lindblad generators. These generators and the corresponding processes of time evolution are analyzed,…
We present a general formalism based on the variational principle for finding the time-optimal quantum evolution of mixed states governed by a master equation, when the Hamiltonian and the Lindblad operators are subject to certain…
The quantum regression theorem is a powerful tool for calculating the muli-time correlators of operators of open quantum systems which dynamics can be described in Markovian approximation. It enables to obtain the closed system of equation…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
We investigate the dynamics of open quantum systems which are initially correlated with their environment. The strategy of our approach is to analyze how given, fixed initial correlations modify the evolution of the open system with respect…
We show that Feynman's Clock construction, in which the time-evolution of a closed quantum system is encoded as a ground state problem, can be extended to open quantum systems. In our formalism, the ground states of an ensemble of…
We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach…
The stroboscopic evolution of a time-periodically driven isolated quantum system can always be described by an effective time-independent Hamiltonian. Whether this concept can be generalized to open Floquet systems, described by a Markovian…
Supersymmetric extensions of Hamilton-Jacobi separable Liouville mechanical systems with two degrees of freedom are defined. It is shown that supersymmetry can be implemented in this type of systems in two independent ways. The structure of…
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…
We prove some Liouville properties for sub- and supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have…
Quantum revivals are investigated for the dynamics of an atom in a driven gravitational cavity. It is demonstrated that the external driving field influences the revival time significantly. Analytical expressions are presented which are…
In this work we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which…
We find analytical solutions to the evolution of interacting two-level atoms when the master equation is symmetric under the permutation of atomic labels. The master equation includes atomic independent dissipation. The method to obtain the…
We analyze the possibility of tomographic reconstruction of a system of three-level atoms in both non-degenerate and degenerate cases. In the non-degenerate case (when both transitions can be accessed independently) a complete…