Related papers: Kraus representation for maps and master equation …
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…
Steady-state observables, such as occupation numbers and currents, are crucial experimental signatures in open quantum systems. The time-convolutionless (TCL) master equation, which is both exact and time-local, is an ideal candidate for…
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…
Transition operator method is proposed for description of the dynamics of spectroscopic transitions. Quantum-mechanical analogue of Landau-Lifshitz equation has been derived for the system representing itself the periodical…
An exactly solvable model of a quantum spin interacting with a spin environment is considered. The interaction is chosen to be such that the state of the environment is conserved. The reduced density matrix of the spin is calculated for…
It is known that the time evolution of a subsystem from an initial state to two later times, t1, t2 (t2 > t1), are both completely positive (CP) but it is shown here that in the intermediate times between t1 and t2, in general, it need not…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
The reduced dynamics of a central spin coupled to a bath of N spin-1/2 particles arranged in a spin star configuration is investigated. The exact time evolution of the reduced density operator is derived, and an analytical solution is…
The quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model in a transverse magnetic field is studied in this paper. An exact solution is obtained by using an extended Jordan and Wigner transformation to the…
There exist two canonical approaches to describe open quantum systems by a time-evolution equation: the Nakajima-Zwanzig quantum master equation, featuring a time-nonlocal memory kernel $\mathcal{K}$, and the time-convolutionless equation…
Quantum dynamical maps provide suitable mathematical representation of quantum evolutions. It is the very notion of complete positivity which provides a proper mathematical representation of quantum evolution and gives rise to the powerful…
Most textbooks introduce the concept of spin by presenting the Stern-Gerlach experiment with the aid of Newtonian atomic trajectories. However, to understand how both spatial and spin degrees of freedom evolve over time and how the latter…
Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative…
The time evolution of an initially uncorrelated system is governed by a completely positive (CP) map. More generally, the system may contain initial (quantum) correlations with an environment, in which case the system evolves according to a…
Accurate and efficient simulation of open quantum systems remains a significant challenge, particularly for Non-Markovian dynamics. We demonstrate the profound utility of expressing the environmental correlation function as a sum of damped…
We propose a family of low-rank, completely positive and trace preserving schemes for the Lindblad equation, a common model for open quantum systems. Low-rank representation is employed at two levels: the density matrix is factorized into…
Given an quantum dynamical semigroup expressed as an exponential superoperator acting on a space of N-dimensional density operators, eigenvalue methods are presented by which canonical Kraus and Lindblad operator sum representations can be…
We address the problem of quantum process tomography with the preparators producing states correlated with the environmental degrees of freedom that play role in the system-environment interactions. We discuss the physical situations, in…
A central problem in the theory of the dynamics of open quantum systems is the derivation of a rigorous and computationally tractable master equation for the reduced system density matrix. Most generally, the evolution of an open quantum…
We propose a computationally efficient method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint…