Related papers: Completely Positive Post-Markovian Master Equation…
We show that complete positivity is not only sufficient but also necessary for the validity of the quantum data-processing inequality. As a consequence, the reduced dynamics of a quantum system are completely positive, even in the presence…
To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion,…
We recall theoretical studies on transient transport through interacting mesoscopic systems. It is shown that a generalized master equation (GME) written and solved in terms of many-body states provides the suitable formal framework to…
Starting from the Liouville-von Neumann equation, under a weak coupling limit we derive the Lindblad master equation for the one-dimensional quantum Ising model in a Markov approximation and a rotating wave approximation. We also prove that…
We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of…
We solve the optimal quantum limit of probing a classical force exactly by a damped oscillator initially prepared in the factorized squeezed state. The memory effects of the thermal bath on the oscillator evolution are investigated. We show…
We suggest a more general than quantum statistical mechanics ($QSM$) microdescription of objects in a heat bath taken into account a vacuum as an object environment - modification of quantum mechanics at finite temperatures; we call it…
We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter.…
An exactly solvable model for a quantum measurement is discussed which is governed by hamiltonian quantum dynamics. The $z$-component $\hat s_z$ of a spin-1/2 is measured with an apparatus, which itself consists of magnet coupled to a bath.…
In this article, we report the recent progress on decoherence dynamics of electrons in quantum dot quantum computing systems using the exact master equation we derived recently based on the Feynman-Vernon influence functional approach. The…
This paper presents a comprehensive review of the wave-function approach for derivation of the number-resolved Master equations, used for description of transport and measurement in mesoscopic systems. The review contains important…
This work makes progress on the issue of global vs. local master equations. Global master equations like the Redfield master equation (following from standard Born and Markov approximation) require a full diagonalization of the system…
We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time…
On its own, the invariance properties of Markovian master equations have mostly played a mathematical or computational role in the evaluation of quantum open system dynamics. Because all forms of the equation lead to the same time evolution…
In this work we introduce and characterize a broad class of quantum operations with a unique fixed point, termed quantum ergodic channels. We derive Lindblad-type master equations for these channels in arbitrary finite dimensions and…
Featuring memory of past inputs is a fundamental requirement for machine learning models processing time-dependent data. In quantum reservoir computing, all architectures proposed so far rely on Markovian dynamics, which, as we prove,…
This is a concise, pedagogical introduction to the dynamic field of open quantum systems governed by Markovian master equations. We focus on the mathematical and physical origins of the widely used Lindblad equation, its unraveling in terms…
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…
We propose to describe the dynamics of phase transitions in terms of a non-stationary Generalized Langevin Equation for the order parameter. By construction, this equation is non-local in time, i.e.~it involves memory effects whose…
A quantum master equation of the Lindblad form is obtained in this paper by considering the spontaneous wave-packet reduction. Different classical equations can be derived after exactly mapping such a quantum master equation to a continuous…