112 research outputs found
A short introduction to the Lindblad master equation
The theory of open quantum systems is one of the most essential tools for the development of quantum technologies. Furthermore, the
Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) master equation plays a key role as it is the most general generator of Markovian
dynamics in quantum systems. In this paper, we present this equation together with its derivation and methods of resolution. The presentation
tries to be as self-contained and straightforward as possible to be useful to readers with no previous knowledge of this field.Spanish Ministry and the
Agencia Española de Investigación (AEI) for financial support under
Grant No. FIS2017-84256-P (FEDER funds)
Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview
Over the past few decades, there has been substantial interest in evolution
equations that involving a fractional-order derivative of order
in time, due to their many successful applications in
engineering, physics, biology and finance. Thus, it is of paramount importance
to develop and to analyze efficient and accurate numerical methods for reliably
simulating such models, and the literature on the topic is vast and fast
growing. The present paper gives a concise overview on numerical schemes for
the subdiffusion model with nonsmooth problem data, which are important for the
numerical analysis of many problems arising in optimal control, inverse
problems and stochastic analysis. We focus on the following aspects of the
subdiffusion model: regularity theory, Galerkin finite element discretization
in space, time-stepping schemes (including convolution quadrature and L1 type
schemes), and space-time variational formulations, and compare the results with
that for standard parabolic problems. Further, these aspects are showcased with
illustrative numerical experiments and complemented with perspectives and
pointers to relevant literature.Comment: 24 pages, 3 figure
Systematic Perturbation Theory for Dynamical Coarse-Graining
We demonstrate how the dynamical coarse-graining approach can be
systematically extended to higher orders in the coupling between system and
reservoir. Up to second order in the coupling constant we explicitly show that
dynamical coarse-graining unconditionally preserves positivity of the density
matrix -- even for bath density matrices that are not in equilibrium and also
for time-dependent system Hamiltonians. By construction, the approach correctly
captures the short-time dynamics, i.e., it is suitable to analyze non-Markovian
effects. We compare the dynamics with the exact solution for highly
non-Markovian systems and find a remarkable quality of the coarse-graining
approach. The extension to higher orders is straightforward but rather tedious.
The approach is especially useful for bath correlation functions of simple
structure and for small system dimensions.Comment: 17 pages, 5 figures, version accepted for publication in PR
Quantum dynamical semigroups for diffusion models with Hartree interaction
We consider a class of evolution equations in Lindblad form, which model the
dynamics of dissipative quantum mechanical systems with mean-field interaction.
Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson
model. The existence and uniqueness of global-in-time, mass preserving
solutions is proved, thus establishing the existence of a nonlinear
conservative quantum dynamical semigroup. The mathematical difficulties stem
from combining an unbounded Lindblad generator with the Hartree nonlinearity.Comment: 30 pages; Introduction changed, title changed, easier and shorter
proofs due to new energy norm. to appear in Comm. Math. Phy
Effects of dipolar coupling on an entanglement storage device
Quantum computation requires efficient long-term storage devices to preserve
quantum states. An attractive candidate for such storage devices is qubits
connected to a common dissipative environment. The common environment gives
rise to persistent entanglements in these qubit systems. Hence these systems
act efficiently as a storage device of entanglement. However, the existence of
a common environment often requires the physical proximity of the qubits and
hence results in direct dipolar coupling between the qubits. In this work, we
investigate the total effect of the dipolar coupling on the environment-induced
entanglement using a recently-proposed fluctuation-regulated quantum master
equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)].
We show that nonsecular part of the dipolar coupling results in reduced
entanglement and hence less efficiency of the storage devices. We also discuss
the properties of efficient storage that mitigates the detrimental effects of
the dipolar coupling on the stored entanglement.Comment: 22 pages, 7 figure
Open Systems, Entanglement and Quantum Optics
The subject of this book is a presentation of some aspects of modern theory of open quantum systems. It introduces several up-to- date topics, such as detecting quantum entanglement, modeling of quantum noise, quantum communication processes, and computational complexity in the analysis of quantum operations. Also discussed are light propagation in optically dressed media, as well as entropy and information measure for quantized electromagnetic fields media. This book is intended for researchers and students interested in the theory of open quantum systems, quantum information theory and quantum systems interacting with electromagnetic fields
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