Extended Theories of Gravity

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.

Background independent quantum gravity: A Status report

The control of individual quantum systems promises a new technology for the 21st century – quantum technology. This book is the first comprehensive treatment of modern quantum measurement and measurement-based quantum control, which are vital elements for realizing quantum technology. Readers are introduced to key experiments and technologies through dozens of recent experiments in cavity QED, quantum optics, mesoscopic electronics, and trapped particles several of which are analyzed in detail. Nearly 300 exercises help build understanding, and prepare readers for research in these exciting areas. This important book will interest graduate students and researchers in quantum information, quantum metrology, quantum control and related fields. Novel topics covered include adaptive measurement; realistic detector models; mesoscopic current detection; Markovian, state-based and optimal feedback; and applications to quantum information processing.

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Quantum Measurement and Control

Journal of Statistical Mechanics: theory and experiment

A nonlinear stochastic Schr\"odinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including measurementlike situations, dissipation, and quantum Brownian motion. Some examples treat this environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In such a quasiperiodic case we see the reversible decay of a macroscopic quantum-superposition (``Schr\"odinger cat''). Finally, our description of open systems is compatible with different positions of the ``Heisenberg cut'' between system and environment.

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Non-Markovian quantum state diffusion

A non-Markovian stochastic Schr\"odinger equation for a quantum system coupled to an environment of harmonic oscillators is presented The ensemble average recovers the reduced density matrix without approximation and hence it allows one to determine open system dynamics with strong and non-Markovian environmental effects in a very efficient way We demonstrate the power of our approach with several illustrative examples First, we discuss a measurement-type situation, then a two-state system strongly coupled to a non-Markovian environment, exhibiting decays and revivals Further examples showing the remarkable features of our new approach to non-Markovian open system dynamics are discussed, for instance, the possibility to shift the ``Heisenberg cut'' between system and environment

Open system dynamics with non-markovian quantum trajectories

http://www.rmki.kfki.hu/~diosi/prints/1997pla235p569.pdf

The non-Markovian stochastic Schrödinger equation for open systems

We present a perturbation theory for non-Markovian quantum state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a bosonic environment [Physical Review A 58, 1699, (1998)]. We establish a systematic expansion in the ratio between the environmental correlation time and the typical system time scale. The leading order recovers the Markov theory, so here we concentrate on the next-order correction corresponding to first-order non-Markovian master equations. These perturbative equations greatly simplify the general nonMarkovian QSD approach, and allow for efficient numerical simulations beyond the Markov approximation. Furthermore, we show that each perturbative scheme for QSD naturally gives rise to a perturbative scheme for the master equation which we study in some detail. Analytical and numerical examples are presented, including the quantum Brownian motion model.

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Non-Markovian quantum state diffusion: Perturbation approach

Stochastic Schr\"odinger equations for quantum trajectories offer an alternative and sometimes superior approach to the study of open quantum system dynamics. Here we show that recently established convolutionless non-Markovian stochastic Schr\"odinger equations may serve as a powerful tool for the derivation of convolutionless master equations for non-Markovian open quantum systems. The most interesting example is quantum Brownian motion (QBM) of a harmonic oscillator coupled to a heat bath of oscillators, one of the most employed exactly soluble models of open system dynamics. We show explicitly how to establish the direct connection between the exact convolutionless master equation of QBM and the corresponding convolutionless exact stochastic Schr\"odinger equation.

https://arxiv.org/pdf/quant-ph/0312103.pdf

Walter T. Strunz

Papers

Non-Markovian quantum state diffusion

Open system dynamics with non-markovian quantum trajectories

The non-Markovian stochastic Schrödinger equation for open systems

Non-Markovian quantum state diffusion: Perturbation approach

Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion