Quantum Stochastic Processes: A Case Study

We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the process allows us to specify and to construct the dilation of the quantum dynamical maps, including conditional quantum expectations. The quantum phase space Brownian motion possesses many properties similar to that of the classical Brownian motion, notably its increments are independent and identically distributed. Possible applications to dissipative phenomena in the quantum Hall effect are suggested.Comment: 35 pages, 1 figure

Fluctuations of Quantum Currents and Unravelings of Master Equations

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system.Comment: 18 pages, v1-->v2, Replaced the former Appendix B by a (thematically) different one. Mainly changes in the introductory Section 2+ added reference

Non-equilibrium states of a photon cavity pumped by an atomic beam

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the energy flux in both the ideal and open cavity and the entropy production for the ideal cavity.Comment: Corrected energy production calculations and made some changes to ease the readin

Non Markovian Quantum Repeated Interactions and Measurements

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions of the integro-differential and time-convolutioness Master equations for the reduced system are derived. Next, an intuitive and rigorous description of the indirect quantum measurement principle is developed and a discrete non Markovian stochastic Master equation for the open system is obtained. Finally, the question of unravelling in a particular model of non-Markovian quantum interactions is discussed.Comment: 22 page

Adiabatic response for Lindblad dynamics

We study the adiabatic response of open systems governed by Lindblad evolutions. In such systems, there is an ambiguity in the assignment of observables to fluxes (rates) such as velocities and currents. For the appropriate notion of flux, the formulas for the transport coefficients are simple and explicit and are governed by the parallel transport on the manifold of instantaneous stationary states. Among our results we show that the response coefficients of open systems, whose stationary states are projections, is given by the adiabatic curvature.Comment: 33 pages, 4 figures, accepted versio

Quantum Fluctuation Relations for the Lindblad Master Equation

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula

Random repeated quantum interactions and random invariant states

We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between $\mathcal{H}$ and $\mathcal{K}_n$. The other involves random quantum states describing each copy $\mathcal{K}_n$. In the limit of a large number of interactions, we present convergence results for the asymptotic state of $\mathcal{H}$. This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the \emph{asymptotic induced ensemble}

Rayleigh-Taylor and Richtmyer-Meshkov instabilities: A journey through scales

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordHydrodynamic instabilities such as Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities usually appear in conjunction with the Kelvin-Helmholtz (KH) instability and are found in many natural phenomenon and engineering applications. They frequently result in turbulent mixing, which has a major impact on the overall flow development and other effective material properties. This can either be a desired outcome, an unwelcome side effect, or just an unavoidable consequence, but must in all cases be characterized in any model. The RT instability occurs at an interface between different fluids, when the light fluid is accelerated into the heavy. The RM instability may be considered a special case of the RT instability, when the acceleration provided is impulsive in nature such as that resulting from a shock wave. In this pedagogical review, we provide an extensive survey of the applications and examples where such instabilities play a central role. First, fundamental aspects of the instabilities are reviewed including the underlying flow physics at different stages of development, followed by an overview of analytical models describing the linear, nonlinear and fully turbulent stages. RT and RM instabilities pose special challenges to numerical modeling, due to the requirement that the sharp interface separating the fluids be captured with fidelity. These challenges are discussed at length here, followed by a summary of the significant progress in recent years in addressing them. Examples of the pivotal roles played by the instabilities in applications are given in the context of solar prominences, ionospheric flows in space, supernovae, inertial fusion and pulsed-power experiments, pulsed detonation engines and scramjets. Progress in our understanding of special cases of RT/RM instabilities is reviewed, including the effects of material strength, chemical reactions, magnetic fields, as well as the roles the instabilities play in ejecta formation and transport, and explosively expanding flows. The article is addressed to a broad audience, but with particular attention to graduate students and researchers that are interested in the state-of-the-art in our understanding of the instabilities and the unique issues they present in the applications in which they are prominent.Science and Technology Facilities CouncilScience and Technology Facilities Counci

Training for managing impacted fetal head at caesarean birth: multimethod evaluation of a pilot

Background Implementation of national multiprofessional training for managing the obstetric emergency of impacted fetal head (IFH) at caesarean birth has potential to improve quality and safety in maternity care, but is currently lacking in the UK. Objectives To evaluate a training package for managing IFH at caesarean birth with multiprofessional maternity teams. Methods The training included an evidence-based lecture supported by an animated video showing management of IFH, followed by hands-on workshops and real-time simulations with use of a birth simulation trainer, augmented reality and management algorithms. Guided by the Kirkpatrick framework, we conducted a multimethod evaluation of the training with multiprofessional maternity teams. Participants rated post-training statements about relevance and helpfulness of the training and pre-training and post-training confidence in their knowledge and skills relating to IFH (7-point Likert scales, strongly disagree to strongly agree). An ethnographer recorded sociotechnical observations during the training. Participants provided feedback in post-training focus groups. Results Participants (N=57) included 21 midwives, 25 obstetricians, 7 anaesthetists and 4 other professionals from five maternity units. Over 95% of participants agreed that the training was relevant and helpful for their clinical practice and improving outcomes following IFH. Confidence in technical and non-technical skills relating to managing IFH was variable before the training (5%–92% agreement with the pre-training statements), but improved in nearly all participants after the training (71%–100% agreement with the post-training statements). Participants and ethnographers reported that the training helped to: (i) better understand the complexity of IFH, (ii) recognise the need for multiprofessional training and management and (iii) optimise communication with those in labour and their birth partners. Conclusions The evaluated training package can improve self-reported knowledge, skills and confidence of multiprofessional teams involved in management of IFH at caesarean birth. A larger-scale evaluation is required to validate these findings and establish how best to scale and implement the training

Measurement of the Lifetime Difference Between B_s Mass Eigenstates

We present measurements of the lifetimes and polarization amplitudes for B_s --> J/psi phi and B_d --> J/psi K*0 decays. Lifetimes of the heavy (H) and light (L) mass eigenstates in the B_s system are separately measured for the first time by determining the relative contributions of amplitudes with definite CP as a function of the decay time. Using 203 +/- 15 B_s decays, we obtain tau_L = (1.05 +{0.16}/-{0.13} +/- 0.02) ps and tau_H = (2.07 +{0.58}/-{0.46} +/- 0.03) ps. Expressed in terms of the difference DeltaGamma_s and average Gamma_s, of the decay rates of the two eigenstates, the results are DeltaGamma_s/Gamma_s = (65 +{25}/-{33} +/- 1)%, and DeltaGamma_s = (0.47 +{0.19}/-{0.24} +/- 0.01) inverse ps.Comment: 8 pages, 3 figures, 2 tables; as published in Physical Review Letters on 16 March 2005; revisions are for length and typesetting only, no changes in results or conclusion