Download or read book Initial Correlations in Open Quantum Systems Constructing Linear Dynamical Maps and Master Equations written by Alessandra Colla and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: 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 to the corresponding uncorrelated dynamical behavior with the same fixed initial environmental state, described by a completely positive dynamical map. We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system which acts like the proper dynamical map on the set of physical states and represents its unique linear extension. Furthermore, we demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure involving time-dependent, possibly negative transition rates. Thus, the general non-Markovian dynamics of an open quantum system can be described by means of a time-local master equation even in the case of arbitrary, fixed initial system-environment correlations. We present some illustrative examples and explain the relation of our approach to several other approaches proposed in the literature

Download or read book Initial Correlations in Non equilibrium Quantum Thermodynamics written by Niklas Felix Neubrand and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Quantum thermodynamics is a relatively young scientific field that tries to extend the phenomenological theory of thermodynamics to the quantum regime. Many dynamical approaches are based on the theory of open quantum systems and assume factorizing initial conditions. In this work we relax this requirement and study an open system which is initially correlated with a thermal environment. For a predetermined environmental state and correlation operator the reduced evolution can be described by affine equations of motion. We prove that these maps can be linearized uniquely from the set of trace-one operators to the set of all bounded operators. Hence, we introduce a linearized dynamical map which acts identical to the affine map on the set of physical system states. Likewise, we obtain a linear time-local master equation with a generalized Lindblad form involving an time-dependent effective Hamiltonian and a time-dependent dissipator with possibly negative coefficients. By applying a principle of minimal dissipation, we prove that the effective Hamiltonian is identical to its uncorrelated version. Then, we generalize the formalism of Colla and Breuer [1] for exact non-equilibrium thermodynamics. We identify the effective Hamiltonian with the internal energy observable and define a first law of thermodynamics. Here, the effects of the initial correlations appear as additional terms in the work, heat and internal energy rates. Similarly, we generalize the entropy production rate. As the expression is non-linear in the system state, the influence of the initial correlations is harder to analyze. Also meaningful conditions for positive entropy production rates, i.e. the second law, have still to be found for correlated initial states. To illustrate our results, we finally consider the application to the Jaynes-Cummings model, where we explicitly compare the thermodynamic quantities for the correlated and uncorrelated cases. [1] A. Colla and H.-P. Breuer, Phys Rev A 105, 052216 (2022)

Download or read book G consistent Subsets and Reduced Dynamical Quantum Maps written by Russell R. Ceballos and published by . This book was released on 2017 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quantum system which evolves in time while interacting with an external environment is said to be an open quantum system (OQS), and the influence of the environment on the unperturbed unitary evolution of the system generally leads to non-unitary dynamics. This kind of open system dynamical evolution has been typically modeled by a Standard Prescription (SP) which assumes that the state of the OQS is initially uncorrelated with the environment state. It is here shown that when a minimal set of physically motivated assumptions are adopted, not only does there exist constraints on the reduced dynamics of an OQS such that this SP does not always accurately describe the possible initial correlations existing between the OQS and environment, but such initial correlations, and even entanglement, can be witnessed when observing a particular class of reduced state transformations termed purity extractions are observed. Furthermore, as part of a more fundamental investigation to better understand the minimal set of assumptions required to formulate well defined reduced dynamical quantum maps, it is demonstrated that there exists a one-to-one correspondence between the set of initial reduced states and the set of admissible initial system-environment composite states when G-consistency is enforced. Given the discussions surrounding the requirement of complete positivity and the reliance on the SP, the results presented here may well be found valuable for determining the ba- sic properties of reduced dynamical maps, and when restrictions on the OQS dynamics naturally emerge.

Download or read book Irreversible Quantum Dynamics written by Fabio Benatti and published by Springer. This book was released on 2008-01-11 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of editing the present volume in the Lecture Notes in Physics series arosewhileorganizingthe“ConferenceonIrreversibleQuantumDynamics”that took place at The Abdus Salam International Center for Theoretical Physics, Trieste, Italy, from July 29 to August 2, 2002. The aim of the Conference was to bring together di?erent groups of - searcherswhoseinterestsandpursuitsinvolveirreversibilityandtimeasymmetry in quantum mechanics. The Conference promoted open and in-depth exchanges of di?erent points of view, concerning both the content and character of qu- tum irreversibility and the methodologies used to study it. The following main themes were addressed: • Theoretical Aspects of Quantum Irreversible Dynamics • Open Quantum Systems and Applications • Foundational Aspects of Irreversible Quantum Dynamics • Asymmetric Time Evolution and Resonances Eachthemewasreviewedbyanexpertinthe?eld,accompaniedbymorespeci?c, research-like shorter talks. The whole topic of quantum irreversibility in all its manifold aspects has always raised a lot of interest, starting with the description of unstable systems in quantum mechanics and the issue of quantum measurement. Further, in - cent years a boost of activity concerning noise, dissipation and open systems has been prompted by the fast developing ?eld of quantum communication and information theory. These considerations motivated the editors to put together a volume that tries to summarize the present day status of the research in the ?eld, with the aim of providing the reader with an accessible and exhaustive introduction to it.

Download or read book Linearity Versus Complete Positivity of the Evolution of Open Quantum Systems written by Russell R. Ceballos and published by . This book was released on 2014 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The title may be a bit misleading. Perhaps, "On the Complete Positivity of Reduced Quantum Dynamics," would be a more fitting title. Determining whether or not completely positive (CP) maps are required to describe open system quantum dynamics is an extremely important issue concerning the fundamental mathematical foundations of QM, as well as many other areas of physics. it had been typically believed that only CP maps actually describe the dynamical evolution of open quantum systems, however there has been speculation as to whether this is a strict constraint on the mathematical and physical structure of stochastic quantum dynamical maps. The objective of this thesis is to demonstrate that given a particular unitary operator, an initial system state, a final system state, and the dimension of the environment state, there exists no CP map with a composite system-environment, product initial state that is compatible with the given constraints on the reduced quantum dynamics of the system under investigation.

Download or read book The Theory of Open Quantum Systems written by Heinz-Peter Breuer and published by Oxford University Press, USA. This book was released on 2002 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.

Download or read book Detecting Initial Correlations in Open Quantum Systems written by Anjala Mullaparambil Babu and published by . This book was released on 2021 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we discuss correlations arising between a system and its environment that lead to errors in an open quantum system. Detecting those correlations would be valuable for avoiding and/or correcting those errors. It was studied previously that we can detect correlations by only measuring the system itself if we know the cause of interaction between the two, for example in the case of a dipole-dipole interaction for a spin 1/2-spin 1/2 interaction Hamiltonian. We investigate the unitary, U which is associated with the exchange Hamiltonian and examine the ability to detect initial correlations between a system and its environment for a spin-1/2(qubit) system interacting with a larger higher dimensional environment. We provide bounds for when we can state with certainty that there are initial system-environment correlations given experimental data.

Download or read book Open Quantum Systems Far from Equilibrium written by Gernot Schaller and published by Springer. This book was released on 2014-01-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides graduate students and also professional researchers aiming to understand the dynamics of open quantum systems with a valuable and self-contained toolbox. Special focus is laid on the link between microscopic models and the resulting open-system dynamics. This includes how to derive the celebrated Lindblad master equation without applying the rotating wave approximation. As typical representatives for non-equilibrium configurations it treats systems coupled to multiple reservoirs (including the description of quantum transport), driven systems and feedback-controlled quantum systems. Each method is illustrated with easy-to-follow examples from recent research. Exercises and short summaries at the end of every chapter enable the reader to approach the frontiers of current research quickly and make the book useful for quick reference.

Download or read book Initialization and Characterization of Open Quantum Systems written by Christopher James Wood and published by . This book was released on 2015 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we address three topics of open quantum systems theory. The first concerns the operational characterization of an open quantum system. We develop a graphical calculus for open quantum systems and use it to review the operational representation and characterization of noisy evolution using completely-positive maps, or quantum channels. These graphical techniques facilitate an intuitive unification of the various representations of CP-maps, and the transformations between these representations. We generalize the channel formalism by introducing quantum superchannels -- effective quantum channels which take another channel as input. Superchannels may be constructed using graphical techniques to rearrange the tensor network for a sequence of channels, and these constructions allow for the description of a strictly greater set of dynamics than is possible with the standard formalism. We demonstrate this by providing a method for the complete characterization of an open system initially correlated with its environment. In doing so we introduce and develop several novel quantitative measures for characterizing the strength and presence of initial correlations in a quantum system. These techniques may be implemented using measurement of the system alone, and do not require any access or prior knowledge about the environment. The second topic we discuss is the parallel initialization of an ensemble quantum system into a high purity state. We describe a dissipative state engineering technique where an ensemble of identical spins may be prepared in its ground state by coupling the spins to the resolved sidebands of a high-Q resonator. This allows for parallel removal of entropy from a large number of quantum systems, enabling an ensemble to achieve a polarization greater than thermal equilibrium, and in principle on a time scale much shorter than thermal relaxation processes. This is achieved by the collective enhancement in coupling strength of the coupled angular momentum subspaces which behave as larger effective spins. Cavity cooling is shown to cool each of these subspaces to their respective ground state, however by including a local $T_2$ dephasing dissipator on each spin we show how one may use this to break the identical spin degeneracy and couple the subspaces to enable cooling to the full ground state of the joint system. The third topic concerns quantum correlations between the momentum and spin subsystems of a neutron in a neutron interferometer. We explore the robustness of these correlations in the presence of dephasing noise due to randomized phase differences between interferometer paths. We demonstrate that even in the presence of strong noise quantum correlations persist and can be detected by introducing post-selected spin measurements at the output of the interferometer. We relate these post-selected experiments to which-way measurements and a quantum eraser.

Download or read book Open Quantum Systems I written by St Phane Attal and published by . This book was released on 2008-08-15 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamics of Open Systems with Affine Maps Supported by the National Natural Science Foundation of China Under Grant written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract : Many quantum systems of interest are initially correlated with their environments and the reduced dynamics of open systems are an interesting while challenging topic. Affine maps, as an extension of completely positive maps, are a useful tool to describe the reduced dynamics of open systems with initial correlations. However, it is unclear what kind of initial state shares an affine map. In this study, we give a sufficient condition of initial states, in which the reduced dynamics can always be described by an affine map. Our result shows that if the initial states of the combined system constitute a convex set, and if the correspondence between the initial states of the open system and those of the combined system, defined by taking the partial trace, is a bijection, then the reduced dynamics of the open system can be described by an affine map.

Download or read book Quantum Dissipative Systems written by Ulrich Weiss and published by World Scientific. This book was released on 2012 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book -- originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions -- delves significantly deeper than ever before into the fundamental concepts, methods and applications of quantum dissipative systems.This fourth edition provides a self-contained and updated account of the quantum mechanics of open systems and offers important new material including the most recent developments. The subject matter has been expanded by about fifteen percent. Many chapters have been completely rewritten to better cater to both the needs of newcomers to the field and the requests of the advanced readership. Two chapters have been added that account for recent progress in the field. This book should be accessible to all graduate students in physics. Researchers will find this a rich and stimulating source.

Download or read book Dynamics of Initially Entangled Open Quantum Systems written by Anil Shaji and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Thermodynamics and Synchronization in Open Quantum Systems written by Gonzalo Manzano Paule and published by Springer. This book was released on 2018-07-04 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores some of the connections between dissipative and quantum effects from a theoretical point of view. It focuses on three main topics: the relation between synchronization and quantum correlations, the thermodynamical properties of fluctuations, and the performance of quantum thermal machines. Dissipation effects have a profound impact on the behavior and properties of quantum systems, and the unavoidable interaction with the surrounding environment, with which systems continuously exchange information, energy, angular momentum and matter, is ultimately responsible for decoherence phenomena and the emergence of classical behavior. However, there is a wide intermediate regime in which the interplay between dissipative and quantum effects gives rise to a plethora of rich and striking phenomena that has just started to be understood. In addition, the recent breakthrough techniques in controlling and manipulating quantum systems in the laboratory have made this phenomenology accessible in experiments and potentially applicable.

Download or read book The Role of System environment Correlations in the Dynamics of Open Quantum Systems written by Ansgar Pernice and published by . This book was released on 2013 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Study on the Lindblad Master Equation of Open Quantum Systems Using Spin 1 2 Chains written by Meng-Wei (Vivian) Chen and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamics of Open Quantum Systems written by Keith H. Hughes and published by . This book was released on 2006 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: