Download or read book A Driven Dissipative Phase Transition in an Open Quantum System written by Jens Benary and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dissipative Phase Transitions written by Pierluigi Colli and published by World Scientific. This book was released on 2006-03-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity.The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area.This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects.
Download or read book Phase Space Representations and Stochastic Simulations of Dissipative Phase Transitions in Nonlinear Quantum Systems written by Sean Muleady and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of generalized P representations allow a phase space description of quantum mechanics which, for certain systems, uniquely maps to a computationally efficient description via stochastic differential equations (SDEs). Recent interest in dissipative phase transitions in many-body open quantum systems has opened up P representations as a potential candidate for efficiently simulating such phenomena, since the exponential growth of the Hilbert space with system size quickly renders standard methods unfeasible. We provide an overview of the various P representations and their associated problems, and discuss ways of dealing with numerical issues that arise. A numerical infrastructure is developed to efficiently simulate SDEs, and this is directly applied to the study of phase transition phenomena in real nonlinear quantum systems. We first study the bistability and first-order phase transition in the single Kerr oscillator. We then extend the positive-P representation to a dimer of coupled Kerr oscillators, and study the emergent spatial-symmetry-breaking phase transition. Our work on the Kerr dimer extends very recent studies into high excitation number regimes unreachable using standard density matrix approaches.
Download or read book Phase Transition Dynamics written by Tian Ma and published by Springer Nature. This book was released on 2019-11-08 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields. This second edition introduces a unified theory for topological phase transitions, provides a first-principle approach to statistical and quantum physics, and offers a microscopic mechanism of quantum condensates (Bose-Einstein condensation, superfluidity, and superconductivity). Reviews of first edition: “The goals of this interesting book are to derive a general principle of dynamic transitions for dissipative systems and to establish a systematic dynamic transition theory for a wide range of problems in the nonlinear sciences. ... The intended audience for this book includes students and researchers working on nonlinear problems in physics, meteorology, oceanography, biology, chemistry, and the social sciences.” (Carlo Bianca, Mathematical Reviews, December, 2014) “This is a clearly written book on numerous types of phase transitions taken in a broad sense when a dynamical dissipative system transforms from one physical state into another. ... The book is a very useful literature not only for the professionals in the field of dynamic systems and phase transitions but also for graduate students due to its interdisciplinary coverage and state-of-the-art level.” (Vladimir Čadež, zbMATH, Vol. 1285, 2014)
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 411 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 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 Understanding Quantum Phase Transitions written by Lincoln Carr and published by CRC Press. This book was released on 2010-11-02 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivit
Download or read book Open Quantum Systems in Biology Cognitive and Social Sciences written by Andrei Y. Khrennikov and published by Springer Nature. This book was released on 2023-06-03 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mathematically analyzes the basic problems of biology, decision making and psychology within the framework of the theory of open quantum systems. In recent years there has been an explosion of interest in applications of quantum theory in fields beyond physics. The main areas include psychology, decision-making, economics, finance, social science as well as genetics and molecular biology. The corresponding models are referred to as quantum-like; they don’t concern any genuine physical processes in the human brain. Quantum-like models reflect the special features of information processing in biological, cognitive, and social systems which match well with the quantum formalism. This formalism gives rise to the quantum probability model (QP) which differs essentially from Kolmogorov's classical probability model. QP also serves as the basis for quantum information theory. Recently QP has been widely applied to the resolution of the basic paradoxes of decision making theory and to modeling experimental data stemming from cognition, psychology, economics, and finance thereby shedding light on probability fallacies and irrational behavior. In this book, the theory of quantum instruments and the quantum master equation are applied to the modeling of biological and cognitive processes, in particular, to the stability of complex biological and social systems interacting with their environment. An essential part of the book is devoted to the theory of the social laser and the Fröhlich condensate.
Download or read book Driven Dissipative Quantum Many Body Systems written by Orazio Scarlatella and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: My PhD was devoted to the study of driven-dissipative quantum many-body systems. These systems represent natural platforms to explore fundamental questions about matter under non-equilibrium conditions, having at the same time a potential impact on emerging quantum technologies. In this thesis, we discuss a spectral decomposition of single-particle Green functions of Markovian open systems, that we applied to a model of a quantum van der Pol oscillator. We point out that a sign property of spectral functions of equilibrium systems doesn't hold in the case of open systems, resulting in a surprising ``negative density of states", with direct physical consequences. We study the phase transition between a normal and a superfluid phase in a prototype system of driven-dissipative bosons on a lattice. This transition is characterized by a finite-frequency criticality corresponding to the spontaneous break of time-translational invariance, which has no analog in equilibrium systems. Later, we discuss the mean-field phase diagram of a Mott insulating phase stabilized by dissipation, which is potentially relevant for ongoing experiments. Our results suggest that there is a trade off between the fidelity of the stationary phase to a Mott insulator and robustness of such a phase at finite hopping. Finally, we present some developments towards using dynamical mean field theory (DMFT) for studying driven-dissipative lattice systems. We introduce DMFT in the context of driven-dissipative models and developed a method to solve the auxiliary problem of a single impurity, coupled simultaneously to a Markovian and a non-Markovian environment. As a test, we applied this novel method to a simple model of a fermionic, single-mode impurity.
Download or read book Progress in Optics written by and published by Elsevier. This book was released on 2023-04-18 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress in Optics, Volume 68 highlights new advances in the field of optics, with this updated volume presenting interesting chapters on a variety of timely topics in the field. Chapters in this release include Nonlinear Optical Polarimetry with application in biomicroscopy, Single-photon Sources, Introduction to Tensor Networks and Matrix Product States with Applications in Cavity and Waveguide Quantum Electrodynamics, Rotated frames, Phase retrieval, and more. Each chapter is written by an international board of authors who review the latest developments in optics. Covers medical imaging, physical optics, integrated optics and quantum optics Includes contributions from leading authorities in the field of optics Presents timely, state-of-the-art reviews on advances in optics
Download or read book Quantum Phase Transitions written by Subir Sachdev and published by Cambridge University Press. This book was released on 2001-04-23 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Phase Transitions is the first book to describe in detail the fundamental changes that can occur in the macroscopic nature of matter at zero temperature due to small variations in a given external parameter. The subject plays a central role in the study of the electrical and magnetic properties of numerous important solid state materials. The author begins by developing the theory of quantum phase transitions in the simplest possible class of non-disordered, interacting systems - the quantum Ising and rotor models. Particular attention is paid to their non-zero temperature dynamic and transport properties in the vicinity of the quantum critical point. Several other quantum phase transitions of increasing complexity are then discussed and clarified. Throughout, the author interweaves experimental results with presentation of theoretical models, and well over 500 references are included. The book will be of great interest to graduate students and researchers in condensed matter physics.
Download or read book Dissipative Systems in Quantum Optics written by R. Bonifacio and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: In studying the radiation-matter interaction, one can take two different approaches. The first is typical of spectroscopy: one considers the interaction between radi ation and a single atom, i. e. , one studies those phenomena in which the presence of other atoms is irrelevant. The other attitude consists, in contrast, in studying those phenomena which arise just from the simultaneous presence of many atoms. In fact, all the atoms interact with the same electromagnetic field; under suitable conditions, this situation creates strong atom-atom correlations, which in turn give rise to a cooperative behavior of the system as a whole. Cooperative means that the overall behavior is quite different from the superposition of the effects arising from single atoms and is completely unpredictable if one neglects the coup ling between the atoms induced by their common electromagnetic field. This book contains five complete and up-to-date contributions on the theory and experiments of three coherence effects in radiation-matter interaction: resonance fluorescences, optical bistability, and superfluorescence. They have raised in creasing interest in recent years from both a fundamental and an applicative view point. Even if their phenomenology appears completely different, these effects be long in the same book because they are striking examples of open systems driven far from thermal equilibrium, as those considered in Haken's synergetics and in Prigogine's theory of dissipative structures. This aspect is discussed in the in troducting chapter, in which we outline the basic physics and the essential features which unify these three effects.
Download or read book Dissipative Phase Transitions written by Pierluigi Colli and published by World Scientific. This book was released on 2006 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity. The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area. This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects. Contents: Mathematical Models Including a Hysteresis Operator (T Aiki); Modelling Phase Transitions via an Entropy Equation: Long-Time Behavior of the Solutions (E Bonetti); Global Solution to a One Dimensional Phase Transition Model with Strong Dissipation (G Bonfanti & F Luterotti); A Global in Time Result for an Integro-Differential Parabolic Inverse Problem in the Space of Bounded Functions (F Colombo et al.); Weak Solutions for Stefan Problems with Convections (T Fukao); Memory Relaxation of the One-Dimensional CahnOCoHilliard Equation (S Gatti et al.); Mathematical Models for Phase Transition in Materials with Thermal Memory (G Gentili & C Giorgi); Hysteresis in a First Order Hyperbolic Equation (J Kopfovi); Approximation of Inverse Problems Related to Parabolic Integro-Differential Systems of Caginalp Type (A Lorenzi & E Rocca); Gradient Flow Reaction/Diffusion Models in Phase Transitions (J Norbury & C Girardet); New Existence Result for a 3-D Shape Memory Model (I Pawlow & W M Zajaczkowski); Analysis of a 1-D Thermoviscoelastic Model with Temperature-Dependent Viscosity (R Peyroux & U Stefanelli); Global Attractor for the Weak Solutions of a Class of Viscous Cahn-Hilliard Equations (R Rossi); Stability for Phase Field Systems Involving Indefinite Surface Tension Coefficients (K Shirakawa); Geometric Features of p -Laplace Phase Transitions (E Valdinoci). Readership: Applied mathematicians and researchers in analysis and differential equations."
Download or read book Phase Transition Dynamics written by Tian Ma and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields.
Download or read book Quantum Many Body Physics in Open Systems Measurement and Strong Correlations written by Yuto Ashida and published by Springer Nature. This book was released on 2020-01-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the fundamental aspects of many-body physics in quantum systems open to an external world. Recent remarkable developments in the observation and manipulation of quantum matter at the single-quantum level point to a new research area of open many-body systems, where interactions with an external observer and the environment play a major role. The first part of the book elucidates the influence of measurement backaction from an external observer, revealing new types of quantum critical phenomena and out-of-equilibrium dynamics beyond the conventional paradigm of closed systems. In turn, the second part develops a powerful theoretical approach to study the in- and out-of-equilibrium physics of an open quantum system strongly correlated with an external environment, where the entanglement between the system and the environment plays an essential role. The results obtained here offer essential theoretical results for understanding the many-body physics of quantum systems open to an external world, and can be applied to experimental systems in atomic, molecular and optical physics, quantum information science and condensed matter physics.
Download or read book Phase Transitions and Diffusion in Dissipative Classical and Quantum Systems written by Julius Bonart and published by . This book was released on 2013 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is structured around three main chapters. In the first chapter I present new results which have been obtained for the out-of-equilibrium critical S\phi^4S-theory. Its dynamics are described by a Langevin equation driven by a colored noise. The temporal correlation of this noise features a power-law decrease which is governed by a certain exponent S\alphaS. It turns out that there exists a crossover S\alpha_cS which depends on the dimension SDS of the system and separates the S(\alpha, D)S-plane into a region where the color of the noise alters the critical behaviour and a region where the color is non relevant. I also discuss the scaling bahaviour of the non equilibrium correlation functions. In the second chapter I introduce a path integral formalism to describe non equilibrium quantum Brownian motion. I present the results which have been obtained during my PhD on the evolution of the non equilibrium correlation functions after a quantum quench. The third part of my thesis focuses on the impurity diffusion in one-dimensional quantum liquids which are commonly called Luttinger liquids. After an introductory part which covers the main issues related to such a system, I present a novel description of the impurity dynamics in the case where an external trapping potential is present. The non-homogeneous density profile of the Luttinger liquid then strongly influences on the impurity dynamics in a fascinating way. Such systems are currently being studied in cold atoms experiments.
Download or read book Dissipative Quantum Phase Transitions of Light Generalized Jaynes Cummings Rabi Model written by Ricardo Gutierrez Jauregui and published by . This book was released on 2018 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dissipative quantum phase transitions experienced by a driven optical system are studied in order to understand the underlying light-matter coupling. The primary system under study is composed of a cavity mode coupled to a two-level system with dissipation being introduced through the interaction with a surrounding environment; an external coherent field is included to drive the system out of the ground state. The coupling is given by a generalized Rabi Hamiltonian, where rotating, gr, and counter-rotating, ngr, couplings are both present and can be adjusted independently. A comprehensive study of the different phases the system can exhibit as gr and n are varied is presented. From this, we construct a bridge between two limiting scenarios: (i) the Jaynes-Cummings limit (n = 0), where the system undergoes a phase transition by means of the breakdown of the photon blockade, and (ii) the driven Dicke limit ( = 1 ), where the normal to super-radiant phase transition is found. Novel behaviour encountered in an intermediate regime (1 > n > 0) is discussed. Attention is drawn towards the strong coupling regime, where changes at the one-photon level induce nonlinear effects and behaviour reminiscent of phase transitions is encountered with just a few photons present. A comparison between weak and strong coupling regimes, and, thus, an exploration of the effect of fluctuations over quantum phase transitions of light, is given through a survey of the phases an auxiliary optical system exhibits. This system is composed of two coupled nonlinear cavities that are driven coherently and damped through the interaction with the environment; it is seen to exhibit three phases. Two phases present high-correlation between the cavities and are differentiated by the photon statistics, transitioning from classical to quantum. The third phase is characterized by a highly localized field in one of the cavities. The departure from mean-field results is highlighted and a new way to characterize the possible phases of the system is proposed. Finally, the crucial role of quantum fluctuations is quantified and used to define the phases at hand.
