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Quantum Trajectories and Measurements in Continuous Time

Alberto Barchielli,Matteo Gregoratti

Author : Alberto Barchielli,Matteo Gregoratti
Publisher : Springer
Page : 325 pages
File Size : 55,9 Mb
Release : 2009-07-11
Category : Science
ISBN : 9783642012983

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Quantum Trajectories and Measurements in Continuous Time by Alberto Barchielli,Matteo Gregoratti Pdf

Quantum trajectory theory is largely employed in theoretical quantum optics and quantum open system theory and is closely related to the conceptual formalism of quantum mechanics (quantum measurement theory). However, even research articles show that not all the features of the theory are well known or completely exploited. We wrote this monograph mainly for researchers in theoretical quantum optics and related ?elds with the aim of giving a self-contained and solid p- sentation of a part of quantum trajectory theory (the diffusive case) together with some signi?cant applications (mainly with purposes of illustration of the theory, but which in part have been recently developed). Another aim of the monograph is to introduce to this subject post-graduate or PhD students. To help them, in the most mathematical and conceptual chapters, summaries are given to ?x ideas. Moreover, as stochastic calculus is usually not in the background of the studies in physics, we added Appendix A to introduce these concepts. The book is written also for ma- ematicians with interests in quantum theories. Quantum trajectory theory is a piece of modern theoretical physics which needs an interplay of various mathematical subjects, such as functional analysis and probability theory (stochastic calculus), and offers to mathematicians a beautiful ?eld for applications, giving suggestions for new mathematical developments.

Quantum Trajectories and Measurements in Continuous Time

Alberto Barchielli,Matteo Gregoratti

Author : Alberto Barchielli,Matteo Gregoratti
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 42,8 Mb
Release : 2009-07-21
Category : Mathematics
ISBN : 9783642012976

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Quantum Trajectories and Measurements in Continuous Time by Alberto Barchielli,Matteo Gregoratti Pdf

This course-based monograph introduces the reader to the theory of continuous measurements in quantum mechanics and provides some benchmark applications. The approach chosen, quantum trajectory theory, is based on the stochastic Schrödinger and master equations, which determine the evolution of the a-posteriori state of a continuously observed quantum system and give the distribution of the measurement output. The present introduction is restricted to finite-dimensional quantum systems and diffusive outputs. Two appendices introduce the tools of probability theory and quantum measurement theory which are needed for the theoretical developments in the first part of the book. First, the basic equations of quantum trajectory theory are introduced, with all their mathematical properties, starting from the existence and uniqueness of their solutions. This makes the text also suitable for other applications of the same stochastic differential equations in different fields such as simulations of master equations or dynamical reduction theories. In the next step the equivalence between the stochastic approach and the theory of continuous measurements is demonstrated. To conclude the theoretical exposition, the properties of the output of the continuous measurement are analyzed in detail. This is a stochastic process with its own distribution, and the reader will learn how to compute physical quantities such as its moments and its spectrum. In particular this last concept is introduced with clear and explicit reference to the measurement process. The two-level atom is used as the basic prototype to illustrate the theory in a concrete application. Quantum phenomena appearing in the spectrum of the fluorescence light, such as Mollow’s triplet structure, squeezing of the fluorescence light, and the linewidth narrowing, are presented. Last but not least, the theory of quantum continuous measurements is the natural starting point to develop a feedback control theory in continuous time for quantum systems. The two-level atom is again used to introduce and study an example of feedback based on the observed output.

Bohmian Mechanics, Open Quantum Systems and Continuous Measurements

Antonio B. Nassar,Salvador Miret-Artés

Author : Antonio B. Nassar,Salvador Miret-Artés
Publisher : Springer
Page : 241 pages
File Size : 47,9 Mb
Release : 2017-03-14
Category : Science
ISBN : 9783319536538

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Bohmian Mechanics, Open Quantum Systems and Continuous Measurements by Antonio B. Nassar,Salvador Miret-Artés Pdf

This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from the violation of the noncrossing rule of quantum trajectories.

Continuous Quantum Measurements and Path Integrals

M.B Mensky

Author : M.B Mensky
Publisher : CRC Press
Page : 212 pages
File Size : 40,9 Mb
Release : 1993-01-01
Category : Science
ISBN : 0750302283

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Continuous Quantum Measurements and Path Integrals by M.B Mensky Pdf

Advances in technology are taking the accuracy of macroscopic as well as microscopic measurements close to the quantum limit, for example, in the attempts to detect gravitational waves. Interest in continuous quantum measurements has therefore grown considerably in recent years. Continuous Quantum Measurements and Path Integrals examines these measurements using Feynman path integrals. The path integral theory is developed to provide formulae for concrete physical effects. The main conclusion drawn from the theory is that an uncertainty principle exists for processes, in addition to the familiar one for states. This implies that a continuous measurement has an optimal accuracy-a balance between inefficient error and large quantum fluctuations (quantum noise). A well-known expert in the field, the author concentrates on the physical and conceptual side of the subject rather than the mathematical.

Time in Quantum Mechanics - Vol. 2

Gonzalo Muga,Andreas Ruschhaupt,Adolfo del Campo

Author : Gonzalo Muga,Andreas Ruschhaupt,Adolfo del Campo
Publisher : Springer
Page : 423 pages
File Size : 55,6 Mb
Release : 2010-01-13
Category : Science
ISBN : 9783642031748

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Time in Quantum Mechanics - Vol. 2 by Gonzalo Muga,Andreas Ruschhaupt,Adolfo del Campo Pdf

But all the clocks in the city Began to whirr and chime: ’O let not Time deceive you, You cannot conquer Time. W. H. Auden It is hard to think of a subject as rich, complex, and important as time. From the practical point of view it governs and organizes our lives (most of us are after all attached to a wrist watch) or it helps us to wonderfully ?nd our way in unknown territory with the global positioning system (GPS). More generally it constitutes the heartbeat of modern technology. Time is the most precisely measured quantity, so the second de?nes the meter or the volt and yet, nobody knows for sure what it is, puzzling philosophers, artists, priests, and scientists for centuries as one of the enduring enigmas of all cultures. Indeed time is full of contrasts: taken for granted in daily life, it requires sophisticated experimental and theoretical treatments to be accurately “produced. ” We are trapped in its web, and it actually kills us all, but it also constitutes the stuff we need to progress and realize our objectives. There is nothing more boring and monotonous than the tick-tock of a clock, but how many fascinating challenges have physicists met to realize that monotony: Quite a number of Nobel Prize winners have been directly motivated by them or have contributed 1 signi?cantly to time measurement.

Quantum Measurement

Andrew N. Jordan,Irfan A. Siddiqi

Author : Andrew N. Jordan,Irfan A. Siddiqi
Publisher : Cambridge University Press
Page : 283 pages
File Size : 53,9 Mb
Release : 2024-02-15
Category : Science
ISBN : 9781009100069

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Quantum Measurement by Andrew N. Jordan,Irfan A. Siddiqi Pdf

A novel, physics-first approach to quantum measurement, using physical experiments to describe the underlying mathematical formalism.

Quantum Probability and Related Topics

Franco Fagnola

Author : Franco Fagnola
Publisher : World Scientific
Page : 280 pages
File Size : 43,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814447546

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Quantum Probability and Related Topics by Franco Fagnola Pdf

This volume contains the current research in quantum probability, infinite dimensional analysis and related topics. Contributions by experts in these fields highlight the latest developments and interdisciplinary connections with classical probability, stochastic analysis, white noise analysis, functional analysis and quantum information theory.This diversity shows how research in quantum probability and infinite dimensional analysis is very active and strongly involved in the modern mathematical developments and applications.Tools and techniques presented here will be of great value to resear.

Quantum Probability and Related Topics

Luigi Accardi,Franco Fagnola

Author : Luigi Accardi,Franco Fagnola
Publisher : World Scientific
Page : 280 pages
File Size : 50,5 Mb
Release : 2012-11-22
Category : Mathematics
ISBN : 9789814447553

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Quantum Probability and Related Topics by Luigi Accardi,Franco Fagnola Pdf

This volume contains the current research in quantum probability, infinite dimensional analysis and related topics. Contributions by experts in these fields highlight the latest developments and interdisciplinary connections with classical probability, stochastic analysis, white noise analysis, functional analysis and quantum information theory. This diversity shows how research in quantum probability and infinite dimensional analysis is very active and strongly involved in the modern mathematical developments and applications. Tools and techniques presented here will be of great value to researchers. Contents:Central Extension of Virasoro Type Subalgebras of the Zamolodchikov–w∞ Lie Algebra (L Accardi and A Boukas)Entanglement Protection and Generation Under Continuous Monitoring (A Barchielli and M Gregoratti)Completely Positive Transformations of Quantum Operations (G Chiribella, A Toigo and V Umanità)Invariant Operators in Schrödinger Setting (V K Dobrev)Generation of Semigroups by Degenerate Elliptic Operators Arising in Open Quantum Systems (F Fagnola and L Pantaleón Martínez)Quantum Observables on a Completely Simple Semigroup (Ph. Feinsilver)A Mathematical Treatment for the Contextual Dependent Bio-Systems (T Hara and M Ohya)On the Spectral Gap of the N-Photon Absorption-Emission Process (R Hermida and R Quezada)Some Recent Topics on White Noise Theory (T Hida and Si Si)Quantum Lévy Area as Quantum Martingale Limit (R L Hudson)On Computational Complexity of Quantum Algorithm for Factoring (S Iriyama, M Ohya and I V Volovich)Prequantum Classical Statistical Field Theory: Derivation of Gaussianity of Probability Distributions (A Khrennikov)A Survey on Extensions of Hilbert C*-Modules (B Kolarec)An Isometry Formula for a New Stochastic Integral (H-H Kuo, A Sae-Tang and B Szozda)Infinite Dimensional Laplacians Associated with Derivatives of White Noise (K Saitô)A New Noise Depending on a Space Parameter and Its Transformations (Si Si)Note on Complexities for Gaussian Communication Processes (N Watanabe) Readership: Researchers in stochastic analysis, quantum probability, quantum information, mathematical modeling, and probability and statistics. Keywords:Quantum Probability;Infinite Dimensional Analysis;Quantum White Noise;Quantum Markov Semigroups;Quantum Stochastic Calculus;Quantum Computation;Quantum Measurement;Quantum OperationsKey Features:Clear and quick information on hot research topicsOriginality of contributionsLeading expects in their field

Quantum Information and Foundations

Giacomo Mauro D’Ariano,Paolo Perinotti

Author : Giacomo Mauro D’Ariano,Paolo Perinotti
Publisher : MDPI
Page : 508 pages
File Size : 53,7 Mb
Release : 2020-03-23
Category : Mathematics
ISBN : 9783039283804

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Quantum Information and Foundations by Giacomo Mauro D’Ariano,Paolo Perinotti Pdf

Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultra-sensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on non-causal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.

Collapse of the Wave Function

Shan Gao

Author : Shan Gao
Publisher : Cambridge University Press
Page : 361 pages
File Size : 53,7 Mb
Release : 2018-04-26
Category : Science
ISBN : 9781108428989

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Collapse of the Wave Function by Shan Gao Pdf

An overview of the collapse theories of quantum mechanics. Written by distinguished physicists and philosophers of physics, it discusses the origin and implications of wave-function collapse, the controversies around collapse models and their ontologies, and new arguments for the reality of wave function collapse.

Quantum Limits on Measurement and Control of a Mechanical Oscillator

Vivishek Sudhir

Author : Vivishek Sudhir
Publisher : Springer
Page : 214 pages
File Size : 51,5 Mb
Release : 2017-11-21
Category : Science
ISBN : 9783319694313

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Quantum Limits on Measurement and Control of a Mechanical Oscillator by Vivishek Sudhir Pdf

This thesis reports on experiments in which the motion of a mechanical oscillator is measured with unprecedented precision. The position fluctuations of the oscillator—a glass nanostring—are measured with an imprecision that is sufficient to resolve its quantum zero-point motion within its thermal decoherence time. The concomitant observation of measurement back-action, in accordance with Heisenberg’s uncertainty principle, verifies the principles of linear quantum measurements on a macroscopic mechanical object. The record of the measurement is used to perform feedback control so as to suppress both classical thermal motion and quantum measurement back-action. These results verify some of the central and long-standing predictions of quantum measurement theory applied to a macroscopic object. The act of measurement not only perturbs the subject of the measurement—the mechanical oscillator—but also changes the state of the light used to make the measurement. This prediction is verified by demonstrating that the optical field, after having interacted with the mechanical oscillator, contains quantum correlations that render its quadrature fluctuations smaller than those of the vacuum – i.e., the light is squeezed. Lastly, the thesis reports on some of the first feedback control experiments involving macroscopic objects in the quantum regime, together with an exploration of the quantum limit of feedback control. The book offers a pedagogical account of linear measurement theory, its realization via optical interferometry, and contains a detailed guide to precision optical interferometry..

Formulation and Numerical Solution of Quantum Control Problems

Alfio Borzi,Gabriele Ciaramella,Martin Sprengel

Author : Alfio Borzi,Gabriele Ciaramella,Martin Sprengel
Publisher : SIAM
Page : 390 pages
File Size : 46,7 Mb
Release : 2017-07-06
Category : Technology & Engineering
ISBN : 9781611974843

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Formulation and Numerical Solution of Quantum Control Problems by Alfio Borzi,Gabriele Ciaramella,Martin Sprengel Pdf

This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the SchrÓdinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods.

Photonics, Volume 1

David L. Andrews

Author : David L. Andrews
Publisher : John Wiley & Sons
Page : 472 pages
File Size : 46,6 Mb
Release : 2015-01-16
Category : Technology & Engineering
ISBN : 9781119009702

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Photonics, Volume 1 by David L. Andrews Pdf

Covers modern photonics accessibly and discusses the basic physical principles underlying all the applications and technology of photonics. This volume covers the basic physical principles underlying the technology and all applications of photonics from statistical optics to quantum optics. The topics discussed in this volume are: Photons in perspective; Coherence and Statistical Optics; Complex Light and Singular Optics; Electrodynamics of Dielectric Media; Fast and slow Light; Holography; Multiphoton Processes; Optical Angular Momentum; Optical Forces, Trapping and Manipulation; Polarization States; Quantum Electrodynamics; Quantum Information and Computing; Quantum Optics; Resonance Energy Transfer; Surface Optics; Ultrafast Pulse Phenomena. Comprehensive and accessible coverage of the whole of modern photonics Emphasizes processes and applications that specifically exploit photon attributes of light Deals with the rapidly advancing area of modern optics Chapters are written by top scientists in their field Written for the graduate level student in physical sciences; Industrial and academic researchers in photonics, graduate students in the area; College lecturers, educators, policymakers, consultants, Scientific and technical libraries, government laboratories, NIH.

Continuous Quantum Measurements and Path Integrals

M.B Mensky

Author : M.B Mensky
Publisher : CRC Press
Page : 188 pages
File Size : 46,9 Mb
Release : 2017-10-19
Category : Science
ISBN : 9781351458030

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Continuous Quantum Measurements and Path Integrals by M.B Mensky Pdf

Advances in technology are taking the accuracy of macroscopic as well as microscopic measurements close to the quantum limit, for example, in the attempts to detect gravitational waves. Interest in continuous quantum measurements has therefore grown considerably in recent years. Continuous Quantum Measurements and Path Integrals examines these measurements using Feynman path integrals. The path integral theory is developed to provide formulae for concrete physical effects. The main conclusion drawn from the theory is that an uncertainty principle exists for processes, in addition to the familiar one for states. This implies that a continuous measurement has an optimal accuracy-a balance between inefficient error and large quantum fluctuations (quantum noise). A well-known expert in the field, the author concentrates on the physical and conceptual side of the subject rather than the mathematical.

Quantum Trajectories

Pratim Kumar Chattaraj

Author : Pratim Kumar Chattaraj
Publisher : CRC Press
Page : 429 pages
File Size : 43,7 Mb
Release : 2016-04-19
Category : Science
ISBN : 9781439825624

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Quantum Trajectories by Pratim Kumar Chattaraj Pdf

The application of quantum mechanics to many-particle systems has been an active area of research in recent years as researchers have looked for ways to tackle difficult problems in this area. The quantum trajectory method provides an efficient computational technique for solving both stationary and time-evolving states, encompassing a large area of quantum mechanics. Quantum Trajectories brings the expertise of an international panel of experts who focus on the epistemological significance of quantum mechanics through the quantum theory of motion. Emphasizing a classical interpretation of quantum mechanics as developed by de Bröglie and Bohm, this volume: Introduces the concept of the quantum theory of motion Explains the connection with conventional quantum mechanics Presents various numerical techniques generated from the Bohmian approach Describes the epistemological significance of quantum trajectories Provides an authoritative account of the foundations of quantum mechanics vis-à-vis that of the Bohmian mechanics The popularity of using the quantum trajectory as a computational tool has exploded over the last decade, finally bringing this methodology to the level of practical applications. Many of the experts in the field who have either developed the methodology or have improved upon it have contributed chapters to this volume, making it a state-of-the-art expression of the field as it exists today and providing insight into the future of this technology.

Quantum Trajectories And Measurements In Continuous Time

Quantum Trajectories and Measurements in Continuous Time by Alberto Barchielli,Matteo Gregoratti Pdf

Quantum Trajectories and Measurements in Continuous Time by Alberto Barchielli,Matteo Gregoratti Pdf

Bohmian Mechanics, Open Quantum Systems and Continuous Measurements by Antonio B. Nassar,Salvador Miret-Artés Pdf

Continuous Quantum Measurements and Path Integrals by M.B Mensky Pdf

Time in Quantum Mechanics - Vol. 2 by Gonzalo Muga,Andreas Ruschhaupt,Adolfo del Campo Pdf

Quantum Measurement by Andrew N. Jordan,Irfan A. Siddiqi Pdf

Quantum Probability and Related Topics by Franco Fagnola Pdf

Quantum Probability and Related Topics by Luigi Accardi,Franco Fagnola Pdf

Quantum Information and Foundations by Giacomo Mauro D’Ariano,Paolo Perinotti Pdf

Collapse of the Wave Function by Shan Gao Pdf

Quantum Limits on Measurement and Control of a Mechanical Oscillator by Vivishek Sudhir Pdf

Formulation and Numerical Solution of Quantum Control Problems by Alfio Borzi,Gabriele Ciaramella,Martin Sprengel Pdf

Photonics, Volume 1 by David L. Andrews Pdf

Continuous Quantum Measurements and Path Integrals by M.B Mensky Pdf

Quantum Trajectories by Pratim Kumar Chattaraj Pdf

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