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Brownian Motion: The Quantum PerspectiveJul 08 2001We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.

Non-Markovian master equations from piecewise dynamicsJan 14 2013We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps, randomly distributed ... More

General structure of quantum collisional modelsApr 02 2014We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time dependent completely ... More

Non-Abelian linear Boltzmann equation and quantum correction to Kramers and Smoluchowski equationApr 19 2002A quantum linear Boltzmann equation is proposed, constructed in terms of the operator-valued dynamic structure factor of the macroscopic system the test particle is interacting with. Due to this operator structure it is a non-Abelian linear Boltzmann ... More

Reply to Comment on "Completely positive quantum dissipation"Jul 08 2001This is the reply to a Comment by R. F. O'Connell (Phys. Rev. Lett. 87 (2001) 028901) on a paper written by the author (B. Vacchini, ``Completely positive quantum dissipation'', Phys.Rev.Lett. 84 (2000) 1374, arXiv:quant-ph/0002094).

Theory of decoherence due to scattering events and Lévy processesOct 17 2005A general connection between the characteristic function of a L\'evy process and loss of coherence of the statistical operator describing the center of mass degrees of freedom of a quantum system interacting through momentum transfer events with an environment ... More

Generalized master equations leading to completely positive dynamicsNov 03 2016We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of memory kernels ... More

Master-equations for the study of decoherenceJan 10 2003Jul 24 2003Different structures of master-equation used for the description of decoherence of a microsystem interacting through collisions with a surrounding environment are considered and compared. These results are connected to the general expression of the generator ... More

Dissipative Systems and Objective Description: Quantum Brownian Motion as an ExampleApr 22 2002A structure of generator of a quantum dynamical semigroup for the dynamics of a test particle interacting through collisions with the environment is considered, which has been obtained from a microphysical model. The related master-equation is shown to ... More

Test Particle in a Quantum GasDec 22 2000A master equation with a Lindblad structure is derived, which describes the interaction of a test particle with a macroscopic system and is expressed in terms of the operator valued dynamic structure factor of the system. In the case of a free Fermi or ... More

Description of decoherence by means of translation-covariant master equations and Levy processesMar 04 2009Translation-covariant Markovian master equations used in the description of decoherence and dissipation are considered in the general framework of Holevo's results on the characterization of generators of covariant quantum dynamical semigroups. A general ... More

Covariant Mappings for the Description of Measurement, Dissipation and Decoherence in Quantum MechanicsJul 04 2007The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to the isochronous ... More

Quantum master equation for collisional dynamics of massive particles with internal degrees of freedomMar 04 2010Oct 26 2010We address the microscopic derivation of a quantum master equation in Lindblad form for the dynamics of a massive test particle with internal degrees of freedom interacting through collisions with a background ideal gas. When either internal or centre ... More

Kinetic description of quantum Brownian motionSep 03 2008We stress the relevance of the two features of translational invariance and atomic nature of the gas in the quantum description of the motion of a massive test particle in a gas, corresponding to the original picture of Einstein used in the characterization ... More

Reduced dynamical maps in the presence of initial correlationsMay 13 2016We introduce a general framework for the construction of completely positive dynamical evolutions in the presence of system-environment initial correlations. The construction relies upon commutativity of the compatibility domain obtained by considering ... More

Comment on "Quantum linear Boltzmann equation with finite intercollision time"Jul 17 2009Sep 27 2010Inconsistencies are pointed out in a recent proposal [L. Diosi, Phys. Rev. A 80, 064104 (2009); arXiv:0905.3908v1] for a quantum version of the classical linear Boltzmann equation.

On the quantum description of Einstein's Brownian motionNov 12 2004A fully quantum treatment of Einstein's Brownian motion is given, showing in particular the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature of the medium. ... More

Quantum Langevin equations for optomechanical systemsMar 23 2015Jun 24 2015We provide a fully quantum description of a mechanical oscillator in the presence of thermal environmental noise by means of a quantum Langevin formulation based on quantum stochastic calculus. The system dynamics is determined by symmetry requirements ... More

Decoherence Versus the Idealization of Microsystems as Correlation Carriers Between MacrosystemsNov 20 2002It is argued that the appropriate framework to describe a microsystem as a correlation carrier between a source and a detector is non-equilibrium statistical mechanics for the compound source-detector system. An attempt is given to elucidate how this ... More

Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level systemMay 10 2010We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The considered system includes the damped and undamped ... More

Monitoring derivation of the quantum linear Boltzmann equationNov 20 2007Feb 21 2008We show how the effective equation of motion for a distinguished quantum particle in an ideal gas environment can be obtained by means of the monitoring approach introduced in [EPL 77, 50007 (2007)]. The resulting Lindblad master equation accounts for ... More

Subdynamics of relevant observables: a field theoretical approachApr 16 2002An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory derivation ... More

Quantum linear Boltzmann equationApr 24 2009Jul 27 2009We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic ... More

Relaxation dynamics of a quantum Brownian particle in an ideal gasJun 29 2007We show how the quantum analog of the Fokker-Planck equation for describing Brownian motion can be obtained as the diffusive limit of the quantum linear Boltzmann equation. The latter describes the quantum dynamics of a tracer particle in a dilute, ideal ... More

Quantum Semi-Markov ProcessesSep 09 2008We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions ... More

Three-dimensional Monte Carlo simulations of the quantum linear Boltzmann equationJul 17 2007Recently the general form of a translation-covariant quantum Boltzmann equation has been derived which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full three-dimensional Monte ... More

Exact master equations for the non-Markovian decay of a qubitFeb 10 2010Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. Employing the exact solution for the model we determine analytical expressions for the memory kernel of the Nakajima-Zwanzig master equation ... More

Signatures of non-Markovianity in classical single-time probability distributionsNov 26 2012We show that the Kolmogorov distance allows to quantify memory effects in classical stochastic processes by studying the evolution of the single-time probability distribution. We further investigate the relation between the Kolmogorov distance and other ... More

On the Energy Increase in Space-Collapse ModelsJun 10 2005A typical feature of spontaneous collapse models which aim at localizing wavefunctions in space is the violation of the principle of energy conservation. In the models proposed in the literature the stochastic field which is responsible for the localization ... More

Generalized trace distance measure connecting quantum and classical non-MarkovianityJul 31 2015We establish a direct connection of quantum Markovianity of an open quantum system to its classical counterpart by generalizing the criterion based on the information flow. Here, the flow is characterized by the time evolution of Helstrom matrices, given ... More

Microscopic modelling of general time-dependent quantum Markov processesMar 14 2019Master equations are typically adopted to describe the dynamics of open quantum systems. Such equations are either in integro-differential or in time-local form, with the latter class more frequently adopted due to the simpler numerical methods developed ... More

Dissipative extension of the Ghirardi-Rimini-Weber modelAug 26 2014Jan 02 2015In this paper we present an extension of the Ghirardi-Rimini-Weber model for the spontaneous collapse of the wavefunction. Through the inclusion of dissipation, we avoid the divergence of the energy on the long time scale, which affects the original model. ... More

Quantum regression theorem and non-Markovianity of quantum dynamicsJun 20 2014We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behaviour in ... More

Energy backflow and non-Markovian dynamicsOct 08 2015Jan 23 2016We explore the behavior in time of the energy exchange between a system of interest and its environment, together with its relationship to the non-Markovianity of the system dynamics. In order to evaluate the energy exchange we rely on the full counting ... More

Entropy production and correlations in a controlled non-Markovian settingApr 11 2018Jul 23 2018We study the relationship between (non-)Markovian evolutions, established correlations, and the entropy production rate. We consider a system qubit in contact with a thermal bath and in addition the system is strongly coupled to an ancillary qubit. We ... More

Nonequilibrium quantum bounds to Landauer's principle: Tightness and effectivenessJul 28 2017Oct 13 2017We assess two different non-equilibrium quantum Landauer bounds: the traditional approach based on the change in entropy, referred to as the `entropic bound', and one based on the details of the dynamical map, referred to as the `thermodynamic bound'. ... More

Quantum non-Markovian piecewise dynamics from collision modelsJun 27 2017Recently, a large class of quantum non-Markovian piecewise dynamics for an open quantum system obeying closed evolution equations has been introduced [B. Vacchini, Phys. Rev. Lett. 117, 230401 (2016)]. These dynamics have been defined in terms of a waiting-time ... More

Universal Markovian reduction of Brownian particle dynamicsOct 22 2010Non-Markovian processes can often be turned Markovian by enlarging the set of variables. Here we show, by an explicit construction, how this can be done for the dynamics of a Brownian particle obeying the generalized Langevin equation. Given an arbitrary ... More

Non-Markovian dynamics in open quantum systemsMay 06 2015The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications ... More

Precursors of non-MarkovianityFeb 08 2019Using the paradigm of information backflow to characterize a non-Markovian evolution, we introduce so-called precursors of non-Markovianity, i.e. necessary properties that the system and environment state must exhibit at earlier times in order for an ... More

Decoherence and noise in open quantum system dynamicsMay 25 2016We consider the description of quantum noise within the framework of the standard Copenhagen interpretation of quantum mechanics applied to a composite system environment setting. Averaging over the environmental degrees of freedom leads to a stochastic ... More

A classical appraisal of quantum definitions of non-Markovian dynamicsJul 17 2012We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a classical process ... More

Quantum optical versus quantum Brownian motion master-equation in terms of covariance and equilibrium propertiesApr 15 2002Jun 26 2002Structures of quantum Fokker-Planck equations are characterized with respect to the properties of complete positivity, covariance under symmetry transformations and satisfaction of equipartition, referring to recent mathematical work on structures of ... More

Non-Markovian dynamics for bipartite systemsMay 05 2008Aug 26 2008We analyze the appearance of non-Markovian effects in the dynamics of a bipartite system coupled to a reservoir, which can be described within a class of non-Markovian equations given by a generalized Lindblad structure. A novel master equation, which ... More

Energy backflow in strongly coupled non-Markovian continuous-variables systemsJul 18 2016By employing the full counting statistics formalism, we characterize the first moment of energy that is exchanged during a generally non-Markovian evolution in non-driven continuous variables systems. In particular, we focus on the evaluation of the energy ... More

System-environment correlations and Markovian embedding of quantum non-Markovian dynamicsMay 24 2018Jul 10 2018We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e. the open dynamics is modelled through sequences of unitary interactions between the system and the individual constituents of the environment, ... More

Interaction-induced correlations and non-Markovianity of quantum dynamicsFeb 08 2013We investigate the conditions under which the trace distance between two different states of a given open system increases in time due to the interaction with an environment, therefore signalling non-Markovianity. We find that the finite-time difference ... More

Quantum interference induced by initial system-environment correlationsJul 23 2012We investigate the quantum interference induced by a relative phase in the correlated initial state of a system which consists in a two-level atom interacting with a damped mode of the radiation field. We show that the initial relative phase has significant ... More

Markovian and non-Markovian dynamics in quantum and classical systemsJun 01 2011We discuss the conceptually different definitions used for the non-Markovianity of classical and quantum processes. The well-established definition for non-Markovianity of a classical stochastic process represents a condition on the Kolmogorov hierarchy ... More

Two-step procedure to discriminate discordant from classical correlated or factorized statesNov 13 2014We devise and experimentally realize a procedure capable of detecting and distinguishing quantum discord and classical correlations as well the presence of factorized states in a joint system-environment setting. Our scheme builds on recent theoretical ... More

Collisional unfolding of quantum DarwinismJan 10 2019We examine the emergence of objectivity via quantum Darwinism through the use of a collision model, i.e. where the dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed ... More

Robust multipartite entanglement generation via a collision modelMar 14 2018Jan 14 2019We examine a simple scheme to generate genuine multipartite entangled states across disjoint qubit registers. We employ a shuttle qubit that is sequentially coupled, in an energy preserving manner, to the constituents within each register through rounds ... More

Quantum probes to assess correlations in a composite systemFeb 01 2013Apr 11 2013We suggest and demonstrate experimentally a strategy to obtain relevant information about a composite system by only performing measurements on a small and easily accessible part of it, which we call quantum probe. We show in particular how quantitative ... More

Experimental investigation of initial system-environment correlations via trace distance evolutionMay 01 2011Sep 19 2011The trace distance between two states of an open quantum system quantifies their distinguishability, and for a fixed environmental state can increase above its initial value only in the presence of initial system-environment correlations. We provide for ... More

All-optical quantum simulator of qubit noisy channelsDec 20 2016Feb 24 2017We suggest and demonstrate an all-optical quantum simulator for single-qubit noisy channels originating from the interaction with a fluctuating field. The simulator employs the polarization degree of freedom of a single photon, and exploits its spectral ... More

Structure of completely positive quantum master equations with memory kernelFeb 13 2009Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is demonstrated to yield ... More

Non-Markovianity by undersampling in quantum optical simulatorsMay 16 2017Dec 05 2017We unveil a novel source of non-Markovianity for the dynamics of quantum systems, which appears when the system does not explore the full set of dynamical trajectories in the interaction with its environment. We term this effect non-Markovianity by undersampling ... More

On the precise connection between the GRW master-equation and master-equations for the description of decoherenceJan 29 2007We point out that the celebrated GRW master-equation is invariant under translations, reflecting the homogeneity of space, thus providing a particular realization of a general class of translation-covariant Markovian master-equations. Such master-equations ... More

Quantum and classical features in the explanation of collisional decoherenceDec 16 2003A most simple theoretical argument is given in order to explain the quantitative estimate of the effect of collisional decoherence in matter-wave interferometry. The argument highlights the relevance of quantum and classical features in the description ... More

Complete positivity and subdynamics in quantum field theoryNov 20 2002The relevance that the property of complete positivity has had in the determination of quantum structures is briefly reviewed, together with recent applications to neutron optics and quantum Brownian motion. A possible useful application and generalization ... More

Translation-covariant Markovian master equation for a test particle in a quantum fluidJul 02 2001A recently proposed master equation in the Lindblad form is studied with respect to covariance properties and existence of a stationary solution. The master equation describes the interaction of a test particle with a quantum fluid, the so-called Rayleigh ... More

Completely Positive Quantum DissipationFeb 29 2000A completely positive master equation describing quantum dissipation for a Brownian particle is derived starting from microphysical collisions, exploiting a recently introduced approach to subdynamics of a macrosystem. The obtained equation can be cast ... More

Time scales in quantum mechanics by a scattering mapNov 29 1999Inside quantum mechanics the problem of decoherence for an isolated, finite system is linked to a coarse-grained description of its dynamics.

Full counting statistics approach to the quantum non-equilibrium Landauer boundApr 04 2017Nov 01 2017We develop the full counting statistics of dissipated heat to explore the relation with Landauer's principle. Combining the two-time measurement protocol for the reconstruction of the statistics of heat with the minimal set of assumptions for Landauer's ... More

Dynamical Semigroup Description of Coherent and Incoherent Particle-Matter InteractionFeb 26 1997The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of non-relativistic quantum field theory is proposed, to describe both coherent and incoherent interaction of a single ... More

Subdynamics through Time Scales and Scattering Maps in Quantum Field TheoryMar 04 1997It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics, e.g., hydrodynamics, ... More

Description of isolated macroscopic systems inside quantum mechanicsOct 09 1999For an isolated macrosystem classical state parameters $\zeta(t)$ are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval $[T,t_0]$ a statistical operator ... More

Quantum theory: the role of microsystems and macrosystemsJan 24 2007We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence for particles. ... More

Subdynamics as a mechanism for objective descriptionDec 13 1999The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship. This ... More

Physics of a microsystem starting from non-equilibrium quantum statistical mechanicsOct 30 2002In this paper we address the problem to give a concrete support to the idea, originally stemming from Niels Bohr, that quantum mechanics must be rooted inside the physics of macroscopic systems. It is shown that, starting from the formalism of the non-equilibrium ... More

Time Scale and Completely Positive Dynamical EvolutionsNov 20 2002It is argued that in the description of macroscopic systems inside quantum mechanics the study of the dynamics of selected degrees of freedom slowly varying on a suitable time scale, corresponding to relevant observables for the given reduced description, ... More

Initial correlations in open system's dynamics: The Jaynes-Cummings modelOct 21 2010Employing the trace distance as a measure for the distinguishability of quantum states, we study the influence of initial correlations on the dynamics of open systems. We concentrate on the Jaynes-Cummings model for which the knowledge of the exact joint ... More

A complete characterization of phase space measurementsMay 05 2004We characterize all the phase space measurements for a non-relativistic particle.

Incoherent dynamics in neutron-matter interactionSep 11 1997Coherent and incoherent neutron-matter interaction is studied inside a recently introduced approach to subdynamics of a macrosystem. The equation describing the interaction is of the Lindblad type and using the Fermi pseudopotential we show that the commutator ... More

Critical assessment of two-qubit post-Markovian master equationsMar 22 2012A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 (R) (2005)]. For a single qubit affected by appropriately ... More

Role of correlations in the thermalization of quantum systemsJul 16 2012We investigate the equilibration and thermalization properties of quantum systems interacting with a finite dimensional environment. By exploiting the concept of time averaged states, we introduce a completely positive map which allows to describe in ... More