Dynamics of collective decoherence and thermalization

Merkli, Marco; Berman, G. P.; Sigal, Israel Michael

doi:10.1016/j.aop.2008.07.004

Cited by 23 publications

(78 citation statements)

References 26 publications

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“…Any real measurement requires finite time and involves interactions with measuring devices and observers [6,[36][37][38][39]. Even the so-called nondemolition and nondestructive measurements may essentially influence the measured system [40][41][42][43]. In what follows, the environment, including measuring apparatuses and observers, acting on the system in the process of measurement, will be called for short a measurer.…”

Section: Quantum State Reductionmentioning

confidence: 99%

Quantum probabilities of composite events in quantum measurements with multimode states

Yukalov

Sornette

2013

Laser Phys.

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The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that the Lüders probability of consecutive measurements is a transition probability between two quantum states and that this probability cannot be treated as a quantum extension of the classical conditional probability. The Wigner distribution is shown to be a weighted transition probability that cannot be accepted as a quantum extension of the classical joint probability. We suggest the definition of quantum joint probabilities by introducing composite events in multichannel measurements. The notion of measurements under uncertainty is defined. We demonstrate that the necessary condition for the mode interference is the entanglement of the composite prospect together with the entanglement of the composite statistical state. As an illustration, we consider an example of a quantum game. A special attention is payed to the application of the approach to systems with multi-mode states, such as atoms, molecules, quantum dots, or trapped Bose-condensed atoms with several coherent modes.

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Section: Quantum State Reductionmentioning

confidence: 99%

Quantum probabilities of composite events in quantum measurements with multimode states

Yukalov

Sornette

2013

Laser Phys.

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“…Recently, a method based on graph expansions of the propagator rather than purely spectral considerations was given in [12]. The spectral approach has been further developed to yield a detailed description of open systems dynamics in terms of resonances in [33,34,35], with applications to quantum information theory [28,30] and quantum chemistry [29]. The spectral analysis and its consequences for "return to equilibrium" based on Mourre theory and positive commutators was carried out in [13,27,18,14].…”

Section: 2mentioning

confidence: 99%

On the irreversible dynamics emerging from quantum resonances

Könenberg

Merkli

2016

Journal of Mathematical Physics

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Abstract. We consider the dynamics of quantum systems which possess stationary states as well as slowly decaying, metastable states arising from the perturbation of bound states. We give a decomposition of the propagator into a sum of a stationary part, one exponentially decaying in time and a polynomially decaying remainder. The exponential decay rates and the directions of decay in Hilbert space are determined, respectively, by complex resonance energies and by projections onto resonance states. Our approach is based on an elementary application of the Feshbach map. It is applicable to open quantum systems and to situations where spectral deformation theory fails. We derive a detailed description of the dynamics of the spin-boson model at arbitrary coupling strength.

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“…While this topic of fundamental interest has a long tradition in physics and mathematics, conventionally explored via master equations [6,9], dynamical semi-groups [3,6] and algebraic scattering theory [16,33], many recent works focus on a quantum resonance theory approach. The latter has been applied successfully to systems close to equilibrium [18,[27][28][29] and far from equilibrium [19,26]. In both situations, one of the main questions is the (time-) asymptotic behaviour of a quantum system consisting of a subsystem S interacting with one or several other subsystems, given by thermal reservoirs R 1 , .…”

Section: Introductionmentioning

confidence: 99%

“…While the initial motivation for the development of the dynamical resonance theory was the investigation of the time-asymptotics, the method is becoming increasingly refined. It has been extended to give a precise picture of the dynamics of open quantum systems for all times t ≥ 0, with applications to the phenomena of decoherence, disentanglement, and their relation to thermalization [24,[27][28][29]. An extension to systems with rather arbitrary time-dependent Hamiltonians has been presented in [30] (see also [2] for time-periodic systems).…”

Section: Introductionmentioning

confidence: 99%

Repeated and Continuous Interactions in Open Quantum Systems

Bruneau

Joye

Merkli

2009

Ann. Henri Poincaré

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We consider a finite quantum system S coupled to two environments of different nature. One is a heat reservoir R (continuous interaction) and the other one is a chain C of independent quantum systems E (repeated interaction). The interactions of S with R and C lead to two simultaneous dynamical processes. We show that for generic such systems, any initial state approaches an asymptotic state in the limit of large times. We express the latter in terms of the resonance data of a reduced propagator of S + R and show that it satisfies a second law of thermodynamics. We analyze a model where both S and E are two-level systems and obtain the asymptotic state explicitly (at lowest order in the interaction strength). Even though R and C are not directly coupled, we show that they exchange energy, and we find the dependence of this exchange in terms of the thermodynamic parameters. We formulate the problem in the framework of W * -dynamical systems and base the analysis on a combination of spectral deformation methods and repeated interaction model techniques. We analyze the full system via rigorous perturbation theory in the coupling strength, and do not resort to any scaling limit, like e.g. weak coupling limits, or any other approximations in order to derive some master equation.A.

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Dynamics of collective decoherence and thermalization

Cited by 23 publications

References 26 publications

Quantum probabilities of composite events in quantum measurements with multimode states

Quantum probabilities of composite events in quantum measurements with multimode states

On the irreversible dynamics emerging from quantum resonances

Repeated and Continuous Interactions in Open Quantum Systems

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