Repeated and Continuous Interactions in Open Quantum Systems

Bruneau, Laurent; Joye, Alain; Merkli, Marco

doi:10.1007/s00023-009-0017-8

Cited by 13 publications

(18 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The reservoir R is a thermal reservoir of free Fermi particles at a temperature T R > 0, in the thermodynamic limit. Its description was originally given in the work by Araki and Wyss [AW] (see also [JP2,BJM4]). The Hilbert space is the anti-symmetric Fock space B(H R ) = Γ − (h) where G is an 'auxiliary space' (typically an angular part like L 2 (S 2 )).…”

Section: The Additional Reservoirmentioning

confidence: 99%

Repeated interactions in open quantum systems

Bruneau

Joye

Merkli

2014

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium.Comment: Lecture notes of the summer school "Non-equilibrium statistical mechanics" (Montreal, July 2011

show abstract

Section: The Additional Reservoirmentioning

confidence: 99%

Repeated interactions in open quantum systems

Bruneau

Joye

Merkli

2014

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The literature on repeated interaction systems we are aware of can be classified into two categories. In a first one, effective evolution equations are derived by taking continuous interaction limits [5,6,2,3,33,34,21] and in a second category, the dynamics is left discrete, but the time-asymptotics is investigated [11,12,13,14,8,9,22,31]. To our knowledge, repeated interaction systems have been first proposed in [27,28] and in [5,6] as approximations for system-environment type models, where it is proven that the discrete evolution converges to that of a quantum Langevin equation, in the limit of ever shorter system-probe interaction times.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…The eigenvalues m of M are the possible measurement outcomes. Due to finite dimensionality, the random variables X n have finite range.The present work can be viewed as the continuation of recently developed techniques for the mathematical analysis of repeated interaction quantum systems [11,12,13,14]. In these references, asymptotic properties of the scatterer have been investigated, without considering the fate of the outcoming probes, and without quantum measurements.…”

mentioning

confidence: 99%

Quantum Measurements of Scattered Particles

Merkli

Penney

2015

Mathematics

Self Cite

View full text Add to dashboard Cite

Abstract:We investigate the process of quantum measurements on scattered probes. Before scattering, the probes are independent, but they become entangled afterwards, due to the interaction with the scatterer. The collection of measurement results (the history) is a stochastic process of dependent random variables. We link the asymptotic properties of this process to spectral characteristics of the dynamics. We show that the process has decaying time correlations and that a zero-one law holds. We deduce that if the incoming probes are not sharply localized with respect to the spectrum of the measurement operator, then the process does not converge. Nevertheless, the scattering modifies the measurement outcome frequencies, which are shown to be the average of the measurement projection operator, evolved for one interaction period, in an asymptotic state. We illustrate the results on a truncated Jaynes-Cummings model.

show abstract

“…We remark that the setup specified so far is identical to the framework of repeated interactions or collisional models as considered in Refs. [17,[45][46][47]. Next, we want to explicitly include measurements and conditioning in the description.…”

Section: Autonomous Modelmentioning

confidence: 99%

Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach

Strasberg

2020

Quantum

View full text Add to dashboard Cite

Operational quantum stochastic thermodynamics is a recently proposed theory to study the thermodynamics of open systems based on the rigorous notion of a quantum stochastic process or quantum causal model. In there, a stochastic trajectory is defined solely in terms of experimentally accessible measurement results, which serve as the basis to define the corresponding thermodynamic quantities. In contrast to this observer-dependent point of view, a 'black box', which evolves unitarily and can simulate any quantum causal model, is constructed here. The quantum thermodynamics of this big isolated system can then be studied using widely accepted arguments from statistical mechanics. It is shown that the resulting definitions of internal energy, heat, work, and entropy have a natural extension to the trajectory level. The canonical choice of them coincides with the proclaimed definitions of operational quantum stochastic thermodynamics, thereby providing strong support in favour of that novel framework. However, a few remaining ambiguities in the definition of stochastic work and heat are also discovered and in light of these findings some other proposals are reconsidered. Finally, it is demonstrated that the first and second law hold for an even wider range of scenarios than previously thought, covering arbitrary quantum causal models based solely on a single assumption about the initial system-bath state.

show abstract

Repeated and Continuous Interactions in Open Quantum Systems

Cited by 13 publications

References 29 publications

Repeated interactions in open quantum systems

Repeated interactions in open quantum systems

Quantum Measurements of Scattered Particles

Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach

Contact Info

Product

Resources

About