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The repeated interaction model provides a framework for emulating and analyzing the dynamics of open quantum systems. We explore here the dynamics generated by this protocol in a system that is simultaneously coupled to two baths through noncommuting system operators. One bath is made to couple to nondiagonal elements of the system, thus it induces dissipative dynamics, while the other couples to diagonal elements, and by itself it generates pure dephasing. By solving the model analytically exactly, we show that when both baths act concurrently, a strong system-bath coupling gives rise to nonadditive effects in the dynamics. A prominent signature of this nonadditivity is the characteristic slowing down of population relaxation, driven by the influence of the dephasing bath. Beyond dynamics, we investigate the thermodynamic behavior of the model. Previous studies, using quantum master equations, showed that strong system-bath coupling created bath-cooperativity in this model, allowing heat exchange to the dephasing (diagonally coupled) bath. We find instead that, under the repeated interaction (RI) scheme, heat flows exclusively to the dissipative bath (coupled through nondiagonal elements). Our results highlight the need for a deeper understanding of the types of open quantum system (OQS) dynamics and steady-state phenomena that emerge within the RI framework and the relation of this protocol to other common OQS techniques.

I study optimal design of a dynamic capital allocation process in an organization in which the division manager with empire-building preferences privately observes the arrival and properties of investment projects, and headquarters can audit projects at a cost. Under certain conditions, a budgeting mechanism with threshold separation of financing is optimal. Headquarters: (1) allocate a spending account to the manager and replenish it over time; (2) set a threshold, such that projects below it are financed from the account, while projects above are financed fully by headquarters upon an audit. Further analysis studies when co-financing of projects is optimal and how the size of the account depends on past performance of projects.

We study linear response theory and entropic fluctuations of finite dimensional non-equilibrium Repeated Interaction Systems (RIS). More precisely, in a situation where the temperatures of the probes can take a finite number of different values, we prove analogs of the Green–Kubo fluctuation–dissipation formula and Onsager reciprocity relations on energy flux observables. Then we prove a Large Deviation Principle, or Fluctuation Theorem, and a Central Limit Theorem on the full counting statistics of entropy fluxes. We consider two types of non-equilibrium RIS: either the temperatures of the probes are deterministic and arrive in a cyclic way, or the temperatures of the probes are described by a sequence of i.i.d. random variables with uniform distribution over a finite set.

Formal contracting addresses the moral hazard problems inherent in interfirm deals via explicit terms designed to achieve incentive alignment. Alternatively, when firms expect to interact repeatedly, relational mechanisms may achieve similar results without the associated costs. However, as we now know from a growing body of theoretical and empirical work, the resulting intuition—that relational mechanisms will be substituted for formal ones whenever possible—does not generally hold. The extent to which firms substitute relational mechanisms for formal ones in the presence of repeated interaction is an empirical question that forms the basis of this paper. We study a sample of 52 joint technology development contracts in the telecommunications and microelectronics industries and devise a coding scheme to allow empirical comparison of contract terms. Counter to the above intuition (but consistent with recent research), we find that a firm's contracts are more detailed and more likely to include penalties when it engages in frequent deals (whether with the same or different partners). Our results suggest complementarity between formal and relational contracts, and have implications for optimal contracting, particularly in high technology sectors.

Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, and quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas. Here we develop a tensor network formalism to address both challenges. We show that the induced correlations in the standard collision model are well captured by a matrix product state (a matrix product density operator) if the colliding particles are in pure (mixed) states. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory-kernel master equation. Analyzing the perturbation series for the memory kernel, we go beyond the recent results concerning the leading role of two-point correlations and consider multipoint correlations (Waldenfelds cumulants) that become relevant in the higher-order stroboscopic limits. These results open an avenue for the further analysis of memory effects in collisional quantum dynamics.

Organizations interacting repeatedly on similar transactions may learn from prior experiences, allowing contracts to be specified in greater detail. In this study, we analyze the conditions under which this learning effect is most likely to manifest itself. We do this by focusing on different parts of a contract as well as differences across transacting parties. Using a survey of information technology procurement contracts from 788 Dutch small- and medium-sized enterprises, we show that the learning effect is stronger for technical than for legal detail in contracts and is stronger for firms with information technology expertise than for firms without such expertise.

Obtaining the total wavefunction evolution of interacting quantum systems provides access to important properties, such as entanglement, shedding light on fundamental aspects, e.g., quantum energetics and thermodynamics, and guiding towards possible application in the fields of quantum computation and communication. We consider a two-level atom (qubit) coupled to the continuum of travelling modes of a field confined in a one-dimensional chiral waveguide. Originally, we treated the light-matter ensemble as a closed, isolated system. We solve its dynamics using a collision model where individual temporal modes of the field locally interact with the qubit in a sequential fashion. This approach allows us to obtain the total wavefunction of the qubit-field system, at any time, when the field starts in a coherent or a single-photon state. Our method is general and can be applied to other initial field states.

A new type of quantum random walks, called Open Quantum Random Walks, has been developed and studied in Attal et al. (Open quantum random walks, preprint) and (Central limit theorems for open quantum random walks, preprint). In this article we present a natural continuous time extension of these Open Quantum Random Walks. This continuous time version is obtained by taking a continuous time limit of the discrete time Open Quantum Random Walks. This approximation procedure is based on some adaptation of Repeated Quantum Interactions Theory (Attal and Pautrat in Annales Henri Poincaré Physique Théorique 7:59–104, 2006) coupled with the use of correlated projectors (Breuer in Phys Rev A 75:022103, 2007). The limit evolutions obtained this way give rise to a particular type of quantum master equations. These equations appeared originally in the non-Markovian generalization of the Lindblad theory (Breuer in Phys Rev A 75:022103, 2007). We also investigate the continuous time limits of the quantum trajectories associated with Open Quantum Random Walks. We show that the limit evolutions in this context are described by jump stochastic differential equations. Finally we present a physical example which can be described in terms of Open Quantum Random Walks and their associated continuous time limits.

We study the Stag Hunt game where two players simultaneously decide whether to cooperate or to choose their outside options (defect). A player’s gain from defection is his private information (the type). The two players’ types are independently drawn from the same cumulative distribution. We focus on the case where only a small proportion of types are dominant (higher than the value from cooperation). It is shown that for a wide family of distribution functions, if the players interact only once, the unique equilibrium outcome is defection by all types of player. Whereas if a second interaction is possible, the players will cooperate with positive probability and already in the first period. Further restricting the family of distributions to those that are sufficiently close to the uniform distribution, cooperation in both period with probability close to 1 is achieved, and this is true even if the probability of a second interaction is very small.

We consider a generalized model of repeated quantum interactions, where a system is interacting in a random way with a sequence of independent quantum systems . Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between and . The other involves random quantum states describing each copy . In the limit of a large number of interactions, we present convergence results for the asymptotic state of . This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the asymptotic induced ensemble .