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A spin (qubit) is in contact with a bosonic reservoir. The state of the reservoir contains a parameter {\varepsilon} interpolating between quantum and classical reservoir features. We derive the explicit expression for the time-dependent reduced spin density matrix, valid for all values of {\varepsilon} and for energy conserving interactions. We study decoherence and markovianity properties. Our main finding is that the spin decoherence is enhanced (full decoherence) when the spin is coupled to quantum reservoir states while it is dampened (partial decoherence) when coupled to classical reservoir states. The markovianity properties depend in a subtle way on the classicality parameter {\varepsilon} and on the finer details of the spin-reservoir interaction. We further examine scattering and periodicity properties for energy exchange interactions.

In this paper we study the semiclassical limit $\hslash\to 0$ of a completely solvable model in quantum field theory: the van Hove model, describing a scalar field created and annihilated by an immovable source. Despite its simplicity, the van Hove model possesses many characterizing features of quantum fields, especially in the infrared region. In particular, the existence of non-Fock ground and equilibrium states in the presence of infrared singular sources makes a representation-independent algebraic approach of utmost importance. We make use of recent representation-independent techniques of infinite dimensional semiclassical analysis to establish the Bohr correspondence principle for the dynamics, equilibrium states, and long-time asymptotics in the van Hove model., Comment: 39 pages, no figures

We study effective models describing systems of quantum particles interacting with quantized (electromagnetic) fields in the quasi-classical regime, i.e., when the field's state shows a large average number of excitations. Once the field's degrees of freedom are traced out on factorized states, the reduced dynamics of the particles' system is described by an effective Schr\"{o}dinger operator keeping track of the field's state. We prove that, under suitable assumptions on the latter, such effective models are well-posed even if the particles are point-like, that is no ultraviolet cut-off is imposed on the interaction with quantum fields., Comment: 24 pages

We consider the quasi-classical limit of Nelson-type regularized polaron models describing a particle interacting with a quantized bosonic field. We break translation-invariance by adding an attractive external potential decaying at infinity, acting on the particle. In the strong coupling limit where the field behaves classically we prove that the model's energy quasi-minimizers strongly converge to ground states of the limiting Pekar-like non-linear model. This holds for arbitrarily small external attractive potentials, hence this binding is fully due to the interaction with the bosonic field. We use a new approach to the construction of quasi-classical measures to revisit energy convergence, and a localization method in a concentration-compactness type argument to obtain convergence of states.

The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation, versatility, and predisposition to be employed in model-free settings, the LP approach has not enjoyed the same popularity as the other methods. The reason is the often poor scalability of the exact LP approach and the difficulty to obtain bounded solutions for a reasonable amount of constraints. We mitigate these issues here, by investigating fundamental geometric features of the LP and developing sufficient conditions to guarantee finite solutions with minimal constraints. In the model-free context, we show that boundedness can be guaranteed by a suitable choice of dataset and objective function.

A new paradigm is proposed for the robustification of the LQG controller against distributional uncertainties on the noise process. Our controller optimizes the closed-loop performances in the worst possible scenario under the constraint that the noise distributional aberrance does not exceed a certain threshold limiting the relative entropy pseudo-distance between the actual noise distribution the nominal one. The main novelty is that the bounds on the distributional aberrance can be arbitrarily distributed along the whole disturbance trajectory. We discuss why this can, in principle, be a substantial advantage and we provide simulation results that substantiate such a principle.

We consider the time evolution of the renormalized Nelson model, which describes $N$ bosons linearly coupled to a quantized scalar field, in the mean-field limit of many particles $N\gg 1$ with coupling constant proportional to $N^{-1/2}$. First, we show that initial states exhibiting Bose-Einstein condensation for the particles and approximating a coherent state for the quantum field retain their structure under the many-body time evolution. Concretely, the dynamics of the reduced densities are approximated by solutions of two coupled PDEs, the Schr\"odinger-Klein-Gordon equations. Second, we construct a renormalized Bogoliubov evolution that describes the quantum fluctuations around the Schr\"odinger-Klein-Gordon equations. This evolution is used to extend the approximation of the evolved many-body state to the full norm topology. In summary, we provide a comprehensive analysis of the Nelson model that reveals the role of renormalization in the mean-field Bogoliubov theory., Comment: 76 pages, 1 figure

With the increase in health consciousness, noninvasive body monitoring has aroused interest among researchers. As one of the most important pieces of physiological information, researchers have remotely estimated the heart rate (HR) from facial videos in recent years. Although progress has been made over the past few years, there are still some limitations, like the processing time increasing with accuracy and the lack of comprehensive and challenging datasets for use and comparison. Recently, it was shown that HR information can be extracted from facial videos by spatial decomposition and temporal filtering. Inspired by this, a new framework is introduced in this paper to remotely estimate the HR under realistic conditions by combining spatial and temporal filtering and a convolutional neural network. Our proposed approach shows better performance compared with the benchmark on the MMSE-HR dataset in terms of both the average HR estimation and short-time HR estimation. High consistency in short-time HR estimation is observed between our method and the ground truth.

This paper deals with the estimation of the hidden factor in Dynamic Generalized Factor Analysis via a generalization of Kalman filtering. Asymptotic consistency is discussed and it is shown that the Kalman one-step predictor is not the right tool while the pure filter yields a consistent estimate.

In this short note we study Spin-Boson Models from the Quasi-Classical standpoint. In the Quasi-Classical limit, the field becomes macroscopic while the particles it interacts with, they remain quantum. As a result, the field becomes a classical environment that drives the particle system with an explicit effective dynamics., Comment: 15 pages