Related papers: Risk-sensitive Dissipativity of Linear Quantum Sto…
This paper is concerned with stochastic Hamiltonian systems which model a class of open dynamical systems subject to random external forces. Their dynamics are governed by Ito stochastic differential equations whose structure is specified…
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…
This paper is concerned with multimode open quantum harmonic oscillators and quadratic-exponential functionals (QEFs) as quantum risk-sensitive performance criteria. Such systems are described by linear quantum stochastic differential…
This paper is concerned with open quantum systems whose dynamic variables satisfy canonical commutation relations and are governed by quantum stochastic differential equations. The latter are driven by quantum Wiener processes which…
This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
This paper is concerned with quadratic-exponential moments (QEMs) for dynamic variables of quantum stochastic systems with position-momentum type canonical commutation relations. The QEMs play an important role for statistical…
This paper is concerned with the original risk-sensitive performance criterion for quantum stochastic systems and its recent quadratic-exponential counterpart. These functionals are of different structure because of the noncommutativity of…
This paper extends the Karhunen-Loeve representation from classical Gaussian random processes to quantum Wiener processes which model external bosonic fields for open quantum systems. The resulting expansion of the quantum Wiener process in…
We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a…
This paper is concerned with the sensitivity of invariant states in linear quantum stochastic systems with respect to nonlinear perturbations. The system variables are governed by a Markovian Hudson-Parthasarathy quantum stochastic…
The concept of dissipativity plays a crucial role in the analysis of control systems. Dissipative energy functionals, also known as Hamiltonians, storage functions, or Lyapunov functions, depending on the setting, are extremely valuable to…
This paper is concerned with a class of open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices pertaining to finite-level systems. The system interacts with external bosonic fields,…
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic…
The unraveling of open quantum system dynamics in terms of stochastic quantum trajectories offers a picture of open system dynamics that consistently considers memory effects stemming from the finite correlation time of environment…
A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…
We discuss dynamical response theory of driven-dissipative quantum systems described by Markovian Master Equations generating semi-groups of maps. In this setting thermal equilibrium states are replaced by non-equilibrium steady states and…
We extend deterministic port-Hamiltonian systems (PHS) to a stochastic framework by means of stochastic differential equations. As the dissipation inequality plays a crucial role for deterministic PHS, we develop several passivity concepts…
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…
In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it…