Related papers: Repeated quantum interactions Quantum Langevin equ…
We consider the general physical situation of a quantum system $\H_0$ interacting with a chain of exterior systems $\bigotimes_\N \H$, one after the other, during a small interval of time $h$ and following some Hamiltonian $H$ on $\H_0…
We consider the physical model of a classical mechanical system (called "small system") undergoing repeated interactions with a chain of identical small pieces (called "environment"). This physical setup constitutes an advantageous way of…
We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in…
We consider a non-interacting bipartite quantum system $\mathcal H_S^A\otimes\mathcal H_S^B$ undergoing repeated quantum interactions with an environment modeled by a chain of independant quantum systems interacting one after the other with…
In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical…
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…
We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal equilibrium at inverse temperature $\beta$. The time evolution is discrete and such that over each time step of…
First weak solutions of generalized stochastic Hamiltonian systems (gsHs) are constructed via essential m-dissipativity of their generators on a suitable core. For a scaled gsHs we prove convergence of the corresponding semigroups and…
The thermodynamic framework of repeated interactions is generalized to an arbitrary open quantum system in contact with a heat bath. Based on these findings the theory is then extended to arbitrary measurements performed on the system. This…
Among the discrete evolution equations describing a quantum system $\rH_S$ undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in…
A quantum system interacting with a dilute gas experiences irreversible dynamics. The corresponding master equation can be derived within two different approaches: The fully quantum description in the low-density limit and the semiclassical…
This paper gives an overview of recent results concerning the long time dynamics of repeated interaction quantum systems in a deterministic and random framework. We describe the non equilibrium steady states (NESS) such systems display and…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
A quantum system $\s$ interacts in a successive way with elements $\ee$ of a chain of identical independent quantum subsystems. Each interaction lasts for a duration $\tau$ and is governed by a fixed coupling between $\s$ and $\ee$. We show…
The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…
We study the evolution of a quantum particle interacting with a random potential in the low density limit (Boltzmann-Grad). The phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear…
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…
The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy.…
We introduce an alternative way to understand the decomposition of a quantum system into interacting parts and show that it is natural in several physical models. This enables us to define a reduced density operator for a working system…
The $XXZ$ model $(s = 1/2)$ in a transverse field on a double chain with a uniform long-range interaction among the $z$ components of the spins is considered. The nearest-neighbour interactions are restricted to the components in the $xy$…