Related papers: Mean field master equation for self-interacting ba…
Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…
We study the response of ideal spin systems which are interacting with both a strong oscillating magnetic field, and a thermal environment, to a weak probing magnetic field. We demonstrate that even the sign of the resulting mean…
Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…
We discuss the dynamics of a spin coupled to a damped harmonic oscillator. This system can be mapped to a spin-boson model with a structured bath, i.e. the spectral function of the bath has a resonance peak. We diagonalize the model by…
We consider a bipartite mean-field model in which both the interaction constant and the external field take different values only depending on the groups particles belong to. We compute the exact value of the thermodynamic limit of the…
Computing the exact dynamics of many-body quantum systems becomes intractable as system size grows. Here, we present a symmetry-based method that provides an exponential reduction in the complexity of a broad class of such problems…
Dynamical mean-field approximation with explicit pairing is utilized to study the properties of a two-component Fermi gas at unitarity. The problem is approximated by the lattice Hubbard Hamiltonian, and the continuum limit is realized by…
We present an efficient impurity solver for the dynamical mean-field theory (DMFT). It is based on the separation of bath degrees of freedom into the low energy and the high energy parts. The former is solved exactly using exact…
We derive the general form of a master equation describing the interaction of an arbitrary multipartite quantum system, consisting of a set of subsystems, with an environment, consisting of a large number of sub-envirobments. Each subsystem…
This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…
A spin version of dynamical mean-field theory is extended for magnetically ordered states in the Heisenberg model. The self-consistency equations are solved with high numerical accuracy by means of the continuous-time quantum Monte Carlo…
We study the dynamical stability of the entanglement between the two spin ensembles in the presence of an environment. For a comparative study, we consider the two cases: a single spin ensemble, and two ensembles linearly coupled to a bath,…
In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations are the complex computations necessary to…
In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework…
The zero-temperature physics of interacting quantum dots attached to superconducting leads is now well understood. The overall qualitative picture is obtained from the static mean-field approximation. The situation drastically changes at…
Periodic boundary conditions are applied to a ferromagnetic spin lattice. A symmetrical lattice and its contributions all over space are being used. Results, for the Ising model with ferromagnetic interaction that decays as a $1/r^{D+\nu}$…
The linear coupling of a rotating heat bath to a quantum field is studied in the framework of the Markovian master equation for the field's non-unitary time evolution. The bath's rotation induces population inversion for the field's…
We present results of existence, regularity and uniqueness of solutions of the master equation associated with the mean field planning problem in the finite state space case, in the presence of a common noise. The results hold under…
In this paper, we address the possibility of generalising the standard analysis of thermal contact between a sample system and a heat bath, by including long range interactions between them. As a concrete example, both system and bath are…
We report the results of a study of the dynamics of a two-state system coupled to an environment with peaked spectral density. An exact analytical expression for the bath correlation function is obtained. Validity range of various…