Related papers: BBGKY Hierarchy and Dynamics of Correlations
A semiconductor Boltzmann equation with a non-linear BGK-type collision operator is analyzed for a cloud of ultracold atoms in an optical lattice: \[ \partial_t f + \nabla_p\epsilon(p)\cdot\nabla_x f - \nabla_x n_f\cdot\nabla_p f = n_f(1-…
We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for small number of atoms, which permits us to…
We present an iterative algorithm to count Feynman diagrams via many-body relations. The algorithm allows us to count the number of diagrams of the exact solution for the general fermionic many-body problem at each order in the interaction.…
We consider the path integral associated to the Moyal formalism for quantum mechanics extended to contain higher differential forms by means of Grassmann odd fields. After revisiting some properties of the functional integral associated to…
We demonstrate how Bose-Einstein correlations emerge from the correlations of fluctuations allowing for their extremely simple and fast numerical modelling. Both the advantages and limitations of this new method of implementation of BEC in…
Using eigen-functional bosonization method, we study quantum many-particle systems, and show that the quantum many-particle problems end in to solve the differential equation of the phase fields which represent the particle correlation…
We extend the results of the FBSDE theory in order to construct a probabilistic representation of a viscosity solution to the Cauchy problem for a system of quasilinear parabolic equations. We derive a BSDE associated with a class of…
The interaction of particles in an electrolytic medium can be calculated by solving the Poisson equation inside the solutes and the linearized Poisson--Boltzmann equation in the solvent, with suitable boundary conditions at the interfaces.…
The Boltzmann equation is a powerful theoretical tool for modeling the collective dynamics of quantum many-body systems subject to external perturbations. Analysis of the equation gives access to linear response properties including…
We analyze the dynamics of an initially trapped cloud of interacting quantum particles on a lattice under a linear (Stark) potential. We reveal a dichotomy: initially trapped interacting systems possess features typical of both…
The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions…
We study the Lindblad master equation in the space of operators and provide simple criteria for closeness of the hierarchy of equations for correlations. We separately consider the time evolution of closed and open systems and show that…
We review methods that allow one to detect and characterise quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without…
The series expansion for the evolution of the correlation functions of a finite system of hard spheres is derived from direct integration of the solution of the Liouville equation, with minimal regularity assumptions on the density of the…
We present a formal derivation of the many-body perturbation theory for a system of electrons and bosons subject to a nonlinear electron-boson coupling. The interaction is treated at an arbitrary high order of bosons scattered. The…
The two-fermion two-point correlation function in the pairing channel is discussed in the equation of motion framework. Starting from the bare two-fermion interaction, we derive the equation of motion for the two-fermion pair propagator in…
We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We…
We complete the existing literature on the kinetic theory of systems with long-range interactions. Starting from the BBGKY hierarchy, or using projection operator technics or a quasilinear theory, a general kinetic equation can be derived…
Many-body properties of a fermionic impurity embedded in a Bose-Einstein condensate are analyzed analytically using a solvable model, the harmonic-interaction model for Bose-Fermi mixtures. The one-particle and two-particle densities,…
We present a systematic theory of dissipation in finite Fermi systems like nuclei and metallic clusters. This theory is based on the application of semiclassical methods and random matrix theory to linear response of many-body systems. The…