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Pair annihilation of heavy stable particle that occurs in the early universe is investigated, and quantum kinetic equation for the momentum distribution of the annihilating particle is derived, using the influence functional method. A…

High Energy Physics - Phenomenology · Physics 2009-10-31 Sh. Matsumoto , M. Yoshimura

In this paper, we solve a set of hierarchy equations for the reduced statistical density operator in a grand canonical ensemble for an identical many-body fermion system without or with two-body interaction. We take the single-particle…

Statistical Mechanics · Physics 2009-11-10 Liqiang Wei , Chiachung Sun

In this paper we motivate, formulate and analyze the Multi-Configuration Time-Dependent Hartree-Fock (MCTDHF) equations for molecular systems under Coulomb interaction. They consist in approximating the N-particle Schrodinger wavefunction…

Mathematical Physics · Physics 2015-05-13 C. Bardos , I. Catto , N. Mauser , S. Trabelsi

This work derives exact solutions to the problem of interacting particle density evolution in relativistic and quasi-relativistic approximations for electromagnetic and gravitational interactions. Two types of radial symmetry for the…

Mathematical Physics · Physics 2025-10-20 E. E. Perepelkin , B. I. Sadovnikov , N. G. Inozemtseva , I. Yu. Baibara

We study the quantum dynamics of a large number of interacting fermionic particles in a constant magnetic field. In a coupled mean-field and semiclassical scaling limit, we show that solutions of the many-body Schr\"odinger equation…

Mathematical Physics · Physics 2025-03-24 Niels Benedikter , Chiara Boccato , Domenico Monaco , Ngoc Nhi Nguyen

The density functional scheme for calculating the pair density is presented by means of the constrained-search technique. The resultant single-particle equation takes the form of the modified Hartree-Fock equation which contains the kinetic…

Strongly Correlated Electrons · Physics 2015-06-25 Masahiko Higuchi , Katsuhiko Higuchi

The finite duration of the collisions in Fermionic systems as expressed by the retardation time in non-Markovian Levinson-type kinetic equations is discussed in the quasiclassical limit. We separate individual contributions included in the…

Statistical Mechanics · Physics 2009-10-31 Klaus Morawetz , Václav Špička , Pavel Lipavský

We analyze the many-particle Schrodinger equation for fermions in a thermal ensemble by introducing an exponential operator expansion, defined in the context of thermofield dynamics. The expansion is optimized variationally at each time…

Statistical Mechanics · Physics 2020-01-10 Edward B. Baker

Methods based on propagation of the one-body reduced density-matrix hold much promise for the simulation of correlated many-electron dynamics far from equilibrium, but difficulties with finding good approximations for the interaction term…

Chemical Physics · Physics 2016-02-12 Peter Elliott , Neepa T. Maitra

We develop the kinetic theory of Hamiltonian systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a general kinetic equation that can be applied to spatially…

Statistical Mechanics · Physics 2009-11-13 Pierre-Henri Chavanis

We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…

Quantum Physics · Physics 2013-04-10 Christina V. Kraus , J. Ignacio Cirac

We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave…

Other Condensed Matter · Physics 2015-05-14 Xianlong Gao , Jianmin Tao , G. Vignale , I. V. Tokatly

The time evolution of a finite fermion system towards statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The…

Statistical Mechanics · Physics 2018-12-07 T. Bartsch , G. Wolschin

We prove long-time contractivity estimates and exponential rates of convergence to equilibrium for solutions of hypoelliptic diffusion equations, which include the well-known Kolmogorov equation and similar kinetic Fokker-Planck equations…

Analysis of PDEs · Mathematics 2025-10-15 Nicolò Forcillo , Alessio Porretta

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…

Statistical Mechanics · Physics 2015-05-18 Pierre-Henri Chavanis

We consider a two-dimensional gas of interacting fermions in presence of an external constant magnetic field: the system is extended and homogeneous, and thus assumed to be invariant under magnetic translations. Working within the…

Mathematical Physics · Physics 2026-02-18 Horia D. Cornean , Emanuela Laura Giacomelli , Domenico Monaco , Mikkel Hviid Thorn

We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise-interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method we…

Quantum Physics · Physics 2009-11-10 L. Tessieri , J. Wilkie , M. Cetinbas

We perform unrestricted Hartree-Fock (HF) calculations for electrons in a parabolic quantum dot at zero magnetic field. The crossover from Fermi liquid to Wigner molecule behavior is studied for up to eight electrons and various spin…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 Boris Reusch , Wolfgang Häusler , Hermann Grabert

This paper derives a kinetic equation for a two-dimensional single species point vortex system. We consider a situation (different from the ones considered previously) of weak mean flow where the time scale of the macroscopic motion is…

Statistical Mechanics · Physics 2016-12-28 Yuichi Yatsuyanagi , Tadatsugu Hatori , Pierre-Henri Chavanis

In recent years it has been shown for hard sphere gas that, by retaining the correlation information, dynamical fluctuation and large deviation of empirical measure around Boltzmann equation could be proved, in addition to the classical…

Analysis of PDEs · Mathematics 2024-09-05 Chenjiayue Qi