171 research outputs found
Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations
In the paper we consider the problem of the rigorous description of the
kinetic evolution in the presence of initial correlations of quantum large
particle systems. One of the developed approaches consists in the description
of the evolution of quantum many-particle systems within the framework of
marginal observables in mean field scaling limit. Another method based on the
possibility to describe the evolution of states within the framework of a
one-particle marginal density operator governed by the generalized quantum
kinetic equation in case of initial states specified by a one-particle marginal
density operator and correlation operators.Comment: 17 page
Kinetic Equations of Active Soft Matter
We consider a new approach to the description of the collective behavior of complex systems of mathematical biology based on the evolution equations for observables of such systems. This representation of the kinetic evolution seems, in fact, the direct mathematically fully consistent formulation modeling the collective behavior of biological systems since the traditional notion of the state in kinetic theory is more subtle and it is an implicit characteristic of the populations of living creatures
A new approach to gravitational clustering: a path-integral formalism and large-N expansions
We show that the formation of large-scale structures through gravitational
instability in the expanding universe can be fully described through a
path-integral formalism. We derive the action S[f] which gives the statistical
weight associated with any phase-space distribution function f(x,p,t). This
action S describes both the average over the Gaussian initial conditions and
the Vlasov-Poisson dynamics. Next, applying a standard method borrowed from
field theory we generalize our problem to an N-field system and we look for an
expansion over powers of 1/N. We describe three such methods and we derive the
corresponding equations of motion at the lowest non-trivial order for the case
of gravitational clustering. This yields a set of non-linear equations for the
mean \fb and the two-point correlation G of the phase-space distribution f,
as well as for the response function R. These systematic schemes match the
usual perturbative expansion on quasi-linear scales but should also be able to
handle the non-linear regime. Our approach can also be extended to non-Gaussian
initial conditions and may serve as a basis for other tools borrowed from field
theory.Comment: 22 pages, final version published in A&
Fractional statistical dynamics and fractional kinetics
We apply the subordination principle to construct kinetic fractional
statistical dynamics in the continuum in terms of solutions to Vlasov-type
hierarchies. As a by-product we obtain the evolution of the density of
particles in the fractional kinetics in terms of a non-linear Vlasov-type
kinetic equation. As an application we study the intermittency of the
fractional mesoscopic dynamics.Comment: Published in Methods of Functional Analysis and Topology (MFAT),
available at http://mfat.imath.kiev.ua/article/?id=890. arXiv admin note:
text overlap with arXiv:1604.0380
Relativistic Quantum Transport Theory for Electrodynamics
We investigate the relationship between the covariant and the
three-dimensional (equal-time) formulations of quantum kinetic theory. We show
that the three-dimensional approach can be obtained as the energy average of
the covariant formulation. We illustrate this statement in scalar and spinor
QED. For scalar QED we derive Lorentz covariant transport and constraint
equations directly from the Klein-Gordon equation rather than through the
previously used Feshbach-Villars representation. We then consider pair
production in a spatially homogeneous but time-dependent electric field and
show that the pair density is derived much more easily via the energy averaging
method than in the equal-time representation. Proceeding to spinor QED, we
derive the covariant version of the equal-time equation derived by
Bialynicki-Birula et al. We show that it must be supplemented by another
self-adjoint equation to obtain a complete description of the covariant spinor
Wigner operator. After spinor decomposition and energy average we study the
classical limit of the resulting three-dimensional kinetic equations. There are
only two independent spinor components in this limit, the mass density and the
spin density, and we derive also their covariant equations of motion. We then
show that the equal-time kinetic equation provides a complete description only
for constant external electromagnetic fields, but is in general incomplete. It
must be supplemented by additional constraints which we derive explicitly from
the covariant formulation.Comment: 32 pages, no figures, standard Late
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