Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userKinetic theory of Calogero particles
178
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We show that the kinetic theory of quantum and classical Calogero particles reduces to the free-particle Boltzmann equation. We reconcile this simple emergent behaviour with the strongly interacting character of the model by developing a Bethe-Lax correspondence in the classical case. This demonstrates explicitly that the freely propagating degrees of freedom are not bare particles, but rather quasiparticles corresponding to eigenvectors of the Lax matrix. We apply the resulting kinetic theory to classical Calogero particles in external trapping potentials and find excellent agreement with numerical simulations in all cases, both for harmonic traps that preserve integrability and exhibit perfect revivals, and for anharmonic traps that break microscopic integrability. Our framework also yields a simple description of multi-soliton solutions in a harmonic trap, with solitons corresponding to sharp peaks in the quasiparticle density. Extensions to quantum systems of Calogero particles are discussed.
rate research
Read More
Recently Mazenko and Das and Mazenko introduced a non-equilibrium field theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy (BBGKY hierarchy) with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
The Navier--Stokes transport coefficients of multicomponent granular suspensions at moderate densities are obtained in the context of the (inelastic) Enskog kinetic theory. The suspension is modeled as an ensemble of solid particles where the influence of the interstitial gas on grains is via a viscous drag force plus a stochastic Langevin-like term defined in terms of a background temperature. In the absence of spatial gradients, it is shown first that the system reaches a homogeneous steady state where the energy lost by inelastic collisions and viscous friction is compensated for by the energy injected by the stochastic force. Once the homogeneous steady state is characterized, a emph{normal} solution to the set of Enskog equations is obtained by means of the Chapman--Enskog expansion around the emph{local} version of the homogeneous state. To first-order in spatial gradients, the Chapman--Enskog solution allows us to identify the Navier--Stokes transport coefficients associated with the mass, momentum, and heat fluxes. In addition, the first-order contributions to the partial temperatures and the cooling rate are also calculated. Explicit forms for the diffusion coefficients, the shear and bulk viscosities, and the first-order contributions to the partial temperatures and the cooling rate are obtained in steady-state conditions by retaining the leading terms in a Sonine polynomial expansion. The results show that the dependence of the transport coefficients on inelasticity is clearly different from that found in its granular counterpart (no gas phase). The present work extends previous theoretical results for emph{dilute} multicomponent granular suspensions [Khalil and Garzo, Phys. Rev. E textbf{88}, 052201 (2013)] to higher densities.
In this work, we introduce an effective model for both ideal and viscous fluid dynamics within the framework of kinetic field theory (KFT). The main application we have in mind is cosmic structure formation where gaseous components need to be gravitationally coupled to dark matter. However, we expect that the fluid model is much more widely applicable. The idea behind the effective model is similar to that of smoothed particle hydrodynamics. By introducing mesoscopic particles equipped with a position, a momentum, and an enthalpy, we construct a free theory for such particles and derive suitable interaction operators. We then show that the model indeed leads to the correct macroscopic evolution equations, namely the continuity, Euler, Navier-Stokes, and energy conservation equations of both ideal and viscous hydrodynamics.
We demonstrate that the clustering statistics and the corresponding phase transition to non-equilibrium clustering found in many experiments and simulation studies with self-propelled particles (SPPs) with alignment can be obtained from a simple kinetic model. The key elements of this approach are the scaling of the cluster cross-section with the cluster mass -- characterized by an exponent $alpha$ -- and the scaling of the cluster perimeter with the cluster mass -- described by an exponent $beta$. The analysis of the kinetic approach reveals that the SPPs exhibit two phases: i) an individual phase, where the cluster size distribution (CSD) is dominated by an exponential tail that defines a characteristic cluster size, and ii) a collective phase characterized by the presence of non-monotonic CSD with a local maximum at large cluster sizes. At the transition between these two phases the CSD is well described by a power-law with a critical exponent $gamma$, which is a function of $alpha$ and $beta$ only. The critical exponent is found to be in the range $0.8 < gamma < 1.5$ in line with observations in experiments and simulations.
A novel formulation of fluid dynamics as a kinetic theory with tailored, on-demand constructed particles removes any restrictions on Mach number and temperature as compared to its predecessors, the lattice Boltzmann methods and their modifications. In the new kinetic theory, discrete particles are determined by a rigorous limit process which avoids ad hoc assumptions about their velocities. Classical benchmarks for incompressible and compressible flows demonstrate that the proposed discrete-particles kinetic theory opens up an unprecedented wide domain of applications for computational fluid dynamics.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
