Heuristic approach to trajectory correlation functions in bounded regions with Lambert scattering walls

Thomas Rao; Robert Golub

Home/Archive/arXiv

arXiv · 2401.13797

Heuristic approach to trajectory correlation functions in bounded regions with Lambert scattering walls

Thomas Rao·Robert Golub

View original source ↗Read source document ↗Export metadata ↓

Abstract

The behavior of spins undergoing Lamor precession in the presence of time varying fields is of interest to many research fields. The frequency shifts and relaxation resulting from these fields are related to their power spectrum and can be determined from the Fourier Transform of the auto-correlation functions of the time varying field. Using the method of images [C. M. Swank, A. K. Petukhov, and R. Golub, Phys. Lett. A 376, 2319 (2012)] calculated the position-position auto-correlation function for particles moving in a rectangular cell with specular scattering walls. In this work we present a heuristic model that extends this work to the case of Lambert scattering walls. The results of this model are compared to simulation and show good agreement from the ballistic to diffusive regime of gas collisions, for both square and general rectangular cells. This model requires three parameters, two of which describe the distribution of images in the case of a square cell, and one of which describes the asymmetry in the mixing of the x and y components of the velocity in the case of non-square rectangular cells.

Explore related subjects

cond-mat.stat-mech physics.atom-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Thomas Rao, Robert Golub. 2024-01-24. Heuristic approach to trajectory correlation functions in bounded regions with Lambert scattering walls. https://arxiv.org/abs/2401.13797

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The free energy of the square lattice Ising model with interactions alternating in horizontal and vertical directions

The free energy of the Ising model on the square lattice with alternating interactions in both horizontal and vertical directions is exactly derived. This model is distinct from the checkerboard Ising model. The result includes Onsager's free energy as a special case, and also includes Lee-Yang's free energy with an imaginary field, and relates these two solutions via continuous parameters. The result includes a generalization of Lee-Yang's result to cases with four different couplings. It is also derived that each imaginary magnetic field $iπ/2$ applied to a lattice site corresponds to a single frustrated square in its dual lattice.

cond-mat.stat-mech↗

arXiv2026

Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond

Given a particular heat engine cycle, what is the optimal working medium that results in the highest efficiency? While one might jump to the conclusion that it must surely be the ideal gas, the situation is actually more intricate. Starting with a general Helmholtz potential that depends polynomially on molar volume and temperature we derive exact expressions for the ideal Stirling, Otto, and Brayton cycles. We find that for the thermodynamic systems described by our ansatz for the Helmholtz potential the maximal efficiency is achieved, if the working medium is described by a fundamental relation linear in temperature. This includes the ideal gas, but also classical harmonic oscillators and phenomenological models of the rubber band.

cond-mat.stat-mech↗

arXiv2026

Local Detailed Balance in the Lorenz Model: Replaces the Butterfly with Frenetic Bursting

The Lorenz system is the canonical low-order model of convective instability, yet its dissipative and driving terms have never been checked against, nor constructed from, an explicit thermodynamic bookkeeping. We derive a modification that satisfies the local-detailed-balance condition for macroscopic relaxation toward nonequilibrium steady states, thereby identifying the thermodynamic force, entropy-production rate and frenesy of the resulting flow. The resulting model produces a transition from a quiescent fixed point to a robust, large-amplitude relaxation oscillation, closely analogous to recharge-discharge oscillator paradigms used for the El Nino-Southern Oscillation. The system alternates between a long, nearly reversible recharge phase and a brief, violently frenetic discharge burst, during which essentially all of the cycle's activity and entropy production is concentrated.

cond-mat.stat-mech↗