2009/12/31 by Punyabrata Pradhan, Udo Seifert · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boundary value problem #Charged particle #Classical mechanics #Condensed matter physics #Diamagnetism #Geometry #Ion #Langevin dynamics #Langevin equation #Magnetic field #Magnetic moment #Mathematics #Moment (physics) #Non-equilibrium thermodynamics #Periodic boundary conditions #Physics #Quantum Electrodynamics and Casimir Effect #Quantum many-body systems #Quantum mechanics #Surface (topology) #cond-mat.stat-mech
paper · pdf · doi:10.1209/0295-5075/89/37001
published as EPL, vol. 89, 37001 (2010) · 6 pages; typos corrected
openalex publication_date 2010/02/01 · arxiv created 2010/02/22 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the classical Langevin dynamics for a charged particle on a closed curved surface in a time-independent magnetic field leads to the canonical distribution in the long time limit. Thus the Bohr-van Leeuwen theorem holds even for a finite system without any boundary and the average magnetic moment is zero. This is contrary to the recent claim by Kumar and Kumar ( EPL , 86 (2009) 17001), obtained from numerical analysis of Langevin dynamics, that a classical charged particle on the surface of a sphere in the presence of a magnetic field has a nonzero average diamagnetic moment. We extend our analysis to a many-particle system on a curved surface and show that the nonequilibrium fluctuation theorems also hold in this geometry.