We study the dynamics of a charged Brownian particle in a 2-D harmonic well under the action of two AC driving forces with different amplitudes as well as with a phase difference, ϕ between them. Interestingly we observed that the system exhibits magnetism even in the absence of magnetic field. We have exactly calculated the magnetic moment and investigated the behaviour in the presence of a linear velocity dependent force. The behaviour of the magnetic moment in various parameter regimes of the model is analyzed. The magnetic moment is found to get suppressed with increase in the amplitude of the linear velocity dependent force. Interestingly we observed that when the phase difference between the AC drives lies in between 0 and π/2 , the system shows a paramagnetic behaviour whereas the system shows a diamagnetic behaviour when the phase difference between the AC drives lies in between π/2 and π. These magnetic behaviours have also been confirmed from the parametric plots. For the phase difference between 0 and π/2 , the orbit of precission of the Brownian particle is in the clockwise direction where as for the phase difference between π/2 and π, the orbit of precission of the Brownian particle is in the anticlockwise direction.
Published in | International Journal of Applied Mathematics and Theoretical Physics (Volume 7, Issue 1) |
DOI | 10.11648/j.ijamtp.20210701.12 |
Page(s) | 10-15 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2021. Published by Science Publishing Group |
DiamaNarrative Strategies, Movie Text, Music Video, Creolized Text, Simulacrum, Simulation, Hyper/Artgnetism, Non-equilibrium Magnetic Moment, Phase Difference, Velocity Dependent Force
[1] | P. Maragakis, F. Ritort, C. Bustamante, M. Karplus, and G. E. Crooks, ”Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise,” The Journal of chemical physics, vol. 129, no. 2, p. 07B609, 2008. |
[2] | K. Mallick, ”Some recent developments in nonequilibrium statistical physics,” Pramana,vol. 73, no. 3, p. 417, 2009. |
[3] | A. Jayannavar and N. Kumar, ”Orbital diamagnetism of a charged brownian particle undergoing a birth-death process,” Journal of Physics A: Mathematical and General, vol. 14, no. 6,p. 1399, 1981. |
[4] | A. Jayannavar and M. Sahoo, ”Charged particle in a magnetic field: Jarzynski equality,”Physical Review E, vol. 75, no. 3, p. 032102, 2007. |
[5] | R. Kubo, M. Toda, and N. Hashitsume,”Statistical physics II: nonequilibrium statistical mechanics”, vol. 31, Springer Science ’&’ Business Media, 2012. |
[6] | G. T. Moore and M. O. Scully, ”Frontiers of nonequilibrium statistical physics”, vol. 135, Springer Science ‘&’ Business Media, 2012. |
[7] | L. Stella, C. Lorenz, and L. Kantorovich, ”Generalized langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems,” Physical Review B, vol. 89,no. 13, p. 134303, 2014. |
[8] | R. Zwanzig, ”Nonlinear generalized langevin equations,” Journal of Statistical Physics, vol. 9, no. 3, pp. 215-220, 1973. |
[9] | B. G. de Grooth, ”A simple model for brownian motion leading to the langevin equation,” American journal of physics, vol. 67, no. 12, pp. 1248-1252, 1999. |
[10] | D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, ”Hot brownian motion,” Physical review letters, vol. 105, no. 9, p. 090604, 2010. |
[11] | N. Pottier, Nonequilibrium statistical physics: linear irreversible processes. Oxford University Press, 2009. |
[12] | L. Chen, ”Nonequilibrium fluctuation-dissipation theorem of brownian dynamics,” The Journal of Chemical Physics, vol. 129, no. 14, p. 144113, 2008. |
[13] | J. Liphardt, S. Dumont, S. B. Smith, I. Tinoco, and C. Bustamante, ”Equilibrium information from nonequilibrium measurements in an experimental test of jarzynski equality,” Science, vol. 296, no. 5574, pp. 1832- 1835, 2002. |
[14] | T. Sagawa and M. Ueda, ”Generalized jarzynski equality under nonequilibrium feedback control,” Physical review letters, vol. 104, no. 9, p. 090602, 2010. |
[15] | J. R. Roth, Plasma stability and the Bohr-van Leeuwen theorem, vol. 3880. Citeseer, 1967. |
[16] | H. Essen and M. C. Fiolhais, ”Meissner effect, diamagnetism, and classical physics review,” American Journal of Physics, vol. 80, no. 2, pp. 164-169, 2012. |
[17] | S. Chandrasekhar, ”Stochastic problems in physics and astronomy,” Reviews of modern physics, vol. 15, no. 1, p. 1, 1943. |
[18] | A. Jayannavar and M. Sahoo, ”Fluctuation theorems and orbital magnetism in nonequilibrium state,” Pramana, vol. 70, no. 2, pp. 201-210, 2008. |
[19] | O. Chubykalo, R. Smirnov-Rueda, J. Gonzalez, M. Wongsam, R. W. Chantrell, and U. Nowak, ”Brownian dynamics approach to interacting magnetic moments,” Journal of magnetism and magnetic materials, vol. 266, no. 1-2, pp. 28-35, 2003. |
[20] | C. Ganguly and D. Chaudhuri, ”Stochastic thermodynamics of active brownian particles,”Physical Review E, vol. 88, no. 3, p. 032102, 2013. |
[21] | Zhao, Zhiyuan, et al. ”Brownian dynamics simulations of magnetic nanoparticles captured in strong magnetic field gradients.” The Journal of Physical Chemistry C 121.1 : 801-810, 2017. |
[22] | Kahmann, Tamara, and Frank Ludwig. ”Magnetic field dependence of the effective magnetic moment of multicore nanoparticles.” Journal of Applied Physics 127.23, 2020. |
[23] | K. Sekimoto, ”Langevin equation and thermodynamics,” Progress of Theoretical Physics Supplement, vol. 130, pp. 17-27, 1998. |
[24] | T. Kaplan and S. Mahanti, ”On the bohr-van leeuwen theorem, the non-existence of classical magnetism in thermal equilibrium,” EPL (Europhysics Letters), vol. 87, no. 1, p. 17002, 2009. |
[25] | R. E. Peierls and R. Peierls, Surprises in theoretical physics. Princeton University Press, 1979. |
[26] | A. A. Deshpande and N. Kumar, ”Classical orbital paramagnetism in non-equilibrium steady state,” Journal of Astrophysics and Astronomy, vol. 38, no. 3, p. 57, 2017. |
APA Style
Midhun A Mohan, M Sahoo. (2021). Magnetic Response of a Charged Brownian Particle Under the Action of Two AC Drive. International Journal of Applied Mathematics and Theoretical Physics, 7(1), 10-15. https://doi.org/10.11648/j.ijamtp.20210701.12
ACS Style
Midhun A Mohan; M Sahoo. Magnetic Response of a Charged Brownian Particle Under the Action of Two AC Drive. Int. J. Appl. Math. Theor. Phys. 2021, 7(1), 10-15. doi: 10.11648/j.ijamtp.20210701.12
AMA Style
Midhun A Mohan, M Sahoo. Magnetic Response of a Charged Brownian Particle Under the Action of Two AC Drive. Int J Appl Math Theor Phys. 2021;7(1):10-15. doi: 10.11648/j.ijamtp.20210701.12
@article{10.11648/j.ijamtp.20210701.12, author = {Midhun A Mohan and M Sahoo}, title = {Magnetic Response of a Charged Brownian Particle Under the Action of Two AC Drive}, journal = {International Journal of Applied Mathematics and Theoretical Physics}, volume = {7}, number = {1}, pages = {10-15}, doi = {10.11648/j.ijamtp.20210701.12}, url = {https://doi.org/10.11648/j.ijamtp.20210701.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20210701.12}, abstract = {We study the dynamics of a charged Brownian particle in a 2-D harmonic well under the action of two AC driving forces with different amplitudes as well as with a phase difference, ϕ between them. Interestingly we observed that the system exhibits magnetism even in the absence of magnetic field. We have exactly calculated the magnetic moment and investigated the behaviour in the presence of a linear velocity dependent force. The behaviour of the magnetic moment in various parameter regimes of the model is analyzed. The magnetic moment is found to get suppressed with increase in the amplitude of the linear velocity dependent force. Interestingly we observed that when the phase difference between the AC drives lies in between 0 and π/2 , the system shows a paramagnetic behaviour whereas the system shows a diamagnetic behaviour when the phase difference between the AC drives lies in between π/2 and π. These magnetic behaviours have also been confirmed from the parametric plots. For the phase difference between 0 and π/2 , the orbit of precission of the Brownian particle is in the clockwise direction where as for the phase difference between π/2 and π, the orbit of precission of the Brownian particle is in the anticlockwise direction.}, year = {2021} }
TY - JOUR T1 - Magnetic Response of a Charged Brownian Particle Under the Action of Two AC Drive AU - Midhun A Mohan AU - M Sahoo Y1 - 2021/02/20 PY - 2021 N1 - https://doi.org/10.11648/j.ijamtp.20210701.12 DO - 10.11648/j.ijamtp.20210701.12 T2 - International Journal of Applied Mathematics and Theoretical Physics JF - International Journal of Applied Mathematics and Theoretical Physics JO - International Journal of Applied Mathematics and Theoretical Physics SP - 10 EP - 15 PB - Science Publishing Group SN - 2575-5927 UR - https://doi.org/10.11648/j.ijamtp.20210701.12 AB - We study the dynamics of a charged Brownian particle in a 2-D harmonic well under the action of two AC driving forces with different amplitudes as well as with a phase difference, ϕ between them. Interestingly we observed that the system exhibits magnetism even in the absence of magnetic field. We have exactly calculated the magnetic moment and investigated the behaviour in the presence of a linear velocity dependent force. The behaviour of the magnetic moment in various parameter regimes of the model is analyzed. The magnetic moment is found to get suppressed with increase in the amplitude of the linear velocity dependent force. Interestingly we observed that when the phase difference between the AC drives lies in between 0 and π/2 , the system shows a paramagnetic behaviour whereas the system shows a diamagnetic behaviour when the phase difference between the AC drives lies in between π/2 and π. These magnetic behaviours have also been confirmed from the parametric plots. For the phase difference between 0 and π/2 , the orbit of precission of the Brownian particle is in the clockwise direction where as for the phase difference between π/2 and π, the orbit of precission of the Brownian particle is in the anticlockwise direction. VL - 7 IS - 1 ER -