Timeline for Computing friction tensor for a colloidal particle in (moving) harmonic potential
Current License: CC BY-SA 4.0
5 events
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| Jun 12, 2023 at 17:05 | comment | added | ZinnTheJackal | @cidrolin Yes, I have assumed a fix value of the control parameters in this calculation. This is based on the equation (12b) from the paper (the average is taken at $\mathbf{\lambda}(t_0)$. The assumption they make is that "control parameter velocities change on timescales slower than the relaxation time of the system’s force fluctuations." Indeed, the resulting friction matrix doesn't explicitly depend on time, but does depend on one of the control parameters $\omega$. | |
| Jun 12, 2023 at 16:55 | history | edited | ZinnTheJackal | CC BY-SA 4.0 |
improved formatting
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| Jun 12, 2023 at 14:47 | vote | accept | cidrolin | ||
| Jun 12, 2023 at 14:45 | comment | added | cidrolin | Thank you! I appreciate your clear explanation, and it solved my problems. Just to clarify, I suppose you are assuming a fixed value of the control parameters at time $\lambda(s)$, since the correlations are all computed at this fixed value along the protocol. Is that correct? Indeed, in my question, I made a typo, and the difference between the instantaneous conjugate force and its equilibrium mean should have been $\delta X_i(t') = X_i(t')-\langle X_i\rangle_{\lambda(s)}$. (Here, I am using $s$ instead of $t$ for better clarity). | |
| Jun 12, 2023 at 9:24 | history | answered | ZinnTheJackal | CC BY-SA 4.0 |