root.bib: Add livadaru03 and burnham03 and mark typos

root.bib: Add livadaru03 and burnham03 and mark typos

Typos in equations listed in bechhoefer02, schlierf06, livadaru03, and
puchner08.  I have contacted the listed author in each case, but so
far there are no published errata :(.  To be fair, I only emailed
Bechhoefer a few hours ago ;).

Excerpts from the relevant emails:

On Tue, Apr 08, 2008 at 07:16:34PM -0400, W. Trevor King wrote:
> ...
> > My double integral is exploding, so I was double checking your formulas.
> I believe you swapped signs in the exponent in your Kramers' rate equation.
>
> It should be
>  k^-1 = 1/D \int_{x_-}^{x_+} e^{  \beta U(x)} [ \int_{0}^{x} e^{- \beta U(x')} dx' ] dx
> not
>  k^-1 = 1/D \int_{x_-}^{x_+} e^{- \beta U(x)} [ \int_{0}^{x} e^{  \beta U(x')} dx' ] dx
>
> See, for example, H\"anggi et al., Rev. Mod. Phys 1990,
>   http://prola.aps.org/abstract/RMP/v62/i2/p251_1
> Equation 4.56b,
> or Socci et al., J Chem Phy 1996
>   http://arxiv.org/pdf/cond-mat/9601091
> Equation 2.

On Wed, Apr 09, 2008 at 09:03:02AM +0200, Michael Schlierf wrote:
> For your second email: So far I am pretty sure about our published
> solution as it worked out. So have you double checked your integral
> borders? Try Kramers first in a simple potential, like a cusp-like or
> flat one. For those some analytical solutions are known and you could
> compare.

On Fri, Sep 07, 2012 at 07:09:17AM -0400, W. Trevor King wrote:
> On Fri, Sep 07, 2012 at 09:28:41AM +0200, Roland Netz wrote:
> > sorry for the confusion: Yes, the formula Eq 46 contains typos, as
> > you correctly point out.
>
> Ah.  Some sort of heads-up on the article page would be useful,
> because at least Puchner [1] quotes the typo-containing version.

On Wed, Sep 12, 2012 at 01:37:23AM +0000, Puchner, Georg Elias Michael wrote:
> thanks for pointing this out, I wasn't aware of this typo and also
> think they should have published and erratum.
>
> I dug into my old data and code (I am not doing force spectroscopy
> andy more since some years) and implemented your corrected
> version. I attached a comparison of my old transformation equation
> (black line with the parameters γ=22° and b=0.4 nm as published) and
> the fixed equation (dashed red line with γ=41° and b=0.11 nm)
>
> As you see, the quality is only slightly increased for some peaks
> but the parameters now make more sense...

On Tue, May 07, 2013 at 07:05:31PM -0400, W. Trevor King wrote:
> I'm citing your thermal spring constant calculation [1] in my thesis
> [2] to confirm my derivation of the overdamped power spectral density
> of a harmonic oscillator.  I was just double-checking my PSD (at the
> end of section 5.2.1 “Highly damped case”, currently around page 48)
> against your equation A12:
>
>   x²(ω) = (2kBTγ) / [k²(1+ω²τ₀²)]       (A12)
>
> It looks like you're missing a factor of 1/π...