Tuesday, August 27, 2013

Back to the Forest

I'm returning to the Haliburton Forest 50 Miler next weekend, and am a bit apprehensive. Deep breaths. Try to keep it simple. Here's the basic, back-of-the-envelope plan.

                   First, my taper needs to be

 |\Psi \rangle \in H_A \otimes H_B.
\rho_T = |\Psi\rangle \; \langle\Psi|.

                   To start the race, my effort should be something like
\rho_A \ \stackrel{\mathrm{def}}{=}\ \sum_j \langle j|_B \left( |\Psi\rangle \langle\Psi| \right) |j\rangle_B = \hbox{Tr}_B \; \rho_T .

                    Oh, and for the uphills
\rho_A = (1/2) \bigg( |0\rangle_A \langle 0|_A + |1\rangle_A \langle 1|_A \bigg)

                  And then the downhills (duh)
\rho_A = |\psi\rangle_A \langle\psi|_A .

               Naturally, for the second half we'll be looking at
|\Phi^\pm\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_B \pm |1\rangle_A \otimes |1\rangle_B)
                     Or, alternatively
H_n(x)=(-1)^n e^{x^2}\frac{d^n}{dx^n}\left(e^{-x^2}\right).

                     (But if I see a bear, I need to run like

\langle\hat{T}\rangle = \bigg\langle\psi \bigg\vert \sum_{i=1}^N \frac{-\hbar^2}{2 m_\text{e}} \nabla^2_i \bigg\vert \psi \bigg\rangle = -\frac{\hbar^2}{2 m_\text{e}} \sum_{i=1}^N \bigg\langle\psi \bigg\vert \nabla^2_i \bigg\vert \psi \bigg\rangle)
                         Happily, my fueling and hydration intake is fool-proof:
|\mathrm{GHZ}\rangle = \frac{|0\rangle^{\otimes M} + |1\rangle^{\otimes M}}{\sqrt{2}},

And finally, though it's out of my control I can't help but hope for ideal weather conditions throughout the day: 
|\psi_\text{NOON} \rangle = \frac{|N \rangle_a |0\rangle_b + |{0}\rangle_a |{N}\rangle_b}{\sqrt{2}}, \,
                    So really, what could go wrong?

Friday, August 2, 2013

Slide Lake Loop Video

A little trail rambling from June 22 that has been sitting on my hard drive.