/ˈtɪdbɪt/ - a small and particularly interesting item of information. – ResearchTidbits

Bogoliubov transformations

tidbit

theory

Consider a set of \(N\) second-quantized creation operators \[\vec{a} = [\hat{a}_1, \hat{a}_2, \cdots, \hat{a}_N]\] which satisfy the canonical (anti-)commutation relations…

Constructing a localized basis

chunk

code

hermite -> fourier transform, roots relation

Imaginary time evolution

chunk

quantum

code

\(i \hbar \partial_t \Psi = -\frac{\partial^2}{\partial x^2} \Psi\)

Superfluidity as a response to phase twists

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theory

Superfluidity and superconductivity might be, in my opinion, one of the most intriguing phenomena that presents quantum behaviour at a macroscopic scale. However, they…

The callback pattern

chunk

code

One of my favourite design patterns is the Callback (also known as the Command pattern in object-oriented contexts). Loosely speaking, a callback is simply a function f whose…

Linearly indexing a 2D grid

nibble

number theory

Recently, I had to write an exact diagonalization routine to solve for the ground state of a system of interacting bosons in the continuum. Generally this simply involves…

Bosons, but not quite

nibble

bec

Automating image cropping

tidbit

code

bec

Sometimes being a (numerical) theorist gets a bit tiring. In those moments, I occasionally peek into what my colleagues are working on with the BEC experiment downstairs. If…

Akshay Shankar, Dhruva Sambrani

Determining phase boundaries

tidbit

code

Given a quantum many-body Hamiltonian, one of the first goals usually is to account for possible ground state phases and map out the corresponding phase diagram in the…