Speaker: Harry Miller (Univ. of Manchester) 

Date: April 9th (Wednesday) 16:30- 

Place: 401, building 5

Title:  Statistical Mechanics of Random Density Matrices

Abstract: Random quantum states play an important role in quantum  theory and can be used to quantify typical properties of states. Normally one considers the uniform distribution on the full state space (ie. Haar distributed pure or mixed states), but it is often more natural to impose energy constraints on this measure. In this talk I will discuss the properties of mixed states that are sampled under a fixed expectation of energy. This leads to an equilibrium ensemble that can be assigned a microcanonical or canonical entropy and temperature. This is then used to compute typical properties of energy-constrained random states such as their average energy spread and purity. I will discuss some physical scenarios where these ensembles might emerge dynamically, as well as their potential applications to quantum state inference and non-equilibrium thermodynamics.