33 research outputs found
On the thermalization of a Luttinger liquid after a sequence of sudden interaction quenches
We present a comprehensive analysis of the relaxation dynamics of a Luttinger
liquid subject to a sequence of sudden interaction quenches. We express the
critical exponent governing the decay of the steady-state propagator as
an explicit functional of the switching protocol. At long distances
depends only on the initial state while at short distances it is also history
dependent. Continuous protocols of arbitrary complexity can be realized with
infinitely long sequences. For quenches of finite duration we prove that there
exist no protocol to bring the initial non-interacting system in the ground
state of the Luttinger liquid. Nevertheless memory effects are washed out at
short-distances. The adiabatic theorem is then investigated with
ramp-switchings of increasing duration, and several analytic results for both
the propagator and the excitation energy are derived.Comment: 7 pages, 4 figure
Zermelo Navigation in the Quantum Brachistochrone
We analyse the optimal times for implementing unitary quantum gates in a constrained finite dimensional controlled quantum system. The family of constraints studied is that the permitted set of (time dependent) Hamiltonians is the unit ball of a norm induced by an inner product on su(n). We also consider a generalisation of this to arbitrary norms. We construct a Randers metric, by applying a theorem of Shen on Zermelo navigation, the geodesics of which are the time optimal trajectories compatible with the prescribed constraint. We determine all geodesics and the corresponding time optimal Hamiltonian for a specific constraint on the control i.e. k (Tr(Hc(t)^2) = 1 for any given value of k > 0. Some of the results of Carlini et. al. are re-derived using alternative methods. A first order system of differential equations for the optimal Hamiltonian is obtained and shown to be of the form of the Euler Poincare equations. We illustrate that this method can form a methodology for determining which physical substrates are effective at supporting the implementation of fast quantum computation