Integrals of motion for one-dimensional Anderson localized systems

Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess `additional' integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

Generation of High Magnetic Fields Using Thyristors

This paper describes the use of high-power thyristors in conjunction with a low-voltage supply for generating pulsed magnetic fields. A modular bank of electrolytic capacitors is charged through a programmable solid-state power supply and then rapidly discharged through a bank of thyristors into a magnetizing coil. The modular construction of capacitor banks enables the discrete control of pulse energy and time. Peak fields up to 15 telsa (150 KOe) and a half period of about 200 microseconds are generated through the discharges. Still higher fields are produced by discharging into a precooled coil ( 77°K). Measurement method for a pulsed field is described.