Laser cooling of fermions to the superfluid transition temperature.

Numerical simulations for realistic experimental parameters demonstrate that laser cooling on the attractive side of the Feshbach resonance can drive fermions much below the superfluid transition. For the assumed set of experimental parameters the transition takes place at 0.35T(F), and laser cooling can drive the system down to at least 0.085T(F) in a time of a few seconds. Superfluid growth is self-consistently included in simulations.

Dynamics of quantum phase transition in an array of Josephson junctions.

We study the dynamics of the Mott insulator-superfluid quantum phase transition in a periodic 1D array of Josephson junctions. We show that crossing the critical point at a finite rate with a quench time tau(Q) induces finite quantum fluctuations of the current around the loop proportional to tau(-1/6)(Q). This scaling could be experimentally verified with an array of weakly coupled Bose-Einstein condensates or superconducting grains.

Domain wall formation in the Cahn-Hilliard-Cook equation.

Formation of domain walls during phase-separating transition in the Cahn-Hilliard-Cook equation is studied. Density of domain wall scales like a sixth root of quench rate for equal concentrations and like a square root of quench rate for unequal concentrations of components. For a slow inhomogeneous transition, the density is linear in a velocity of temperature front.

Stochastic gene expression: density of defects frozen into permanent Turing patterns.

We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. Self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern together with its defects. Defects frozen into the pattern are a permanent record of the transition-they give an animal its own characteristic lifelong "fingerprints" or, as for vital organ formation, they can be fatal. Density of defects scales like the fourth root of the transition rate. This dependence is so weak that there is not enough time during morphogenesis to get rid of defects simply by slowing down the rate. A defect-free pattern can be obtained by spatially inhomogeneous activation of the genes. If the supercritical density of activator spreads slower than certain threshold velocity, then the Turing pattern is expressed without any defects.

Unconditional pointer states from conditional master equations.

When part of the environment responsible for decoherence is used to extract information about the decohering system, the preferred pointer states remain unchanged. This conclusion--reached for a specific class of models--is investigated in a general setting of conditional master equations using suitable generalizations of predictability sieve. We also find indications that the einselected states are easiest to infer from the measurements carried out on the environment.