Weakly nonlinear degrees of freedom in dissipative quantum systems tend to localize near manifolds of quasi-classical states. We present a family of analytical and computational methods for deriving optimal unitary model transformations based on representations of finite dimensional Lie groups. The transformations are optimal in that they minimize the quantum relative entropy distance between a...

defined over Sobolev spaces is connected to the convexity of the potential w. In the scalar case, that is for functions u with domain or range in R, the functional I is weakly W 1,p lower semi-continuous (weakly * W ) if and only if w is convex, provided it is continuous and satisfies some growth conditions. The notion which replaces convexity in the vector case is quasi-convexity (introduced b...

In this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSSbased iteration methods are proposed for solving weakly nonlinear systems base...

We investigated the temperature–dependent conductance of a long and narrow highmobility channel, which is formed from an AlGaAs/GaAs heterostructure using the split-gate technique. When the channel is wider than 100 nm, in the range of 1-10 K we observe logarithmic temperature dependence, which is a key signature of the interaction correction in the quasi-onedimensional weakly-disordered Fermi ...

We introduce a bandwidth-unlimited, dispersion- and shear-self-calibrated, timing-jitter-free pulse measurement technique based on a quasi-linear temporal phase modulation in a gas weakly ionized by a long pump pulse. Results of a 5 fs pulse characterization are reported.

We answer a question of Blass, Di Nasso, and Forti [2, 7] by proving, assuming Continuum Hypothesis or Martin’s Axiom, that (1) there exists a P -point which is not interval-to-one and (2) there exists an interval-to-one P -point which is neither quasi-selective nor weakly Ramsey.

If G is an abelian torsion group with generating subset G0, then by a classical result in the theory of non-unique factorizations, the block monoid B(G0) is a half-factorial monoid if each of its atoms has cross number 1. In this case, G0 is called a half-factorial set. In this note, we introduce the notion of a k-quasihalf-factorial set and show for many abelian torsion groups that G0 k-quasi-...

Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.

We develop a transport theory to describe the dynamics of (weakly) localized waves in a quasi-1D tube geometry both in reflection and in transmission. We compare our results to recent experiments with microwaves and to other theories, such as random matrix theory and supersymmetric theory.