Two Dimensional Quantum Chromodynamics as the Limit of Higher Dimensional Theories

We define pure gauge $QCD$ on an infinite strip of width $L$. Techniques similar to those used in finite $TQCD$ allow us to relate $3D$-observables to pure $QCD_2$ behaviors. The non triviality of the L \arrow 0 limit is proven and the generalization to four dimensions described. The glueball spectrum of the theory in the small width limit is calculated and compared to that of the two dimensional theory.Comment: 12 pages written in LaTeX, figure available from the authors, preprint Univ. of Valencia, FTUV/94-4

Engineering orthogonal dual transcription factors for multi-input synthetic promoters

Synthetic biology has seen an explosive growth in the capability of engineering artificial gene circuits from transcription factors (TFs), particularly in bacteria. However, most artificial networks still employ the same core set of TFs (for example LacI, TetR and cI). The TFs mostly function via repression and it is difficult to integrate multiple inputs in promoter logic. Here we present to our knowledge the first set of dual activator-repressor switches for orthogonal logic gates, based on bacteriophage λ cI variants and multi-input promoter architectures. Our toolkit contains 12 TFs, flexibly operating as activators, repressors, dual activator–repressors or dual repressor–repressors, on up to 270 synthetic promoters. To engineer non cross-reacting cI variants, we design a new M13 phagemid-based system for the directed evolution of biomolecules. Because cI is used in so many synthetic biology projects, the new set of variants will easily slot into the existing projects of other groups, greatly expanding current engineering capacities

Renormings of Lp(Lq)L^p(L^q)

We investigate the best order of smoothness of $L^p(L^q)$. We prove in particular that there exists a $C^\infty$-smooth bump function on $L^p(L^q)$ if and only if $p$ and $q$ are both even integers and $p$ is a multiple of $q$.Comment: 18 pages; AMS-Te

Scaling-up quantum heat engines efficiently via shortcuts to adiabaticity

The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inverse-square pairwise interactions, that includes noninteracting and hard-core bosons as limiting cases.Comment: 15 pages, 3 figures; typo in Eq. (51) fixed. Feature paper in the Special Issue "Quantum Thermodynamics" edited by Prof. Dr. Ronnie Koslof