Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that are not universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner [Phys. Rev. A 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation.

Numerical analysis of capacities for two-qubit unitary operations

We present numerical results on the capacities of two-qubit unitary operations for performing communication and creating entanglement. The capacities for communication considered are based upon the increase in Holevo information of an ensemble. Our results indicate that the capacity may be accurately estimated using ensemble sizes and ancilla dimensions of 4. In addition, the calculated values of these capacities were close to, and in some cases equal to, the similarly defined entangling capacities; this result indicates connections between these capacities.

Primary Fields and Screening Currents of gl (2/2) non-unitary conformal field theory

The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields. (C) 2004 Elsevier B.V All rights reserved.

Differential use of signal peptides and membrane domains is a common occurrence in the protein output of transcriptional units

Membrane organization describes the orientation of a protein with respect to the membrane and can be determined by the presence, or absence, and organization within the protein sequence of two features: endoplasmic reticulum signal peptides and alpha-helical transmembrane domains. These features allow protein sequences to be classified into one of five membrane organization categories: soluble intracellular proteins, soluble secreted proteins, type I membrane proteins, type II membrane proteins, and multi- spanning membrane proteins. Generation of protein isoforms with variable membrane organizations can change a protein's subcellular localization or association with the membrane. Application of MemO, a membrane organization annotation pipeline, to the FANTOM3 Isoform Protein Sequence mouse protein set revealed that within the 8,032 transcriptional units ( TUs) with multiple protein isoforms, 573 had variation in their use of signal peptides, 1,527 had variation in their use of transmembrane domains, and 615 generated protein isoforms from distinct membrane organization classes. The mechanisms underlying these transcript variations were analyzed. While TUs were identified encoding all pairwise combinations of membrane organization categories, the most common was conversion of membrane proteins to soluble proteins. Observed within our highconfidence set were 156 TUs predicted to generate both extracellular soluble and membrane proteins, and 217 TUs generating both intracellular soluble and membrane proteins. The differential use of endoplasmic reticulum signal peptides and transmembrane domains is a common occurrence within the variable protein output of TUs. The generation of protein isoforms that are targeted to multiple subcellular locations represents a major functional consequence of transcript variation within the mouse transcriptome.

Temperature of a trapped unitary Fermi gas at finite entropy

We present theoretical predictions for the equation of state of a harmonically trapped Fermi gas in the unitary limit. Our calculations compare Monte Carlo results with the equation of state of a uniform gas using three distinct perturbation schemes. We show that in experiments the temperature can be usefully calibrated by making use of the entropy, which is invariant during an adiabatic conversion into the weakly interacting limit of molecular BEC. We predict the entropy dependence of the equation of state.

Student Difficulties with units in differential equations in modelling contexts

First-year undergraduate engineering students' understanding of the units of factors and terms in first-order ordinary differential equations used in modelling contexts was investigated using diagnostic quiz questions. Few students appeared to realize that the units of each term in such equations must be the same, or if they did, nevertheless failed to apply that knowledge when needed. In addition, few students were able to determine the units of a proportionality factor in a simple equation. These results indicate that lecturers of modelling courses cannot take this foundational knowledge for granted and should explicitly include it in instruction.