Fluid machines: Expanding the limits, past and future

During the 40 yr period from 1940 to 1980, the capabilities and operating limits of fluid machines were greatly extended. This was due to a research program, carried out to meet the needs of aerospace programs. Some of the events are reviewed. Overall advancements of all machinery components are discussed followed by a detailed examination of technology advancements in axial compressors and pumps. Future technology needs are suggested

Scaling behavior of interactions in a modular quantum system and the existence of local temperature

We consider a quantum system of fixed size consisting of a regular chain of $n$-level subsystems, where $n$ is finite. Forming groups of $N$ subsystems each, we show that the strength of interaction between the groups scales with $N^{- 1/2}$. As a consequence, if the total system is in a thermal state with inverse temperature $\beta$, a sufficient condition for subgroups of size $N$ to be approximately in a thermal state with the same temperature is $\sqrt{N} \gg \beta \bar{\delta E}$, where $\bar{\delta E}$ is the width of the occupied level spectrum of the total system. These scaling properties indicate on what scale local temperatures may be meaningfully defined as intensive variables. This question is particularly relevant for non-equilibrium scenarios such as heat conduction etc.Comment: 7 pages, accepted for publication in Europhysics Letter

On Which Length Scales Can Temperature Exist in Quantum Systems?

We consider a regular chain of elementary quantum systems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of $n$ subsystems each, and when these groups have the same temperature $T$. While in classical mechanics the validity of this procedure only depends on the size of the groups $n$, in quantum mechanics the minimum group size $n_{\text{min}}$ also depends on the temperature $T$! As examples, we apply our analysis to different types of Heisenberg spin chains.Comment: To appear in: Proceedings of the SPQS conference, J. Phys. Soc. Jpn. 74 (2005) Supp

RNA secondary structure design

We consider the inverse-folding problem for RNA secondary structures: for a given (pseudo-knot-free) secondary structure find a sequence that has that structure as its ground state. If such a sequence exists, the structure is called designable. We implemented a branch-and-bound algorithm that is able to do an exhaustive search within the sequence space, i.e., gives an exact answer whether such a sequence exists. The bound required by the branch-and-bound algorithm are calculated by a dynamic programming algorithm. We consider different alphabet sizes and an ensemble of random structures, which we want to design. We find that for two letters almost none of these structures are designable. The designability improves for the three-letter case, but still a significant fraction of structures is undesignable. This changes when we look at the natural four-letter case with two pairs of complementary bases: undesignable structures are the exception, although they still exist. Finally, we also study the relation between designability and the algorithmic complexity of the branch-and-bound algorithm. Within the ensemble of structures, a high average degree of undesignability is correlated to a long time to prove that a given structure is (un-)designable. In the four-letter case, where the designability is high everywhere, the algorithmic complexity is highest in the region of naturally occurring RNA.Comment: 11 pages, 10 figure

Nonlinear nanomechanical resonators for quantum optoelectromechanics

We present a scheme for tuning and controlling nano mechanical resonators by subjecting them to electrostatic gradient fields, provided by nearby tip electrodes. We show that this approach enables access to a novel regime of optomechanics, where the intrinsic nonlinearity of the nanoresonator can be explored. In this regime, one or several laser driven cavity modes coupled to the nanoresonator and suitably adjusted gradient fields allow to control the motional state of the nanoresonator at the single phonon level. Some applications of this platform have been presented previously [New J. Phys. 14, 023042 (2012), Phys. Rev. Lett. 110, 120503 (2013)]. Here, we provide a detailed description of the corresponding setup and its optomechanical coupling mechanisms, together with an in-depth analysis of possible sources of damping or decoherence and a discussion of the readout of the nanoresonator state.Comment: 15 pages, 6 figure

Spin Domains Generate Hierarchical Ground State Structure in J=+/-1 Spin Glasses

Unbiased samples of ground states were generated for the short-range Ising spin glass with Jij=+/-1, in three dimensions. Clustering the ground states revealed their hierarchical structure, which is explained by correlated spin domains, serving as cores for macroscopic zero energy "excitations".Comment: 4 pages, 5 figures, accepted to Phys. Rev. Let

Reduction of Two-Dimensional Dilute Ising Spin Glasses

The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large systems. Low-temperature domain-wall excitations are studied to determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found, consistent with previous results obtained on undiluted lattices. This comparison demonstrates the validity of the reduction method for bond-diluted spin systems and provides strong support for similar studies proclaiming accurate results for stiffness exponents in dimensions d=3,...,7.Comment: 7 pages, RevTex4, 6 ps-figures included, for related information, see http://www.physics.emory.edu/faculty/boettcher

Spectral densities and partition functions of modular quantum systems as derived from a central limit theorem

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite number of subsystems. Even for only small numbers of subsystems we find good accordance with some known, exact results.Comment: 6 pages, 4 figures, some steps added to derivation, accepted for publication in J. Stat. Phy

Reply to the Comment on `Glassy Transition in a Disordered Model for the RNA Secondary Structure'

We reply to the Comment by Hartmann (cond-mat/9908132) on our paper Phys. Rev. Lett. 84 (2000) 2026 (also cond-mat/9907125).Comment: 1 page, no figures. Accepted for publication in Phys. Rev. Let