Plasma contactors for use with electodynamic tethers for power generation

Plasma contactors are proposed as a means of making good electrical contact between biased surfaces such as found at the ends of an electrodynamic tether and the space environment. The plasma contactor emits a plasma cloud which facilitates the electrical connection. The physics of this plasma cloud is investigated for contactors used as electron collectors. The central question addressed is whether the electrons collected by a plasma contactor come from the far field or by ionization of local neutral gas. This question is important because the system implications are different for the two mechanisms. It is shown that contactor clouds in space will consist of a spherical core possibly containing a shock wave. Outside of the core the cloud will expand anisotropically across the magnetic field leading to a turbulent cigar shape structure along the field. This outer region is itself divided into two regions by the ion response to the electric field. A two-dimensional theory for the outer regions of the cloud is developed. The current voltage characteristic of an Argon plasma contactor cloud is estimated for several ion currents in the range of 1 to 100 Amperes. It is suggested that the major source of collected electrons comes by ionization of neutral gas while collection of electrons from the far field is relatively small

A short proof of stability of topological order under local perturbations

Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological quantum order for which the unperturbed Hamiltonian $H_0$ can be written as a sum of local pairwise commuting projectors on a $D$-dimensional lattice. We consider a perturbed Hamiltonian $H=H_0+V$ involving a generic perturbation $V$ that can be written as a sum of short-range bounded-norm interactions. We prove that if the strength of $V$ is below a constant threshold value then $H$ has well-defined spectral bands originating from the low-lying eigenvalues of $H_0$. These bands are separated from the rest of the spectrum and from each other by a constant gap. The width of the band originating from the smallest eigenvalue of $H_0$ decays faster than any power of the lattice size.Comment: 15 page

Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity

We apply the technique of quasi-adiabatic continuation to study systems with continuous symmetries. We first derive a general form of Goldstone's theorem applicable to gapped nonrelativistic systems with continuous symmetries. We then show that for a fermionic system with a spin gap, it is possible to insert $\pi$-flux into a cylinder with only exponentially small change in the energy of the system, a scenario which covers several physically interesting cases such as an s-wave superconductor or a resonating valence bond state.Comment: 19 pages, 2 figures, final version in press at JSTA

Multi-level, multi-party singlets as ground states and their role in entanglement distribution

We show that a singlet of many multi-level quantum systems arises naturally as the ground state of a physically-motivated Hamiltonian. The Hamiltonian simply exchanges the states of nearest-neighbours in some network of qudits (d-level systems); the results are independent of the strength of the couplings or the network's topology. We show that local measurements on some of these qudits project the unmeasured qudits onto a smaller singlet, regardless of the choice of measurement basis at each measurement. It follows that the entanglement is highly persistent, and that through local measurements, a large amount of entanglement may be established between spatially-separated parties for subsequent use in distributed quantum computation.Comment: Corrected method for physical preparatio

Entanglement vs. gap for one-dimensional spin systems

We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state, the entanglement of any interval is upper-bounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap Delta is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small Delta. To help resolve this asymptotic behavior, we construct a family of one-dimensional local systems for which some intervals have entanglement entropy which is polynomial in 1/Delta, whereas previously studied systems, such as free fermion systems or systems described by conformal field theory, had the entropy of all intervals bounded by a constant times log(1/Delta).Comment: 16 pages. v2 is final published version with slight clarification

Exact Multifractal Spectra for Arbitrary Laplacian Random Walks

Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the measure near the growth tip, and of the measure away from the growth tip. The spectra away from the tip coincide with those of conformally invariant equilibrium systems with arbitrary central charge $c\leq 1$, with $c$ related to the particular walk chosen, while the scaling in time and near the tip cannot be obtained from the equilibrium properties.Comment: 4 pages, 3 figures; references added, minor correction

Physical consequences of P≠\neqNP and the DMRG-annealing conjecture

Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and, thus, these theorems do not apply directly to it. But {\em classical simulations} of physical processes are programs running on Turing machines and, as such, are subject to them. In this work, computational complexity theory is applied to classical simulations of systems performing an adiabatic quantum computation (AQC), based on an annealed extension of the density matrix renormalization group (DMRG). We conjecture that the computational time required for those classical simulations is controlled solely by the {\em maximal entanglement} found during the process. Thus, lower bounds on the growth of entanglement with the system size can be provided. In some cases, quantum phase transitions can be predicted to take place in certain inhomogeneous systems. Concretely, physical conclusions are drawn from the assumption that the complexity classes {\bf P} and {\bf NP} differ. As a by-product, an alternative measure of entanglement is proposed which, via Chebyshev's inequality, allows to establish strict bounds on the required computational time.Comment: Accepted for publication in JSTA

Almost Commuting Matrices, Localized Wannier Functions, and the Quantum Hall Effect

For models of non-interacting fermions moving within sites arranged on a surface in three dimensional space, there can be obstructions to finding localized Wannier functions. We show that such obstructions are $K$-theoretic obstructions to approximating almost commuting, complex-valued matrices by commuting matrices, and we demonstrate numerically the presence of this obstruction for a lattice model of the quantum Hall effect in a spherical geometry. The numerical calculation of the obstruction is straightforward, and does not require translational invariance or introducing a flux torus. We further show that there is a $Z_2$ index obstruction to approximating almost commuting self-dual matrices by exactly commuting self-dual matrices, and present additional conjectures regarding the approximation of almost commuting real and self-dual matrices by exactly commuting real and self-dual matrices. The motivation for considering this problem is the case of physical systems with additional antiunitary symmetries such as time reversal or particle-hole conjugation. Finally, in the case of the sphere--mathematically speaking three almost commuting Hermitians whose sum of square is near the identity--we give the first quantitative result showing this index is the only obstruction to finding commuting approximations. We review the known non-quantitative results for the torus.Comment: 35 pages, 2 figure

The effect of local thermal fluctuations on the folding kinetics: a study from the perspective of the nonextensive statistical mechanics

Protein folding is a universal process, very fast and accurate, which works consistently (as it should be) in a wide range of physiological conditions. The present work is based on three premises, namely: ($i$) folding reaction is a process with two consecutive and independent stages, namely the search mechanism and the overall productive stabilization; ($ii$) the folding kinetics results from a mechanism as fast as can be; and ($iii$) at nanoscale dimensions, local thermal fluctuations may have important role on the folding kinetics. Here the first stage of folding process (search mechanism) is focused exclusively. The effects and consequences of local thermal fluctuations on the configurational kinetics, treated here in the context of non extensive statistical mechanics, is analyzed in detail through the dependence of the characteristic time of folding ($\tau$) on the temperature $T$ and on the nonextensive parameter $q$.The model used consists of effective residues forming a chain of 27 beads, which occupy different sites of a $3-$D infinite lattice, representing a single protein chain in solution. The configurational evolution, treated by Monte Carlo simulation, is driven mainly by the change in free energy of transfer between consecutive configurations. ...Comment: 19 pages, 3 figures, 1 tabl