4,350 research outputs found
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 can be written as a sum of local pairwise
commuting projectors on a -dimensional lattice. We consider a perturbed
Hamiltonian involving a generic perturbation that can be written
as a sum of short-range bounded-norm interactions. We prove that if the
strength of is below a constant threshold value then has well-defined
spectral bands originating from the low-lying eigenvalues of . 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
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
-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 , with 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 PNP 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
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: () folding reaction is a
process with two consecutive and independent stages, namely the search
mechanism and the overall productive stabilization; () the folding kinetics
results from a mechanism as fast as can be; and () 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 () on the temperature and on the
nonextensive parameter .The model used consists of effective residues
forming a chain of 27 beads, which occupy different sites of a 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
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 -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 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
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