1,482 research outputs found
Magnetically Defined Qubits on 3D Topological Insulators
We explore potentials that break time-reversal symmetry to confine the
surface states of 3D topological insulators into quantum wires and quantum
dots. A magnetic domain wall on a ferromagnet insulator cap layer provides
interfacial states predicted to show the quantum anomalous Hall effect (QAHE).
Here we show that confinement can also occur at magnetic domain
heterostructures, with states extended in the inner domain, as well as
interfacial QAHE states at the surrounding domain walls. The proposed geometry
allows the isolation of the wire and dot from spurious circumventing surface
states. For the quantum dots we find that highly spin-polarized quantized QAHE
states at the dot edge constitute a promising candidate for quantum computing
qubits.Comment: 5 pages, 4 figure
Flow Fragmentalism
In this paper, we articulate a version of non-standard A-theory – which we call Flow Fragmentalism – in relation to its take on the issue of supervenience of truth on being. According to the Truth Supervenes on Being (TSB) Principle, the truth of past- and future-tensed propositions supervenes, respectively, on past and future facts. Since the standard presentist denies the existence of past and future entities and facts concerning them that do not obtain in the present, she seems to lack the resources to accept both past and future-tensed truths and the TSB Principle. Contrariwise, positions in philosophy of time that accept an eternalist ontology (e.g., B-theory, moving spotlight, and Fine’s and Lipman’s versions of fragmentalism) allow for a “direct” supervenience base for past- and future-tensed truths. We argue that Flow Fragmentalism constitutes a middle ground, which retains most of the advantages of both views, and allows us to articulate a novel account of the passage of time
Relativistic hydrogenic atoms in strong magnetic fields
In the Dirac operator framework we characterize and estimate the ground state
energy of relativistic hydrogenic atoms in a constant magnetic field and
describe the asymptotic regime corresponding to a large field strength using
relativistic Landau levels. We also define and estimate a critical magnetic
field beyond which stability is lost
Variational study of the nu=1 quantum Hall ferromagnet in the presence of spin-orbit interaction
We investigate the nu=1 quantum Hall ferromagnet in the presence of
spin-orbit coupling of the Rashba or Dresselhaus type by means of
Hartree-Fock-typed variational states. In the presence of Rashba (Dresselhaus)
spin-orbit coupling the fully spin-polarized quantum Hall state is always
unstable resulting in a reduction of the spin polarization if the product of
the particle charge and the effective -factor is positive (negative). In
all other cases an alternative variational state with O(2) symmetry and finite
in-plane spin components is lower in energy than the fully spin-polarized state
for large enough spin-orbit interaction. The phase diagram resulting from these
considerations differs qualitatively from earlier studies.Comment: 9 pages, 3 figures included, version to appear in Phys. Rev.
Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces
This paper is motivated by the characterization of the optimal symmetry
breaking region in Caffarelli-Kohn-Nirenberg inequalities. As a consequence,
optimal functions and sharp constants are computed in the symmetry region. The
result solves a longstanding conjecture on the optimal symmetry range.
As a byproduct of our method we obtain sharp estimates for the principal
eigenvalue of Schr\"odinger operators on some non-flat non-compact manifolds,
which to the best of our knowledge are new.
The method relies on generalized entropy functionals for nonlinear diffusion
equations. It opens a new area of research for approaches related to carr\'e du
champ methods on non-compact manifolds. However key estimates depend as much on
curvature properties as on purely nonlinear effects. The method is well adapted
to functional inequalities involving simple weights and also applies to general
cylinders. Beyond results on symmetry and symmetry breaking, and on optimal
constants in functional inequalities, rigidity theorems for nonlinear elliptic
equations can be deduced in rather general settings.Comment: 33 pages, 1 figur
Decoherence of Majorana qubits by noisy gates
We propose and study a realistic model for the decoherence of topological
qubits, based on Majorana fermions in one-dimensional topological
superconductors. The source of decoherence is the fluctuating charge on a
capacitively coupled gate, modeled by non-interacting electrons. In this
context, we clarify the role of quantum fluctuations and thermal fluctuations
and find that quantum fluctuations do not lead to decoherence, while thermal
fluctuations do. We explicitly calculate decay times due to thermal noise and
give conditions for the gap size in the topological superconductor and the gate
temperature. Based on this result, we provide simple rules for gate geometries
and materials optimized for reducing the negative effect of thermal charge
fluctuations on the gate
Probing entanglement via Rashba-induced shot noise oscillations
We have recently calculated shot noise for entangled and spin-polarized
electrons in novel beam-splitter geometries with a local Rashba s-o interaction
in the incoming leads. This interaction allows for a gate-controlled rotation
of the incoming electron spins. Here we present an alternate simpler route to
the shot noise calculation in the above work and focus on only electron pairs.
Shot noise for these shows continuous bunching and antibunching behaviors. In
addition, entangled and unentangled triplets yield distinctive shot noise
oscillations. Besides allowing for a direct way to identify triplet and singlet
states, these oscillations can be used to extract s-o coupling constants
through noise measurements. Incoming leads with spin-orbit interband mixing
give rise an additional modulation of the current noise. This extra rotation
allows the design of a spin transistor with enhanced spin control.Comment: 7 pages, 3 figures; to appear in the special issue of the Journal of
Superconductivity in honor of E. I. Rashb
Characterization of the critical magnetic field in the Dirac-Coulomb equation
We consider a relativistic hydrogenic atom in a strong magnetic field. The
ground state level depends on the strength of the magnetic field and reaches
the lower end of the spectral gap of the Dirac-Coulomb operator for a certain
critical value, the critical magnetic field. We also define a critical magnetic
field in a Landau level ansatz. In both cases, when the charge Z of the nucleus
is not too small, these critical magnetic fields are huge when measured in
Tesla, but not so big when the equation is written in dimensionless form. When
computed in the Landau level ansatz, orders of magnitude of the critical field
are correct, as well as the dependence in Z. The computed value is however
significantly too big for a large Z, and the wave function is not well
approximated. Hence, accurate numerical computations involving the Dirac
equation cannot systematically rely on the Landau level ansatz. Our approach is
based on a scaling property. The critical magnetic field is characterized in
terms of an equivalent eigenvalue problem. This is our main analytical result,
and also the starting point of our numerical scheme
An analytical proof of Hardy-like inequalities related to the Dirac operator
We prove some sharp Hardy type inequalities related to the Dirac operator by
elementary, direct methods. Some of these inequalities have been obtained
previously using spectral information about the Dirac-Coulomb operator. Our
results are stated under optimal conditions on the asymptotics of the
potentials near zero and near infinity.Comment: LaTex, 22 page
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