2,994 research outputs found
Theory of valley-orbit coupling in a Si/SiGe quantum dot
Electron states are studied for quantum dots in a strained Si quantum well,
taking into account both valley and orbital physics. Realistic geometries are
considered, including circular and elliptical dot shapes, parallel and
perpendicular magnetic fields, and (most importantly for valley coupling) the
small local tilt of the quantum well interface away from the crystallographic
axes. In absence of a tilt, valley splitting occurs only between pairs of
states with the same orbital quantum numbers. However, tilting is ubiquitous in
conventional silicon heterostructures, leading to valley-orbit coupling. In
this context, "valley splitting" is no longer a well defined concept, and the
quantity of merit for qubit applications becomes the ground state gap. For
typical dots used as qubits, a rich energy spectrum emerges, as a function of
magnetic field, tilt angle, and orbital quantum number. Numerical and
analytical solutions are obtained for the ground state gap and for the mixing
fraction between the ground and excited states. This mixing can lead to valley
scattering, decoherence, and leakage for Si spin qubits.Comment: 18 pages, including 4 figure
B\"acklund Transformations of MKdV and Painlev\'e Equations
For there are and actions on the space of solutions of
the first nontrivial equation in the Z_2$ actions on the space of solutions of the standard MKdV equation.
These actions survive scaling reduction, and give rise to transformation groups
for certain (systems of) ODEs, including the second, fourth and fifth
Painlev\'e equations.Comment: 8 pages, plain te
Noise resistance of adiabatic quantum computation using random matrix theory
Besides the traditional circuit-based model of quantum computation, several
quantum algorithms based on a continuous-time Hamiltonian evolution have
recently been introduced, including for instance continuous-time quantum walk
algorithms as well as adiabatic quantum algorithms. Unfortunately, very little
is known today on the behavior of these Hamiltonian algorithms in the presence
of noise. Here, we perform a fully analytical study of the resistance to noise
of these algorithms using perturbation theory combined with a theoretical noise
model based on random matrices drawn from the Gaussian Orthogonal Ensemble,
whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure
Anomalous diffusion in quantum Brownian motion with colored noise
Anomalous diffusion is discussed in the context of quantum Brownian motion
with colored noise. It is shown that earlier results follow simply and directly
from the fluctuation-dissipation theorem. The limits on the long-time
dependence of anomalous diffusion are shown to be a consequence of the second
law of thermodynamics. The special case of an electron interacting with the
radiation field is discussed in detail. We apply our results to wave-packet
spreading
Vacuum Polarization and the Electric Charge of the Positron
We show that higher-order vacuum polarization would contribute a measureable
net charge to atoms, if the charges of electrons and positrons do not balance
precisely. We obtain the limit for the sum of
the charges of electron and positron. This also constitutes a new bound on
certain violations of PCT invariance.Comment: 9 pages, 1 figure attached as PostScript file, DUKE-TH-92-38. Revised
versio
Applications of Automata and Graphs: Labeling-Operators in Hilbert Space I
We show that certain representations of graphs by operators on Hilbert space
have uses in signal processing and in symbolic dynamics. Our main result is
that graphs built on automata have fractal characteristics. We make this
precise with the use of Representation Theory and of Spectral Theory of a
certain family of Hecke operators. Let G be a directed graph. We begin by
building the graph groupoid G induced by G, and representations of G. Our main
application is to the groupoids defined from automata. By assigning weights to
the edges of a fixed graph G, we give conditions for G to acquire fractal-like
properties, and hence we can have fractaloids or G-fractals. Our standing
assumption on G is that it is locally finite and connected, and our labeling of
G is determined by the "out-degrees of vertices". From our labeling, we arrive
at a family of Hecke-type operators whose spectrum is computed. As
applications, we are able to build representations by operators on Hilbert
spaces (including the Hecke operators); and we further show that automata built
on a finite alphabet generate fractaloids. Our Hecke-type operators, or
labeling operators, come from an amalgamated free probability construction, and
we compute the corresponding amalgamated free moments. We show that the free
moments are completely determined by certain scalar-valued functions.Comment: 69 page
Computing the spectrum of black hole radiation in the presence of high frequency dispersion: an analytical approach
We present a method for computing the spectrum of black hole radiation of a
scalar field satisfying a wave equation with high frequency dispersion. The
method involves a combination of Laplace transform and WKB techniques for
finding approximate solutions to ordinary differential equations. The modified
wave equation is obtained by adding a higher order derivative term suppressed
by powers of a fundamental momentum scale to the ordinary wave equation.
Depending on the sign of this new term, high frequency modes propagate either
superluminally or subluminally. We show that the resulting spectrum of created
particles is thermal at the Hawking temperature, and further that the out-state
is a thermal state at the Hawking temperature, to leading order in , for
either modification.Comment: 26 pages, plain latex, 6 figures included using psfi
Equivalence Theorems for Pseudoscalar Coupling
By a unitary transformation a rigorous equivalence theorem is established for the pseudoscalar coupling of pseudoscalar mesons (neutral and charged) to a second-quantized nucleon field. By the transformation the linear pseudoscalar coupling is eliminated in favor of a nonlinear pseudovector coupling term together with other terms. Among these is a term corresponding to a variation of the effective rest mass of the nucleons with position through its dependence on the meson potentials. The question of the connection of the nonlinear pseudovector coupling with heuristic proposals that such a coupling may account for the saturation of nuclear forces and the independence of single nucleon motions in nuclei is briefly discussed. The new representation of the Hamiltonian may have particular value in constructing a strong coupling theory of pseudoscalar coupled meson fields. Some theorems on a class of unitary transformations of which the present transformation is an example are stated and proved in an appendix.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86126/1/PhysRev.87.1061-RKO.pd
The general-covariant and gauge-invariant theory of quantum particles in classical backgrounds
A new approach to the concept of particles and their production in quantum
field theory is developed. A local operator describing the current of particle
density is constructed for scalar and spinor fields in arbitrary gravitational
and electromagnetic backgrounds. This enables one to describe particles in a
local, general-covariant and gauge-invariant way. However, the current depends
on the choice of a 2-point function. There is a choice that leads to the local
non-conservation of the current in a gravitational or an electromagnetic
background, which describes local particle production consistent with the usual
global description based on the Bogoliubov transformation. The most natural
choice based on the Green function calculated using the Schwinger-DeWitt method
leads to the local conservation of the current, provided that interactions with
quantum fields are absent. Interactions with quantum fields lead to the local
non-conservation of the current which describes local particle production
consistent with the usual global description based on the interaction picture.Comment: 34 pages, revised, to appear in Int. J. Mod. Phys.
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