59,141 research outputs found
Nonperturbative results for the mass dependence of the QED fermion determinant
The fermion determinant in four-dimensional quantum electrodynamics in the
presence of O(2)XO(3) symmetric background gauge fields with a nonvanishing
global chiral anomaly is considered. It is shown that the leading mass
singularity of the determinant's nonperturbative part is fixed by the anomaly.
It is also shown that for a large class of such fields there is at least one
value of the fermion mass at which the determinant's nonperturbative part
reduces to its noninteracting value.Comment: This is an extended version of the author's paper in
Phys.Rev.D81(2010)10770
Hamilton's turns as visual tool-kit for designing of single-qubit unitary gates
Unitary evolutions of a qubit are traditionally represented geometrically as
rotations of the Bloch sphere, but the composition of such evolutions is
handled algebraically through matrix multiplication [of SU(2) or SO(3)
matrices]. Hamilton's construct, called turns, provides for handling the latter
pictorially through the as addition of directed great circle arcs on the unit
sphere S, resulting in a non-Abelian version of the
parallelogram law of vector addition of the Euclidean translation group. This
construct is developed into a visual tool-kit for handling the design of
single-qubit unitary gates. As an application, it is shown, in the concrete
case wherein the qubit is realized as polarization states of light, that all
unitary gates can be realized conveniently through a universal gadget
consisting of just two quarter-wave plates (QWP) and one half-wave plate (HWP).
The analysis and results easily transcribe to other realizations of the qubit:
The case of NMR is obtained by simply substituting and pulses
respectively for QWPs and HWPs, the phases of the pulses playing the role of
the orientation of fast axes of these plates.Comment: 16 Pages, 14 Figures, Published versio
Generalized Wannier Functions
We consider single particle Schrodinger operators with a gap in the en ergy
spectrum. We construct a complete, orthonormal basis function set for the inv
ariant space corresponding to the spectrum below the spectral gap, which are
exponentially localized a round a set of closed surfaces of monotonically
increasing sizes. Estimates on the exponential dec ay rate and a discussion of
the geometry of these surfaces is included
On the existence of impurity bound excitons in one-dimensional systems with zero range interactions
We consider a three-body one-dimensional Schr\"odinger operator with zero
range potentials, which models a positive impurity with charge
interacting with an exciton. We study the existence of discrete eigenvalues as
is varied. On one hand, we show that for sufficiently small
there exists a unique bound state whose binding energy behaves like ,
and we explicitly compute its leading coefficient. On the other hand, if
is larger than some critical value then the system has no bound
states
Monte Carlo Renormalization of 2d Simplicial Quantum Gravity Coupled to Gaussian Matter
We extend a recently proposed real-space renormalization group scheme for
dynamical triangulations to situations where the lattice is coupled to
continuous scalar fields. Using Monte Carlo simulations in combination with a
linear, stochastic blocking scheme for the scalar fields we are able to
determine the leading eigenvalues of the stability matrix with good accuracy
both for c = 1 and c = 10 theories.Comment: 17 pages, 7 figure
Pauli-Fierz model with Kato-class potentials and exponential decays
Generalized Pauli-Fierz Hamiltonian with Kato-class potential \KPF in
nonrelativistic quantum electrodynamics is defined and studied by a path
measure. \KPF is defined as the self-adjoint generator of a strongly
continuous one-parameter symmetric semigroup and it is shown that its bound
states spatially exponentially decay pointwise and the ground state is unique.Comment: We deleted Lemma 3.1 in vol.
Designing colloidal ground state patterns using short-range isotropic interactions
DNA-coated colloids are a popular model system for self-assembly through
tunable interactions. The DNA-encoded linkages between particles theoretically
allow for very high specificity, but generally no directionality or long-range
interactions. We introduce a two-dimensional lattice model for particles of
many different types with short-range isotropic interactions that are pairwise
specific. For this class of models, we address the fundamental question whether
it is possible to reliably design the interactions so that the ground state is
unique and corresponds to a given crystal structure. First, we determine lower
limits for the interaction range between particles, depending on the complexity
of the desired pattern and the underlying lattice. Then, we introduce a
`recipe' for determining the pairwise interactions that exactly satisfies this
minimum criterion, and we show that it is sufficient to uniquely determine the
ground state for a large class of crystal structures. Finally, we verify these
results using Monte Carlo simulations.Comment: 19 pages, 7 figure
Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees
We present examples of rooted tree graphs for which the Laplacian has
singular continuous spectral measures. For some of these examples we further
establish fractional Hausdorff dimensions. The singular continuous components,
in these models, have an interesting multiplicity structure. The results are
obtained via a decomposition of the Laplacian into a direct sum of Jacobi
matrices
A quantum Mermin--Wagner theorem for quantum rotators on two--dimensional graphs
This is the first of a series of papers considering symmetry properties of
quantum systems over 2D graphs or manifolds, with continuous spins, in the
spirit of the Mermin--Wagner theorem. In the model considered here (quantum
rotators) the phase space of a single spin is a dimensional torus, and
spins (or particles) are attached to sites of a graph satisfying a special
bi-dimensionality property. The kinetic energy part of the Hamiltonian is minus
a half of the Laplace operator. We assume that the interaction potential is
C-smooth and invariant under the action of a connected Lie group {\ttG}.
A part of our approach is to give a definition (and a construction) of a class
of infinite-volume Gibbs states for the systems under consideration (the class
\fG). This class contains the so-called limit Gibbs states, with or without
boundary conditions. We use ideas and techniques originated from various past
papers, in combination with the Feynman--Kac representation, to prove that any
state lying in the class \fG (defined in the text) is {\ttG}-invariant. An
example is given where the interaction potential is singular and there exists a
Gibbs state which is not {\ttG}-invariant.
In the next paper under the same title we establish a similar result for a
bosonic model where particles can jump from a vertex of the graph to one of its
neighbors (a generalized Hubbard model).Comment: 27 page
Quantum tunneling on graphs
We explore the tunneling behavior of a quantum particle on a finite graph, in
the presence of an asymptotically large potential. Surprisingly the behavior is
governed by the local symmetry of the graph around the wells.Comment: 18 page
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