75,380 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

### Spinoza today: the current state of Spinoza scholarship

What I plan to do in this paper is to provide a survey of the ways in which Spinozaâ€™s philosophy has been deployed in relation to early modern thought, in the history of ideas and in a number of different domains of contemporary philosophy, and to offer an account of how some of this research has developed. The past decade of research in Spinoza studies has been characterized by a number of tendencies; however, it is possible to identify four main domains that characterize these different lines of research: studies of Spinozaâ€™s individual works, of its problematic concepts, from the point of view of the history of ideas, and comparative studies of Spinozaâ€™s ideas

### 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$^2 \subset \mathbb{R}^3$, 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 $\pi/2$ and $\pi$ 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

### Approach to Equilibrium for a Forced Burgers Equation

We show that approach to equilibrium in certain forced Burgers equations is
implied by a decay estimate on a suitable intrinsic semigroup estimate, and we
verify this estimate in a variety of cases including a periodic force.Comment: To appear in Journal of Evolution Equation

### On Local Borg-Marchenko Uniqueness Results

We provide a new short proof of the following fact, first proved by one of us
in 1998: If two Weyl-Titchmarsh m-functions, $m_j(z)$, of two Schr\"odinger
operators H_j = -\f{d^2}{dx^2} + q_j, j=1,2 in $L^2 ((0,R))$, $0<R\leq
\infty$, are exponentially close, that is, |m_1(z)- m_2(z)|
\underset{|z|\to\infty}{=} O(e^{-2\Ima (z^{1/2})a}), 0<a<R, then $q_1 = q_2$
a.e.~on $[0,a]$. The result applies to any boundary conditions at x=0 and x=R
and should be considered a local version of the celebrated Borg-Marchenko
uniqueness result (which is quickly recovered as a corollary to our proof).
Moreover, we extend the local uniqueness result to matrix-valued Schr\"odinger
operators.Comment: LaTeX, 18 page

### Uniqueness theorems in inverse spectral theory for one-dimensional SchrÃ¶dinger operators

New unique characterization results for the potential V(x) in connection with SchrÃ¶dinger operators on R and on the half-line [0,âˆž)are proven in terms of appropriate Krein spectral shift functions. Particular results obtained include a generalization of a well-known uniqueness theorem of Borg and Marchenko for SchrÃ¶dinger operators on the half-line with purely discrete spectra to arbitrary spectral types and a new uniqueness result for SchrÃ¶dinger operators with confining potentials on the entire real line

### Positive Lyapunov Exponents for Quasiperiodic Szego cocycles

In this paper we first obtain a formula of averaged Lyapunov exponents for
ergodic Szego cocycles via the Herman-Avila-Bochi formula. Then using
acceleration, we construct a class of analytic quasi-periodic Szego cocycles
with uniformly positive Lyapunov exponents. Finally, a simple application of
the main theorem in [Y] allows us to estimate the Lebesgue measure of support
of the measure associated to certain class of C1 quasiperiodic 2- sided
Verblunsky coefficients. Using the same method, we also recover the [S-S]
results for Schrodinger cocycles with nonconstant real analytic potentials and
obtain some nonuniform hyperbolicity results for arbitrarily fixed Brjuno
frequency and for certain C1 potentials.Comment: 27 papge

### Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

We prove that for any $n\times n$ matrix, $A$, and $z$ with $|z|\geq \|A\|$,
we have that \|(z-A)^{-1}\|\leq\cot (\frac{\pi}{4n}) \dist (z,
\spec(A))^{-1}. We apply this result to the study of random orthogonal
polynomials on the unit circle.Comment: 27 page

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