8,812 research outputs found
Coherent population transfer beyond the adiabatic limit: generalized matched pulses and higher-order trapping states
We show that the physical mechanism of population transfer in a 3-level
system with a closed loop of coherent couplings (loop-STIRAP) is not equivalent
to an adiabatic rotation of the dark-state of the Hamiltonian but coresponds to
a rotation of a higher-order trapping state in a generalized adiabatic basis.
The concept of generalized adiabatic basis sets is used as a constructive tool
to design pulse sequences for stimulated Raman adiabatic passage (STIRAP) which
give maximum population transfer also under conditions when the usual condition
of adiabaticty is only poorly fulfilled. Under certain conditions for the
pulses (generalized matched pulses) there exists a higher-order trapping state,
which is an exact constant of motion and analytic solutions for the atomic
dynamics can be derived.Comment: 15 pages, 9 figure
Large-order trend of the anomalous-dimensions spectrum of trilinear twist-3 quark operators
The anomalous dimensions of trilinear-quark operators are calculated at
leading twist by diagonalizing the one-gluon exchange kernel of the
renormalization-group type evolution equation for the nucleon distribution
amplitude. This is done within a symmetrized basis of Appell polynomials of
maximum degree for (up to order 400) by combining analytical and
numerical algorithms. The calculated anomalous dimensions form a degenerate
system, whose upper envelope shows asymptotically logarithmic behavior.Comment: 12 pages; 1 table; 4 figures as PS files; RevTex styl
On the Relation between Rigging Inner Product and Master Constraint Direct Integral Decomposition
Canonical quantisation of constrained systems with first class constraints
via Dirac's operator constraint method proceeds by the thory of Rigged Hilbert
spaces, sometimes also called Refined Algebraic Quantisation (RAQ). This method
can work when the constraints form a Lie algebra. When the constraints only
close with nontrivial structure functions, the Rigging map can no longer be
defined.
To overcome this obstacle, the Master Constraint Method has been proposed
which replaces the individual constraints by a weighted sum of absolute squares
of the constraints. Now the direct integral decomposition methods (DID), which
are closely related to Rigged Hilbert spaces, become available and have been
successfully tested in various situations.
It is relatively straightforward to relate the Rigging Inner Product to the
path integral that one obtains via reduced phase space methods. However, for
the Master Constraint this is not at all obvious. In this paper we find
sufficient conditions under which such a relation can be established. Key to
our analysis is the possibility to pass to equivalent, Abelian constraints, at
least locally in phase space. Then the Master Constraint DID for those Abelian
constraints can be directly related to the Rigging Map and therefore has a path
integral formulation.Comment: 25 page
Effect of current corrugations on the stability of the tearing mode
The generation of zonal magnetic fields in laboratory fusion plasmas is
predicted by theoretical and numerical models and was recently observed
experimentally. It is shown that the modification of the current density
gradient associated with such corrugations can significantly affect the
stability of the tearing mode. A simple scaling law is derived that predicts
the impact of small stationary current corrugations on the stability parameter
. The described destabilization mechanism can provide an explanation
for the trigger of the Neoclassical Tearing Mode (NTM) in plasmas without
significant MHD activity.Comment: Accepted to Physics of Plasma
The Gelfand map and symmetric products
If A is an algebra of functions on X, there are many cases when X can be
regarded as included in Hom(A,C) as the set of ring homomorphisms. In this
paper the corresponding results for the symmetric products of X are introduced.
It is shown that the symmetric product Sym^n(X) is included in Hom(A,C) as the
set of those functions that satisfy equations generalising f(xy)=f(x)f(y).
These equations are related to formulae introduced by Frobenius and, for the
relevant A, they characterise linear maps on A that are the sum of ring
homomorphisms. The main theorem is proved using an identity satisfied by
partitions of finite sets.Comment: 14 pages, Late
Coordinate time and proper time in the GPS
The Global Positioning System (GPS) provides an excellent educational example
as to how the theory of general relativity is put into practice and becomes
part of our everyday life. This paper gives a short and instructive derivation
of an important formula used in the GPS, and is aimed at graduate students and
general physicists.
The theoretical background of the GPS (see \cite{ashby}) uses the
Schwarzschild spacetime to deduce the {\it approximate} formula, ds/dt\approx
1+V-\frac{|\vv|^2}{2}, for the relation between the proper time rate of a
satellite clock and the coordinate time rate . Here is the gravitational
potential at the position of the satellite and \vv is its velocity (with
light-speed being normalized as ). In this note we give a different
derivation of this formula, {\it without using approximations}, to arrive at
ds/dt=\sqrt{1+2V-|\vv|^2 -\frac{2V}{1+2V}(\n\cdot\vv)^2}, where \n is the
normal vector pointing outward from the center of Earth to the satellite. In
particular, if the satellite moves along a circular orbit then the formula
simplifies to ds/dt=\sqrt{1+2V-|\vv|^2}.
We emphasize that this derivation is useful mainly for educational purposes,
as the approximation above is already satisfactory in practice.Comment: 5 pages, revised, over-over-simplified... Does anyone care that the
GPS uses an approximate formula, while a precise one is available in just a
few lines??? Physicists don'
Weak Localization Coexisting with a Magnetic Field in a Normal-Metal--Superconductor Microbridge
A random-matrix theory is presented which shows that breaking time-reversal
symmetry by itself does {\em not} suppress the weak-localization correction to
the conductance of a disordered metal wire attached to a superconductor.
Suppression of weak localization requires applying a magnetic field as well as
raising the voltage, to break both time-reversal symmetry and electron-hole
degeneracy. A magnetic-field dependent contact resistance obscured this anomaly
in previous numerical simulations.Comment: 8 pages, REVTeX-3.0, 1 figur
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