10,964 research outputs found
Field theory of bicritical and tetracritical points. III. Relaxational dynamics including conservation of magnetization (Model C)
We calculate the relaxational dynamical critical behavior of systems of
symmetry including conservation of magnetization by
renormalization group (RG) theory within the minimal subtraction scheme in two
loop order. Within the stability region of the Heisenberg fixed point and the
biconical fixed point strong dynamical scaling holds with the asymptotic
dynamical critical exponent where is the crossover
exponent and the exponent of the correlation length. The critical
dynamics at and is governed by a small dynamical transient
exponent leading to nonuniversal nonasymptotic dynamical behavior. This may be
seen e.g. in the temperature dependence of the magnetic transport coefficients.Comment: 6 figure
Field theory of bi- and tetracritical points: Relaxational dynamics
We calculate the relaxational dynamical critical behavior of systems of
symmetry by renormalization group method within the
minimal subtraction scheme in two loop order. The three different bicritical
static universality classes previously found for such systems correspond to
three different dynamical universality classes within the static borderlines.
The Heisenberg and the biconical fixed point lead to strong dynamic scaling
whereas in the region of stability of the decoupled fixed point weak dynamic
scaling holds. Due to the neighborhood of the stability border between the
strong and the weak scaling dynamic fixed point corresponding to the static
biconical and the decoupled fixed point a very small dynamic transient
exponent, of , is present in the dynamics for the
physically important case and in .Comment: 8 figure
Average output entropy for quantum channels
We study the regularized average Renyi output entropy \bar{S}_{r}^{\reg} of
quantum channels. This quantity gives information about the average noisiness
of the channel output arising from a typical, highly entangled input state in
the limit of infinite dimensions. We find a closed expression for
\beta_{r}^{\reg}, a quantity which we conjecture to be equal to \Srreg. We
find an explicit form for \beta_{r}^{\reg} for some entanglement-breaking
channels, and also for the qubit depolarizing channel as a
function of the parameter . We prove equality of the two quantities in
some cases, in particular we conclude that for both are
non-analytic functions of the variable .Comment: 32 pages, several plots and figures; positivity condition added for
Theorem on entanglement breaking channels; new result for entrywise positive
channel
A few things I learnt from Jurgen Moser
A few remarks on integrable dynamical systems inspired by discussions with
Jurgen Moser and by his work.Comment: An article for the special issue of "Regular and Chaotic Dynamics"
dedicated to 80-th anniversary of Jurgen Mose
Cayley-Type Conditions for Billiards within Quadrics in
The notions of reflection from outside, reflection from inside and signature
of a billiard trajectory within a quadric are introduced. Cayley-type
conditions for periodical trajectories for the billiard in the region bounded
by quadrics in and for the billiard ordered game within
ellipsoids in are derived. In a limit, the condition describing periodic
trajectories of billiard systems on a quadric in is obtained.Comment: 10 pages, some corractions are made in Section
Longitudinal Losses Due to Breathing Mode Excitation in Radiofrequency Linear Accelerators
Transverse breathing mode oscillations in a particle beam can couple energy
into longitudinal oscillations in a bunch of finite length and cause
significant losses. We develop a model that illustrates this effect and explore
the dependence on mismatch size, space-charge tune depression, longitudinal
focusing strength, bunch length, and RF bucket length
Discrete Lagrangian systems on the Virasoro group and Camassa-Holm family
We show that the continuous limit of a wide natural class of the
right-invariant discrete Lagrangian systems on the Virasoro group gives the
family of integrable PDE's containing Camassa-Holm, Hunter-Saxton and
Korteweg-de Vries equations. This family has been recently derived by Khesin
and Misiolek as Euler equations on the Virasoro algebra for
-metrics. Our result demonstrates a universal nature of
these equations.Comment: 6 pages, no figures, AMS-LaTeX. Version 2: minor changes. Version 3:
minor change
Geodesic Flow on the Normal Congruence of a Minimal Surface
We study the geodesic flow on the normal line congruence of a minimal surface
in induced by the neutral K\"ahler metric on the space of
oriented lines. The metric is lorentz with isolated degenerate points and the
flow is shown to be completely integrable. In addition, we give a new
holomorphic description of minimal surfaces in and relate it to
the classical Weierstrass representation.Comment: AMS-LATEX 8 pages 2, figure
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