1,626 research outputs found
The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions
We show that for two dimensional manifolds M with negative Euler
characteristic there exists subsets of the space of smooth Riemannian metrics
which are invariant and either parabolic or backwards-parabolic for the 2nd
order RG flow. We also show that solutions exists globally on these sets.
Finally, we establish the existence of an eternal solution that has both a UV
and IR limit, and passes through regions where the flow is parabolic and
backwards-parabolic
Dynamical heat channels
We consider heat conduction in a 1D dynamical channel. The channel consists
of a group of noninteracting particles, which move between two heat baths
according to some dynamical process. We show that the essential thermodynamic
properties of the heat channel can be evaluated from the diffusion properties
of the underlying particles. Emphasis is put on the conduction under anomalous
diffusion conditions. \\{\bf PACS number}: 05.40.+j, 05.45.ac, 05.60.cdComment: 4 figure
No classical limit of quantum decay for broad states
Though the classical treatment of spontaneous decay leads to an exponential
decay law, it is well known that this is an approximation of the quantum
mechanical result which is a non-exponential at very small and large times for
narrow states. The non exponential nature at large times is however hard to
establish from experiments. A method to recover the time evolution of unstable
states from a parametrization of the amplitude fitted to data is presented. We
apply the method to a realistic example of a very broad state, the sigma meson
and reveal that an exponential decay is not a valid approximation at any time
for this state. This example derived from experiment, shows the unique nature
of broad resonances
Smoluchowski-Kramers approximation in the case of variable friction
We consider the small mass asymptotics (Smoluchowski-Kramers approximation)
for the Langevin equation with a variable friction coefficient. The limit of
the solution in the classical sense does not exist in this case. We study a
modification of the Smoluchowski-Kramers approximation. Some applications of
the Smoluchowski-Kramers approximation to problems with fast oscillating or
discontinuous coefficients are considered.Comment: already publishe
Chaos edges of -logistic maps: Connection between the relaxation and sensitivity entropic indices
Chaos thresholds of the -logistic maps are numerically analysed at accumulation points of cycles 2, 3
and 5. We verify that the nonextensive -generalization of a Pesin-like
identity is preserved through averaging over the entire phase space. More
precisely, we computationally verify , where the entropy (), the sensitivity to the initial
conditions , and
(). The entropic index
depend on
both and the cycle. We also study the relaxation that occurs if we start
with an ensemble of initial conditions homogeneously occupying the entire phase
space. The associated Lebesgue measure asymptotically decreases as
(). These results led to (i) the first
illustration of the connection (conjectured by one of us) between sensitivity
and relaxation entropic indices, namely , where the positive numbers depend on the
cycle; (ii) an unexpected and new scaling, namely ( for , and for ).Comment: 5 pages, 5 figure
A gyro-gauge independent minimal guiding-center reduction by Lie-transforming the velocity vector field
International audienceWe introduce a gyro-gauge independent formulation of a simplified guiding-center reduction, which removes the fast time-scale from particle dynamics by Lie-transforming the velocity vector field. This is close to Krylov-Bogoliubov method of averaging the equations of motion, although more geometric. At leading order, the Lie-transform consists in the generator of Larmor gyration, which can be explicitly inverted, while working with gauge-independent coordinates and operators, by using the physical gyro-angle as a (constrained) coordinate. This brings both the change of coordinates and the reduced dynamics of the minimal guiding-center reduction order by order in a Larmor radius expansion. The procedure is algorithmic and the reduction is systematically derived up to full second order, in a more straightforward way than when Lie-transforming the phase-space Lagrangian or averaging the equations of motion. The results write up some structures in the guiding-center expansion. Extensions and limitations of the method are considered
On the Green function of linear evolution equations for a region with a boundary
We derive a closed-form expression for the Green function of linear evolution
equations with the Dirichlet boundary condition for an arbitrary region, based
on the singular perturbation approach to boundary problems.Comment: 9 page
Towards a feasible implementation of quantum neural networks using quantum dots
We propose an implementation of quantum neural networks using an array of
quantum dots with dipole-dipole interactions. We demonstrate that this
implementation is both feasible and versatile by studying it within the
framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic
phonons. Using numerically exact Feynman integral calculations, we have found
that the quantum coherence in our neural networks survive for over a hundred ps
even at liquid nitrogen temperatures (77 K), which is three orders of magnitude
higher than current implementations which are based on SQUID-based systems
operating at temperatures in the mK range.Comment: revtex, 5 pages, 2 eps figure
GPU accelerated shake and rattle algorithms for systems with holonomic constraints
The dynamic of complex fluid can be described by including viscoelastic stress tensor
into the equation of Non-Newtonian fluid. Different models are used to evaluate the stress tensor at
various levels, with the multi-scale model being the most effective
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