scholarly journals LONG-TIME RELAXATION ON SPIN LATTICE AS A MANIFESTATION OF CHAOTIC DYNAMICS

2004 ◽  
Vol 18 (08) ◽  
pp. 1119-1159 ◽  
Author(s):  
BORIS V. FINE
Keyword(s):  
Correlation Functions ◽  
Time Scale ◽  
Inelastic Neutron Scattering ◽  
Spin Correlation ◽  
Inelastic Neutron ◽  
Theoretical Explanation ◽  
Characteristic Time Scale ◽  
Time Behavior ◽  
Intermediate Structure ◽  
Long Time

The long-time behavior of the infinite temperature spin correlation functions describing the free induction decay in nuclear magnetic resonance and intermediate structure factors in inelastic neutron scattering is considered. These correlation functions are defined for one-, two- and three-dimensional infinite lattices of interacting spins, both classical and quantum. It is shown that, even though the characteristic time-scale of the long-time decay of the correlation functions considered is non-Markovian, the generic functional form of this decay is either simple exponential or exponential multiplied by cosine. This work contains (i) the summary of the existing experimental and numerical evidence of the above asymptotic behavior; (ii) theoretical explanation of this behavior; and (iii) semi-empirical analysis of various factors discriminating between the monotonic and the oscillatory long-time decays. The theory is based on a fairly strong conjecture that, as a result of chaos generated by spin dynamics, a Brownian-like Markovian description can be applied to the long-time properties of ensemble average quantities on a non-Markovian time-scale. The formalism resulting from that conjecture can be described as "correlated diffusion in finite volumes."

scholarly journals The investigation of Neutron Scattering In Spin Waves Theory of Ferromagnetic Crystals

2014 ◽  
Vol 8 (4) ◽  
Author(s):  
Azadeh Farzaneh ◽  
Mohammad Reza Abdi ◽  
Khadije Rezaee Ebrahim Saraee
Keyword(s):  
Neutron Scattering ◽  
Spin Wave ◽  
Cross Section ◽  
Inelastic Neutron Scattering ◽  
Spin Waves ◽  
Wave Theory ◽  
Spin Correlation ◽  
Inelastic Neutron ◽  
Magnetic Behaviour ◽  
Spin Interaction

Inelastic neutron scattering, probing the temporal spin-spin correlation at the different microscopic scale, is a powerful technique to study the magnetic behaviour of ferromagnetic crystals. In addition, high penetration power of neutron in samples has made it as a useful way for spin-spin interaction in neutron scattering. Changes in the magnetic cross section in term of different energy transfer and temperatures are calculated for nickel and iron as transition metals in Heisenberg model versus spin wave theory by considering atomic form factor. Finally, the effect of magnetic structure and behaviour of crystal in measuring cross-section shows that increasing temperature results in the Cross-section increase Also, the existence of propagating spin waves below Tc is compared in Ni and Fe in different momentum transfers. The relation of spin wave energy with temperature dependence of nickel has created different behaviour in the changes of cross section rather than iron.

STUDY OF SLOW DYNAMICAL PROCESSES BY NEUTRON-SPIN-ECHO

1993 ◽  
Vol 07 (16n17) ◽  
pp. 2885-2907 ◽  
Author(s):  
FERENC MEZEI
Keyword(s):  
Time Scale ◽  
Soft Matter ◽  
Inelastic Neutron Scattering ◽  
Spin Echo ◽  
Slow Motion ◽  
Inelastic Neutron ◽  
Neutron Spin ◽  
Neutron Spin Echo ◽  
Relaxation Effects ◽  
Atomic Vibrations

Conventional resolution inelastic neutron scattering spectroscopy allows us to explore the behaviour of condensed matter essentially on the time scale of thermal atomic vibrations. By the application of the Neutron Spin Echo trick, which enables us to get around the Liouville theorem limitation of conventional methods, the resolution can be improved very substantially. This opened up the field for the study of a large variety of slow motion phenomena (critical slowing down, relaxation effects, disordered dynamics, soft matter), i.e. the investigation of processes on a mesoscopic time scale between microscopic collision times and macroscopic dynamics.

Averaging of Attractors and Inertial Manifolds for Parabolic PDE With Random Coefficients

2005 ◽  
Vol 5 (4) ◽  
Author(s):  
Igor D. Chueshov ◽  
Björn Schmalfuß
Keyword(s):  
Evolution Equation ◽  
Time Scale ◽  
Inertial Manifolds ◽  
Inertial Manifold ◽  
Fast Time ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Scaling Parameter ◽  
Fast Time Scale ◽  
Long Time

AbstractThe averaging method has been used to study random or non-autonomous systems on a fast time scale. We apply this method to a random abstract evolution equation on a fast time scale whose long time behavior can be characterized by a random attractor or a random inertial manifold. The main purpose is to show that the long-time behavior of such a system can be described by a deterministic evolution equation with averaged coefficients. Our first result provides an averaging result on finite time intervals which we use to show that under a dissipativity assumption the attractors of the fast time scale systems are upper semicontinuous when the scaling parameter goes to zero. Our main result deals with a global averaging procedure. Under some spectral gap condition we show that inertial manifolds of the fast time scale system tend to an inertial manifold of the averaged system when the scaling parameter goes to zero. These general results can be applied to semilinear parabolic differential equations containing a scaled ergodic noise on a fast time scale which includes scaled almost periodic motions.

scholarly journals LONG TIME BEHAVIOR OF THE TWO-DIMENSIONAL VLASOV EQUATION WITH A STRONG EXTERNAL MAGNETIC FIELD

2000 ◽  
Vol 10 (04) ◽  
pp. 539-553 ◽  
Author(s):  
E. FRÉNOD ◽  
E. SONNENDRÜCKER
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Vlasov Equation ◽  
Time Scale ◽  
Observation Time ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time ◽  
Field Lines ◽  
The Magnetic Field

When charged particles are submitted to a large external magnetic field, their movement in first approximation occurs along the magnetic field lines and obeys a one-dimensional Vlasov equation along these field lines. However, when observing the particles on a sufficiently long time scale, a drift phenomenon perpendicular to the magnetic field lines superposes to this first movement. In this paper, we present a rigorous asymptotic analysis of the two-dimensional Vlasov equation when the magnetic field tends to infinity, the observation time scale increases accordingly. Techniques based on the two-scale convergence and the introduction of a second problem enable us to find an equation verified by the weak limit of the distribution function.

scholarly journals An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number

2007 ◽  
Vol 574 ◽  
pp. 405-427 ◽  
Author(s):  
MICHELE GUALA ◽  
ALEXANDER LIBERZON ◽  
ARKADY TSINOBER ◽  
WOLFGANG KINZELBACH
Keyword(s):  
Reynolds Number ◽  
Time Scales ◽  
Correlation Functions ◽  
Time Scale ◽  
Cross Correlation ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Small Scale ◽  
Production Term ◽  
Long Time

Lagrangian auto- and cross-correlation functions of the rate of strain s2, enstrophy ω2, their respective production terms −sijsjkski and ωiωjsij, and material derivatives, Ds2/Dt and Dω2/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Reλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensor sij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2 to the relatively shorter time scales of s2, ωiωjsij and −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s2 and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkski and s2 and between −sijsjkski and Ds2/Dt, in addition to a marked anti-correlation between ωiωjsij and Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s2 and its production term, −sijsjkski.

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