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7
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85088178434
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15)
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15.
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8
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70349430009
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Low frequency phenomena permit long time scale averages giving mean field like homogeneity to statistical quantities.5,14,15)
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Low frequency phenomena permit long time scale averages giving mean field like homogeneity to statistical quantities.5,14,15).
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9
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70349422460
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An isolated, stationary macrostate would make no N-body transition
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An isolated, stationary macrostate would make no N-body transition.
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10
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70349413323
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note
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An isolated particle, e.g. an electron, has attributes of mass, charge and spin. In an electron quasiparticle approximation to a macroscopic state these quantities are no longer unique, either the particle or the attributes must be redefined. Following convention we redefine the particle giving the conceptual pure 'spin fluctuation' quasiparticle as a mixture of the basic electronic and nuclear spin, charge and motional degrees of freedom. It is then not evident that, for example, the neutron will act as an appropriate 'spin fluctuation' filter since it couples electromagnetically to the total b field (electron and nucleus) and via the strong force to the ionic mass. With changing constraints of the imposed thermodynamic state it does not follow either that the initial quasiparticle representation will rappropriate to the evolved macrostate, nor that the probe projection of the quasiparticle will rconstant. This may restrict e.g. the temperature and pressure range of interpretation. Changing the probe to, for example, magnetic x-ray scattering or NMR may alter the projected quasiparticle properties in a significant manner both on account of the coupling constant and the relative space-time coherence scales of probe and quasiparticle an isolated particle, e.g. an electron, has attributes of mass, charge and spin. In an electron quasiparticle approximation to a macroscopic state these quantities are no longer unique, either the particle or the attributes must be redefined. Following convention we redefine the particle giving the (conceptual) pure 'spin fluctuation' quasiparticle as a mixture of the basic electronic and nuclear spin, charge and motional degrees of freedom. It is then not evident that, for example, the neutron will act as an appropriate 'spin fluctuation' filter since it couples electromagnetically to the total b field (electron and nucleus) and via the strong force to the ionic mass. With changing constraints of the imposed thermodynamic state it does not follow either that the initial quasiparticle representation will rappropriate to the evolved macrostate, nor that the probe projection of the quasiparticle will rconstant. This may restrict e.g. the temperature and pressure range of interpretation. Changing the probe to, for example, magnetic x-ray scattering or NMR may alter the projected quasiparticle properties in a significant manner both on account of the coupling constant and the relative space-time coherence scales of probe and quasiparticle.
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11
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70349421198
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Construction of a PDF is based on the implicit assumption of an incoherent sum
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Construction of a PDF is based on the implicit assumption of an incoherent sum.
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12
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85088180581
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13
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I.e. have a maximum likelihood as assessed by number of possible configurations.13
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14
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0004055640
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5,14 in other classes of problem it may prove convenient to make short time scale spatially extended averages to enable a temporal decomposition
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TL Hill: Thermodynamics of Small Systems (Dover Publications, New York, 1994). Whilst statistical equivalence of such sub-systems is generally ensured by long time averages5,14) in other classes of problem it may prove convenient to make short time scale spatially extended averages to enable a temporal decomposition.
-
(1994)
Thermodynamics of Small Systems
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Hill, T.L.1
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15
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70349431471
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A concept of motion may be central to define dimension and time; this invokes a degree of localisation of the evolving microstate
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A concept of motion may be central to define dimension and time; this invokes a degree of localisation of the evolving microstate.
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19
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70349436264
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The q index is suppressed for notational convenience
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The q index is suppressed for notational convenience.
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21
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85088179069
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23
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Mode incoherence allows the entropy to be estimated by direct summation.23
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23
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70349432543
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Whilst there are clear analogies with the conventional superconductor order parameter, here the observable is associated with the modulus rather than the phase variable
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Whilst there are clear analogies with the conventional superconductor order parameter, here the observable is associated with the modulus rather than the phase variable.
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24
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70349414690
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Roughly, for ω « 1 the dynamic heterogeneity may establish a modified Brillioun zone by Bragg reflection and hence effective local magnetic order
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Roughly, for ω « 1 the dynamic heterogeneity may establish a modified Brillioun zone by Bragg reflection and hence effective local magnetic order.
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25
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85088177584
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27-29
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27-29)
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26
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0034601474
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S Yau et al: Nature 406 (2000) 494.
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(2000)
Nature
, vol.406
, pp. 494
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Yau, S.1
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29
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85088179696
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6
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6
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31
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85088178597
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3,14
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Which are stabilised by the energy saving on approach to local order; mean field arguments are advanced in.3,14).
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32
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70349435631
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note
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An interesting counter intutative example is provided by the doping dependence of the response in Hi-Tc materials where, contary to expectations, in both La1-xBax;Cu04 and La11-xSrxCu04 the susceptibility is most FL like (SED) in the immediate vicinity of the critical composition for anti- ferromagnetism (i.e. x ∼ 0.04).6) In a classical scenario, the presence of an incipient phase transition would be anticipated to result in strong NER. From the present perspective, the disordered, spin-glass like, nature coupled with a diverging susceptibility, Xo, suggests the distribution of fluctuating volumes not to exceed V2 with resultant SED. Increased doping reduces X0 (v2 falls with increased disorder and γ2 rises) andNER (i.e. NFL behaviour) emerges with the renormalised distribution, D(γ) biased to higher frequencies. The coincidenceof maximal NFL behaviour with optimal doping for superconductivity suggests such renormalised high frequency modes toplay a sensitive role.
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33
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70349426037
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note
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A degree of self consistency may then be sought in the behaviour of the SED (FL) contribution to the susceptibility,the volume of such fluctuating modes and bulk thermodynamic measurements. The calculations outlined in section 3neglect this contribution.
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34
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0004095757
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quoted in M Sargent et al,(Addison-Wesley)
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C Huygens: quoted in M Sargent et al.: Laser Physics p.52(Addison-Wesley 1974).
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(1974)
Laser Physics
, pp. 52
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Huygens, C.1
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37
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85088178906
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i tends to a common (low) value
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i tends to a common (low) value.
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38
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70349435629
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E.g. on account of thermal contraction
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E.g. on account of thermal contraction.
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41
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0032474839
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ND Mathur et al. : Nature 394 (1998) 39;
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(1998)
Nature
, vol.394
, pp. 39
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Mathur, N.D.1
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43
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0035913344
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K Shimizu et al : Nature 412 (2001) 316.
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(2001)
Nature
, vol.412
, pp. 316
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Shimizu, K.1
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44
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0034632726
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SS Saxena et al. : Nature 406 (2000) 587;
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(2000)
Nature
, vol.406
, pp. 587
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Saxena, S.S.1
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47
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0000969306
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refs. therein
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N Bernhoeft: Eur. Phys. J. B13 (2000) 685 and refs. therein.
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(2000)
Eur. Phys. J.
, vol.B13
, pp. 685
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Bernhoeft, N.1
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48
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0002182040
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Where the possibility of a geometrically projected static magnetic moment coexisting with a dynamic order parameter is discussed
-
N Bernhoeft: J; Phys. Soc. Jpn. 70 (2001) Suppl A 7 where the possibility of a geometrically projected static magnetic moment coexisting with a dynamic order parameter is discussed.
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(2001)
J.Phys. Soc. Jpn.
, vol.70
, Issue.SUPPL. A
, pp. 7
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Bernhoeft, N.1
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