bjoernp/1-sentence-level-gutenberg-en_arxiv_pubmed_soda

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it is given by @xmath103}+ e^{-\lambda _ c^{-2}[({\bf r - r^\prime}_1)^2+({\bf r^\prime -r_1})^2]-2\nu^2\tau ^2},\ ] ] where @xmath104 ^ 2\rangle = 2\nu^2 $ ] .
as we see , the effect of the phase screen can be described by two parameters , @xmath93 and @xmath105 , which characterize the spatial and temporal coherence of the laser beam .
in the limiting case , @xmath106 , the second term in eq .
[ twenty ] vanishes and the problem is reduced to the case considered in refs .
@xcite,@xcite .
in the opposite case , @xmath107 , both terms in eq .
[ twenty ] are important .
this is shown in ref .
@xcite .
in what follows , we will see that these two limiting cases have physical interpretations where where @xmath108 ( slow detector ) and @xmath109 ( fast detector ) , respectively .
there is a specific realization of the diffuser in which a random phase distribution moves across the beam .
( this situation can be modeled by a rotating transparent disk with large diameter and varying thickness . )
the phase depends here on the only variable @xmath110 , i.e.
@xmath111 where @xmath112 is the velocity of the drift .
then we have @xmath113}+e^{-\lambda _ c^{-2}[({\bf r - r^\prime_1+v}\tau)^2+({\bf r^\prime -r_1+v}\tau)^2]}.\ ] ] comparing eqs .
[ twenty ] and [ twtw ] , we see that the quantity , @xmath114 , stands for the characteristic parameter describing the efficiency of the phase diffuser .
the criterion of slow " detector requires @xmath115 .
qualitatively , the two scenarios of phase variations , given by eqs .
[ twenty ] and [ twtw ] , affect in a similar way the intensity fluctuations .
in what follows , we consider the first of them as the simplest one .
( this is because the spatial and temporal variables in @xmath102 , given by eq .
[ twenty ] , are separable . )
_ vs _ propagation distance @xmath28 in the case of `` slow '' detector : @xmath116 .
the parameter @xmath117 indicates different initial coherence length .
in the absence of phase diffuser @xmath118 ( solid line ) .
@xmath119 is the conventional parameter describing a strength of the atmospheric turbulence . ]
substituting the expressions for operators given by eq .
[ fourteen ] with account for the phase factors @xmath120 and averaging over time as shown in eq .
[ one ] , we obtain @xmath121 @xmath122\bigg > , \ ] ] where the notation @xmath16 after sums indicates averaging over different realizations of the atmospheric refractive index .
the parameter @xmath123 describes the initial coherence length modified by the phase diffuser .
other notations are defined by following relations @xmath124 @xmath125 @xmath126 further calculations follow the scheme described in ref @xcite .
2 illustrates the effect of the phase diffuser on scintillations in the limit of a slow " detector ( @xmath127 ) .
we can see a considerable decrease in @xmath128 caused by the phase diffuser .
at the same time , the effect of the phase screen on @xmath128 becomes weaker for finite values of @xmath129 .
moreover , comparing the two upper curves in fig .
3 , we see the opposite effect : slow phase variations ( @xmath130 ) result in increased scintillations .
there is a simple explanation for this phenomenon : the noise generated by the turbulence is complemented by the noise arising from the random phase screen .
the integration time of the detector , @xmath3 , is not sufficiently large for averaging phase variations generated by the diffuser .
the function , @xmath131 , has a very simple form in the two limits : ( i)@xmath132 , when @xmath133 ; and ( ii ) @xmath134 , when @xmath109 .
then , in case ( i ) and for small values of the initial coherence [ @xmath135 , the asymptotic term for the scintillation index ( @xmath136 ) is given by @xmath137 the right - hand side of eq .
[ twfo ] differs from analogous one in ref .
@xcite by the value @xmath138 that is much less than unity but , nevertheless , can be comparable or even greater than @xmath139 .
in case ( ii ) , the asymptotic value of @xmath26 is close to unity , coinciding with the results of refs .
@xcite and @xcite .
this agrees with well known behavior of the scintillation index to approach unity for any source distribution , provided the response time of the recording instrument is short compared with the source coherence time .
( see , for example , survey @xcite ) .
a similar tendency can be seen in both figs .
3 and 4 : the curves with the smallest @xmath129 , used for numerical calculations ( @xmath130 ) , are close to the curves without diffuser " in spite of the small initial coherence length [ @xmath140 .
it can also be seen that all curves approach their asymptotic values very slowly .
describing diffuser dynamics .
the solid curve is calculated for @xmath118 ( without diffuser ) .
other curves are for @xmath141 . ]
. ]
it follows from our analysis that the scintillation index is very sensitive to the diffuser parameters , @xmath0 and @xmath142 , for long propagation paths .
on the other hand , the characteristics of the irradience such as beam radius , @xmath143 , and angle - of - arrival spread , @xmath144 , do not depend on the presence of the phase diffuser for large values of @xmath28 .
to see this , the following analysis is useful .
the beam radius expressed in terms of the distribution function is given by @xmath145 straightforward calculations using eq .
[ ten ] with @xmath69 ( see ref .
@xcite ) result in the following explicit form : @xmath146 where @xmath147 and @xmath148 is the inner radius of turbulent eddies , which in our previous calculations was assumed to be equal @xmath149 m .
as we see , the third term does not depend on the diffuser parameters and it dominates when @xmath150 .
a similar situation holds for the angle - of - arrival spread , @xmath144 .
( this physical quantity is of great importance for the performance of communication systems based on frequency encoded information @xcite . )
it is defined by the distribution function as @xmath151 simple calculations , which are very similar to those while obtaining @xmath152 , result in @xmath153 ^ 2=\frac 2{r_1 ^ 2q_0 ^ 2}+12tz-\frac { 4z^2}{q_0 ^ 4r^2}(r_1^{-2}+3tq_0 ^ 2z)^2.\ ] ] for long propagation paths , .
[ twei ] reduces to @xmath154 , which like @xmath152 does not depend on the diffuser parameters .
as we see , for large distances @xmath28 , the quantities @xmath152 and @xmath144 do not depend on @xmath93 and @xmath105 .
this contrasts with the case of the scintillation index .
so pronounced differences can be explained by differences in the physical nature of these characteristics .
it follows from eq .
[ two ] that the functional , @xmath26 , is quadratic in the distribution function , @xmath155 .
hence , four - wave correlations determine the value of scintillation index .
the main effect of a phase diffuser on @xmath26 is to destroy correlations between waves exited at different times .
( see more explanations in ref .
this is achieved at sufficiently small parameters @xmath93 and @xmath156 .
in contrast , @xmath152 and @xmath144 depend on two wave - correlations , both waves being given at the same instant .
therefore , the values of @xmath152 and @xmath144 do not depend on the rate of phase variations [ @xmath105 does not enter the factor ( [ seventeen ] ) describing the effect of phase diffuser ] .
moreover , these quantities become independent of @xmath93 at long propagation paths because light scattering on atmospheric inhomogeneities prevails in this case .
the plots in figs .
3 anf 4 show that the finite - time effect is quite sizable even for very slow " detectors ( @xmath157 ) .
our paper makes it possible to estimate the actual utility of phase diffusers in several physical regimes .
we have analyzed the effects of a diffuser on scintillations for the case of large - amplitude phase fluctuations .
this specific case is very convenient for theoretial analysis because only two parameters are required to describe the effects of the diffuser .
phase fluctuations may occur independently in space as well as in time .
also , our formalism can be applied for the physical situation in which a spatially random phase distribution drifts across the beam .
[ twtw ] . )
our results show the importance of both parameters , @xmath93 and @xmath142 , on the ability of a phase diffuser to suppress scintillations .
this work was carried out under the auspices of the national nuclear security administration of the u.s .
department of energy at los alamos national laboratory under contract no .
de - ac52 - 06na25396 .
we thank onr for supporting this research .
with a special intention of clarifying the underlying spin contents of the nucleon , we investigate the generalized form factors of the nucleon , which are defined as the @xmath0-th @xmath1-moments of the generalized parton distribution functions , within the framework of the chiral quark soliton model .
a particular emphasis is put on the pion mass dependence of final predictions , which we shall compare with the predictions of lattice qcd simulations carried out in the so - called heavy pion region around @xmath2 .
we find that some observables are very sensitive to the variation of the pion mass .
it will be argued that the negligible importance of the quark orbital angular momentum indicated by the lhpc and qcdsf lattice collaborations might be true in the unrealistic heavy pion world , but it is not necessarily the case in our real world close to the chiral limit .
the so - called `` nucleon spin crisis '' raised by the european muon collaboration ( emc ) measurement in 1988 is one of the most outstanding findings in the field of hadron physics @xcite,@xcite .
the renaissance of the physics of high energy deep inelastic scatterings is greatly indebted to this epoch - making finding .
probably , one of the most outstanding progresses achieved recently in this field of physics is the discovery and the subsequent research of completely new observables called generalized parton distribution functions ( gpd ) .
it has been revealed that the gpds , which can be measured through the so - called deeply - virtual compton scatterings ( dvcs ) or the deeply - virtual meson productions ( dvmp ) , contain surprisingly richer information than the standard parton distribution functions @xcite@xcite .
roughly speaking , the gpds are generalization of ordinary parton distributions and the elastic form factors of the nucleon .
the gpds in the most general form are functions of three kinematical variables : the average longitudinal momentum fraction @xmath1 of the struck parton in the initial and final states , a skewdness parameter @xmath3 which measures the difference between two momentum fractions , and the four - momentum - transfer square @xmath4 of the initial and final nucleon .
in the forward limit @xmath5 , some of the gpds reduce to the usual quark , antiquark and gluon distributions .

it is given by @xmath103}+ e^{-\lambda _ c^{-2}[({\bf r - r^\prime}_1)^2+({\bf r^\prime -r_1})^2]-2\nu^2\tau ^2},\ ] ] where @xmath104 ^ 2\rangle = 2\nu^2 $ ] .

as we see , the effect of the phase screen can be described by two parameters , @xmath93 and @xmath105 , which characterize the spatial and temporal coherence of the laser beam .

in the limiting case , @xmath106 , the second term in eq .

[ twenty ] vanishes and the problem is reduced to the case considered in refs .

@xcite,@xcite .

in the opposite case , @xmath107 , both terms in eq .

[ twenty ] are important .

this is shown in ref .

@xcite .

in what follows , we will see that these two limiting cases have physical interpretations where where @xmath108 ( slow detector ) and @xmath109 ( fast detector ) , respectively .

there is a specific realization of the diffuser in which a random phase distribution moves across the beam .

( this situation can be modeled by a rotating transparent disk with large diameter and varying thickness . )

the phase depends here on the only variable @xmath110 , i.e.

@xmath111 where @xmath112 is the velocity of the drift .

then we have @xmath113}+e^{-\lambda _ c^{-2}[({\bf r - r^\prime_1+v}\tau)^2+({\bf r^\prime -r_1+v}\tau)^2]}.\ ] ] comparing eqs .

[ twenty ] and [ twtw ] , we see that the quantity , @xmath114 , stands for the characteristic parameter describing the efficiency of the phase diffuser .

the criterion of slow " detector requires @xmath115 .

qualitatively , the two scenarios of phase variations , given by eqs .

[ twenty ] and [ twtw ] , affect in a similar way the intensity fluctuations .

in what follows , we consider the first of them as the simplest one .

( this is because the spatial and temporal variables in @xmath102 , given by eq .

[ twenty ] , are separable . )

_ vs _ propagation distance @xmath28 in the case of `` slow '' detector : @xmath116 .

the parameter @xmath117 indicates different initial coherence length .

in the absence of phase diffuser @xmath118 ( solid line ) .

@xmath119 is the conventional parameter describing a strength of the atmospheric turbulence . ]

substituting the expressions for operators given by eq .

[ fourteen ] with account for the phase factors @xmath120 and averaging over time as shown in eq .

[ one ] , we obtain @xmath121 @xmath122\bigg > , \ ] ] where the notation @xmath16 after sums indicates averaging over different realizations of the atmospheric refractive index .

the parameter @xmath123 describes the initial coherence length modified by the phase diffuser .

other notations are defined by following relations @xmath124 @xmath125 @xmath126 further calculations follow the scheme described in ref @xcite .

2 illustrates the effect of the phase diffuser on scintillations in the limit of a slow " detector ( @xmath127 ) .

we can see a considerable decrease in @xmath128 caused by the phase diffuser .

at the same time , the effect of the phase screen on @xmath128 becomes weaker for finite values of @xmath129 .

moreover , comparing the two upper curves in fig .

3 , we see the opposite effect : slow phase variations ( @xmath130 ) result in increased scintillations .

there is a simple explanation for this phenomenon : the noise generated by the turbulence is complemented by the noise arising from the random phase screen .

the integration time of the detector , @xmath3 , is not sufficiently large for averaging phase variations generated by the diffuser .

the function , @xmath131 , has a very simple form in the two limits : ( i)@xmath132 , when @xmath133 ; and ( ii ) @xmath134 , when @xmath109 .

then , in case ( i ) and for small values of the initial coherence [ @xmath135 , the asymptotic term for the scintillation index ( @xmath136 ) is given by @xmath137 the right - hand side of eq .

[ twfo ] differs from analogous one in ref .

@xcite by the value @xmath138 that is much less than unity but , nevertheless , can be comparable or even greater than @xmath139 .

in case ( ii ) , the asymptotic value of @xmath26 is close to unity , coinciding with the results of refs .

@xcite and @xcite .

this agrees with well known behavior of the scintillation index to approach unity for any source distribution , provided the response time of the recording instrument is short compared with the source coherence time .

( see , for example , survey @xcite ) .

a similar tendency can be seen in both figs .

3 and 4 : the curves with the smallest @xmath129 , used for numerical calculations ( @xmath130 ) , are close to the curves without diffuser " in spite of the small initial coherence length [ @xmath140 .

it can also be seen that all curves approach their asymptotic values very slowly .

describing diffuser dynamics .

the solid curve is calculated for @xmath118 ( without diffuser ) .

other curves are for @xmath141 . ]

. ]

it follows from our analysis that the scintillation index is very sensitive to the diffuser parameters , @xmath0 and @xmath142 , for long propagation paths .

on the other hand , the characteristics of the irradience such as beam radius , @xmath143 , and angle - of - arrival spread , @xmath144 , do not depend on the presence of the phase diffuser for large values of @xmath28 .

to see this , the following analysis is useful .

the beam radius expressed in terms of the distribution function is given by @xmath145 straightforward calculations using eq .

[ ten ] with @xmath69 ( see ref .

@xcite ) result in the following explicit form : @xmath146 where @xmath147 and @xmath148 is the inner radius of turbulent eddies , which in our previous calculations was assumed to be equal @xmath149 m .

as we see , the third term does not depend on the diffuser parameters and it dominates when @xmath150 .

a similar situation holds for the angle - of - arrival spread , @xmath144 .

( this physical quantity is of great importance for the performance of communication systems based on frequency encoded information @xcite . )

it is defined by the distribution function as @xmath151 simple calculations , which are very similar to those while obtaining @xmath152 , result in @xmath153 ^ 2=\frac 2{r_1 ^ 2q_0 ^ 2}+12tz-\frac { 4z^2}{q_0 ^ 4r^2}(r_1^{-2}+3tq_0 ^ 2z)^2.\ ] ] for long propagation paths , .

[ twei ] reduces to @xmath154 , which like @xmath152 does not depend on the diffuser parameters .

as we see , for large distances @xmath28 , the quantities @xmath152 and @xmath144 do not depend on @xmath93 and @xmath105 .

this contrasts with the case of the scintillation index .

so pronounced differences can be explained by differences in the physical nature of these characteristics .

it follows from eq .

[ two ] that the functional , @xmath26 , is quadratic in the distribution function , @xmath155 .

hence , four - wave correlations determine the value of scintillation index .

the main effect of a phase diffuser on @xmath26 is to destroy correlations between waves exited at different times .

( see more explanations in ref .

this is achieved at sufficiently small parameters @xmath93 and @xmath156 .

in contrast , @xmath152 and @xmath144 depend on two wave - correlations , both waves being given at the same instant .

therefore , the values of @xmath152 and @xmath144 do not depend on the rate of phase variations [ @xmath105 does not enter the factor ( [ seventeen ] ) describing the effect of phase diffuser ] .

moreover , these quantities become independent of @xmath93 at long propagation paths because light scattering on atmospheric inhomogeneities prevails in this case .

the plots in figs .

3 anf 4 show that the finite - time effect is quite sizable even for very slow " detectors ( @xmath157 ) .

our paper makes it possible to estimate the actual utility of phase diffusers in several physical regimes .

we have analyzed the effects of a diffuser on scintillations for the case of large - amplitude phase fluctuations .

this specific case is very convenient for theoretial analysis because only two parameters are required to describe the effects of the diffuser .

phase fluctuations may occur independently in space as well as in time .

also , our formalism can be applied for the physical situation in which a spatially random phase distribution drifts across the beam .

[ twtw ] . )

our results show the importance of both parameters , @xmath93 and @xmath142 , on the ability of a phase diffuser to suppress scintillations .

this work was carried out under the auspices of the national nuclear security administration of the u.s .

department of energy at los alamos national laboratory under contract no .

de - ac52 - 06na25396 .

we thank onr for supporting this research .

with a special intention of clarifying the underlying spin contents of the nucleon , we investigate the generalized form factors of the nucleon , which are defined as the @xmath0-th @xmath1-moments of the generalized parton distribution functions , within the framework of the chiral quark soliton model .

a particular emphasis is put on the pion mass dependence of final predictions , which we shall compare with the predictions of lattice qcd simulations carried out in the so - called heavy pion region around @xmath2 .

we find that some observables are very sensitive to the variation of the pion mass .

it will be argued that the negligible importance of the quark orbital angular momentum indicated by the lhpc and qcdsf lattice collaborations might be true in the unrealistic heavy pion world , but it is not necessarily the case in our real world close to the chiral limit .

the so - called `` nucleon spin crisis '' raised by the european muon collaboration ( emc ) measurement in 1988 is one of the most outstanding findings in the field of hadron physics @xcite,@xcite .

the renaissance of the physics of high energy deep inelastic scatterings is greatly indebted to this epoch - making finding .

probably , one of the most outstanding progresses achieved recently in this field of physics is the discovery and the subsequent research of completely new observables called generalized parton distribution functions ( gpd ) .

it has been revealed that the gpds , which can be measured through the so - called deeply - virtual compton scatterings ( dvcs ) or the deeply - virtual meson productions ( dvmp ) , contain surprisingly richer information than the standard parton distribution functions @xcite@xcite .

roughly speaking , the gpds are generalization of ordinary parton distributions and the elastic form factors of the nucleon .

the gpds in the most general form are functions of three kinematical variables : the average longitudinal momentum fraction @xmath1 of the struck parton in the initial and final states , a skewdness parameter @xmath3 which measures the difference between two momentum fractions , and the four - momentum - transfer square @xmath4 of the initial and final nucleon .

in the forward limit @xmath5 , some of the gpds reduce to the usual quark , antiquark and gluon distributions .