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recently , in the context of the jet - quenching phenomena @xcite , exciting jet - associated particle correlations @xcite have been observed in heavy - ion collisions at bnl s relativistic heavy - ion collider ( rhic ) .
this indicates the formation of shock waves in form of mach cones @xcite induced by supersonic partons moving through the quark - gluon plasma ( qgp ) and could give a direct access to the equation of state of the qgp .
shock waves can be observed if the matter , where the shock waves are induced , behaves like a fluid .
the large measured elliptic flow coefficient @xmath2 @xcite implies that the qgp created at rhic could be a nearly perfect fluid with a small viscosity .
calculations of viscous hydrodynamics @xcite and microscopic transport theory @xcite have estimated the shear viscosity to the entropy density ratio @xmath0 to be less than 0.4 .
still , it is not known , if this upper limit of the @xmath0 ratio is sufficiently small to allow the formation of relativistic shock waves .    in this work
we address the question , whether and when relativistic shock waves can develop in viscous gluon matter for given @xmath0 values . for this purpose
we consider the relativistic riemann problem .
its initial conditions are two regions of equilibrated matter with different constant pressure separated by a membrane which is removed at @xmath3 .
the matter evolves in form of a one - dimensional expansion .
we solve the relativistic riemann problem employing both the parton cascade bamps ( boltzmann approach of multiparton scatterings ) @xcite and the vshasta approach ( viscous sharp and smooth transport algorithm ) @xcite of viscous hydrodynamics .
we demonstrate the transition from ideal shock waves to free diffusion by varying the @xmath0 ratio from zero to infinity .
we estimate the upper limit of the @xmath0 value , for which shocks can still be observed experimentally on the time scale typical at rhic .
bamps is a microscopic transport model solving the boltzmann equation @xmath4 for on - shell gluons with the collision integral @xmath5 .
the algorithm for collisions is based on the stochastic interpretation of the transition rate @xcite . in this study
, we consider only binary gluon scattering processes with an isotropic cross section , which is adjusted locally at each time step to keep a constant @xmath0 value @xcite .
vshasta solves the israel - stewart ( is ) equations of dissipative hydrodynamics . in 1 + 1 dimensions
is equations reduce to @xcite @xmath6 where @xmath7 and @xmath8 . for vanishing shear viscous pressure , @xmath9 , eqs .
( [ cons_e ] ) and ( [ cons_m ] ) reduce to the equations of ideal hydrodynamics .
figure [ fig01 ] shows the solution of the relativistic riemann problem for various @xmath0 values as computed with bamps .    , the pressure is @xmath10 for @xmath11 and @xmath12 for @xmath13 .
the left panel shows the pressure and the right panel the velocity at time @xmath14 fm / c .
, width=491 ]    the results demonstrate a gradual transition from ideal hydrodynamic limit ( @xmath15 ) to free streaming of particles ( @xmath16 ) .
the ideal solution @xcite is reproduced with a very good precision for @xmath17 .
we see that a shock wave is traveling into matter with lower pressure ( on the right ) with a velocity @xmath18 larger than the velocity of sound @xmath19 .
the region behind the shock front is the so - called shock plateau , where matter is equilibrated and moves collectively with @xmath20 , shown on the right panel of fig .
[ fig01 ] .
simultaneously a rarefaction wave is propagating with @xmath19 into matter of higher pressure ( on the left ) .    a larger @xmath0 value results in a finite transition layer where the quantities change smoothly rather than discontinuously as in the case of a perfect fluid .
furthermore a non - zero viscosity , if large enough , impedes the formation of a shock plateau and a clear separation of the shock front from the rarefaction fan .    .
results are obtained using bamps and vshasta.,width=491 ]    in fig .
[ fig03 ] we compare the results from bamps and vshasta for @xmath21 and @xmath22 .
we see a perfect agreement for @xmath21 , whereas for larger value of @xmath23 small deviations in the region of the shock front and rarefaction wave are found .
the reason for the difference is that in these regions the local knudsen number @xmath24 @xcite is large and thus the applicability of is equations is questionable .
transport calculations do not suffer from that drawback .
results are obtained using bamps for @xmath25.,width=491 ]    the formation of a shock wave takes a certain amount of time , as demonstrated in fig .  [ fig02 ] for @xmath25 . at early times
a shock has not yet developed , the profile looks like a free streaming of particles .
but at later times we observe the creation of a shock plateau .
formally we define the time of formation of the shock plateau when the maximum of the velocity distribution @xmath26 reaches the value @xmath20 of the ideal - fluid solution in fig .
[ fig01 ] . from the right panel of fig .
[ fig02 ] , we see that this happens at @xmath14 fm / c .    in ref .
@xcite we have found the scaling behavior of the riemann problem : the time scale of the formation of shock waves @xmath27 is proportional to the @xmath0 ratio . from fig .
[ fig02 ] we also infer that , for @xmath28 , a shock plateau has not yet developed at @xmath14 fm / c , whereas for @xmath29 , it has already fully formed .
for @xmath30 we obtain @xmath31 fm / c , which is the typical lifetime of the qgp produced in heavy - ion collisions at rhic .
therefore , an imperfect quark gluon fluid with @xmath30 will prevent the observation of mach cone signals at rhic .
using the parton cascade bamps we have solved the relativistic riemann problem .
the transition from ideal - fluid behavior to free streaming is demonstrated .
numerical results from bamps agree well with those obtained from viscous hydrodynamical calculations using vshasta .
considering the scaling behavior we found that the formation of shock waves in gluon matter with @xmath30 probably takes longer than the lifetime of the qgp at rhic .
this work was supported by the helmholtz international center for fair within the framework of the loewe program launched by the state of hesse .
e.  molnr acknowledges support by the alexander von humboldt foundation . the work of h.  niemi was supported by the extreme matter institute ( emmi ) .
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to investigate the formation and the propagation of relativistic shock waves in viscous gluon matter we solve the relativistic riemann problem using a microscopic parton cascade . 
 we demonstrate the transition from ideal to viscous shock waves by varying the shear viscosity to entropy density ratio @xmath0 . we show that an @xmath0 ratio larger than @xmath1 prevents the development of well - defined shock waves on time scales typical for ultrarelativistic heavy - ion collisions . 
 these findings are confirmed by viscous hydrodynamic calculations .