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energy localization in the form of breathers has been intensely investigated over the past several years @xcite .
these highly localized long - lived excitations in translationally invariant nonlinear arrays are of great interest because they provide a mechanism for energy storage that does not rely on defects . indeed , the fact that these excitations are often mobile ( which they would in general not be if the localization were defect - induced ) makes them particularly interesting in the context of efficient transport of vibrational energy  @xcite .
exact breather excitations , that is , breathers that persist forever , can be confirmed analytically and constructed numerically for certain nonlinear infinite arrays of interacting masses , among them nonlinear arrays with no local potentials and interactions between neighboring sites that vary as @xmath0 with @xmath1 @xcite .
the @xmath2 s denote displacements of the masses at sites @xmath3 and @xmath4 .
when the interactions are not precisely of this form , or when the array is finite , or when other excitations ( for example , phonons or other localized excitations ) are present in the system , it is no longer possible to prove that there are exact breather solutions .
nevertheless , it is possible to explore the problem numerically . in particular , in this paper we study the asymptotic dynamics of localized excitations in the one - dimensional fermi - pasta - ulam ( fpu ) @xmath5-model at zero temperature and during thermal relaxation .
we corroborate that long - wavelength thermal excitations have a profound effect on breather stability .
since thermal fluctuations are inevitable in any real system , zero - temperature results must be applied with appropriate caution .
these results extend our earlier work to much longer time regimes  @xcite , and agree with and complement those of piazza et al .
the conditions for breather stationarity and longevity are thereby further clarified .
we present our numerical results in secs .  [ zero ] and [ nonzero ] , and end with a brief summary in sec .
[ summation ] .
the hamiltonian for the fpu @xmath5-model is @xmath6 where @xmath7 is the number of sites , and @xmath8 and @xmath9 are the harmonic and anharmonic force constants , respectively .
we set @xmath10 throughout .
the equations of motion with free - end boundary conditions are integrated using a fourth order runge - kutta method with time interval @xmath11 ( further reduction leads to no significant improvement ) .
the total energy of the array is the sum over individual symmetrized site energies @xmath12  @xcite .
a zero temperature environment with the least disturbance to the dynamics in the chain is achieved by connecting only the ends of the chain to such an environment via a dissipation term .
this is accomplished by adding a term of the form @xmath13 to the equations of motion for sites @xmath14 and @xmath15  @xcite .    since we do not _ a priori _ know the form of the longest - lived localized excitation
, we initially create an excitation of the  odd parity " breather configuration with amplitudes @xmath16 , and zero velocity at each site .
the frequency of the resulting oscillatory motion increases with increasing @xmath17 , which must be chosen so that this frequency is above the phonon band edge at @xmath18 .
this excitation is not an exact stationary solution of the equations of motion , so it typically sheds some energy while re - accommodating amplitudes and frequencies , and settles into an excitation that is very long - lived .
the discarded energy appears in the form of phonons that travel away from the localized excitation and dissipate quickly , in a time @xmath19 , across the ends of the chain .
the balance of the energy remains localized , most of it ( @xmath20 for @xmath21 ) on the three initially excited sites , and decays exponentially with an extremely long characteristic time @xmath22 .
= 3.0 in    to extract exponents and characteristic times , it is crucial to have data that covers both time scales , and to normalize the data in such a way that one behavior does not mask or distort the other  @xcite .
we introduce the _ normalized energy _ @xmath23 and the _ modified normalized energy _
@xmath24 : @xmath25 the denominator in the first contains the initial energies , and in the second the energies after the discarded phonons have dissipated ( but before the remaining localized excitation has decayed appreciably ) . in our illustrations we take @xmath26 .
= 3.0 in    in fig .  [ fig1 ] we show typical results for the normalized energy for three excitation amplitudes over more than six decades of time .
the modified normalized energy shows essentially the same behavior .
if the decay of the long - lived excitation is exponential , we expect @xmath27 $ ] and @xmath28 $ ] vs @xmath29 to be straight lines over the appropriate long time intervals . in fig .
[ fig2 ] we clearly see this behavior , which extends over the entire time interval for the higher ( but not the lower ) amplitude excitation .
the slope for the @xmath21 curve leads to a decay time of @xmath30 , a number reported here merely to stress its enormous magnitude .
the frequency of the localized breather increases with increasing amplitude and hence is more separated from the phonon band for larger @xmath17 , leading to a slower decay of more energetic breathers .
as the breather loses its energy , its frequency decreases , and eventually as it approaches the phonon band edge the decay becomes more rapid .
this behavior is evident in the @xmath31 curve in fig .
we also find that longer chains exhibit a longer decay time : residual amplitude of the breather at sites far from its center decreases rapidly with increasing distance and thus the chain end sites have less energy to dissipate .
figure  [ fig3 ] confirms the exponential behavior of the breather decay  @xcite . for two initial amplitudes
, the figure shows @xmath32 $ ] vs @xmath33 , which yields a straight line of slope @xmath5 if the decay is of the form @xmath34 .
the inset shows the values of the slopes as a function of time .
for @xmath21 pure exponential behavior @xmath35 is confirmed throughout the time range presented .
the deviation from pure exponential decay for the lower amplitude breather is evident .
= 3.0 in    a breather of a given amplitude has a well - defined characteristic frequency . in fig .
[ fig4 ] we show this frequency in relation to the phonon band edge as a function of time for the cases discussed above . for 31-site chains ,
the frequency of the breather of initial amplitude @xmath21 decreases very little over the entire simulation , while that of initial amplitude @xmath31 decreases more markedly .
consistent with the fact that the breather does not disappear entirely in the time range shown , its frequency never reaches the phonon band edge . if the initial amplitude of the excitation were even smaller , or the simulation time much longer , or the chain shorter , the breather would eventually disappear .
this last case is illustrated in fig .
the disappearance of the breather coincides with its frequency reaching the band edge .
the inset shows @xmath36 , the ratio of the energy on the five sites around the breather to the total energy .
this parameter is of order unity when most of the energy is localized on a small number of sites .
the situation is less certain when a localized excitation evolves in a thermal environment .
other excitations in the medium perturb the breather , and its eventual fate varies from one realization to another . to illustrate the complexity of the situation , we present two scenarios .
= 3.0 in    we begin with a chain that is initially in thermal equilibrium at a nonzero temperature @xmath37  @xcite . at time @xmath38
, the end sites of the thermalized chain are connected to a zero temperature bath via a purely dissipative term  @xcite .
we follow the thermal relaxation of the chain and , in particular , the dynamics of breathers that may spontaneously appear during relaxation if the initial temperature is sufficiently high .
figure  [ fig5 ] shows the evolution of the total energy in a chain of @xmath39 sites initially thermalized at temperature @xmath40 .
the figure also shows the energy in only the four sites @xmath41 . after a relatively short time ( @xmath42 time units in this particular realization ) almost all of the energy settles in these sites and remains there .
the excitation around the four sites turns out to be an  even parity " breather , with maximum displacements @xmath17 and @xmath43 alternating on sites @xmath44 and @xmath45 , smaller but not negligible amplitudes at sites @xmath46 and @xmath47 , and essentially no motion of the other sites .
the frequency of the breather , initially @xmath48 , decreases very little for the duration of the simulation . in fig .
[ fig5 ] we also present the modified normalized energy .
its decay is clearly exponential , with an enormously long time constant , @xmath49 .
thus this breather , even in our relatively short chain , is essentially stationary .
this decay time is much longer than that reported in the previous section , consistent with the fact that the amplitude of the breather that has emerged spontaneously is larger .
the thermal relaxation process has swept the lattice clean of all other excitations , allowing the breather to survive undisturbed .
this process was described in our earlier work  @xcite .
there we reported a stretched exponential rather than a purely exponential decay , a conclusion that relied on the normalized rather than the modified normalized energy  @xcite , on a time history that was not sufficiently long , and on a statistical average over a thermal ensemble that included realizations where no breather appeared during the thermal relaxation process ( and where the energy dissipation was consequently much more rapid ) .    in our second scenario , at @xmath38 a breather is explicitly injected into a chain that is in thermal equilibrium at a very low temperature ( too low for the spontaneous formation of breathers ) .
the chain is then allowed to relax into a zero temperature heat bath .
we find that the thermal background invariably sets the breather in motion , and causes the breather to collide with other excitations and with the chain boundaries .
collision events not only cause the breather to keep moving , but also lead to breather degradation through loss of energy upon collision  @xcite .
the resulting lifetime @xmath22 of the breather is then in general much smaller than in the first scenario .
the lifetime is also much smaller than that of a breather of the same amplitude injected into a zero temperature chain .
we find this behavior even when the temperature is extremely low ( all the way down to @xmath50 ) . as a quantitative check
we have explicitly injected a breather of initial amplitude @xmath21 into a chain thermalized at @xmath51 .
the system is then allowed to relax into a zero temperature bath , as before .
compared to the lifetime of the breather in the zero temperature chain , the lifetime of the breather is now much reduced , @xmath52 .
a similar comparison with @xmath53 again leads to dramatically different lifetimes , @xmath54 ( @xmath55 ) and @xmath56 ( @xmath51 ) .
note that it does not much matter whether the injected breather is of even or odd parity ( we inject an odd one ) .
why is a breather created spontaneously during thermal relaxation more stable than one explicitly injected into a thermalized chain , even at extremely low temperatures ?
the answer lies in the effect of different phonons on breather dynamics  @xcite .
whereas short wavelength zone - boundary phonons contribute to spontaneous breather formation (  modulational instability " ) , breathers are most strongly perturbed by the longest wavelength phonons .
these are also the phonons that dissipate most rapidly out of a chain with free - end boundaries into a zero - temperature bath . in the higher temperature system ,
when the breather is created spontaneously the long wavelength phonons have already dissipated and , as dissipation continues up the phonon spectrum , the breather is increasingly less disturbed until it reaches a spatially stationary very long - lived configuration  @xcite . on the other hand ,
if the breather is injected into a thermalized system , the breather is subject to strong disturbance by long wavelength phonons even at the very lowest temperatures until these phonons dissipate .
an injected breather in the thermalized scenario is therefore a more fragile excitation than a spontaneously created breather of the same amplitude . to confirm this description
we have followed the dynamics of a breather injected into a relaxing chain _
after _ the long wavelength phonons have decayed , and find the breather to be almost as stable as one in a zero - temperature simulation .
for example , for a zero - temperature injected breather of initial amplitude @xmath57 in a chain of 31 sites ( @xmath58 ) , we find a lifetime @xmath59 . in a chain
initially thermalized at @xmath60 and then allowed to relax , if we wait until @xmath61 before injecting the same breather we find a somewhat shortened but still very long lifetime of @xmath62 , in any case much longer than it would be if injected at @xmath38 .
we have also observed a breather in a chain whose temperature is maintained at an extremely low but nonzero value .
the breather in this case is always fragile , continuing to move and lose energy until it degrades completely .
the zero temperature stability of the breather is therefore a somewhat singular result .
our work supports three main conclusions concerning the dynamics of breathers in fpu @xmath5-chains : 1 ) at zero temperature in finite chains , breather - like excitations remain stationary and localized , and their energy decays exponentially with time ; 2 ) the decay time at zero temperature is extremely long , increasing with increasing chain length and with increasing initial breather amplitude ; 3 ) long wavelength thermal background sets the breather in motion , which in turn leads to a more rapid decay of the breather .
the zero - temperature result is in this sense fragile .
we have confirmed that breather decay for any particular realization is exponential  @xcite until the breather frequency closely approaches the phonon band edge .
however , since the characteristic exponential time varies considerably from one realization to another , an ensemble averaged decay may be of stretched exponential or other form .
the authors are grateful to f. piazza for enlightening discussions .
this work was supported by the engineering research program of the office of basic energy sciences at the u. s. department of energy under grant no .
de - fg03 - 86er13606 .
support was also provided by a grant from the university of california institute for mxico and the united states ( uc mexus ) and the consejo nacional de ciencia y tecnologa de mxico ( conacyt ) .
a. j. sievers and s. takeno , phys .
lett . * 61 * , 970 ( 1988 ) ; s. aubry , physica d * 103 * , 201 ( 1997 ) ; s. flach and c. r. willis , physics reports * 295 * , 181 ( 1998 ) ; t. rssler and j. b. page , phys .
b * 62 * , 11460 ( 2000 ) ; m. peyrard and j. farago , physica a * 288 * , 199 ( 2000 ) ; s. aubry and g. kopidakis , cond - mat/0102162 .
we study the asymptotic dynamics of breathers in finite fermi - pasta - ulam chains at zero and non - zero temperatures . 
 while such breathers are essentially stationary and very long - lived at zero temperature , thermal fluctuations tend to lead to breather motion and more rapid decay .