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Breakdown of the adiabatic limit in low dimensional gapless systems  Anatoli Polkovnikov
; Vladimir Gritsev
;  Date: 
1 Jun 2007  Abstract:  It is generally believed that a generic system can be reversibly transformed
from one state into another by sufficiently slow change of parameters and that
the entropy of the system is conserved in such a slow (adiabatic) process. A
standard argument favoring this assertion is based on possibility of the
expansion of the energy, entropy, number of excitations (quasiparticles) or
other thermodynamic quantities into the Taylor series in the ramp speed
$delta$. In this paper we examine this assertion for gapless systems. We show
that the general argumentation is indeed valid at high enough dimensions.
However, in low dimensional gapless systems it can break down. We identify
three possible generic regimes of a system response to a slow ramp: ({f A})
meanfield, where the energy density in the final state $mathcal E$ is an
analytic function of $delta$: $mathcal E(delta)approx mathcal E_0+eta
delta^2$, ({f B}) nonanalytic, where $mathcal E(delta)approx mathcal
E_0+etadelta^
u$ with some universal power $
u<2$, and ({f C})
nonadiabatic, where $mathcal E(delta)approx mathcal E_0+etadelta^
u
L^eta$ with $L$ being the system size. In the third regime the limits
$delta o 0$ and $L oinfty$ do not commute and the adiabatic process does
not exist for large enough $L$. Our analysis directly applies to integrable and
weakly nonintegrable systems. In the latter case, if the system is allowed to
rethermalize at long times then regimes {f A}, {f B}, and {f C} apply to
the entropy and the temperature of the system. We give specific examples where
all three regimes are realized and support our results by numerical
simulations. Our results can be relevant to condensedmatter and atomic
physics, quantum computing, quantum optics, inflationary cosmology and others.  Source:  arXiv, arxiv.0706.0212  Services:  Forum  Review  PDF  Favorites 


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