8 research outputs found
Shortcuts to adiabaticity from linear response theory
A shortcut to adiabaticity is a finite-time process that produces the same
final state as would result from infinitely slow driving. We show that such
shortcuts can be found for weak perturbations from linear response theory. With
the help of phenomenological response functions a simple expression for the
excess work is found -- quantifying the nonequilibrium excitations. For two
specific examples, the quantum parametric oscillator and the spin-1/2 in a
time-dependent magnetic field, we show that finite-time zeros of the excess
work indicate the existence of shortcuts. Finally, we propose a degenerate
family of protocols, which facilitate shortcuts to adiabaticity for specific
and very short driving times.Comment: 9 pages, 8 figure; published versio
Degenerate optimal paths in thermally isolated systems
CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTĂFICO E TECNOLĂGICOFAPESP - FUNDAĂĂO DE AMPARO Ă PESQUISA DO ESTADO DE SĂO PAULOWe present an analysis of the work performed on a system of interest that is kept thermally isolated during the switching of a control parameter. We show that there exists, for a certain class of systems, a finite-time family of switching protocols for which the work is equal to the quasistatic value. These optimal paths are obtained within linear response for systems initially prepared in a canonical distribution. According to our approach, such protocols are composed of a linear part plus a function which is odd with respect to time reversal. For systems with one degree of freedom, we claim that these optimal paths may also lead to the conservation of the corresponding adiabatic invariant. This points to an interesting connection between work and the conservation of the volume enclosed by the energy shell. To illustrate our findings, we solve analytically the harmonic oscillator and present numerical results for certain anharmonic examples.We present an analysis of the work performed on a system of interest that is kept thermally isolated during the switching of a control parameter. We show that there exists, for a certain class of systems, a finite-time family of switching protocols for which the work is equal to the quasistatic value. These optimal paths are obtained within linear response for systems initially prepared in a canonical distribution. According to our approach, such protocols are composed of a linear part plus a function which is odd with respect to time reversal. For systems with one degree of freedom, we claim that these optimal paths may also lead to the conservation of the corresponding adiabatic invariant. This points to an interesting connection between work and the conservation of the volume enclosed by the energy shell. To illustrate our findings, we solve analytically the harmonic oscillator and present numerical results for certain anharmonic examples.914112CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTĂFICO E TECNOLĂGICOFAPESP - FUNDAĂĂO DE AMPARO Ă PESQUISA DO ESTADO DE SĂO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTĂFICO E TECNOLĂGICOFAPESP - FUNDAĂĂO DE AMPARO Ă PESQUISA DO ESTADO DE SĂO PAULOCNPq [134296/2013-3]FAPESP [2012/07429-0]134296/2013-32012/07429-0Both authors thank C. Jarzynski for his hospitality during their visit to the University of Maryland, where most of this work was developed. It is also a pleasure to thank S. Deffner and M. de Koning for enriching discussions and Y. Subasi and R. Freitas for useful comments and suggestions about the manuscript. T.A. acknowledges financial support from the Physics Institute of the Universidade Estadual de Campinas and CNPq (Brazil), Project No. 134296/2013-3. M.B. acknowledges financial support from FAPESP (Brazil), Project No. 2012/07429-0