TY - JOUR

T1 - What it takes to avoid equilibration

AU - Gallego, R.

AU - Wilming, H.

AU - Eisert, J.

AU - Gogolin, C.

N1 - Funding Information: The group at FUB thanks the DFG (EI 519/7-1, GA 2184/2-1, CRC 183-project B02), the European Research Council (TAQ), and the EC (AQuS) for support. H.W. further thanks the Studienstiftung des Deutschen Volkes for support. C.G. is supported by a Marie Skodowska-Curie Individual Fellowships (IF-EF) program under GA: 700140 by the European Union and acknowledges financial support from the European Research Council (CoG QITBOX and AdG OSYRIS), the Axa Chair in Quantum Information Science, Spanish MINECO (FOQUS FIS2013-46768, QIBEQI FIS2016-80773-P, and Severo Ochoa Grant No. SEV-2015-0522), and the Fundació Privada Cellex, and Generalitat de Catalunya (Grant No. SGR 874 and 875, and the CERCA Program).

PY - 2018/8/27

Y1 - 2018/8/27

N2 - Numerous works have shown that under mild assumptions, unitary dynamics inevitably leads to equilibration of physical expectation values if many energy eigenstates contribute to the initial state. Here, we consider systems driven by arbitrary time-dependent Hamiltonians as a protocol to prepare systems that do not equilibrate. We introduce a measure of the resilience against equilibration of such states, and we show, under natural assumptions, that in order to increase the resilience against equilibration of a given system, one needs to possess a resource system that itself has a large resilience. In this way, we establish a link between the theory of equilibration and resource theories by quantifying the resilience against equilibration and the resources that are needed to produce it. We connect these findings with insights into local quantum quenches, and we investigate the (im)possibility of formulating a second law of equilibration by studying how resilience can be either only redistributed among subsystems, if these remain completely uncorrelated, or in turn created in a catalytic process if subsystems are allowed to build up some correlations.

AB - Numerous works have shown that under mild assumptions, unitary dynamics inevitably leads to equilibration of physical expectation values if many energy eigenstates contribute to the initial state. Here, we consider systems driven by arbitrary time-dependent Hamiltonians as a protocol to prepare systems that do not equilibrate. We introduce a measure of the resilience against equilibration of such states, and we show, under natural assumptions, that in order to increase the resilience against equilibration of a given system, one needs to possess a resource system that itself has a large resilience. In this way, we establish a link between the theory of equilibration and resource theories by quantifying the resilience against equilibration and the resources that are needed to produce it. We connect these findings with insights into local quantum quenches, and we investigate the (im)possibility of formulating a second law of equilibration by studying how resilience can be either only redistributed among subsystems, if these remain completely uncorrelated, or in turn created in a catalytic process if subsystems are allowed to build up some correlations.

UR - http://www.scopus.com/inward/record.url?scp=85052684016&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.98.022135

DO - 10.1103/PhysRevA.98.022135

M3 - Article

AN - SCOPUS:85052684016

VL - 98

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 022135

ER -