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This paper is a Reply paper to the Comment paper by Mondaini et.al.
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H. Tasaki, Typicality of Thermal Equilibrium and Thermalization in Isolated Macroscopic Quantum Systems
2016
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Our description “ It may be then tempting to conjecture that the above (i)-iii) are necessary and sufficient conditions for the validity of ETH and also for the system to thermalize
Cited in the paper.
All the definitions of the off-diagonal ETH require the decay of all the off-diagonal elements in the thermodynamic limit. However, some definitions Gol put no requirement on the speed of decay, some definitions AGH require exponential decay but do not require its coefficient and functional form, and some other definitions DAl require the explicit functional form of decay. The comment paper comment employs the last one, the most strict definition, and we follow this strict definition in this Reply
Cited in the paper.
The word “no LCQ” is used for each sector of interest. Suppose that a system conserves total magnetization. We can say that this system has no LCQ if we treat a sector with a particular total magnetization. In contrast, if we do not separate sector, we say that this system has some LCQ. In case with LCQ, (d1) no longer holds Ham and separation into sectors associated with this LCQ is necessary to recover (d1)
Cited in the paper.
T. Mori and N. Shiraishi, Thermalization without eigenstate thermalization hypothesis after a quantum quench
2017
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2017
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