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Schr\"odinger's illustration of an imaginary cat in a box, neither alive nordead, leads to a question of whether and how long a macroscopic quantumsuperposition can exist in various situations. It is well known that amacroscopic superposition is destroyed very quickly by environmental effectscalled decoherence. On the contrary, it is often believed that a macroscopicsuperposition continues to "survive" if it is ideally isolated from itsenvironment. In this paper, using a well-established measure of macroscopicsuperpositions and the eigenstate thermalization hypothesis, we show thatmacroscopic superpositions even in ideally closed systems are destroyed bythermalization processes. We further investigate specific examples of adisordered Heisenberg spin chain varied between the thermalization phase andthe many-body localized (MBL) phase. This leads to consistent results; initialmacroscopic superpositions disappear under thermalization while they may bepreserved in the MBL phase in which thermalization does not occur.

Disappearance of macroscopic superpositions in perfectly isolated systems