Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four
Mathematical Perspectives
- URL: http://arxiv.org/abs/2011.10349v2
- Date: Mon, 30 Nov 2020 12:23:39 GMT
- Title: Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four
Mathematical Perspectives
- Authors: Cristhiano Duarte, Barbara Amaral, Marcelo Terra Cunha, Matthew Leifer
- Abstract summary: It is crucial to build effective quantum theories aiming to understand how the description in one scale emerges from the description of a deeper scale.
This contribution explores different mathematical tools to the study of emergent effective dynamics in scenarios where a system is subject to a unitary evolution.
We see that a well-defined effective dynamics can only be defined when some sort of matching between the underlying unitary and the coarse-graining map is satisfied.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: With the birth of quantum information science, many tools have been developed
to deal with many-body quantum systems. Although a complete description of such
systems is desirable, it will not always be possible to achieve this goal, as
the complexity of such description tends to increase with the number of
particles. It is thus crucial to build effective quantum theories aiming to
understand how the description in one scale emerges from the description of a
deeper scale. This contribution explores different mathematical tools to the
study of emergent effective dynamics in scenarios where a system is subject to
a unitary evolution and the coarse-grained description of it is given by a CPTP
map taking the original system into an \emph{effective} Hilbert space of
smaller dimension. We see that a well-defined effective dynamics can only be
defined when some sort of matching between the underlying unitary and the
coarse-graining map is satisfied. Our main goal is to use these different tools
to derive necessary and sufficient conditions for this matching in the general
case.
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