Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Emergence of Time from Unitary Equivalence   We implement the unitary equivalence of modular Hamiltonian
$\hat{H}_{\mathrm{mod}}$ and Hamiltonian $\hat{H}$,
$\hat{H}\sim\hat{U}^{\dagger}\hat{H}_{\mathrm{mod}}\hat{U}$, to realize the
emergence of time from an unitary operator $\hat{U}$. The unitary equivalence
relation implies a duality between the modular flow and time evolution.
Requiring the unitary equivalence also implies "Modular Chaos Bound = Chaos
Bound". We demonstrate the duality of quantum chaos quantities in the
thermofield double state defined in a fermionic system. We then show the
explicit duality between a specific form of correlators, the spectral form
factor, and the Loschmidt echo with $\hat{H}_{\mathrm{mod}}$. In the end, we
also consider a two-qubit system to demonstrate that a different entanglement
spectrum does not provide the same constraint to $\hat{H}$.

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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math