Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum return probability of a system of $N$ non-interacting lattice
  fermions   We consider $N$ non-interacting fermions performing continuous-time quantum
walks on a one-dimensional lattice. The system is launched from a most compact
configuration where the fermions occupy neighboring sites. We calculate exactly
the quantum return probability (sometimes referred to as the Loschmidt echo) of
observing the very same compact state at a later time $t$. Remarkably, this
probability depends on the parity of the fermion number -- it decays as a power
of time for even $N$, while for odd $N$ it exhibits periodic oscillations
modulated by a decaying power law. The exponent also slightly depends on the
parity of $N$, and is roughly twice smaller than what it would be in the
continuum limit. We also consider the same problem, and obtain similar results,
in the presence of an impenetrable wall at the origin constraining the
particles to remain on the positive half-line. We derive closed-form
expressions for the amplitudes of the power-law decay of the return probability
in all cases. The key point in the derivation is the use of Mehta integrals,
which are limiting cases of the Selberg integral.

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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
18
The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess