Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Does Hohenberg-Kohn Theorem apply to a general quantum system?   Hohenberg-Kohn (HK) theorem is the foundation of density function theory. For
interacting electrons, given that the internal part of the Hamiltonian ($\hat
H_{int}$), containing the kinetic energy and Couloumb interaction of electrons,
has a fixed form, the theorem states that when the electrons are subject to an
external electrostatic field $V(r)$, the ground-state density can inversely
determine $V(r)$, and thus the full Hamiltonian completely. We ask, for a
general HK-type Hamiltonian $\hat H_{hk}\{g_i\}=\hat H_{int}+\sum_i g_i \hat
O_i$ with arbitrarily chosen Hermitian operators $\hat H_{int}$ and $\{\hat
O_i\}$, whether the ground-state expectation values of $\{\hat O_i\}$ as the
generalized density can equally determine $\{g_i\}$. We prove that $\hat
H_{hk}$ bears an "all-or-nothing" classification by the ground-state
correlation matrix defined with respect to the $\{\hat O_i\}$ operators. For
one class of $\hat H_{hk}$, the answer is generically "yes" throughout the
$\{g_i\}$ parameter space, and for the other class, the answer is always "no".

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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th