Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schroedinger Operator: Heat Kernel and Its Applications   In this paper, we study the geometry associated with Schroedinger operator
via Hamiltonian and Lagrangian formalism. Making use of a multiplier technique,
we construct the heat kernel with the coefficient matrices of the operator both
diagonal and non-diagonal. For applications, we compute the heat kernel of a
Schroedinger operator with terms of lower order, and obtain a globally closed
solution to a matrix Riccati equations as a by-product. Besides, we finally
recover and generalise several classical results on some celebrated operators.

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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex