Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a probabilistic interpretation of shape derivatives of Dirichlet
  groundstates with application to Fermion nodes   This paper considers Schr\"odinger operators, and presents a probabilistic
interpretation of the variation (or shape derivative) of the Dirichlet
groundstate energy when the associated domain is perturbed. This interpretation
relies on the distribution on the boundary of a stopped random process with
Feynman-Kac weights. Practical computations require in addition the explicit
approximation of the normal derivative of the groundstate on the boundary. We
then propose to use this formulation in the case of the so-called fixed node
approximation of fermion groundstates, defined by the bottom eigenelements of
the Schr\"odinger operator of a fermionic system with Dirichlet conditions on
the nodes (the set of zeros) of an initially guessed skew-symmetric function.
We show that the shape derivative of the fixed node energy vanishes if and only
if either (i) the distribution on the nodes of the stopped random process is
symmetric; or (ii) the nodes are exactly the zeros of a skew-symmetric
eigenfunction of the operator. We propose an approximation of the shape
derivative of the fixed node energy that can be computed with a Monte-Carlo
algorithm, which can be referred to as Nodal Monte-Carlo (NMC). The latter
approximation of the shape derivative also vanishes if and only if either (i)
or (ii) holds.

25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int