Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Schr\"odinger equation from generalized exact uncertainty
  principle   Inspired by the generalized uncertainty principle (GUP), which adds
gravitational effects to the standard description of quantum uncertainty, we
extend the exact uncertainty principle (EUP) approach by Hall and Reginatto [J.
Phys. A: Math. Gen. (2002) 35 3289], and obtain a (quasi)nonlinear
Schr\"odinger equation. This quantum evolution equation of unusual form, enjoys
several desired properties like separation of non-interacting subsystems or
planewave solutions for free particles. Starting with the harmonic oscillator
example, we show that every solution of this equation respects the
gravitationally-induced minimal position uncertainty proportional to the Planck
length. Quite surprisingly, our result successfully merges the core of
classical physics with non-relativistic quantum mechanics in its extremal form.
We predict that the commonly accepted phenomenon, namely a modification of a
free-particle dispersion relation due to quantum gravity might not occur in
reality.

21
The categories of this paper are: adap-org
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom