Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum-jump vs stochastic Schr\"{o}dinger dynamics for Gaussian states
  with quadratic Hamiltonians and linear Lindbladians   The dynamics of Gaussian states for open quantum systems described by
Lindblad equations can be solved analytically for systems with quadratic
Hamiltonians and linear Lindbladians, showing the familiar phenomena of
dissipation and decoherence. It is well known that the Lindblad dynamics can be
expressed as an ensemble average over stochastic pure-state dynamics, which can
be interpreted as individual experimental implementations, where the form of
the stochastic dynamics depends on the measurement setup. Here we consider
quantum-jump and stochastic Schr\"odinger dynamics for initially Gaussian
states. While both unravellings converge to the same Lindblad dynamics when
averaged, the individual dynamics can differ qualitatively. For the stochastic
Schr\"odinger equation, Gaussian states remain Gaussian during the evolution,
with stochastic differential equations governing the evolution of the
phase-space centre and a deterministic evolution of the covariance matrix. In
contrast to this, individual pure-state dynamics arising from the quantum-jump
evolution do not remain Gaussian in general. Applying results developed in the
non-Hermitian context for Hagedorn wavepackets, we formulate a method to
generate quantum-jump trajectories that is described entirely in terms of the
evolution of an underlying Gaussian state. To illustrate the behaviours of the
different unravellings in comparison to the Lindblad dynamics, we consider two
examples in detail, which can be largely treated analytically, a harmonic
oscillator subject to position measurement and a damped harmonic oscillator. In
both cases, we highlight the differences as well as the similarities of the
stochastic Schr\"odinger and the quantum-jump dynamics.

17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con