Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: General solution and main properties

@article{Bassi2009NonMarkovianDF,
  title={Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: General solution and main properties},
  author={Angelo Bassi and Luca Ferialdi},
  journal={Physical Review A},
  year={2009},
  volume={80},
  pages={012116}
}
We analyze the non-Markovian dynamics of a quantum system subject to spontaneous collapse in space. After having proved, under suitable conditions, the separation of the center-of-mass and relative motions, we focus our analysis on the time evolution of the center of mass of an isolated system (free-particle case). We compute the explicit expression of the Green's function, for a generic Gaussian noise, and analyze in detail the case of an exponential correlation function. We study the time… 

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References

SHOWING 1-10 OF 39 REFERENCES
Collapse models: analysis of the free particle dynamics
We study a model of spontaneous wavefunction collapse for a free quantum particle. We analyse in detail the time evolution of the single-Gaussian solution and the double-Gaussian solution, showing
Collapse models with non-white noises
We set up a general formalism for models of spontaneous wavefunction collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white
Non-Markovian quantum state diffusion: Perturbation approach
We present a perturbation theory for non-Markovian quantum state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a bosonic environment [Physical Review A 58, 1699,
Non-Markovian quantum state diffusion
A nonlinear stochastic Schr\"odinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides
Collapse models with non-white noises: II. Particle-density coupled noises
We continue the analysis of models of spontaneous wavefunction collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical ‘noise’ field, with
Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles.
TLDR
Stochastic differential equations describing the Markovian evolution of state vectors in the quantum Hilbert space are studied as possible expressions of a universal dynamical principle and the stochastic evolution is proved to induce continuous dynamical reduction of the state vector onto mutually orthogonal subspaces.
Quantum state diffusion, density matrix diagonalization, and decoherent histories: A model.
TLDR
The quantum evolution of a particle moving in a potential in interaction with an environment of harmonic oscillators in a thermal state is analysed, using the quantum state diffusion (QSD) picture of Gisin and Percival, to exemplify the general connection between the QSD picture and the decoherent histories approach to quantum mechanics.
On the energy increase in space-collapse models
A typical feature of spontaneous collapse models which aim at localizing wavefunctions in space is the violation of the principle of energy conservation. In the models proposed in the literature, the
Dynamical reduction models with general Gaussian noises
TLDR
It is proved that the effect of replacing in stochastic differential equations leading to the dynamical collapse of the state vector, white-noise Stochastic processes with nonwhite ones with the aim of overcoming intractable divergences in relativistic models.
On the long-time behavior of Hilbert space diffusion
Stochastic differential equations in Hilbert space as random nonlinear modified Schrödinger equations have achieved great attention in recent years; of particular interest is the long-time behavior
...
...