Dissipative collapse models with nonwhite noises

@article{Ferialdi2012DissipativeCM,
  title={Dissipative collapse models with nonwhite noises},
  author={Luca Ferialdi and Angelo Bassi},
  journal={Physical Review A},
  year={2012},
  volume={86},
  pages={022108}
}
We study the generalization of the QMUPL model which accounts both for memory and dissipative effects. This is the first model where both features are combined. After having derived the non-local Action describing the system, we solve the equation for a quantum harmonic oscillator via the path integral formalism. We give the explicit expression for the Green's function of the process. We focus on the case of an exponential correlation function and we analyze in detail the behavior Gaussian wave… 

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References

SHOWING 1-10 OF 29 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
Non-markovian quantum trajectories: an exact result.
TLDR
For the first time, the explicit general solution for the free particle case (H=p(2)/2m) is given and the main properties are discussed.
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.
Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: General solution and main properties
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
On the long time behavior of free stochastic Schrödinger evolutions
We discuss the time evolution of the wave function which is the solution of a stochastic Schrodinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations
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
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.
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
The non-Markovian stochastic Schrödinger equation for open systems
Dynamical reduction models
...
...