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

  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},
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… 

Figures from this paper

Particle mixing and the emergence of classicality: A spontaneous-collapse-model view
Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying
Exact solution for a non-Markovian dissipative quantum dynamics.
This work provides the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment and compute the Green's function.
Non-Markov Processes in Quantum Theory
Basic notions in the framework of open quantum systems are introduced, stressing in particular analogies and differences with models used for introducing modifications of quantum mechanics which should help in dealing with the measurement problem.
Colored collapse models from the non-interferometric perspective
Abstract Models of spontaneous wave function collapse describe the quantum-to-classical transition by assuming a progressive breakdown of the superposition principle when the mass of the system
Stochastic unravelings of non-Markovian completely positive and trace-preserving maps
We consider open quantum systems with factorized initial states, providing the structure of the reduced system dynamics, in terms of environment cumulants. We show that such completely positive (CP)
Testing continuous spontaneous localization with Fermi liquids
Collapse models describe phenomenologically the quantum-to-classical transition by adding suitable nonlinear and stochastic terms to the Schrodinger equation, thus (slightly) modifying the dynamics
Dissipative collapse models with nonwhite noises
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
Non-Markovian trajectories involving future in semi-classical path integral expression
  • Fei Wang
  • Mathematics
    European Journal of Physics
  • 2020
Semi-classical path integral expression for a quantum system coupled to a harmonic bath is derived based on the stationary phase condition. It is discovered that the system path is non-Markovian.
Bounds on quantum collapse models from matter-wave interferometry: calculational details
We present a simple derivation of the interference pattern in matter-wave interferometry predicted by a class of quantum master equations. We apply the obtained formulae to the following collapse
Path Integrals, Spontaneous Localisation, and the Classical Limit
Abstract The measurement problem and the absence of macroscopic superposition are two foundational problems of quantum mechanics today. One possible solution is to consider the Ghirardi–Rimini–Weber


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.
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.
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
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