Exact solution for a non-Markovian dissipative quantum dynamics.
@article{Ferialdi2012ExactSF, title={Exact solution for a non-Markovian dissipative quantum dynamics.}, author={Luca Ferialdi and Angelo Bassi}, journal={Physical review letters}, year={2012}, volume={108 17}, pages={ 170404 } }
We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the…
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References
SHOWING 1-10 OF 88 REFERENCES
Non-markovian quantum trajectories: an exact result.
- Mathematics, PhysicsPhysical review letters
- 2009
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.
On the long time behavior of free stochastic Schrödinger evolutions
- Mathematics, Physics
- 2010
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…
Non-Markovian quantum state diffusion
- Physics
- 1998
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…
Open system dynamics with non-markovian quantum trajectories
- Physics
- 1999
A non-Markovian stochastic Schr\"odinger equation for a quantum system coupled to an environment of harmonic oscillators is presented. The ensemble average recovers the reduced density matrix without…
Non-Markovian quantum jumps.
- Physics, MathematicsPhysical review letters
- 2008
This approach is a generalization of the standard Monte Carlo wave function method for Markovian dynamics and provides an efficient unraveling of the ensemble dynamics of open quantum systems that interact with structured reservoirs.
Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: General solution and main properties
- Physics
- 2009
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 Hilbert space diffusion
- Mathematics
- 2008
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…
Quantum semi-Markov processes.
- Physics, MathematicsPhysical review letters
- 2008
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the…
On dissipative stochastic equations in a Hilbert space
- Mathematics
- 1996
SummaryA general existence and uniqueness theorem for solutions of linear dissipative stochastic differential equation in a Hilbert space is proved. The dual equation is introduced and the duality…