The Open Quantum Brownian Motion

Abstract

Using quantum parallelism on random walks as original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers -- with internal degrees of freedom which serve as random gyroscopes -- interacting with series of probes. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: quantum trajectory, quantum dynamical map, and quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as internal gyroscope, illustrating the interplay between ballistic and diffusive behaviors at work in these processes.

50 pages, 5 figures

References in corpus (4)

• Progressive field-state collapse and quantum non-demolition photon counting
• Open Quantum Random Walks
• Existence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case
• The Lyapunov exponent of products of random $2\times 2$ matrices close to the identity

Cited by in corpus (15)

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• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Spikes in quantum trajectories
• Exponential Stability of Subspaces for Quantum Stochastic Master Equations
• Diffusion and signatures of localization in stochastic conformal field theory
• KPZ physics and phase transition in a classical single random walker under continuous measurement
• Microscopic derivation of Open Quantum Walks
• General quantum-classical dynamics as measurement based feedback
• Exact signal correlators in continuous quantum measurements
• Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum Walks
• Lazy Open Quantum Walks
• Digital homodyne and heterodyne detection for stationary bosonic modes
• Noise Induced Universal Diffusive Transport in Fermionic Chains