83 citations · 87 across the 7 of their papers we have counts for
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Quantum Dynamics, Minkowski-Hilbert space, and A Quantum Stochastic Duhamel Principle
Matthew F. Brown
In this paper we shall re-visit the well-known Schrödinger and Lindblad dynamics of quantum mechanics. However, these equations may be realized as the consequence of a more general…
The Generation of Quantum Hamiltonian Evolution from A Pseudo-Measurement Process
Matthew F. Brown
Here we shall consider the idea that the Hamiltonian evolution of a quantum system is generated by sequential observations of the system by a `pseudo-apparatus'. This representatio…
Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space
Viacheslav P. Belavkin, Matthew F. Brown
We study the continuity property of multiple Q-adapted quantum stochastic integrals with respect to noncommuting integrands given by the non-adapted multiple integral kernels in Fo…
Q-Adapted Quantum Stochastic Integrals and Differentials in Fock Scale
Viacheslav P. Belavkin, Matthew F. Brown
In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic integration, then the four fundamental processes of the dynamics are introduced in the can…
The Stochastic Representation of Hamiltonian Dynamics and The Quantization of Time
Matthew F. Brown
Here it is shown that the unitary dynamics of a quantum object may be obtained as the conditional expectation of a counting process of object-clock interactions. Such a stochastic…