• Corpus ID: 6589635

# Quantum Dynamics, Minkowski-Hilbert space, and A Quantum Stochastic Duhamel Principle

@article{Brown2014QuantumDM,
title={Quantum Dynamics, Minkowski-Hilbert space, and A Quantum Stochastic Duhamel Principle},
author={Matthew F. Brown},
journal={ArXiv},
year={2014},
volume={abs/1407.2875}
}
In this paper we shall re-visit the well-known Schr\"odinger and Lindblad dynamics of quantum mechanics. However, these equations may be realized as the consequence of a more general, underlying dynamical process. In both cases we shall see that the evolution of a quantum state $P_\psi=\varrho(0)$ has the not so well-known pseudo-quadratic form $\partial_t\varrho(t)=\mathbf{V}^\star\varrho(t)\mathbf{V}$ where $\mathbf{V}$ is a vector operator in a complex Minkowski space and the pseudo-adjoint…

## References

SHOWING 1-10 OF 27 REFERENCES

### Stochastic Evolutions As Boundary Value Problems (Infinite Dimensional Analysis and Quantum Probability Theory)

• Mathematics
• 2001
Solutions to linear stochastic and quantum stochastic equations are proved to provide the interaction representations for the solutions to certain Dirac type equations with boundary conditions in

### Quantum causality, stochastics, trajectories and information

A history of the discovery of `new' quantum mechanics and the paradoxes of its probabilistic interpretation are briefly reviewed from the modern point of view of quantum probability and information.

### QUANTUM CAUSALITY, DECOHERENCE, TRAJECTORIES AND INFORMATION

A history of the discovery of “new” quantum mechanics and the paradoxes of its probabilistic interpretation are briefly reviewed from the modern point of view of quantum probability and information.

### Quantum Trajectories, State Diffusion, and Time-Asymmetric Eventum Mechanics

We show that the quantum stochastic Langevin model for continuous in time measurements provides an exact formulation of the von Neumann uncertainty error-disturbance principle. Moreover, as it was

### A stochastic Hamiltonian approach for quantum jumps, spontaneous localizations, and continuous trajectories

• Physics
• 1996
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that

### Q-Adapted Quantum Stochastic Integrals and Differentials in Fock Scale

• Physics, Mathematics
ArXiv
• 2011
The Fock-Guichardet formalism for the quantum stochastic integration is introduced, and the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures of the QS integration over a space-time.

### Quantum Stochastics, Dirac Boundary Value Problem, and the Ultra Relativistic Limit

We prove that a single-jump quantum stochastic unitary evolution is equivalent to a Dirac boundary value problem on the half line in an extra dimension. This amounts to the equivalence of the quantum