• 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)

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

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

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 stochastic calculus and quantum nonlinear filtering

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