arXiv subjects

Herschel A. Rabitz

Publications and source records attributed to Herschel A. Rabitz.

23 records · Page 2Linked to original sources

arXiv2013

Conceptual inconsistencies in finite-dimensional quantum and classical mechanics

Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012); arXiv:1105.4014], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities are also revealed, including the nonexistence of the free particle and ambiguity in defining potential forces. Non-Hermitian mechanics is shown to have the same problems. This work compromises a popular belief that finite-dimensional mechanics is a straightforward discretization of the corresponding infinite-dimensional formulation.

quant-ph↗

arXiv2013

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

We introduce a general and systematic theoretical framework for Operational Dynamic Modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

quant-ph↗

arXiv2012

NMR quantum gate factorization through canonical cosets

The block canonical coset decomposition is developed as a universal algorithmic tool to synthesize n-qubit quantum gates out of experimentally realizable NMR elements. The two-, three-, and four-qubit quantum Fourier transformations are worked out as examples. The proposed decomposition bridges the state of the art numerical analysis with NMR quantum gate synthesis.

quant-ph↗

arXiv2012

Relativistic Wigner function and consistent classical limit for spin 1/2 particles

The relativistic Wigner function for spin 1/2 particles is the subject of active research due to diverse applications. However, further progress is hindered by the fabulous complexity of the integro-differential equations of motion. We simplify these equations to partial differential equations of the Dirac type that are not only well suited for numerical computation, but also posses a well defined classical limit in a manifestly covariant form.

quant-ph↗

arXiv2003

Efficient extraction of quantum Hamiltonians from optimal laboratory data

Optimal Identification (OI) is a recently developed procedure for extracting optimal information about quantum Hamiltonians from experimental data using shaped control fields to drive the system in such a manner that dynamical measurements provide maximal information about its Hamiltonian. However, while optimal, OI is computationally expensive as initially presented. Here, we describe the unification of OI with highly efficient global, nonlinear map-facilitated data inversion procedures. This combination is expected to make OI techniques more suitable for laboratory implementation. A simulation of map-facilitated OI is performed demonstrating that the input-output maps can greatly accelerate the inversion process.

quant-ph↗