Time Derivatives as a Special Set of Observables

Arijit Dutta, Marcin Wieśniak, Marek Żukowski

Bell's theorem for systems more complicated than two qubits faces a hidden, as yet undiscussed, problem. One of the methods to derive Bell inequalities is to assume the existence of a joint probability distribution for measurement results for all settings in the given experiment. However, for spin-1 systems, one faces the problem that the eigenvalues of observables do not allow a consistent algebra if one allows all possible settings on each side (Bell's 1966 contradiction), or some specific sets (leading to a Kochen-Specker 1967 contradiction). We show here that by choosing a special set of settings which never lead to inconsistent algebra of eigenvalues, one can still derive multisetting Bell inequalities, and that they are robustly violated. Violation factors increase with the number of subsystems. The inequalities involve only spin observables, we do not allow all possible qutrit observables, still the violations are strong.

Bernard W. Banks

Hermanns, Sebastian

The framework of nonequilibrium Green functions is developed to accurately describe interacting quantum systems evolving in the presence of strongly exciting ultra-fast fields. At its core stands the selfconsistent determination of the selfenergy, a functional of the single-particle Green function, which incorporates all relevant many-body physics. The single-particle Green function is the solution of a coupled set of kinetic equations. Its intrinsic dependence on two independent time-arguments, ranging over the complete past of the system, not only enables the determination of all single-particle observables but also provides access to important two-particle observables and spectral information. With this coupling to the history, though, comes the practical necessity to apply physically motivated approximation techniques to the structure of the selfenergy and the Green functions, to achieve numerical tractability. This thesis is devoted to provide a thorough overview of the possible approximation techniques including perturbative and non-perturbative approaches. Starting from the exact coupled set of equations of motion for the Green functions, the expressions for all selfenergy approximations are derived in the most general basis representation and the special cases of a diagonal basis and the Hubbard basis with scalar interaction. In the second part of this thesis, the quality of the selfenergy approximations to describe time-dependent as well as ground-state properties of interacting systems is tested. A special focus lies on fermionic Hubbard nano-clusters, where the effect of the interaction strength and the filling factor on the performance of the approximations is studied.

Bryan Wilson Roberts

Hennadii Kovalov

We derive a direct, non-linear relation between the internal phase time per radian , the macroscopically observable coordinate time , and the relative energy fluctuation . Through rigorous differentiation and integration of these phase relations, we demonstrate that for topologically synchronized systems, the product of energy and observable time constitutes a strict dynamic process invariant: . Moving beyond phenomenological interpretations, we deduce the classical Heisenberg uncertainty relation without invoking independent quantum postulates, showing it to be a special boundary limit governing a single elementary phase cycle () under critical fluctuation. Finally, we bridge the gap between microscopic quantum reversibility and the macroscopic thermodynamic arrow of time by analyzing the dynamics of synchronization breakdown and phase slippage ().

Ian M Davies