An extended approach to the field-theoretical time operators

Iason Vakondios, Charis Anastopoulos

We study the time-of-arrival problem for relativistic particles constrained to move on a ring, formulating the problem entirely within Quantum Field Theory (QFT). In contrast to its counterpart for motion in a line, the circle topology implies that particles may encounter the detector multiple times before detection, making a field-theoretic treatment of the measurement interaction essential. We employ the Quantum Temporal Probabilities (QTP) method to derive a class of Positive-Operator-Valued Measures (POVMs) for time-of-arrival observables directly from QFT. We analyze the resulting detection probabilities in both semiclassical and fully quantum regimes, identifying the relevant timescales and their dependence on the field-theoretic parameters. For ensembles of particles, the detection signal is a periodic function, providing a realization of a quantum clock whose operation reflects the local spacetime structure. We also extend the formalism to rotating rings and show that rotation induces additional noise in detection probabilities, interpretable as a manifestation of the rotational Unruh effect. Finally, we investigate multi-time measurements and demonstrate the emergence of non-classical temporal correlations due to entanglement.

Tadashi Fujimoto

Volodymyr Turkowski, James K. Freericks

We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform, time-dependent electric field. The moments are similar to the well-known moments in equilibrium, but we extend those results to systems in arbitrary time-dependent electric fields. Moment sum rules can be employed to estimate the accuracy of numerical calculations; we compare our theoretical results to numerical calculations for the nonequilibrium dynamical mean-field theory solution of the Falicov-Kimball model at half-filling.

Ilya Prigogine, Evgueni Karpov, Tomio Petrosky +1 more

G E Stedman

The application of quasispin in nuclear, atomic and ligand field theory is extended here to systems of electron and hole states in a metallic systems. Conversely, results known in connection with particle-hole conjugation in metals are generalised to shell theoretic applications of quasispin. The analogy between the relationship of particle hole conjugation with quasispin and the relationship of time reversal with ordinary spin is extended to the development of selection rules parallelling those associated through Kramers with time reversal. Hamiltonians such as the BCS Hamiltonian which are composed of quasispin operators with real or imaginary coefficients have definite conjugation signature and so have a special interest. Several old and new results for matrix elements within a half-filled shell are derived from this viewpoint.

Alexander Macfarlane