As a microscopic theory to express the electromagnetic response of the system to the external fields, we present the time-dependent current-density-functional theory (td-CDFT), taking into account the effect of the energy dissipation from the system. In order to express such an effect, the non-Hermitian term which corresponds to the lifetime of the higher-energy component of the many-electron state is added to the Hamiltonian of the system. Specifically, the occupation number of the Bloch states, the energies of which are higher than the Fermi energy, is chosen as a basic variable in addition to the electron density and paramagnetic current density. In order to confirm its validity, the present td-CDFT is applied to the two-level system. We successfully revisit the electric susceptibility of the Drude-Lorentz model via the present theory.
Abstract We investigate open quantum Brownian motions as quantum analogues of classical diffusion processes under interaction with an external environment. Building upon the microscopic derivation by Sinayskiy and Petruccione (2015 Phys. Scr. T165 014017), we revisit the associated master equation and study its formulation as a generalized parabolic system. Employing Fourier transform methods, we derive exact analytical solutions for one-dimensional evolutions of particles with two-level internal degree of freedom.
Microscopic two-level systems (TLS) -- ubiquitous atomic-scale defects in solid-state quantum devices -- are a dominant source of qubit decoherence, yet their role is often considered local and short-memoried. Here, we report the observation of a coherent TLS that couples simultaneously to two spatially distant superconducting qubits. The TLS is identified to reside within the tunable coupler linking the qubits, enabling controllability of the TLS-qubit coupling strength via coupler frequency -- a capability absent in earlier studies. This tunability allows us to systematically probe how TLS distorts qubit dynamics, revisiting the decoherence model in the presence of non-Markovian TLS dephasing noise. This is corroborated by the reconstructed
1/f noise spectrum of TLS frequency fluctuation spanning more than ten orders of magnitude (0.1\,mHz -- 1\,MHz) that reveals discrete fluctuator signatures. Quantum process tomography further unveils TLS-induced correlated qubit dynamics, highlighting the long-lived TLS as an effective source of non-Markovianity. Our findings expose a previously overlooked interaction mechanism in scalable quantum architectures: defects embedded in coupling elements can simultaneously affect multiple qubits with variable impact. Beyond immediate implications for system characterization and calibration, this situation provides a powerful testbed for studying defect-driven quantum dynamics, refining error suppression strategies, and advancing architecture design for scalable quantum technologies.