arXiv subjects

Dragomir Davidovic

Publications and source records attributed to Dragomir Davidovic.

8 recordsLinked to original sources

arXiv2026

TCL4 Asymptotic Redundancy and Canonically Consistent Master Equations

Left alone, open quantum systems relax toward a Kubo--Martin--Schwinger (KMS) equilibrium state, yet the inner workings of this process remain opaque. It remains unclear why the intricate fourth-order time-convolutionless (TCL4) population generator reproduces the comparatively simple second-order stationary state corrections. Even more surprisingly, stationary-state corrections of such precision can be compressed into a simple virtual coherence pathway: an open quantum systems analogue of virtual transitions, in which populations communicate through coherences that are never occupied. Here we show that this simplification arises through a sequence of stationary-state-preserving transformations that progressively eliminate asymptotically redundant components while preserving the stationary state, ultimately yielding the virtual coherence pathway. This resolves the longstanding stationary-state problem of the Redfield equation and reveals that much of the apparent complexity of the TCL4 generator is asymptotically redundant.

quant-ph↗

arXiv2026

Nonperturbative Resummation of Divergent Time-Local Generators

Perturbative van Kampen cumulant expansions of time-local generators of open quantum systems generically diverge at long times, even though the reduced dynamics remains regular. Here we show that these divergent cumulants nevertheless contain sufficient information to reconstruct the nonperturbative dynamical map. The resulting dynamical map reveals that the divergence does not signal a breakdown of the reduced dynamics, but the approach to isolated times at which the dynamical map becomes noninvertible. Rather than arising from special Lindblad-type constructions, the corresponding singular time-local generators emerge generically from microscopic open-system Hamiltonians. The onset of recurrent noninvertibility identifies the reduced-dynamical-map manifestation of the Khalfin effect, a transition from exponential to algebraic relaxation, establishing a direct connection between long-time quantum decay and noninvertibility of reduced open-system dynamics. Nevertheless, the distinguishability of quantum superposition states remains governed by an exponential decay law throughout the Khalfin regime, demonstrating that the Markovian loss of distinguishability survives even in the presence of long-lived non-Markovian memory.

quant-ph↗

arXiv2025

Regulated reconstruction of long-time spin--boson dynamics and emergent zero-bias transverse measurement primitive

Time--convolutionless (TCL) master equations can break down at long times: time-local perturbative generators develop secular growth in correlation-dominated regimes. We mitigate this by a regulated, partially resummed reconstruction of the dynamical map around a Davies reference semigroup, expressed through a non--Markovian density-matrix correlator C(t) that remains bounded at late times. An exactly solvable rotating-wave benchmark links generator growth to interference-induced near-zeros of the coherence and shows how the reconstruction regulates the map. Applying the method to the unbiased spin--boson model reveals an emergent transverse measurement primitive: bath memory and counter--rotating terms induce phase lock-in that irreversibly erases the relative phase between $\sigma_x$ eigenspaces on a finite timescale $t_P$, yielding an effective zero-bias transverse ($\sigma_x$) measurement channel. The selected transverse basis is not assumed a priori; it follows from the reconstructed reduced dynamics. The effect disappears in the rotating-wave approximation and in the Davies weak-coupling limit, demonstrating its non--Markovian interference origin.

quant-ph↗

arXiv2025

Benchmarking TCL4: Assessing the Usability and Reliability of Fourth-Order Approximations

The non-Markovian dynamics of an open quantum system can be rigorously derived using the Feynman-Vernon influence functional approach. Although this formalism is exact, practical numerical implementations often require compromises. The time-convolutionless (TCL) master equation offers an exact framework, yet its application typically relies on a perturbative expansion of both the time forward and time backward state propagators. Due to the significant computational effort involved - and the scarcity of analytical solutions for most open quantum systems - the fourth-order perturbative TCL generator (TCL4) has only been benchmarked on a limited range of systems and parameter spaces. Recent advancements, however, have made the computation of TCL4 faster and more accessible. In this paper, we benchmark the TCL4 master equation against numerically exact methods for the biased spin-boson model. We focus on the regime near critical bath coupling where perturbative master equations are expected to become inaccurate. Our findings reveal that the TCL4 approach is most reliable at low temperature and more efficient than the numerical exact methods. This study aims to delineate the conditions under which the TCL4 perturbative master equation enhances the accuracy of the TCL2.

quant-ph↗

arXiv2021

Geometric-Arithmetic Master Equation in Large and Fast Open Quantum Systems

Understanding nonsecular dynamics in open quantum systems is addressed here, with emphasis on systems with large numbers of Bohr frequencies, zero temperature, and fast driving. We employ the master equation, which replaces arithmetic averages of the decay rates in the open system, with their geometric averages, and find that it can improve the second order perturbation theory, known as the Redfield equation, while enforcing complete positivity on quantum dynamics. The characteristic frequency scale that governs the approximation is the minimax frequency: the minimum of the maximum system oscillation frequency and the bath relaxation rate; this needs to be larger than the dissipation rate for it to be valid. The concepts are illustrated on the Heisenberg ferromagnetic spin-chain model. To study the accuracy of the approximation, a Hamiltonian is drawn from the Gaussian unitary ensemble, for which we calculate the fourth order time convolutionless master equation, in the Ohmic bath at zero temperature. Enforcing the geometric average, decreases the trace distance to the exact solution. Dynamical decoupling of a qubit is examined by applying the Redfield and the geometric-arithmetic master equations, in the interaction picture of the time dependent system Hamiltonian, and the results are compared to the exact path integral solution. The geometric-arithmetic approach is significantly simpler and can be super-exponentially faster compared to the Redfield approach.

quant-ph↗

arXiv2021

Hamiltonian Model for Fault Tolerant Singlet-Like Excitation: First Principles Approach

Deriving quantum error correction and quantum control from the Schrodinger equation for a unified qubit-environment Hamiltonian will give insights into how microscopic degrees of freedom affect the capability to control and correct quantum information beyond that of phenomenological theory. Here, we investigate the asymptotic reduced state of two qubits coupled to each other solely via a common heat bath of linear harmonic oscillators and search for evidence of fault-tolerant excited qubit states. We vary the Hamiltonian parameters, including the qubit-qubit and qubit-bath detuning, the bath spectral density, and whether or not we use the Markov approximation in the calculation of our dynamics. In proximity to special values of these parameters, we identify these states as asymptotic reduced states that are arbitrarily pure, excited, unique, and have high singlet fidelity. We emphasize the central role of the Lamb-shift as an agent responsible for fault tolerant excitations. To learn how these parameters relate to performance, we discuss numerical studies on fidelity and error recovery time.

quant-ph↗

arXiv2020

Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation

Here we present a Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfield equation. Instead of full-scale coarse-graining, this approximation only truncates terms in the Redfield equation that average out over a time-scale typical of the quantum system. The first step in this approximation is to properly renormalize the system Hamiltonian, to symmetrize the gains and losses of the state due to the environmental coupling. In the second step, we swap out an arithmetic mean of the spectral density with a geometric one, in these gains and losses, thereby restoring complete positivity. This completely positive approximation, GAME (geometric-arithmetic master equation), is adaptable between its time-independent, time-dependent, and Floquet form. In the exactly solvable, three-level, Jaynes-Cummings model, we find that the error of the approximate state is almost an order of magnitude lower than that obtained by solving the coarse-grained stochastic master equation. As a test-bed, we use a ferromagnetic Heisenberg spin-chain with long-range dipole-dipole coupling between up to 25-spins, and study the differences between various master equations. We find that GAME has the highest accuracy per computational resource.

quant-ph↗

arXiv2018

Probing the Magnetodynamics of Magnetic Tunnel Junctions with the Aid of SiGe HBTs

High impedance (about 1 Megaohm) magnetic tunnel junctions (MTJs) are used to observe and record the magnetodynamics of the nanomagnets that form the junctions themselves. To counteract the bandwidth limitations caused by the high impedance of the junction and the parasitic capacitance intrinsic to any cryogenic system, silicon-germanium heterojunction bipolar transistors (SiGe HBTs) are used as cryogenic preamplifiers for the MTJs. The resulting measurement improvements include an increase in bandwidth by a factor of 3.89, an increase in signal-to-noise ratio by a factor of 6.62, and a gain of 7.75 of the TMR signal produced by the MTJ. The limitation to the measurement system was found to be from the external, room temperature electronics. Despite this limitation, these improvements allow for better time-resolved magnetodynamics measurements of the MTJs. These experiments pave the way for future cryogenic, magnetodynamics measurement improvements, and could even be useful in cryogenic memory applications.

cond-mat.mes-hall↗