arXiv subjects

J. T. Stockburger

Publications and source records attributed to J. T. Stockburger.

12 recordsLinked to original sources

arXiv2026

Markovian Embeddings of Non-Markovian Open System Dynamics

Embedding non-Markovian open quantum dynamics into an enlarged Markovian space offers a powerful route to nonperturbative simulations, where the dynamics of the extended space can be governed by multiple distinct Markovian equations. We show that these distinct embeddings arise from different unravelings of Gaussian bath self-energies, generating a family of deterministic, time-local equations for the extended system. Using the Brownian-oscillator spectral density as an illustrative example, we clarify the relationships among existing approaches, including the Hierarchical Equations of Motion (HEOM) and the Lindblad--pseudomode formalism, and demonstrate how this framework enables numerically stable and efficient simulations. This work provides both a transparent theoretical foundation for embedding techniques and a flexible platform for developing new methods to simulate non-Markovian quantum dynamics.

quant-ph↗

arXiv2026

Simulating Non-Markovian Dynamics in Open Quantum Systems

Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects (non-Markovianity), system-environment hybridization, and the necessity for accuracy beyond the Born-Markov approximation form particular challenges. Approaches to meet these challenges have been introduced, originating from different fields, such as hierarchical equations of motion, Lindblad-pseudomode formulas, chain-mapping approaches, quantum Brownian motion master equations, stochastic unravelings, and refined quantum master equations. This diversity, while indicative of the field's relevance, has inadvertently led to a fragmentation that hinders cohesive advances and their effective cross-community application to current problems for complex systems. How are different approaches related to each other? What are their strengths and limitations? Here we give a systematic overview and concise discussion addressing these questions. We make use of a unified framework which very conveniently allows to link different schemes and, this way, may also catalyze further progress. In line with the state of the art, this framework is formulated not in a fully reduced space of the system but in an extended state space which in a minimal fashion includes effective reservoir modes. This in turn offers a comprehensive understanding of existing methods, elucidating their physical interpretations, interconnections, and applicability.

quant-ph↗

arXiv2025

Nonlinear response theory for lossy superconducting quantum circuits

We introduce a numerically exact and computationally feasible nonlinear-response theory developed for lossy superconducting quantum circuits based on a framework of quantum dissipation in a minimally extended state space. Starting from the Feynman--Vernon path integral formalism for open quantum systems with the system degrees of freedom being the nonlinear elements of the circuit, we eliminate the temporally non-local influence functional of all linear elements by introducing auxiliary harmonic modes with complex-valued frequencies coupled to the nonlinear elements. In our work, we propose a concept of time-averaged observables, inspired by experiment, and provide an explicit formula for producing their quasiprobability distribution. We illustrate the consistency of our formalism with the well-established Markovian input-output theory by applying them the dispersive readout of a superconducting transmon qubit. For an important demonstration of our approach beyond weak coupling, we analyze the low-frequency linear response of a capacitively and resistively shunted Josephson junction and observe signatures of a much-debated quantum phase transition at a finite temperature. The developed framework enables a comprehensive fully quantum-mechanical treatment of nonlinear quantum circuits coupled to their environment, without the limitations of typical approaches to weak dissipation, high temperature, and weak drive. This versatile tool paves the way for accurate models of quantum devices and increased fundamental understanding of quanutm mechanics such as that of the quantum measurement.

quant-ph↗

arXiv2024

Environment-Mediated Long-Ranged Correlations in Many-Body System

Quantum states in complex aggregates are unavoidably affected by environmental effects, which typically cannot be accurately modeled by simple Markovian processes. As system sizes scale up, nonperturbative simulation become thus unavoidable but they are extremely challenging due to the intimate interplay of intrinsic many-body interaction and time-retarded feedback from environmental degrees of freedom. In this work, we utilize the recently developed Quantum Dissipation with Minimally Extended State Space (QD-MESS) approach to address reservoir induced long-ranged temporal correlations in finite size Ising-type spin chains. For thermal reservoirs with ohmic and subohmic spectral density we simulate the quantum time evolution from finite to zero temperature. The competition between thermal fluctuations, quantum fluctuations, and anti-/ferromagnetic interactions reveal a rich pattern of dynamical phases including dissipative induced phase transitions and spatiotemporal correlations.

cond-mat.stat-mech↗

arXiv2023

A Universal Framework for Quantum Dissipation:Minimally Extended State Space and Exact Time-Local Dynamics

The dynamics of open quantum systems is formulated in a minimally extended state space comprising the degrees of freedom of a system of interest and a finite set of non-unitary, pure-state reservoir modes. This formal structure, derived from the Feynman-Vernon path integral for the reduced density, is shown to lead to an exact time-local evolution equation in a mixed Liouville-Fock space. The crucial ingredient is a mathematically consistent decomposition of the reservoir auto-correlation in terms of harmonic modes with complex-valued frequencies and amplitudes, which are obtained from any given spectral noise power of the physical reservoir. This formulation provides a universal framework to obtain a family of equivalent representations which are directly related to new and established schemes for efficient numerical simulations. By restricting some of the complex-valued mode parameters and performing linear transformations, we make connections to previous approaches, whose auxiliary degrees of freedom are thus revealed as restricted versions of the minimally extended state space presented here. From a practical perspective, the new framework offers a computational tool which combines numerical efficiency and accuracy with long time stability and broad applicability over the whole temperature range and also for strongly structured reservoir mode densities. It can thus deliver high precision data with modest computational resources and simulation times for actual quantum technological devices.

quant-ph↗

arXiv2023

Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model

The hierarchical equations of motion (HEOM) approach is an accurate method to simulate open system quantum dynamics, which allows for systematic convergence to numerically exact results. To represent the effects of the bath, the reservoir correlation functions are usually decomposed into the summation of multiple exponential terms in the HEOM method. Since the reservoir correlation functions become highly non-Markovian at low temperatures or when the bath has complex band structures, a present challenge is to obtain accurate exponential decompositions that allow efficient simulation with the HEOM. In this work, we employ the barycentric representation to approximate the Fermi function and hybridization functions in the frequency domain. The new method, by approximating these functions with optimized rational decomposition, greatly reduces the number of basis functions in decomposing the reservoir correlation functions, which further allows the HEOM method to be applied to ultra-low temperature and general bath structures. We demonstrate the efficiency, accuracy, and long-time stability of the new decomposition scheme by applying it to the Anderson impurity model (AIM) in the low-temperature regime with the Lorentzian and tight-binding hybridization functions.

cond-mat.str-el↗

arXiv2022

Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems

The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems that are embedded in thermal environments. However, its applicability is restricted to specific forms of spectral reservoir distributions and relatively elevated temperatures. Here we solve this problem and introduce an effective treatment of quantum noise in frequency space by systematically clustering higher order Matsubara poles equivalent to an optimized rational decomposition. This leads to an elegant extension of the HEOM to arbitrary temperatures and very general reservoirs in combination with efficiency, high accuracy and long-time stability. Moreover, the technique can directly be implemented in alternative approaches such as Green's function, stochastic, and pseudo-mode formulations. As one highly non-trivial application, for the sub-ohmic spin-boson model at vanishing temperature the Shiba relation is quantitatively verified which predicts the long-time decay of correlation functions.

quant-ph↗

arXiv2022

Minimal quantum thermal machine in a bandgap environment: non-Markovian features and anti-Zeno advantage

A minimal model of a quantum thermal machine is analyzed, where a driven two level working medium (WM) is embedded in an environment (reservoir) whose spectrum possesses bandgaps. overlap with hot or cold reservoirs whose spectra are separated by a bandgap. Approximate and exact treatments supported by analytical considerations yield a complete characterization of this thermal machine in the deep quantum domain. For slow to moderate modulation, the spectral response of the reservoirs is close to equilibrium, exhibiting sideband (Floquet) resonances in the heat currents and power output. In contrast, for faster modulation, strong-coupling and non-Markovian features give rise to correlations between the WM and the reservoirs and between the two reservoirs. Power boost of strictly quantum origin ('quantum advantage') is then found for both continuous and segmental fast modulation that leads to the anti-Zeno effect of enhanced spectral reservoir response. Such features cannot be captured by standard Markovian treatments.

quant-ph↗

arXiv2021

Heat transport through a superconducting artificial atom

Quantum heat transfer through a generic superconducting set-up consisting of a tunable transmon qubit placed between resonators that are termined by thermal reservoirs is explored. Two types of architectures are considered, a sequential and a beam splitter setting. Applying the numerical exact hierarchical equation of motion (HEOM) approach, steady state properties are revealed, and experimentally relevant parameter sets are identified. Benchmark results are compared with predictions based on approximate treatments to demonstrate their failure in broad ranges of parameter space. These findings may allow to improve future designs for heat control in superconducting devices.

quant-ph↗

arXiv2015

Resonators coupled to voltage-biased Josephson junctions: From linear response to strongly driven nonlinear oscillations

Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the dissipative motion of a single degree of freedom in a nonlinear time-dependent potential, where in contrast to conventional settings the nonlinearity appears in the driving while the static potential is purely harmonic. For long times the system approaches steady states which are analyzed in the underdamped regime over the full range of driving parameters including the fundamental resonance as well as higher and sub-harmonics. Observables such as the dc-Josephson current and the radiated microwave power give direct information about the underlying dynamics covering phenomena as bifurcations, irregular motion, up- and down conversion. Due to their tunability, present and future set-ups provide versatile platforms to explore the changeover from linear response to strongly nonlinear behavior in driven dissipative systems under well defined conditions.

cond-mat.mes-hall↗

arXiv2004

Negative differential conductance induced by spin-charge separation

Spin-charge states of correlated electrons in a one-dimensional quantum dot attached to interacting leads are studied in the non-linear transport regime. With non-symmetric tunnel barriers, regions of negative differential conductance induced by spin-charge separation are found. They are due to a correlation-induced trapping of higher-spin states without magnetic field, and associated with a strong increase in the fluctuations of the electron spin.

cond-mat.str-el↗

arXiv2003

Simulating spin-boson dynamics with stochastic Liouville-von Neumann equations

Based on recently derived exact stochastic Liouville-von Neumann equations, several strategies for the efficient simulation of open quantum systems are developed and tested on the spin-boson model. The accuracy and efficiency of these simulations is verified for several test cases including both coherent and incoherent dynamics, involving timescales differing by several orders of magnitude. Using simulations with a time-dependent field, the time evolution of coherences in the reduced density matrix is investigated. Even in the case of weak damping, pronounced preparation effects are found. These indicate hidden coherence in the interacting system which can only be indirectly observed in the basis of the reduced quantum dynamics.

cond-mat↗