arXiv subjects

Daochi Zhang

Publications and source records attributed to Daochi Zhang.

6 recordsLinked to original sources

arXiv2026

Error Propagation Theory for Variational Non-Markovian Open Quantum Dynamics

Variational approaches based on neural quantum states and physics-informed neural networks provide powerful paradigms for simulating non-Markovian open quantum dynamics. However, extending these methods into the strongly non-Markovian regime reveals a critical bottleneck: even minute errors in the time evolution can translate into substantial deviations in physical observables. The fundamental origin of this stringent precision requirement, as well as how non-Markovianity governs it, remains an open question. Here, we develop a theoretical framework that systematically characterizes error propagation in variational non-Markovian dynamics. By combining analytical derivations with numerical verification, we present the first quantitative description of variational error evolution over time. Our analysis uncovers an intrinsic error-backflow mechanism driven by long-lived environmental memory. This mechanism establishes a fundamental precision barrier and provides concrete guidance for designing robust variational algorithms for strongly non-Markovian quantum systems.

quant-ph↗

arXiv2026

Simulating non-Markovian open quantum dynamics by exploiting physics-informed neural network

This work integrates the physics-informed neural network (PINN) approach into the neural quantum state framework to simulate open quantum system dynamics, to circumvent the computationally expensive time-dependent variational principle required in conventional variational methods. The proposed PINN-DQME method employs time-encoded neural networks within a time-domain decomposition strategy to represent the evolution governed by the dissipaton-embedded quantum master equation (DQME). We implement and validate this approach in the single-impurity Anderson model, benchmarking the PINN-DQME results against the numerically exact hierarchical equations of motion. The PINN-DQME method demonstrates high accuracy in simulating quantum dissipative dynamics at high temperatures, where non-Markovian effects are weak. However, for strongly non-Markovian dynamics at low temperatures, it encounters challenges with error accumulation during time propagation, highlighting an area for future refinement in applying PINNs to complex quantum dynamical settings.

quant-ph↗

arXiv2024

Simulating Non-Markovian Open Quantum Dynamics with Neural Quantum States

Reducing computational scaling for simulating non-Markovian dissipative dynamics using artificial neural networks is both a major focus and formidable challenge in open quantum systems. To enable neural quantum states (NQSs), we encode environmental memory in dissipatons (quasiparticles with characteristic lifetimes), yielding the dissipaton-embedded quantum master equation (DQME). The resulting NQS-DQME framework achieves compact representation of many-body correlations and non-Markovian memory. Benchmarking against numerically exact hierarchical equations of motion confirms NQS-DQME maintains comparable accuracy while enhancing scalability and interpretability. This methodology opens new paths to explore non-Markovian open quantum dynamics in previously intractable systems.

quant-ph↗

arXiv2024

HEOM-QUICK2: a general-purpose simulator for fermionic many-body open quantum systems -- An Update

Many-body open quantum systems (OQS) have a profound impact on various subdisciplines of physics, chemistry, and biology. Thus, the development of a computer program capable of accurately, efficiently, and versatilely simulating many-body OQS is highly desirable. In recent years, we have focused on the advancement of numerical algorithms based on the fermionic hierarchical equations of motion (HEOM) theory. Being in-principle exact, this approach allows for the precise characterization of many-body correlations, non-Markovian memory, and non-equilibrium thermodynamic conditions. These efforts now lead to the establishment of a new computer program, HEOM for QUantum Impurity with a Correlated Kernel, version 2 (HEOM-QUICK2), which, to the best of our knowledge, is currently the only general-purpose simulator for fermionic many-body OQS. Compared with version 1, the HEOM-QUICK2 program features more efficient solvers for stationary states, more accurate treatment of non-Markovian memory, and improved numerical stability for long-time dissipative dynamics. Integrated with quantum chemistry software, HEOM-QUICK2 has become a valuable theoretical tool for the precise simulation of realistic many-body OQS, particularly the single atomic or molecular junctions. Furthermore, the unprecedented precision achieved by HEOM-QUICK2 enables accurate simulation of low-energy spin excitations and coherent spin relaxation. The unique usefulness of HEOM-QUICK2 is demonstrated through several examples of strongly correlated quantum impurity systems under non-equilibrium conditions. Thus, the new HEOM-QUICK2 program offers a powerful and comprehensive tool for studying many-body OQS with exotic quantum phenomena and exploring applications in various disciplines.

cond-mat.str-el↗

arXiv2021

Effect of quantum resonances on local temperature in nonequilibrium open systems

Measuring local temperatures of open systems out of equilibrium is emerging as a novel approach to study the local thermodynamic properties of nanosystems. An operational protocol has been proposed to determine the local temperature by coupling a probe to the system and then minimizing the perturbation to a certain local observable of the probed system. In this paper, we first show that such a local temperature is unique for a single quantum impurity and the given local observable. We then extend this protocol to open systems consisting of multiple quantum impurities by proposing a local minimal perturbation condition (LMPC). The influence of quantum resonances on the local temperature is elucidated by both analytic and numerical results. In particular, we demonstrate that quantum resonances may give rise to strong oscillations of the local temperature along a multiimpurity chain under a thermal bias.

cond-mat.mes-hall↗

arXiv2019

Local Temperatures Out of Equilibrium

The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in view of the zeroth law of thermodynamics: when the system and the thermometer have reached equilibrium, the "thermometer degrees of freedom" can be traced out and the temperature read by the thermometer can be uniquely assigned to the system. Unfortunately, such a procedure cannot be straightforwardly extended to a system out of equilibrium, where local excitations may be spatially inhomogeneous and the zeroth law of thermodynamics does not hold. With the advent of several experimental techniques that attempt to extract a single parameter characterizing the degree of local excitations of a (mesoscopic or nanoscale) system out of equilibrium, this issue is making a strong comeback to the forefront of research. In this paper, we will review the difficulties to define a unique temperature out of equilibrium, the majority of definitions that have been proposed so far, and discuss both their advantages and limitations. We will then examine a variety of experimental techniques developed for measuring the non-equilibrium local temperatures under various conditions. Finally we will discuss the physical implications of the notion of local temperature, and present the practical applications of such a concept in a variety of nanosystems out of equilibrium.

cond-mat.stat-mech↗