Article
Astronomy & Astrophysics
Lajos Diosi
Summary: The celebrated GKLS master equation, known as the Lindblad equation, serves as the universal dynamical equation for nonrelativistic open quantum systems in their Markovian approximation. However, it is uncertain whether GKLS equations can have sensible relativistic forms. In 2017, Poulin proposed a Lorentz invariant GKLS master equation, but further investigation reveals a hidden defect that prevents the existence of Lorentz invariant Markovian master equations.
Article
Optics
Anton Trushechkin
Summary: The study addresses a long-standing problem in the theory of open quantum systems by providing a fully rigorous derivation of a quantum master equation that takes into account nonsecular effects while maintaining mathematical correctness and thermodynamic properties. The nonsecular terms are essential when energy levels of the system are nearly degenerate, and the derivation is based on a formalization of the weak-coupling limit for the general case.
Article
Multidisciplinary Sciences
Alexander A. Andrianov, Mikhail Ioffe, Ekaterina A. Izotova, Oleg O. Novikov
Summary: In this study, we thoroughly investigate the evolution of open quantum systems in a dynamical semigroup in a 2-dimensional Hilbert space. We discover the final fixed states and obtain a general solution that converges to a fixed state. We also examine the behavior of solutions for weak interactions with an environment and differentiate between interacting and non-interacting cases. Finally, we prove the absence of oscillating solutions resembling closed quantum systems.
Article
Quantum Science & Technology
Ralf Betzholz, Bruno G. Taketani, Juan Mauricio Torres
Summary: In this work, the differences between a common phenomenological model for the master equation and the more rigorous dressed-state master equation for optomechanical systems are investigated. An analytical method to obtain the absorption spectrum of the system for both models is provided, showing the breakdown of the phenomenological model in both the bad cavity and the ultra-strong coupling limit. The role of indirect dephasing of the optical cavity in both models and its impact on the predicted absorption spectra differences is discussed. This work offers a simple experimental test to determine whether the phenomenological model can accurately describe the system and is a step towards better understanding the role of coupling between subsystems for open-quantum-system dynamics.
QUANTUM SCIENCE AND TECHNOLOGY
(2021)
Article
Physics, Multidisciplinary
Jonathan Dubois, Ulf Saalmann, Jan M. Rost
Summary: In this study, the semi-classical Lindblad master equation is derived in phase space for both canonical and non-canonical Poisson brackets using the Wigner-Moyal formalism and the Moyal star-product. The analysis generalizes the classical limit of the Fokker-Planck equation to non-canonical Poisson brackets, such as gyro-Poisson brackets. The equations of motion for collective spin variables are shown to be governed by the Bloch equations of nuclear magnetization with relaxation in this framework.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Physics, Multidisciplinary
Chang-Yao Liao, Xian-Ting Liang
Summary: This paper derives the Lindblad and Redfield forms of the master equation based on the Born-Markov master equation, with coefficients re-evaluated as complex numbers rather than real numbers. Dynamics of two models are studied, showing that different environments may cause small or large distortions in dynamics due to the secular approximation and simplified real coefficients. The effects are discussed by studying the dynamics of multi-level systems in the presence of dissipation.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2021)
Article
Mechanics
Thomas Barthel, Yikang Zhang
Summary: This article investigates the dynamics of Markovian open quantum systems, deriving the equation of motion for the covariance matrix in quasi-free systems. The use of ladder super-operators allows for the transformation of the Liouvillian to a many-body Jordan normal form, uncovering the full many-body spectrum. The article extends previous work, treating fermionic and bosonic systems equally and covering additional phenomena such as non-diagonalizable Liouvillians and quadratic systems.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Physics, Multidisciplinary
Simon B. Jaeger, Tom Schmit, Giovanna Morigi, Murray J. Holland, Ralf Betzholz
Summary: We present a general approach to derive Lindblad master equations for subsystems coupled to dissipative bosonic modes. We apply this approach to the dissipative Dicke model and successfully predict the Dicke phase transition and quantum metastability. The performance of our formalism is validated by comparing with exact diagonalization and numerical integration results.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
K. El Anouz, A. El Allati, F. Saif
Summary: This paper proposes a realizable model based on the interaction between an excited atom and a radiation field. By calculating the entanglement, the entanglement rate in the total field-field system is evaluated, and a comparative study of different levels of entanglement in the quantum teleportation scheme is conducted.
Article
Optics
Jacob R. Lindale, Shannon L. Eriksson, Warren S. Warren
Summary: The theoretical description of the interplay between coherent evolution and chemical exchange, which was originally developed for magnetic resonance and later applied to other spectroscopic regimes, was derived under incorrect statistical assumptions. Correcting these assumptions allows access to the exact form of the chemical exchange interaction, derived within the Lindblad master equation formalism for generality. The exact form of the interaction differs from the traditional equation only by a scalar correction factor derived from higher-order interactions, and it regularly improves the convergence radius of the solution (thus increasing the allowable step size in calculations) by up to an order of magnitude, without any additional computational cost.
Article
Physics, Multidisciplinary
Dragomir Davidovic
Summary: This article discusses the understanding of nonsecular dynamics in open quantum systems, with an emphasis on systems with large numbers of Bohr frequencies, zero temperature, and fast driving. By employing the master equation and replacing arithmetic averages of decay rates with geometric averages, improvements can be made to the second order perturbation theory (known as the Redfield equation) while maintaining the complete positivity of quantum dynamics. The accuracy of the approximation is studied using the Heisenberg ferromagnetic spin-chain model and a Gaussian unitary ensemble. The geometric-arithmetic approach is found to be significantly simpler and faster compared to the Redfield approach.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Vaibhav Chimalgi, Bihalan Bhattacharya, Suchetana Goswami, Samyadeb Bhattacharya
Summary: This article investigates the problem of entanglement detection in quantum information theory, particularly focusing on constructing suitable mappings for non-completely positive maps. The study presents a class of positive maps derived from Lindblad structures, showing that famous positive maps such as transposition, reduction map, and Choi map can be obtained as special cases within this class. By generalizing the transposition map, the authors successfully detect genuine multipartite entanglement and define a similar measure to assess it.
Article
Physics, Multidisciplinary
Frederic Barbaresco
Summary: This article discusses the application of the canonical ensemble extended by Lie groups on symplectic manifolds, introduces the concept of Lie group thermodynamics and information geometry, and investigates the geometric structure of the heat equation and entropy. The study of information geometry for Lie groups leads to the derivation of the Fisher metric, and analyzing dissipative dynamics on symplectic leaves helps interpret phenomena in Lie group thermodynamics.
Article
Physics, Multidisciplinary
Francesco Carnazza, Federico Carollo, Dominik Zietlow, Sabine Andergassen, Georg Martius, Igor Lesanovsky
Summary: In the study of many-body quantum systems, it is often sufficient to consider the dynamical or stationary properties of local observables. By formulating the problem of finding the generator of the subsystem dynamics as a variational problem and using machine learning techniques, we are able to learn a physically consistent open quantum time-evolution and predict the stationary state of the subsystem dynamics.
NEW JOURNAL OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
Alexei D. Kiselev, Ranim Ali, Andrei Rybin
Summary: This paper investigates the thermal bath Lindblad master equation to describe the nonunitary dynamics of quantum states in a multi-mode bosonic system, and analyzes how the coupling between modes and with the environment affect entanglement dynamics. It discusses how entanglement revivals can be induced by dynamic coupling between different modes, and shows that reorientation of the relaxation rate vector can significantly increase the time of disentanglement in the regime of finite-time disentanglement.
Article
Automation & Control Systems
Sophie G. Schirmer, Edmond A. Jonckheere, Frank C. Langbein
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2018)
Article
Automation & Control Systems
E. Jonckheere, S. Schirmer, F. Langbein
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2018)
Article
Radiology, Nuclear Medicine & Medical Imaging
Ziyafer Gizem Portakal, Sophie Shermer, Christopher Jenkins, Emiliano Spezi, Teresa Perrett, Nina Tuncel, Jonathan Phillips
Article
Statistics & Probability
Simon Apers, Alain Sarlette, Francesco Ticozzi
Summary: This paper explores various methods to accelerate Markov chain mixing, finding that some approaches can speed up mixing time while others do not allow for any speedup.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2021)
Article
Engineering, Electrical & Electronic
B. Thorpe, S. Schirmer, K. Kalna
Summary: In this study, spin-based metal-oxide-semiconductor field-effect transistors (MOSFETs) with a high-mobility III-V channel were investigated using self-consistent quantum corrected ensemble Monte Carlo device simulations. The simulations examined the role of spin-orbit coupling mechanisms in electron spin transport in the MOSFET and showed that the spin-dependent drain current modulation can be controlled by adjusting the transistor lateral dimensions and temperature.
SEMICONDUCTOR SCIENCE AND TECHNOLOGY
(2022)
Article
Automation & Control Systems
Sophie G. Schirmer, Frank C. Langbein, Carrie Ann Weidner, Edmond Jonckheere
Summary: This study investigates the robust performance of control schemes for open quantum systems under classical and non-classical uncertainties. A formalism is developed to measure performance based on the transmission of perturbations and errors to the quantum state. Classical robust control tools are applied, overcoming difficulties arising from singularity and symmetry. The concepts are applied to specific system examples, introducing a nonclassical performance index.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Automation & Control Systems
S. P. O'Neil, I. Khalid, A. A. Rompokos, C. A. Weidner, F. C. Langbein, S. Schirmer, E. A. Jonckheere
Summary: Recent advancements in quantum control have provided advanced techniques for designing robust controllers in quantum systems. This letter investigates the correlation between the time-domain log-sensitivity and the recently introduced robustness infidelity measure (RIM) for evaluating controller robustness in the presence of dephasing. The study shows that the differential sensitivity of the error agrees with the differential sensitivity of the RIM, indicating that the two measures are highly concordant.
IEEE CONTROL SYSTEMS LETTERS
(2023)
Article
Automation & Control Systems
Tommaso Grigoletto, Francesco Ticozzi
Summary: This paper proposes a new method for pure-state and subspace preparation in quantum systems, which improves convergence speed and robustness by utilizing the output of a continuous measurement process and switching dissipative control.
IEEE CONTROL SYSTEMS LETTERS
(2022)
Article
Computer Science, Theory & Methods
Giacomo Baggio, Francesco Ticozzi, Peter D. Johnson, Lorenza Viola
Summary: This paper formalizes the problem of dissipative quantum encoding and explores the advantages of using Markovian evolution to prepare quantum codes in the desired logical space, with a focus on discrete-time dynamics and exact finite-time convergence. It is shown that even for stabilizer quantum codes, dissipative encoders can be constructed in finite time using a number of quantum maps determined by the number of stabilizer generators.
QUANTUM INFORMATION & COMPUTATION
(2021)
Proceedings Paper
Automation & Control Systems
Francesco Ticozzi, Giacomo Baggio, Lorenza Viola
2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC)
(2019)
Proceedings Paper
Automation & Control Systems
Francesco Ticozzi, Salini Karuvade, Lorenza Viola
2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC)
(2019)
Proceedings Paper
Automation & Control Systems
E. Jonckheere, S. Schirmer, F. Langbein
2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC)
(2019)
Article
Optics
Salini Karuvade, Peter D. Johnson, Francesco Ticozzi, Lorenza Viola
Article
Optics
Re-Bing Wu, Haijin Ding, Daoyi Dong, Xiaoting Wang
Article
Optics
Simon Apers, Alain Sarlette, Francesco Ticozzi
