and related topics
Date & Time: 24 Sep 2025 (Wed) from 13:00
Venue: Shibaura Institute of Technology,
Omiya Campus, Bldg. 5 (3F) Room 5351
This workshop is dedicated to sharing the latest insights on Markovian and non‑Markovian dynamics in open quantum systems. We are pleased to welcome Professor Dariusz Chruściński from Poland as our special guest. If you would like to participate, please contact us.
Nearest station: JR Utsunomiya Line Higashi‑Ōmiya.
University shuttle bus: about 5 minutes
-- bus time table.
-- bus stop.
Abstract: Relaxation rates are key characteristics of quantum processes, as they determine how quickly a
quantum system thermalizes, equilibrates, decoheres, and dissipates. While they play a crucial role
in theoretical analyses, relaxation rates are also often directly accessible through experimental measurements.
Recently, it was shown that for quantum processes governed by Markovian semigroups,
the relaxation rates satisfy a universal constraint: the maximal rate is upper-bounded by the sum
of all rates divided by the dimension of the Hilbert space. This bound, initially conjectured a few
years ago, was only recently proven using classical Lyapunov theory.
In this talk I briefly review the link between classical Lyapunov theory and relaxation rates for quantum evolution. Moreover, I present a new,
purely algebraic proof of this constraint. Remarkably, this new technique is not only more direct but also
allows for a natural generalization beyond completely positive semigroups. It is shown that complete
positivity can be relaxed to 2-positivity without affecting the validity of the constraint. This reveals
that the bound is more subtle than previously understood: 2-positivity is necessary, but even when
further relaxed to Schwarz maps, a slightly weaker—yet still non-trivial—universal constraint still
holds. Possible application of the universal bound are also discussed.
The talk is based on a recent work arXiv:2505.24467 (to appear in Reports on Progress in Physics)
Abstract: The quantum master equation stands as a cornerstone for understanding open quantum systems. In this presentation, I will provide a comprehensive review of the microscopic derivation of the quantum master equation and explore its powerful extensions, including full counting statistics, the Heisenberg picture, and the complex susceptibility under initial correlations between the system and its environment. Join me as we delve into these critical concepts that enhance our comprehension of quantum dynamics and pave the way for future advancements in the field.
Abstract: The dynamics of Markovian open quantum systems are governed by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation. A fundamental property of this equation is the possible degeneracy of its steady states. In particular, when the steady state is unique, any initial state will eventually relax to it.
There has been extensive research on the uniqueness of steady states for GKSL equations with time-independent generators.
Recently, the interplay between periodic driving and dissipation has attracted growing interest. However, general results concerning the uniqueness of steady states in time-periodic settings remain limited.
In this talk, we present a general and rigorous criterion for the uniqueness of steady states in GKSL equations with time-periodic generators, assuming Hermitian jump operators.
Abstract:
We have been interested in the dynamics of a system in an environment, or an open system, since 2007. Such phenomena as crossover from Markovian to non-Markovian relaxation, Bang-Bang control, and quantum Zeno effects are of our interest. Open systems have been experimentally studied using ultra-cold atoms, ions in traps, optics, and cold electric circuits, as they are well-isolated systems. Thus, one can control the effects of their environments. We point out that some molecules dissolved in an isotropic liquid are well isolated, and they can also be employed for studying open systems in Nuclear Magnetic Resonance (NMR) experiments.
In this talk, we will show several of our experiments related to an open system.
Abstract: Since the quantum geometric tensor (QGT) captures the local geometric structure inherent in quantum states, in contrast to topological invariants that characterize global features, its singular behavior near the critical point of a quantum phase transition has attracted much attention.
The conventional framework is suitable for compact systems, where the Hermitian metric is well defined in a finite-dimensional Hilbert space.
However, there also exist physically important non-compact systems exhibiting critical phenomena, such as superradiant phase transitions, exponentially growing parametric amplification, and vacuum instabilities represented by the inverted oscillator.
In these systems, quantum states do not belong to a Hilbert space when the system becomes unstable, and thus the Hermitian inner product cannot be properly defined, which calls for a new definition of the Berry connection.
In this talk, I will present a new formulation of quantum geometry applicable to non-compact quantum systems, based on the principal bundle structure of operator space.
Specifically, we employ the Ehresmann connection on the total space of the principal frame bundle, which provides a geometric formulation independent of the Hilbert space inner product.
I will also show that the geometric structure of the projective operator space manifold changes from a Kähler structure to a pseudo-Kähler structure across the transition.
Abstract: Understanding quantum systems open to their surroundings is essential for comprehending fluctuations, dissipation, and decoherence. While the environment or bath is typically modeled as a set of harmonic oscillators exhibiting Gaussian statistics, deviations arise when the bath comprises two-state systems, spins, or anharmonic oscillators, introducing non-Gaussian properties. However, a theoretical framework to describe quantum systems under the influence of such non-Gaussian baths is not well established.
To tackle this problem, we first review the so-called pseudo-mode method for Gaussian baths, a technique that reproduces the non-Markovian dynamics of the target system by a Markovian dynamics for the enlarged system including the auxiliary modes (pseudo-modes). We extend the Feynman-Vernon influence functional formalism to a non-unitary time evolution and clarify the conditions that the pseudo-mode model must satisfy to reproduce the time-evolution of the target system.
Next, we consider the non-Gaussian bath that produces random telegraph noise and Poisson noise, which are renowned examples of non-Gaussian noise. In particular, the Levi-Ito decomposition theorem asserts that any white noise can be decomposed into Gaussian white noise and a sum of Poisson white noises. We introduce a random telegraph noise and Poisson noise bath model in the enlarged system including the auxiliary modes and discuss the time-evolution of the target system based on the non-unitary extension of the generalized master equation.
Gen Kimura <gen[at]sic.shibaura-it.ac.jp>
Gen Kimura (Shibaura Institute of Technology),
Chikako Uchiyama (Yamanashi Univ.)