RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences

Developing a framework for inferring spatial biodiversity: quantifying the "beta-diversity" patterns

An international research team led by Ryosuke Iritani, Senior Research Scientist at RIKEN iTHEMS, has developed a theoretical framework to estimate the probability distribution of spatial biodiversity. This interdisciplinary work uses fuzzy set theory to formulate species presence-absence in a community, armed with analytical techniques and concepts from mathematics and theoretical physics. This work enables a quantitative assessment of differences and variations in species richness across regions, contributing to the prediction of how environmental changes in the biosphere influence biodiversity. For more details, please refer to the related link.

2025-06-12

Understanding dynamics and quantum chaos through Krylov space

In everyday life, we often associate chaos with randomness, disorder, or unpredictability—phenomena that appear to lack any discernible pattern. However, from a physics standpoint, understanding chaos requires a more rigorous and precise mathematical framework. In classical physics, chaos is often perceived through its sensitive dependence on initial conditions. Small perturbations in an initial state of a system can lead to vastly different outcomes over time, a behavior commonly known as “butterfly effect”, and typically analyzed within the framework of phase space trajectories, and its detailed topological properties. In contrast, chaos in the quantum realm presents unique challenges. The notion of sharp trajectories in phase space clashes with Heisenberg’s uncertainty principle in quantum mechanics, and initial perturbations cannot be treated in a way that mirrors classical intuition. As a result, quantum chaos requires distinct formulations, relying on diagnostic tools like spectral statistics, out-of-time-order correlators, and entanglement measures. However, the relationships between these different probes are not always clear, and a unified understanding remains an open area of research. In recent years, significant progress has been made in understanding quantum chaos through the lens of operator growth, where localized quantum information encoded in simple operators spreads across a system—a process known as information scrambling. Such phenomena is crucial in understanding the thermalization of a system. Krylov space, a subspace of the operator Hilbert space, provides an elegant framework to describe such operator growth. By decomposing operator dynamics using an orthonormal basis, it traces how simple operators evolve into increasingly complex ones—quantified by a complexity measure in Krylov space. A parallel formulation exists for the evolution of quantum states, offering a complementary perspective. Importantly, to make these ideas applicable to realistic physical scenarios, one must consider open quantum systems—systems that interact with their environment. In such contexts, the dynamics become richer, requiring more generic theoretical and computational techniques. Furthermore, efficient quantum control protocols often leverage the structured Hilbert space, with Krylov subspace methods providing computationally efficient frameworks. These methods facilitate guiding systems along desired adiabatic trajectories, reducing runtime and mitigating decoherence effects, as often required for quantum technologies. These developments form the core focus of this review article.

2025-06-04

Information entropy untangles vortices and flows in turbulent plasmas: A turbulence analysis inspired by quantum information theory

A research team including Motoki Nakata (Visiting Scientist, iTHEMS) has proposed a novel method that interprets structural transitions and nonlinear interactions in turbulent fields from the perspective of “information,” inspired from information entropy and its mathematical formalism used in quantum mechanics theory. This approach has enabled the discovery of new turbulent states in plasma—states that had been overlooked by conventional energy-based analysis methods—and the extraction of key interactions among vortices and flows in various scales. The team also proposes an application of this method to experimental measurements that observe turbulence and fluctuations. Looking ahead, this technique is expected to be applied beyond turbulent plasmas to a wide range of research domains involving “complex flows” and “mutually correlated fluctuations,” appearing in atmospheric, oceanic, and social systems. For more details, please refer to the press release available through the related links.

2025-06-03

International and Interdisciplinary Collaboration at the RIKEN-Berkeley Center - Yuuka Kanakubo

"I’m leaving for the U.S. tomorrow," says Yuuka Kanakubo, who joined iTHEMS in October 2024 as a Postdoctoral Researcher and RIKEN-Berkeley Fellow. Her specialty is elementary particle and nuclear theory. She will be conducting research during a long-term stay at the RIKEN-Berkeley Center, iTHEMS' satellite office. "This position is perfect for me," Kanakubo says. We asked her about her journey so far and what makes this opportunity ideal. Please see the full article via the related link.

2025-05-22

Yoshimasa Hidaka received the 25th Soryushi Medal for his unified description of the Nambu-Goldstone theorem

Yoshimasa Hidaka, our Deputy Director, is awarded 25th SORYUSHI MEDAL (Paricle Physics Medal) from Japanese Particle Theory Community. The title of the achievement is “Unified Description of the Nambu-Goldstone Theorem”. The award will be presented at the 80th Annual Meeting of the Physical Society of Japan, to be held at Hiroshima University from September 16 to 19, 2025. Congratulations!!

2025-05-22

Haruki Emori received the “Second Prize”

Our colleague Haruki Emori (Junior Research Associate, iTHEMS) has received the “Second Prize’” in the Poster Session for the Quantinuum 2025 May Training Session. The outstanding presentation poster is entitled “Quantum algorithm for implementing arbitrary quantum instruments based on parameterized quantum circuits”. Congratulations, Haruki!

2025-05-22

Looking for “Overlap” to Connect - Akihisa Yamamoto

"I have always walked along the boundaries between different fields," says Research Scientist Akihisa Yamamoto. Currently, he is focusing on the interdisciplinary field between medicine and mathematics, seeking to identify patterns in doctors' experiential knowledge, translating them into mathematical models, and applying them to deepen our understanding of biological phenomena while contributing to clinical practice. We spoke with him about the encounters that led him to this path, as well as the unique challenges and excitement of working at the intersection of disciplines. Please see the full article via the related link.

2025-05-20

Utilizing Every Possible Method to Challenge the Ultimate Goal - Masazumi Honda

What are the fundamental building blocks of the universe? What is the ultimate physical law that govern the universe? How did the universe begin? Theoretical high energy physics, which seeks to answer these profound questions, is the main research field for Masazumi Honda. We spoke with Honda about his journey to iTHEMS, the breadth of his research approaches and disciplines, and his recent research on applying quantum computers to high energy physics. Please see the full article via the related link.

2025-05-15

iTHEMS x academist online event was held on April 19, 2025

iTHEMS held an online lecture event for the general public with the help of Academist Inc., on April 19, 2025. This year’s speakers were Yuuka Kanakubo, Kan Kitamura, Leo Speidel, and Yuki Yokokura, who delivered clear and easy-to-understand lectures that even middle school students could comprehend. Each speaker also served as a commentator for other lectures and facilitated Q&A sessions based on audience questions. During the lunch break, as part of the lunch program, Director Iso, a physicist, and Prof. Fumiharu Kato, a mathematician, engaged in a discussion about the future possibilities of mathematics, moderated by Ms. Shinozaki. The event was organized and hosted by Ms. Michibayashi and Mr. Katada from Academist, who helped make the event a success. The event was attended by 414 people, and at one point there were over 250 in the audience.

2025-04-23

Masazumi Honda received "Commendation for Science and Technology: the Young Scientists' Award"

Our colleague Masazumi Honda received "Commendation for Science and Technology: the Young Scientists' Award" in recognition of his outstanding research achievements in the theoretical studies of strong-coupling dynamics in quantum field theories. Congratulations to Masazumi !

2025-04-17

A Century of Quantum Mechanics

Interview with Mathematician Takashi Tsuboi [Part Ⅱ]

Interview with Physicist Yasunori Nomura - Part Ⅳ

Interview with Physicist Yasunori Nomura - Part Ⅲ

Interview with Mathematician Takashi Tsuboi [Part Ⅰ]

Interview with Mathematician Yuto Moriwaki [Part2]

Interview with Mathematician Yuto Moriwaki [Part 1]

Interview with Mathematician Eiji Inoue [Part 2] (in Japanese)

Interview with Physicist Yasunori Nomura - Part Ⅱ

The Connection Between Mathematics and Microbial Research: From Fisheries Science to the Path of Mathematics

Contributed to the 'One Poster per Household' Project – Like the Ones You See in Science Classrooms

Interview with Dr. Misako Tatsuma, a Planetary Formation Theorist

Interview with Mathematician Eiji Inoue [Part 1]

Interview with Physicist Yasunori Nomura - Part I

Interview with Physicist Ryo Namba [Part 2]

Interview with Physicist Ryo Namba [Part 1]

Interview with Ryosuke Iritani, Mathematical Biologist [Part 1]

Theoretical Physicist Tetsuo Hatsuda Interview Vol.2: About Research and Mathematics

Theoretical Physicist Tetsuo Hatsuda Interview Vol.1: About RIKEN iTHEMS

What about climate change in actuality?

Statistical Signatures of Quantum Chaos in Non-Hermitian Systems

Computers as a Playground for Mathematics

The Free Will Theorem in Quantum Mechanics

Renormalization revisited

Renormalization: Awareness of Ignorance

Recipe for soup of quarks and gluons

A subjective view on what is a quantum effect

Mathematical aspects of the entropic uncertainty relation

Forming black holes from stars

Singularity Theorems

Resurgence: making sense out of non-convergent series

How can we use a quantum computer to study the ground state of the hydrogen molecule?

Applications and Extensions of the Nielsen-Ninomiya Theorem in Condensed Matter Physics

COVID-19: then, now, and into the future

Exploring Quantum Spacetime

Classical simulations of quantum computers

When a Cretan says all Cretans are liars

Physical and local observables in gravitational theory

Can you hear the shape of a drum?

Quantum many-body physics with cold atoms

complexity in non-unitary dynamics of photons

Physics Through the Looking Glass

A new B.O.A.T. in astrophysics

Evolution and our daily rhythms

Area law of entanglement entropy in quantum many body systems and its implication in tensor network calculation

Comparison between conventional computers and quantum computers

A glimpse of enumerative geometry

Message-passing algorithms for graphical models

Canonical form of tensor networks in one and two dimensions

The basics of topological band theory

Building something from nothing: a mathematical framework for aperiodic/amorphous sets

Planetary lightning: Current State-of-the-art and outstanding questions

Collective Power of Science ~ from the High-Energy Atmospheric Physics to our New Exploration of the Universe ~

Morse theory and Floer theory

Knot theory and topological semimetals

On Dark Matter