ncku-talk2023-12-28

Colloquium

DATE 2023-12-28　16:10-17:00

PLACE 數學系館 1F3174教室

SPEAKER 邱聖夫博士（國立清華大學數學系）

TITLE Quantum Speed Limit and Relative Categorical Energy

ABSTRACT Heisenberg's Uncertainty Principle is one of the most celebrated features of quantum mechanics, which states that one cannot simultaneously obtain the precise measurements of two conjugated physical quantities such as the pair of position and momentum or the pair of electric potential and charge density. Among the different formulations of this fundamental quantum property, the uncertainty between energy and time has a special place. This is because the time is rather a variable parametrizing the system evolution than a physical quantity waiting for determination. Physicists working in quantum information theory have understood this energy-time relation by a universal bound of how fast any quantum system with given energy can evolve from one state to another in a distinguishable (orthogonal) way. Recently, there have been many arguing that this bound is not a pure quantum phenomenon but a general dynamical property of Hilbert space. In this talk, in contrast to the usual Hilbert space formalism, we will provide a dual viewpoint of this evolutional speed limit based on a persistence-like distance of the derived category of sheaves : during a fixed time period what is the minimal energy needed for a system to evolve from one sheaf to a status that is distinguishable from a given subcategory? As an application, we will show that such categorical energy with respect to open subsets gives rise to a nontrivial lower bound of Hofer displacement energy.

Colloquium

DATE	2023-12-28　16:10-17:00

PLACE	數學系館 1F3174教室

SPEAKER	邱聖夫博士（國立清華大學數學系）

TITLE	Quantum Speed Limit and Relative Categorical Energy

ABSTRACT	Heisenberg's Uncertainty Principle is one of the most celebrated features of quantum mechanics, which states that one cannot simultaneously obtain the precise measurements of two conjugated physical quantities such as the pair of position and momentum or the pair of electric potential and charge density. Among the different formulations of this fundamental quantum property, the uncertainty between energy and time has a special place. This is because the time is rather a variable parametrizing the system evolution than a physical quantity waiting for determination. Physicists working in quantum information theory have understood this energy-time relation by a universal bound of how fast any quantum system with given energy can evolve from one state to another in a distinguishable (orthogonal) way. Recently, there have been many arguing that this bound is not a pure quantum phenomenon but a general dynamical property of Hilbert space. In this talk, in contrast to the usual Hilbert space formalism, we will provide a dual viewpoint of this evolutional speed limit based on a persistence-like distance of the derived category of sheaves : during a fixed time period what is the minimal energy needed for a system to evolve from one sheaf to a status that is distinguishable from a given subcategory? As an application, we will show that such categorical energy with respect to open subsets gives rise to a nontrivial lower bound of Hofer displacement energy.