Three Lectures on Complexity and Black Holes

ISBN-13: 9783030451080 / Angielski / Miękka / 2020 / 100 str.

Leonard Susskind

Opis

These three lectures cover a certain aspect of complexity and black holes, namely the relation to the second law of thermodynamics. The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity.

Spis treści

Lecture I: Hilbert Space is Huge

1 Preface

2 How Huge?

3 Volume of CP(N)

4 Relative Complexity

5 Dual Role of Unitaries

6 Volume of SU(2K)

7 Exploring SU(2K)

7.1 Relative Complexity of Unitaries

7.2 Complexity is Discontinuous

8 Graph Theory Perspective

8.1 Collisions and Loops

9 The Second Law of Quantum Complexity

9.1 Hamiltonian Evolution

II Lecture II: Black Holes and the Second Law of Complexity

10 Preface

11 The Black Hole-Quantum Circuit Correspondence

11.1 Two Problems

11.2 Circuits and Black Holes

12 The Growth of Wormholes

12.1 Properties of Growth

12.2 Rindler Time and CV

13 Exponential Time Breakdown of GR

13.1 C=V

14 Precursors

14.1 The Epidemic Model

14.2 Lyapunov and Rindler

15 Precursors and Black Holes

15.1 Instability of White Holes

16 Complexity and Firewalls

16.1 Firewalls are Fragile

16.2 What Happens After Exponential Time?

16.3 The Fragility of Complexity Equilibrium

17 Do Typical States have Firewalls?

17.1 AdS Black Holes

17.2 Evaporating Black Holes

Lecture III: The Thermodynamics of Complexity

18 Preface

19 Negentropy

20 Uncomplexity

20.1 The Auxiliary System

20.2 Combining Auxiliary Systems

21 Uncomplexity as a Resource

22 The Power of One Clean Qubit

22.1 The Protocol

22.2 Expending Uncomplexity and Negentropy

23 Spacetime and Uncomplexity

23.1 CA

23.2 Geometric Interpretation of Uncomplexity

Conclusion

O autorze

Leonard Susskind is an American physicist, who is professor of theoretical physics at Stanford University, and founding director of the Stanford Institute for Theoretical Physics. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology.

He is a member of the US National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study.

Susskind is widely regarded as one of the fathers of string theory. He was the first to give a precise string-theoretic interpretation of the holographic principle in 1995 and the first to introduce the idea of the string theory landscape in 2003.

Susskind was awarded the 1998 J. J. Sakurai Prize, and the 2018 Oskar Klein Medal.