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Updated: Jan 8, 2026
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
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No Massless Goldstone Bosons in Hamiltonian Time Crystals
1University of Science and Technology of China, Nordita, Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden and Wilczek Quantum Center, Shanghai Institute for Advanced Studies, Shanghai 201315, China.
Physical Review Letters
|December 19, 2025
Summary
This study introduces a geometric framework for quantum time crystals, revealing how continuous symmetries enable their existence. The research demonstrates that time crystals can circumvent theoretical barriers, offering new insights into quantum many-body physics.
Area of Science:
- Quantum Many-Body Physics
- Quantum Field Theory
- Condensed Matter Physics
Background:
- Quantum time crystals are exotic phases of matter exhibiting periodic behavior without external driving.
- Existing theoretical frameworks face challenges in describing stable quantum time-crystalline order.
- Continuous symmetries and conserved charges are fundamental to understanding quantum phases.
Purpose of the Study:
- To develop a geometric framework for Hamiltonian quantum time crystals.
- To elucidate the role of continuous symmetries and conserved charges in their formation.
- To circumvent existing no-go theorems and enable the study of quantum time-crystalline order.
Main Methods:
- Geometric formulation of quantum time crystals.
- Identification of time crystals as minimum-energy ground states undergoing parallel transport.
- Implementation of time evolution via generalized, time-dependent Bogoliubov transformations.
- Revisiting Goldstone's analysis in the context of time crystals.
Main Results:
- A time crystal is characterized by a ground state parallel transported along Fock spaces.
- Time evolution is realized as a symmetry transformation.
- The Goldstone mode acquires mass and oscillates periodically in Higgs space within a time crystal.
- The proposed framework bypasses theoretical obstacles to quantum time-crystalline order.
Conclusions:
- The geometric framework provides a novel perspective on quantum time crystals.
- Continuous symmetries are crucial for realizing time-crystalline states.
- This work offers new avenues for exploring quantum phenomena in time-dependent systems and their analogies to superconductivity.
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