Mathematical Theory for Quantum Phase Transitions
Tian Ma, Da-peng Li, Ruikuan Liu, Jiayan Yang
TL;DR
This paper develops a general mathematical model for quantum phase transitions using Hamiltonian and Lagrangian principles, applying it to Bose-Einstein Condensates and analyzing bifurcation solutions to understand quantum state changes.
Contribution
It introduces a novel QPT model based on Hamiltonian and Lagrangian dynamics and applies bifurcation theory to analyze quantum states in BECs.
Findings
Established a general QPT model using PHD and PLD
Derived bifurcation solutions for BEC quantum states
Provided a new mathematical framework for quantum phase transitions
Abstract
Quantum Phase Transition (QPT) is a phase transition between different quantum states by adjusting some control parameters. Based on the Principle of Hamilton Dynamics (PHD) and the Principle of Lagrangian Dynamics (PLD), a general QPT model is established. Also, a definition of QPT is given. The important point is that the QPT model is applied to Bose-Einstein Condensate (BEC) and the corresponding bifurcation solutions (i.e., the quantum states) are obtained by using steady state bifurcation theory.
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Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Quantum, superfluid, helium dynamics · Quantum many-body systems