Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1205.4773 · American Journal of Physics

Spontaneous symmetry breakdown in non-relativistic quantum mechanics

Rodrigo Muñoz-Vega, Alberto García-Quiroz, Ernesto López-Chávez, E. Salinas-Hernández

Published Sep 18, 2012• 2 citations
arXivHTMLPDF

Abstract

The advantages and disadvantages of some pedagogical non-relativistic quantum-mechanical models, used to illustrate spontaneous symmetry breakdown, are discussed. A spinor on the line subject to a magnetostatic interaction is presented as a toy model of the spontaneous breakdown of an internal symmetry.
DOI
10.1119/1.4739927

Related papers

Simple models exhibiting spontaneous symmetry breakdown in classical and non-relativistic quantum mechanics

Rodrigo Muñoz-Vega, Alberto García-Quiroz, Ernesto López-Chávez +1 more

First, the properties of a classical model of spontaneous symmetry breakdown are analyzed. Then, the pros and cons of some pedagogical non-relativistic quantum-mechanical models, also used to illustrate spontaneous symmetry breakdown, are discussed. Finally, a simple quantum-mechanical toy model (a spinor on the line, with a spin-dependent interaction) is presented, that exhibits the spontaneous breaking of an internal symmetry.

arXiv:1111.1213•Nov 4, 2011•0 citations

Observing the spontaneous breakdown of unitarity

Jasper van Wezel

During the past decade, the experimental development of being able to create ever larger and heavier quantum superpositions has brought the discussion of the connection between microscopic quantum mechanics and macroscopic classical physics back to the forefront of physical research. Under equilibrium conditions this connection is in fact well understood in terms of the mechanism of spontaneous symmetry breaking, while the emergence of classical dynamics can be described within an ensemble averaged description in terms of decoherence. The remaining realm of individual-state quantum dynamics in the thermodynamic limit was addressed in a recent paper proposing that the unitarity of quantum mechanical time evolution in macroscopic objects may be susceptible to a spontaneous breakdown. Here we will discuss the implications of this theory of spontaneous unitarity breaking for the modern experiments involving truly macroscopic Schrodinger cat states.

arXiv:0807.2368•Journal of Physics Conference Series•Mar 1, 2009•1 citation

Spontaneous symmetry breaking in spinor Bose-Einstein condensates

M. Scherer, B. Lücke, J. Peise +7 more

We present an analytical model for the theoretical analysis of spin dynamics and spontaneous symmetry breaking in a spinor Bose-Einstein condensate (BEC). This allows for an excellent intuitive understanding of the processes and provides good quantitative agreement with the experimental results of Scherer et al. [Phys. Rev. Lett. 105, 135302 (2010)]. It is shown that the dynamics of a spinor BEC initially prepared in an unstable Zeeman state ${m}_{F}=0$ ($\left|0\right\ensuremath{\rangle}$) can be understood by approximating the effective trapping potential for the state $\left|\ifmmode\pm\else\textpm\fi{}1\right\ensuremath{\rangle}$ with a cylindrical box potential. The resonances in the creation efficiency of these atom pairs can be traced back to excitation modes of this confinement. The understanding of these excitation modes allows for a detailed characterization of the symmetry-breaking mechanism, showing how a twofold spontaneous breaking of spatial and spin symmetry can occur. In addition, a detailed account of the experimental methods for the preparation and analysis of spinor quantum gases is given.

arXiv:1309.0424•Physical Review A•Nov 19, 2013•14 citations

Breakdown of agreement between non-relativistic and relativistic quantum dynamical predictions in the non-relativistic regime

Boon Leong Lan, Mehdi Pourzand, Rui Jian Chu

To study quantum dynamics in the non-relativistic regime, the standard practice is to use non-relativistic quantum mechanics, instead of the relativistic theory, because it is thought the approximate non-relativistic result is always close to the relativistic one. Here we present a theoretical argument that this expectation is not true in general. In addition, supporting numerical evidence for the free rotor and hydrogen atom also shows the agreement between the two theories can break down quickly. For the radial Rydberg wave packet in hydrogen atom, the breakdown can occur before spontaneous emission and thus could be tested experimentally. Our surprising result shows relativistic quantum mechanics must be used, instead of the approximate non-relativistic theory, to correctly study quantum dynamics in the non-relativistic regime after the breakdown time. This paradigm shift opens a new avenue of research in a wide range of fields from atomic to molecular, chemical and condensed-matter physics.

arXiv:1808.10096•Results in Physics•Nov 17, 2018•2 citations

Precision tests of models of spontaneous wave function collapse

Angelo Bassi

Quantum mechanics is grounded on the superposition principle, which is the source both of its tremendous success and technological power, as well as of the problems in understanding it. The reason why superpositions do not propagate from the microscopic to the macroscopic world are subject to debate. Spontaneous wave function collapse models have been formulated to take into account a progressive breakdown of quantum superpositions when systems are large enough; they do so by modifying the Schrödinger dynamics, and therefore they are empirically testable. Deviations are tiny, and require precision measurements. I will review collapse models, and present the most recent experimental tests.

Optical and Quantum Sensing and Precision Metrology II•Mar 8, 2023•0 citations

Spontaneous Supersymmetry Breaking and Nambu-Goldstone Modes in Interacting Majorana Chains

Noriaki Sannomiya

In modern physics, spontaneous symmetry breaking is one of the most important and ubiquitous ideas. It is well known that the breakdown of global and continuous symmetry gives rise to gapless excitations called Nambu-Goldstone (NG) bosons. This is called NG theorem. Since the generators of broken symmetries are bosonic, the excitations are also bosons. On the other hand, excitations are thought of as fermionic when a generator of broken symmetry is fermionic. The most famous example of fermionic symmetry is supersymmetry (SUSY). SUSY is a symmetry that exchanges bosons and fermions. In high-energy physics, it is known that spontaneous SUSY breaking gives rise to massless modes called NG fermions or Nambu- Goldstinos. In non-relativistic systems, fewer examples of models with SUSY are studied. Therefore, spontaneous SUSY breaking in non-relativistic systems is less understood than that in nonrelativistic systems or spontaneous symmetry breaking. In this thesis, we introduce interacting Majorana models with supersymmetry (SUSY) and discuss the properties in terms of spontaneous SUSY breaking and NG modes.

arXiv:2401.07419•Jan 15, 2024•1 citation
During the past decade, the experimental development of being able to create ever larger and heavier quantum superpositions has brought the discussion of the connection between microscopic quantum mechanics and macroscopic classical physics back to the forefront of physical research. Under equilibrium conditions this connection is in fact well understood in terms of the mechanism of spontaneous symmetry breaking, while the emergence of classical dynamics can be described within an ensemble averaged description in terms of decoherence. The remaining realm of individual-state quantum dynamics in the thermodynamic limit was addressed in a recent paper proposing that the unitarity of quantum mechanical time evolution in macroscopic objects may be susceptible to a spontaneous breakdown. Here we will discuss the implications of this theory of spontaneous unitarity breaking for the modern experiments involving truly macroscopic Schrodinger cat states.
We present an analytical model for the theoretical analysis of spin dynamics and spontaneous symmetry breaking in a spinor Bose-Einstein condensate (BEC). This allows for an excellent intuitive understanding of the processes and provides good quantitative agreement with the experimental results of Scherer et al. [Phys. Rev. Lett. 105, 135302 (2010)]. It is shown that the dynamics of a spinor BEC initially prepared in an unstable Zeeman state mF=0{m}_{F}=0mF​=0 ($\left|0\right\ensuremath{\rangle}$) can be understood by approximating the effective trapping potential for the state $\left|\ifmmode\pm\else\textpm\fi{}1\right\ensuremath{\rangle}$ with a cylindrical box potential. The resonances in the creation efficiency of these atom pairs can be traced back to excitation modes of this confinement. The understanding of these excitation modes allows for a detailed characterization of the symmetry-breaking mechanism, showing how a twofold spontaneous breaking of spatial and spin symmetry can occur. In addition, a detailed account of the experimental methods for the preparation and analysis of spinor quantum gases is given.
To study quantum dynamics in the non-relativistic regime, the standard practice is to use non-relativistic quantum mechanics, instead of the relativistic theory, because it is thought the approximate non-relativistic result is always close to the relativistic one. Here we present a theoretical argument that this expectation is not true in general. In addition, supporting numerical evidence for the free rotor and hydrogen atom also shows the agreement between the two theories can break down quickly. For the radial Rydberg wave packet in hydrogen atom, the breakdown can occur before spontaneous emission and thus could be tested experimentally. Our surprising result shows relativistic quantum mechanics must be used, instead of the approximate non-relativistic theory, to correctly study quantum dynamics in the non-relativistic regime after the breakdown time. This paradigm shift opens a new avenue of research in a wide range of fields from atomic to molecular, chemical and condensed-matter physics.
Quantum mechanics is grounded on the superposition principle, which is the source both of its tremendous success and technological power, as well as of the problems in understanding it. The reason why superpositions do not propagate from the microscopic to the macroscopic world are subject to debate. Spontaneous wave function collapse models have been formulated to take into account a progressive breakdown of quantum superpositions when systems are large enough; they do so by modifying the Schrödinger dynamics, and therefore they are empirically testable. Deviations are tiny, and require precision measurements. I will review collapse models, and present the most recent experimental tests.
In modern physics, spontaneous symmetry breaking is one of the most important and ubiquitous ideas. It is well known that the breakdown of global and continuous symmetry gives rise to gapless excitations called Nambu-Goldstone (NG) bosons. This is called NG theorem. Since the generators of broken symmetries are bosonic, the excitations are also bosons. On the other hand, excitations are thought of as fermionic when a generator of broken symmetry is fermionic. The most famous example of fermionic symmetry is supersymmetry (SUSY). SUSY is a symmetry that exchanges bosons and fermions. In high-energy physics, it is known that spontaneous SUSY breaking gives rise to massless modes called NG fermions or Nambu- Goldstinos. In non-relativistic systems, fewer examples of models with SUSY are studied. Therefore, spontaneous SUSY breaking in non-relativistic systems is less understood than that in nonrelativistic systems or spontaneous symmetry breaking. In this thesis, we introduce interacting Majorana models with supersymmetry (SUSY) and discuss the properties in terms of spontaneous SUSY breaking and NG modes.