Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken. Here, we consider the possibility that the time evolution governing quantum dynamics may be similarly subject to an instability, at which its unitarity spontaneously breaks down owing to an extreme sensitivity towards perturbations. We find that indeed such an instability exists, and we explore its immediate consequences. Interpretations of the results both in terms of extreme sensitivity to the influence of environmental degrees of freedom, and in terms of a possible fundamental violation of unitarity are discussed.Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken. Here, we consider the possibility that the time evolution governing quantum dynamics may be similarly subject to an instability, at which its unitarity spontaneously breaks down owing to an extreme sensitivity towards perturbations. We find that indeed such an instability exists, and we explore its immediate consequences. Interpretations of the results both in terms of extreme sensitivity to the influence of environmental degrees of freedom, and in terms of a possible fundamental violation of unitarity are discussed.

arXiv:1502.07527Feb 26, 20150 citations

Phase transitions as a manifestation of spontaneous unitarity violation

Jasper van Wezel

Abstract Spontaneous symmetry breaking is well understood under equilibrium conditions as a consequence of the singularity of the thermodynamic limit. How a single global orientation of the order parameter dynamically emerges from an initially symmetric state during a phase transition, however, is not captured by this paradigm. Here, we present a series of symmetry arguments suggesting that singling out a global choice for the ordered state is in fact forbidden under unitary time evolution, even in the presence of an environment and infinitesimal symmetry breaking perturbations. We thus argue that the observation of phase transitions in our everyday world presents a manifestation of the unitarity of quantum dynamics itself being spontaneously broken. We argue that this agrees with the observation that Schrödinger’s time dependent equation is rendered unstable for macroscopic objects owing to the same singular thermodynamic limit that affects equilibrium configurations.Abstract Spontaneous symmetry breaking is well understood under equilibrium conditions as a consequence of the singularity of the thermodynamic limit. How a single global orientation of the order parameter dynamically emerges from an initially symmetric state during a phase transition, however, is not captured by this paradigm. Here, we present a series of symmetry arguments suggesting that singling out a global choice for the ordered state is in fact forbidden under unitary time evolution, even in the presence of an environment and infinitesimal symmetry breaking perturbations. We thus argue that the observation of phase transitions in our everyday world presents a manifestation of the unitarity of quantum dynamics itself being spontaneously broken. We argue that this agrees with the observation that Schrödinger’s time dependent equation is rendered unstable for macroscopic objects owing to the same singular thermodynamic limit that affects equilibrium configurations.

arXiv:2209.04272Journal of Physics A Mathematical and TheoreticalSep 27, 20224 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.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:0807.2368Journal of Physics Conference SeriesMar 1, 20091 citation

An Intrinsic Limit to Quantum Coherence due to Spontaneous Symmetry Breaking

Jasper van Wezel, Jeroen van den Brink, Jan Zaanen

We investigate the influence of spontaneous symmetry breaking on the decoherence of a many-particle quantum system. This decoherence process is analyzed in an exactly solvable model system that is known to be representative of symmetry broken macroscopic systems in equilibrium. It is shown that spontaneous symmetry breaking imposes a fundamental limit to the time that a system can stay quantum coherent. This universal time scale is t(spon) approximately = 2piNH/(kBT), given in terms of the number of microscopic degrees of freedom N, temperature T, and the constants of Planck (h) and Boltzmann (kB).We investigate the influence of spontaneous symmetry breaking on the decoherence of a many-particle quantum system. This decoherence process is analyzed in an exactly solvable model system that is known to be representative of symmetry broken macroscopic systems in equilibrium. It is shown that spontaneous symmetry breaking imposes a fundamental limit to the time that a system can stay quantum coherent. This universal time scale is t(spon) approximately = 2piNH/(kBT), given in terms of the number of microscopic degrees of freedom N, temperature T, and the constants of Planck (h) and Boltzmann (kB).

arXiv:cond-mat/0408357Physical Review LettersJun 13, 200547 citations

Quantum State Reduction of General Initial States through Spontaneous Unitarity Violation

Aritro Mukherjee, Srinivas Gotur, Jelle Aalberts +3 more

The inability of Schrödinger's unitary time evolution to describe the measurement of a quantum state remains a central foundational problem. It was recently suggested that the unitarity of Schrödinger dynamics can be spontaneously broken, resulting in measurement as an emergent phenomenon in the thermodynamic limit. Here, we introduce a family of models for spontaneous unitarity violation that apply to generic initial superpositions over arbitrarily many states, using either single or multiple state-independent stochastic components. Crucially, we show that Born's probability rule emerges spontaneously in all cases.The inability of Schrödinger's unitary time evolution to describe the measurement of a quantum state remains a central foundational problem. It was recently suggested that the unitarity of Schrödinger dynamics can be spontaneously broken, resulting in measurement as an emergent phenomenon in the thermodynamic limit. Here, we introduce a family of models for spontaneous unitarity violation that apply to generic initial superpositions over arbitrarily many states, using either single or multiple state-independent stochastic components. Crucially, we show that Born's probability rule emerges spontaneously in all cases.

arXiv:2301.03233EntropyJan 31, 20248 citations

Nonlocal Quantum Phase Transitions

Alessandro Coppo, Aanal Jayesh Shah, Hadiseh Alaeian +3 more

Phase transitions are paradigmatic examples of emergent phenomena, in which symmetries present at the microscopic level can be spontaneously broken in the thermodynamic limit. Two primary physical mechanisms can drive this symmetry breaking: thermal fluctuations in classical phase transitions and quantum fluctuations in quantum critical phenomena. Here, we introduce $nonlocal$ $quantum$ $fluctuations$ as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations diverges, quantum correlations in the environments govern the system critical behavior. While these correlations manifest locally only as effective thermal fluctuations, at the global level they give rise to an emergent nonlocal phase transition, marked by the spontaneous symmetry breaking of a collective mode shared by the two remote systems.Phase transitions are paradigmatic examples of emergent phenomena, in which symmetries present at the microscopic level can be spontaneously broken in the thermodynamic limit. Two primary physical mechanisms can drive this symmetry breaking: thermal fluctuations in classical phase transitions and quantum fluctuations in quantum critical phenomena. Here, we introduce $nonlocal$ $quantum$ $fluctuations$ as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations diverges, quantum correlations in the environments govern the system critical behavior. While these correlations manifest locally only as effective thermal fluctuations, at the global level they give rise to an emergent nonlocal phase transition, marked by the spontaneous symmetry breaking of a collective mode shared by the two remote systems.

quant-pharXiv:2606.25061Jun 25, 20260 citations

nonlocal

quantum

fluctuations

as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations diverges, quantum correlations in the environments govern the system critical behavior. While these correlations manifest locally only as effective thermal fluctuations, at the global level they give rise to an emergent nonlocal phase transition, marked by the spontaneous symmetry breaking of a collective mode shared by the two remote systems.