We show that the quantum Jarzynski equality generalizes to $\mathcal{P}\mathcal{T}$ -symmetric quantum mechanics with unbroken $\mathcal{P}\mathcal{T}$ symmetry. In the regime of broken $\mathcal{P}\mathcal{T}$ symmetry, the Jarzynski equality does not hold as also the $\mathcal{C}\mathcal{P}\mathcal{T}$ norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system---two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken $\mathcal{P}\mathcal{T}$ symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.We show that the quantum Jarzynski equality generalizes to $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics with unbroken $\mathcal{P}\mathcal{T}$ symmetry. In the regime of broken $\mathcal{P}\mathcal{T}$ symmetry, the Jarzynski equality does not hold as also the $\mathcal{C}\mathcal{P}\mathcal{T}$ norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system---two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken $\mathcal{P}\mathcal{T}$ symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.

arXiv:1501.06545Physical Review LettersApr 13, 201573 citations

The problem of symmetry in quantum mechanics

H. Weyl

Journal of the Franklin InstituteApr 1, 19293 citations

On the Strangeness of Quantum Mechanics

Marcello Poletti

arXiv:2112.15503Foundations of PhysicsJun 1, 20222 citations

Entanglement of boundary conditions giving rise to spontaneous symmetry breaking in quantum mechanics

A. Restuccia, A. Sotomayor, Vladimir Strauss

We study spontaneous symmetry breaking in one dimensional quantum mechanical problems in terms of two-point boundary problems which lead to singular potentials containing Dirac delta functions and its derivatives. We search for broken-symmetry bound states. For a particular entanglement of boundary conditions, we show the existence of a ground state, giving rise to a spontaneous symmetry breaking, stable under the phenomenon of decoherence generated from external fluctuations. We discuss the model in the context of the "chiral" broken-symmetry states of molecules like $NH_3$ .We study spontaneous symmetry breaking in one dimensional quantum mechanical problems in terms of two-point boundary problems which lead to singular potentials containing Dirac delta functions and its derivatives. We search for broken-symmetry bound states. For a particular entanglement of boundary conditions, we show the existence of a ground state, giving rise to a spontaneous symmetry breaking, stable under the phenomenon of decoherence generated from external fluctuations. We discuss the model in the context of the "chiral" broken-symmetry states of molecules like $NH_3$.

arXiv:1902.05836Feb 15, 20190 citations

We show that the quantum Jarzynski equality generalizes to

\mathcal{P}\mathcal{T}

-symmetric quantum mechanics with unbroken

\mathcal{P}\mathcal{T}

symmetry. In the regime of broken

\mathcal{P}\mathcal{T}

symmetry, the Jarzynski equality does not hold as also the

\mathcal{C}\mathcal{P}\mathcal{T}

norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system---two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken

\mathcal{P}\mathcal{T}

symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.

NH_3