Abstract Particle fluctuations in systems, exhibiting Bose–Einstein condensation, are reviewed in order to clarify the basic points that attract high interest and often confront misunderstanding. It is explained that the so-called ‘grand canonical catastrophe’, claiming the occurrence of catastrophic particle fluctuations in the condensed phase, treated by grand canonical ensemble, does not exist. What exists is the incorrect use of the grand canonical ensemble, where gauge symmetry is not broken, while the correct description of the condensed phase necessarily requires gauge symmetry breaking. The ideal Bose gas has no catastrophic condensate fluctuations, and moreover there are no condensate fluctuations at all, as soon as gauge symmetry is broken. However it does have anomalous fluctuations of uncondensed particles, which implies its instability. For interacting particles, there are no condensate fluctuations, as soon as gauge symmetry is broken, and anomalous fluctuations of uncondensed particles, when correctly calculated, do not appear. Particle fluctuations in the systems of trapped atoms are discussed. Canonical ensemble and grand canonical ensemble with broken gauge symmetry are equivalent with respect to the number of particle scaling.Abstract Particle fluctuations in systems, exhibiting Bose–Einstein condensation, are reviewed in order to clarify the basic points that attract high interest and often confront misunderstanding. It is explained that the so-called ‘grand canonical catastrophe’, claiming the occurrence of catastrophic particle fluctuations in the condensed phase, treated by grand canonical ensemble, does not exist. What exists is the incorrect use of the grand canonical ensemble, where gauge symmetry is not broken, while the correct description of the condensed phase necessarily requires gauge symmetry breaking. The ideal Bose gas has no catastrophic condensate fluctuations, and moreover there are no condensate fluctuations at all, as soon as gauge symmetry is broken. However it does have anomalous fluctuations of uncondensed particles, which implies its instability. For interacting particles, there are no condensate fluctuations, as soon as gauge symmetry is broken, and anomalous fluctuations of uncondensed particles, when correctly calculated, do not appear. Particle fluctuations in the systems of trapped atoms are discussed. Canonical ensemble and grand canonical ensemble with broken gauge symmetry are equivalent with respect to the number of particle scaling.

arXiv:2410.08717Laser PhysicsOct 10, 20249 citations

Fluctuations and Geometry

Springer eBooksJan 1, 20060 citations

Symmetry and the thermodynamics of currents in open quantum systems

Daniel Manzano, Pablo I. Hurtado

Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and statistics in open quantum systems. Such control is enabled by a first-order-type dynamic phase transition in current statistics and the associated coexistence of different transport channels (or nonequilibrium steady states) classified by symmetry. Microreversibility then ensues, via the Gallavotti-Cohen fluctuation theorem, a twin dynamic phase transition for rare current fluctuations. Interestingly, the symmetry present in the initial state is spontaneously broken at the fluctuating level, where the quantum system selects the symmetry sector that maximally facilitates a given fluctuation. We illustrate these results in a qubit network model motivated by the problem of coherent energy harvesting in photosynthetic complexes, and introduce the concept of a symmetry-controlled quantum thermal switch, suggesting symmetry-based design strategies for quantum devices with controllable transport properties.Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and statistics in open quantum systems. Such control is enabled by a first-order-type dynamic phase transition in current statistics and the associated coexistence of different transport channels (or nonequilibrium steady states) classified by symmetry. Microreversibility then ensues, via the Gallavotti-Cohen fluctuation theorem, a twin dynamic phase transition for rare current fluctuations. Interestingly, the symmetry present in the initial state is spontaneously broken at the fluctuating level, where the quantum system selects the symmetry sector that maximally facilitates a given fluctuation. We illustrate these results in a qubit network model motivated by the problem of coherent energy harvesting in photosynthetic complexes, and introduce the concept of a symmetry-controlled quantum thermal switch, suggesting symmetry-based design strategies for quantum devices with controllable transport properties.

arXiv:1310.7370Physical Review BSep 22, 201480 citations

The force of fluctuations

S. Balibar

NatureJan 1, 20083 citations

Information and Symmetry

Springer eBooksMay 10, 20070 citations

Controlled pairing symmetry of the superfluid state in systems of three-component repulsive fermionic atoms in optical lattices

Sei-ichiro Suga

We investigate the pairing symmetry of the superfluid state in repulsively interacting three-component (color) fermionic atoms in optical lattices. When two of the three color-dependent repulsions are much stronger than the other, pairing symmetry is an extended $s$ wave, although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. On the other hand, when two of the three color-dependent repulsions are weaker than the other, pairing symmetry is a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave. This change in pairing symmetry is attributed to the change in the dominant quantum fluctuations from the density fluctuations of unpaired atoms and the color-density wave fluctuations to the color-selective antiferromagnet fluctuations. This phenomenon can be studied using existing experimental techniques.We investigate the pairing symmetry of the superfluid state in repulsively interacting three-component (color) fermionic atoms in optical lattices. When two of the three color-dependent repulsions are much stronger than the other, pairing symmetry is an extended $s$ wave, although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. On the other hand, when two of the three color-dependent repulsions are weaker than the other, pairing symmetry is a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave. This change in pairing symmetry is attributed to the change in the dominant quantum fluctuations from the density fluctuations of unpaired atoms and the color-density wave fluctuations to the color-selective antiferromagnet fluctuations. This phenomenon can be studied using existing experimental techniques.

arXiv:1408.6582Physical Review AAug 12, 20152 citations

s

wave, although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. On the other hand, when two of the three color-dependent repulsions are weaker than the other, pairing symmetry is a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave. This change in pairing symmetry is attributed to the change in the dominant quantum fluctuations from the density fluctuations of unpaired atoms and the color-density wave fluctuations to the color-selective antiferromagnet fluctuations. This phenomenon can be studied using existing experimental techniques.