Integrability and chemical potential in the (3 + 1)-dimensional Skyrme model

Alvarez, Pedro D.; Canfora, Fabrizio; Dimakis, N.; Paliathanasis, Andronikos

doi:10.1016/j.physletb.2017.08.073

Cited by 50 publications

(105 citation statements)

References 69 publications

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“…where H ∈ [0, π/2], while A ∈ [0, 2πk 1 ], G ∈ [0, 2πk 2 ] are both periodic Killing coordinates of S 3 , with k 1 and k 2 positive integers (there is clearly some redundancy in this choice of the periodicities -the standard choice k 1 = k 2 = 1 already covers the whole S 3 -but this will become physically meaningful later on). In [19] and [25] it has been shown that similar parametrizations are extremely useful both in curved and in flat spaces. The tensor S µν (11) takes the form…”

Section: The Actionmentioning

confidence: 99%

“…However, the recent generalization of the boson star ansatz to SU (2)-valued scalar fields (introduced in [12][13][14][15][16][17][18][19][20][21][22] and [23][24][25]) allows to construct also non-trivial gravitating soliton solutions (see in particular [13] and [19]) as well as to analyse explicitly thermodynamic properties of solitons (see [25]).…”

Section: Introductionmentioning

confidence: 99%

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Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear σ-model system

et al. 2018

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An exact hairy asymptotically locally AdS black hole solution with a flat horizon in the Einsteinnonlinear sigma model system in (3+1) dimensions is constructed. The ansatz for the nonlinear SU (2) field is regular everywhere and depends explicitly on Killing coordinates, but in such a way that its energy-momentum tensor is compatible with a metric with Killing fields. The solution is characterized by a discrete parameter which has neither topological nor Noether charge associated with it and therefore represents a hair. A U (1) gauge field interacting with Einstein gravity can also be included. The thermodynamics is analyzed. Interestingly, the hairy black hole is always thermodynamically favored with respect to the corresponding black hole with vanishing Pionic

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Section: The Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear σ-model system

et al. 2018

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“…Time crystals are quantum systems where a crystalline structure emerges in time with no initial crystalline structure in space [1][2][3][4][5] (for the classical version of time crystals, including topologically protected systems, see [6][7][8][9][10][11]). A crystalline structure in time is related to the periodic dynamics of a system.…”

Section: Introductionmentioning

confidence: 99%

Topological time crystals

et al. 2019

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By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system. 5 Note that due to the negative effective mass m eff , the first energy band is the highest in energy. 2 New J. Phys. 21 (2019) 052003 where = ¢ J J i 2and J 2i−1 =J, which is identical to the SSH model [86]. The latter describes spinless fermions hopping on a 1D-lattice with staggered hopping amplitudes. Changing the ratio λ 1 /λ in (1), allows one to control the ratio ¢ J J . This effective Hamiltonian belongs to the BDI class of the periodic table of the topological insulators and superconductors [87] and is characterized by a  topological invariant, the winding number ν. For an infinite system with ¢ > J J ( ¢ < J J ), the system is in a topological (trivial) phase with winding number ν=1 (ν=0). For a finite system, the topological phase exhibits zero energy edge states protected by the topology of the bulk. The SSH model has been experimentally realized in quantum simulators and both the presence of edge states and the winding number have been measured [63][64][65]. Let us emphasize that the Wannier states w i (x, t) of equation (2) are localized wavepackets of the effective SSH Hamiltonian of equation (3). We then discuss how such states allow one to detect the topology of the SSH Hamiltonian. corresponding to quasi-energies closest to zero, see top panel. In the topological phase, these eigenstates have zero quasi-energy and are linear combinations of the edge states localized at the edge of time. That is, in the laboratory frame, a detector is placed close to the oscillating mirror (x≈0) and the probability density of clicking of the detector is shown versus time for different values of the ratio ¢ J J of the tunneling amplitudes in (3). This behavior is repeated with the period 2π/ω. At sωt/(2π)=1 and sωt/(2π)=40 there are edges where the eigenstate localizes if ¢ > J J 1. The results correspond to ω=0.067, λ=0.06 in (1) and are obtained within the quantum secular approach [84], see the appendix.

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“…For instance, in the Skyrme model in flat spaces, it was well known that if one includes a too large isospin chemical potential then the Skyrmion becomes unstable. However, only very recently in[34] it was derived an analytic formula for this critical chemical potential.…”

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confidence: 99%

Spherical Skyrmion black holes as gravitational lenses

2018

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In this article, we extend the strong deflection limit to calculate the deflection angle for a class of geometries which are asymptotically locally flat. In particular, we study the deflection of light in the surroundings of spherical black holes in Einstein-Skyrme theory. We find the deflection angle in this limit, from which we obtain the positions and the magnifications of the relativistic images. We compare our results with those corresponding to the Schwarzschild and the global monopole (Barriola-Vilenkin) spacetimes.

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Integrability and chemical potential in the (3 + 1)-dimensional Skyrme model

Cited by 50 publications

References 69 publications

Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear σ-model system

Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear σ-model system

Topological time crystals

Spherical Skyrmion black holes as gravitational lenses

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