Cosmological time crystal: Cyclic universe with a small cosmological constant in a toy model approach

Das, Praloy; Pan, Supriya; Ghosh, Subir; Pal, Partha Sarathi

doi:10.1103/physrevd.98.024004

Cited by 35 publications

(32 citation statements)

References 46 publications

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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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Section: Introductionmentioning

confidence: 99%

Topological time crystals

et al. 2019

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“…So, in this case, the gravitational waves do not affect the BBN success. Moreover, for the value m χ = 5 × 10 −4 M pl one obtains the bound 6 × 10 −11 ≤ h ≤ 10 −10 , and for these values, taking g * = 107, the reheating temperature (27) is around 240 TeV.…”

Section: Bbn Constraints From the Logarithmic Spectrum Of Gwsmentioning

confidence: 79%

Reheating in quintessential inflation via gravitational production of heavy massive particles: a detailed analysis

Haro

Yang

Pan

2019

J. Cosmol. Astropart. Phys.

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An improved version of the well-known Peebles-Vilenkin model unifying early inflationary era to current cosmic acceleration, is introduced in order to match with the theoretical values of the spectral quantities provided by it with the recent observational data about the early universe.Since the model presents a sudden phase transition, we consider the simplest way to reheat the universe − via the gravitational production of heavy massive particles − which assuming that inflation starts at GUT scales ∼ 10 16 GeV, allows us to use the Wentzel-Kramers-Brillouin (WKB) approximation and consequently this enables us to perform all the calculations in an analytic way.Our results show that the model leads to a maximum temperature at the TeV regime, and passes the bounds to ensure the success of the Big Bang Nucleosynthesis. Finally, we have constrained the quintessence piece of the proposed improved version of the Peebles-Vilenkin model using various astronomical datasets available at present. *

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“…Regarding the extended phase space, it is worth mentioning that recent developments involving the nature of time crystals [24][25][26][27][28][29], in which the time-translation symmetry is spontaneously broken, suggest that the extended phase space formalism might be considered as the natural arena to study these phenomena, since, in this extended phase space, the time reparametrization invariance is explicit. Additionally, other recent results in the study of quantum speed limits [30][31][32] suggest that the extended phase space can be used to explore these limits in the context of the path integral formalism.…”

Section: Introductionmentioning

confidence: 99%

Dirac’s Formalism for Time-Dependent Hamiltonian Systems in the Extended Phase Space

2021

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Dirac’s formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant, and we calculate the Feynman propagator using the extended phase space description. We show that the Feynman propagator’s quantum phase is given by the boundary term of the canonical transformation of the extended phase space. We propose a new canonical transformation within the extended phase space that leads to a Lewis invariant generalization, and we sketch some possible applications.

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Cosmological time crystal: Cyclic universe with a small cosmological constant in a toy model approach

Cited by 35 publications

References 46 publications

Topological time crystals

Topological time crystals

Reheating in quintessential inflation via gravitational production of heavy massive particles: a detailed analysis

Dirac’s Formalism for Time-Dependent Hamiltonian Systems in the Extended Phase Space

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