DSpace Collection:http://hdl.handle.net/2289/1442021-05-15T18:13:38Z2021-05-15T18:13:38ZEntanglement entropy of causal set de Sitter horizonsSurya, SumatiX, NomaanYazdi K, Yasamanhttp://hdl.handle.net/2289/77692021-05-15T12:58:50Z2021-06-01T00:00:00ZTitle: Entanglement entropy of causal set de Sitter horizons
Authors: Surya, Sumati; X, Nomaan; Yazdi K, Yasaman
Abstract: de Sitter (dS) cosmological horizons are known to exhibit thermodynamic properties similar to black hole horizons. In this work we study causal set dS horizons, using Sorkin's spacetime entanglement entropy (SSEE) formula, for a conformally coupled quantum scalar field. We calculate the causal set SSEE for the Rindler-like wedge of a symmetric slab of dS spacetime in d = 2, 4 spacetime dimensions using the Sorkin–Johnston vacuum state. We find that the SSEE obeys an area law when the spectrum of the Pauli–Jordan operator is appropriately truncated in both the dS slab as well as its restriction to the Rindler-like wedge. Without this truncation, the SSEE satisfies a volume law. This is in agreement with Sorkin and Yazdi's calculations for the causal set SSEE for nested causal diamonds in ${\mathbb{M}}^{2}$, where they showed that an area law is obtained only after truncating the Pauli–Jordan spectrum. In this work we explore different truncation schemes with the criterion that the SSEE so obtained obeys an area law
Description: Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)2021-06-01T00:00:00ZTopological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger modelVyas, Vivek MRoy, Dibyenduhttp://hdl.handle.net/2289/77532021-04-07T08:25:22Z2021-02-01T00:00:00ZTitle: Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model
Authors: Vyas, Vivek M; Roy, Dibyendu
Abstract: A non-Hermitian generalization of the Su-Schrieffer-Heeger model driven by a periodic external potential is investigated, and its topological features are explored. We find that the bi-orthonormal geometric phase acts as a topological index, well capturing the presence/absence of the zero modes. The model is observed to display trivial and nontrivial insulator phases and a topologically nontrivial Möbius metallic phase. The driving field amplitude is shown to be a control parameter causing topological phase transitions in this model. While the system displays zero modes in the metallic phase apart from the nontrivial insulator phase, the metallic zero modes are not robust, as are the ones found in the insulating phase. We further find that zero modes' energy converges slowly to zero as a function of the number of dimers in the Möbius metallic phase compared to the nontrivial insulating phase.
Description: Open Access2021-02-01T00:00:00ZGravitational Dynamics—A Novel Shift in the Hamiltonian ParadigmAshtekar, AbhayVaradarajan, Madhavanhttp://hdl.handle.net/2289/76822021-02-17T10:07:28Z2021-02-01T00:00:00ZTitle: Gravitational Dynamics—A Novel Shift in the Hamiltonian Paradigm
Authors: Ashtekar, Abhay; Varadarajan, Madhavan
Abstract: It is well known that Einstein’s equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that time evolution of the gravitational field can be re-expressed as (a gauge covariant generalization of) the Lie derivative along a novel shift vector field in spatial directions. Thus, the canonical transformation enerated by the Hamiltonian constraint acquires a geometrical interpretation on the Yang-Mills phase space, similar to that generated by the diffeomorphism constraint. In classical general relativity this geometrical interpretation significantly simplifies calculations and also illuminates the relation between dynamics in the ‘integrable’ (anti)self-dual sector and in the full theory. For quantum gravity, it provides a point of departure to complete the Dirac quantization program for general relativity in a more satisfactory fashion. This gauge theory perspective may also be helpful in extending the ‘double copy’ ideas relating the Einstein and Yang-Mills dynamics to a non-perturbative regime. Finally, the notion of generalized, gauge covariant Lie derivative may also be of interest to the mathematical physics community as it hints at some potentially rich structures that have not been explored.
Description: Open Access2021-02-01T00:00:00ZEntropy and the link action in the causal set path-sumMathur, AbhishekSingh, Anup AnandSurya, Sumatihttp://hdl.handle.net/2289/76612021-02-03T09:24:05Z2021-02-01T00:00:00ZTitle: Entropy and the link action in the causal set path-sum
Authors: Mathur, Abhishek; Singh, Anup Anand; Surya, Sumati
Abstract: In causal set theory the gravitational path integral is replaced by a path-sum over a sample space Ωn of n-element causal sets. The contribution from nonmanifold- like orders dominates Ωn for large n and therefore must be tamed by a suitable action in the low energy limit of the theory. We extend the work of Loomis and Carlip on the contribution of sub-dominant bilayer orders to the causal set path-sum and show that the ‘link action’ suppresses the dominant Kleitman–Rothschild orders for the same range of parameters
Description: Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)2021-02-01T00:00:00Z