اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDomain structures in quantum graphity
128
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Quantum graphity offers the intriguing notion that space emerges in the low energy states of the spatial degrees of freedom of a dynamical lattice. Here we investigate metastable domain structures which are likely to exist in the low energy phase of lattice evolution. Through an annealing process we explore the formation of metastable defects at domain boundaries and the effects of domain structures on the propagation of bosons. We show that these structures should have observable background independent consequences including scattering, double imaging, and gravitational lensing-like effects.
قيم البحث
اقرأ أيضاً
Quantum Graphity (QG) is a model of emergent geometry in which space is represented by a dynamical graph. The graph evolves under the action of a Hamiltonian from a high-energy pre-geometric state to a low-energy state in which geometry emerges as a
coarse-grained effective property of space. Here we show the results of numerical modelling of the evolution of the QG Hamiltonian, a process we term ripening by analogy with crystallographic growth. We find that the model as originally presented favours a graph composed of small disjoint subgraphs. Such a disconnected space is a poor representation of our universe. A new term is introduced to the original QG Hamiltonian, which we call the hypervalence term. It is shown that the inclusion of a hypervalence term causes a connected lattice-like graph to be favoured over small isolated subgraphs.
We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In t
his approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This proper time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in the companion work Symplectic quantization II.
Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such
an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional {em polymer} quantum systems: an ensemble of oscillators that describe a solid and a bunch of non-interacting particles in a box, which thus form an ideal gas. We first study the spectra of these polymer systems. It turns out useful for the analysis to consider the length scale required by the quantization and which we shall refer to as polymer length. The dynamics of the polymer oscillator can be given the form of that for the standard quantum pendulum. Depending on the dominance of the polymer length we can distinguish two regimes: vibrational and rotational. The first occur for small polymer length and here the standard oscillator in Schrodinger quantization is recovered at leading order. The second one, for large polymer length, features dominant polymer effects. In the case of the polymer particles in the box, a bounded and oscillating spectrum that presents a band structure and a Brillouin zone is found. The thermodynamical quantities calculated with these spectra have corrections with respect to standard ones and they depend on the polymer length. For generic polymer length, thermodynamics of both systems present an anomalous peak in their heat capacity $C_V$.
We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the R{e}nyi entropy of such states and recover the Ryu-Takayanagi for
mula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.
The symplectic quantization scheme proposed for matter scalar fields in the companion paper Symplectic quantization I is generalized here to the case of space-time quantum fluctuations. Symplectic quantization considers an explicit dependence of the
metric tensor $g_{mu u}$ on an additional time variable, named proper time at variance with the coordinate time of relativity. The physical meaning of proper time is to label the sequence of $g_{mu u}$ quantum fluctuations at a given point of the four-dimensional space-time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative $dot{g}_{mu u}$ of the metric field with respect to proper time, corresponding to the conjugated momentum $pi_{mu u}$. Symplectic quantization describes the quantum fluctuations of gravity by means of the symplectic dynamics generated by a generalized action functional $mathcal{A}[g_{mu u},pi_{mu u}] = mathcal{K}[g_{mu u},pi_{mu u}] - S[g_{mu u}]$, playing formally the role of a Hamilton function, where $S[g_{mu u}]$ is the Einstein-Hilbert action and $mathcal{K}[g_{mu u},pi_{mu u}]$ is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define a pseudo-microcanonical ensemble for the quantum fluctuations of $g_{mu u}$, built on the conservation of the generalized action $mathcal{A}[g_{mu u},pi_{mu u}]$ rather than of energy. $S[g_{mu u}]$ plays the role of a potential term along the symplectic action-preserving dynamics: its fluctuations are the quantum fluctuations of $g_{mu u}$. It is shown how symplectic quantization maps to the path-integral approach to gravity. By doing so we explain how the integration over the conjugated momentum field $pi_{mu u}$ gives rise to a cosmological constant term in the path-integral.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
