Related papers: Emergence of Lie group symmetric classical spaceti…
We study the wave function of a tensor model in the canonical formalism by Hamiltonian Monte Carlo method for Lie group symmetric or nearby values for the argument of the wave function, and show that there emerge Lie-group symmetric…
The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent model of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general…
To understand spacetime dynamics in the canonical tensor model of quantum gravity for the positive cosmological constant case, we analytically and numerically study the phase profile of its exact wave function in a coordinate…
It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
In this paper, we investigate the behavior of the Fourier transform on finite dimensional 2-step Lie groups and develop a general theory akin to that of the whole space or the torus. We provide a familiar framework in which computations are…
We show that classicality emerges during quantum phase transitions due to parametric interactions without coupling to environments. The Wigner functions are explicitly calculated for the Gaussian vacuum, number, and thermal states of a free…
A classical phase space with a suitable symplectic structure is constructed together with functions which have Poisson brackets algebraically identical to the Lie algebra structure of the Lie group SU(n). In this phase space we show that…
Recent developments in quantum gravity have shown the Lorentzian treatment to be a fruitful approach towards the emergence of macroscopic spacetimes. In this paper, we discuss another related aspect of the Lorentzian treatment: we argue…
Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference…
Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
Advances in the study of relativistic quantum phase space have established the set of Linear Canonical Transformations (LCTs) as a candidate for the fundamental symmetry group associated with relativistic quantum physics. In this framework,…
We explore the transient dynamics associated with the emergence of the classical signal in the full quantum system. We start our study from the instability which promotes the squeezing of the quantum system. This is often interpreted as the…
We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and…
The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a…
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
We formulate non-relativistic classical and quantum mechanics in the non-commutative two dimensional plane. The approach we use is based on the Galilei group, where the non-commutativity is seen as a central extension upon identification of…
Understanding the emergence of classical behavior from a quantum theory is vital to establishing the quantum origin for the temperature fluctuations observed in the Cosmic Microwave Background (CMB). We show that a real-space approach can…
The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of…