Related papers: Quantum Complexity and Negative Curvature
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…
Complexity will be more and more essential in high-energy physics. It is naturally extended into the very early universe. Considering the universe as a quantum chaotic system, the curvature perturbation of the scalar field is identified…
The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space C, but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating "spacetime foam". To improve this situation, we…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
The rate of complexification of a quantum state is conjectured to be bounded from above by the average energy of the state. A different conjecture relates the complexity of a holographic CFT state to the on-shell gravitational action of a…
Building on the recently introduced notion of quantum Ricci curvature and motivated by considerations in nonperturbative quantum gravity, we advocate a new, global observable for curved metric spaces, the curvature profile. It is obtained…
We explore how quantum properties of spacetime, specifically the curvature of momentum space, can backreact on classical gravity within a tractable semiclassical (2+1)-dimensional framework with a negative cosmological constant. Motivated…
As evidenced by a great number of works, it is common practice to assume that the Universe is flat. However, the majority of studies which make use of observational data to constrain the curvature density parameter are premised on the…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
Often, geometries with horizons offer insights into the intricate relationships between general relativity and quantum physics. However, some subtle aspects of gravitating quantum systems might be difficult to ascertain using static…
An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to interpret perceived quantum dynamics as classical. This…
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal,…
We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
Quantum complexity is conjectured to probe inside of black hole horizons (or wormhole) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for generic…