Related papers: Spacetime Density Matrix: Formalism and Properties
We consider quantum quench in large-N singlet sector quantum mechanics of a single hermitian matrix in the double scaling limit. The time dependent parameter is the self-coupling of the matrix. We find exact classical solutions of the…
Direct numerical evaluation of the real-time path integral has a well-known sign problem that makes convergence exponentially slow. One promising remedy is to use Picard-Lefschetz theory to flow the domain of the field variables into the…
We present a general construction of two types of differential forms, based on any $(n{-}3)$-dimensional subspace in the kinematic space of $n$ massless particles. The first type is the so-called projective, scattering forms in kinematic…
An approximate statistical description of the formation and evolution of structure of the universe based on the Zel'dovich theory of gravitational instability is proposed. It is found that the evolution of DM structure shows features of…
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…
In the framework of formal deformation quantization, we apply our formal moment map construction on the space of almost complex structures to recover the Donaldson-Fujiki moment map picture of the Hermitian scalar curvature. In the…
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. We prove that given initial data on a maximal compact spacelike hypersurface $\Sigma \simeq \overline{B(0,1)} \subset \mathbb{R}^3$ and…
The mapping of time-dependent densities on potentials in quantum mechanics is critically examined. The issue is of significance ever since Runge and Gross (Phys. Rev. Lett. 52, 997 (1984)) established the uniqueness of the mapping, forming…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…
The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug…
An intrinsic time in Geometrodynamics is obtained with using a scaled Dirac's mapping. By addition of a background metric, one can construct a scalar field. It is suitable to play a role of intrinsic time. Cauchy problem was successfully…
We develop analytical and numerical methods for the matrix thermofield in the large $N$ limit. Through the double collective representation on the Schwinger-Keldysh contour, it provides thermodynamical properties and finite temperature…
This work constitutes the second part of a series of studies that aim to utilise tools from Hamiltonian mechanics to investigate the motion of an extended body in general relativity. The first part of this work [Refs. [1, 2]] constructed a…
The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that representing instead the $\mathit{logarithm}$ of the density…
Complex metrics are a double-edged sword: they allow one to replace singular spacetimes, such as those containing a big bang, with regular metrics, yet they can also describe unphysical solutions in which quantum transitions may be more…
In stochastic quantization, ordinary 4-dimensional Euclidean quantum field theory is expressed as a functional integral over fields in 5 dimensions with a fictitious 5th time. This is advantageous, in particular for gauge theories, because…
We introduce a witness-based framework for certifying quantum temporal correlations via the pseudo-density matrix (PDM) formalism, which is a spatiotemporal generalization of the density matrix. We define spatial incompatibility (SI) as the…
We formulate a stochastic generalisation of the Schwinger effect, extending pair production to statistically fluctuating gauge-field backgrounds. Our approach captures realistic field configurations that are transient, inhomogeneous, and…
Motivated by the Hawking-King-McCarthy-Malament (HKMM) theorem and the associated reconstruction of spacetime geometry from its causal structure $(M,\prec)$ and local volume element $\epsilon$, we define a one-parameter family of spatial…