Related papers: Classical and Quantum Integrability in Laplacian G…
V. Drinfeld proposed conjectures on geometric Langlands correspondence and its quantum deformation. We refine these conjectures and propose their relationship with algebraic conformal field theory.
In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
We study examples where conformal invariance implies rational critical indices, triviality of the underlying quantum field theory and emergence of hypergeometric functions as solutions of the field equations.
New classes of classically integrable models in the cosmological theories with a scalar field are obtained by using freedoms of defining time and fields. In particular, some models with the sum of exponential potentials in the flat spatial…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
A covariant description of the canonical theory for interacting classical fields is developed on a space-like hypersurface. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in…
We consider a stochastic Laplacian growth problem in the framework of normal random matrices. In the large $N$ limit the support of eigenvalues of random matrices is a planar domain with a sharp boundary which evolves under a change in the…
We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the…
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been…
In this paper we present the problem of quantum to classical transition of quantum fluctuations during inflation and in particular the question of evolution of entanglement. After a general introduction, three specific very recent works are…
We scrutize the commonly used criteria for classicality and examine their underlying issues. The two major issues we address here are that of decoherence and fluctuations. We borrow the insights gained in the study of the semiclassical…
We derive the quantum states corresponding to classical scalar fields in the representation expanded by the eigenstates of quantum field operators. This allows us to directly observe the spatial entanglement structure of quantum states and…
With advanced micro- and nano-photonic structures, the vacuum photon-photon coupling rate is anticipated to approach the intrinsic loss rate and lead to unconventional quantum effects. Here, we investigate the classical-to-quantum…
Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
We discuss the behavior of quantum and classical pairwise correlations in critical systems, with the quantumness of the correlations measured by the quantum discord. We analytically derive these correlations for general real density…
The general equations of motion for two dimensional Laplacian growth are derived using the conformal mapping method. In the singular case, all singularities of the conformal map are on the unit circle, and the map is a degenerate…
The relationship between classical and quantum mechanics is usually understood via the limit $\hbar \rightarrow 0$. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…