We map the quantum problem of a free bosonic field in a space-time dependent background into a classical problem. $N$ degrees of freedom of a real field in the quantum theory are mapped into $2N^2$ classical simple harmonic oscillators with specific initial conditions. We discuss how this classical-quantum correspondence (CQC) may be used to evaluate quantum radiation and fully treat the backreaction of quantum fields on classical backgrounds. The technique has widespread application, including to the quantum evaporation of classical breathers ("oscillons").
We work in the Heisenberg picture to demonstrate the classical-quantum correspondence (CQC) in which the dynamics of a quantum variable is equivalent to that of a complexified classical variable. The correspondence provides a tool for analyzing quantum backreaction problems which we illustrate by a toy model in which a rolling particle slows down due to quantum radiation. The dynamics found using the CQC is in excellent agreement with that found using the much more laborious full quantum analysis.
A recently discovered classical-quantum correspondence (CQC) maps certain quantum problems to corresponding classical problems. We illustrate the CQC for a quantum scalar field in the gravitational background of a collapsing spherical shell. By truncating the problem to a small set of variables, we show how the CQC can yield Hawking radiation as well as the slow down of the collapse due to radiation backreaction.
Derived from semi-classical quantum field theory in curved spacetime, Unruh effect was known as a quantum effect. We find that there does exist a classical correspondence of this effect in electrodynamics. The thermal nature of the vacuum in correlation function for the uniformly accelerated detector is coming from the non-linear relationship between the proper time and the propagating length of the electromagnetic wave. Both the Coulomb field of the detector itself and the radiation supporting the detector's uniformly accelerating motion contribute to the non-vanishing vacuum energy. From thi…
We present an example of the string correspondence: a relation between two classical string solutions - one in Minkowski spacetime and another one in the AdS spacetime. The first solution describes a $2$d motion of the string with massive ends and was derived in (https://doi.org/10.1103/PhysRevD.13.2364). The second solution is the accelerating string solution in the $\textrm{AdS}_3$ spacetime and describes a heavy quark-antiquark pair (arXiv:0804.1343).
We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras $B_N$, $C_N$, $D_N$ to the case of supersymmetric ${\rm gl}(m|n)$ Gaudin models with $m+n=2$. Namely, we show that the spectra of quantum Hamiltonians for all such magnets being identified with the classical particles velocities provide the zero level of the classical action variables.
We discuss the correspondence between the Knizhnik-Zamolodchikov equations associated with $GL(N)$ and the $n$-particle quantum Calogero model in the case when $n$ is not necessarily equal to $N$. This can be viewed as a natural "quantization" of the quantum-classical correspondence between quantum Gaudin and classical Calogero models.
A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers - connections on the projective line with extra structure. In this paper, we describe a deformation of this correspondence for $SL(N)$. We introduce a difference equation version of opers called $q$-opers and prove a $q$-Langlands correspondence between nondegenerate solutions of the Bethe ansatz equations for the XXZ model and nondegenerate twisted $q$-opers with regular singularities on the projective line. We show that the quant…
Embedding Quantum Information into Classical Spacetime: Information Geometrical Perspectives on anti-de Sitter space / conformal field theory Correspondence
We discuss the Matsuo-Cherednik type correspondence between the quantum Knizhnik-Zamolodchikov equations associated with $GL(N)$ and the $n$-particle quantum Ruijsenaars model, with $n$ being not necessarily equal to $N$. The quasiclassical limit of this construction yields the quantum-classical correspondence between the quantum spin chains and the classical Ruijsenaars models.
In this work, a classical-quantum correspondence for two-level pseudo-Hermitian systems is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-Hermitian Hamiltonian if there is a suitable canonical transformation that links it to a real field. We construct a covariant quantization scheme which maps canonically related pseudoclassical theories to unitarily equivalent quantum realizations, such that there is a unique metric-inducing isometry between the distinct Hilbert spaces. In this setting, the pseudo-Hermiticity condition for the operato…
In the Color Glass Condensate(CGC) effective theory, the physics of valence gluons with large longitudinal momentum is reflected in the distribution of color charges in the transverse plane. Averaging over the valence degrees of freedom is effected by integrating over classical color charges with some quasi probability weight functional $W[{\mathbf{j}}]$ whose evolution with rapidity is governed by the JIMWLK equation. In this paper, we reformulate this setup in terms of effective quantum field theory on valence Hilbert space governed by the reduced density matrix $\hatρ$ for hard gluons, whic…
