No Intrinsic Decoherence of Inflationary Cosmological Perturbations

After a brief summary of the four main veins in the treatment of decoherence and quantum to classical transition in cosmology since the 1980s, we focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when it does not rely on any environment. This is what ‘intrinsic’ in the title refers to—a closed quantum system, consisting of a quantum field which drives inflation. The question is whether its quantum perturbations, which interact with the density contrast giving rise to structures in the universe, decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These measures amount to taking only the leading order in the relevant parameters in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrödinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed, it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflation field. All this points to the invariant fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not decohere by themselves.

Dispersion chain of Vlasov equations

On the basis of the Vlasov chain of equations, a new infinite dispersion chain of equations is obtained for the distribution functions of mixed higher order kinematical values. In contrast to the Vlasov chain, the dispersion chain contains distribution functions with an arbitrary set of kinematical values and has a tensor form of writing. For the dispersion chain, new equations for mixed Boltzmann functions and the corresponding chain of conservation laws for fluid dynamics are obtained. The probability is proved to be a constant value for a particle to belong the region where the quasi-probability density is negative (Wigner function).

Ideal Spin Hydrodynamics from the Wigner Function Approach

Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Compared with ideal hydrodynamics without spin, additional terms at the first and second orders in the Knudsen number Kn and the average spin polarization χs have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motion for these parameters are derived by conservation laws at the leading and next-to-leading order Kn and χs .

Covariant chiral kinetic equation in non-Abelian gauge field from “covariant gradient expansion”

We derive the chiral kinetic equation in 8 dimensional phase space in non- Abelian SU(N) gauge field within the Wigner function formalism. By using the “covariant gradient expansion”, we disentangle the Wigner equations in four-vector space up to the first order and find that only the time-like component of the chiral Wigner function is independent while other components can be explicit derivative. After further decomposing the Wigner function or equations in color space, we present the non-Abelian covariant chiral kinetic equation for the color singlet and multiplet phase-space distribution functions. These phase-space distribution functions have non-trivial Lorentz transformation rules when we define them in different reference frames. The chiral anomaly from non-Abelian gauge field arises naturally from the Berry monopole in Euclidian momentum space in the vacuum or Dirac sea contribution. The anomalous currents as non-Abelian counterparts of chiral magnetic effect and chiral vortical effect have also been derived from the non-Abelian chiral kinetic equation.

Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians

The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems described by a quadratic Hamiltonian are obtained. This is done by using the covariance matrix of the mentioned states. The area of the Wigner function and the width of the tomogram of quantum systems are proposed to define a temperature scale for this type of states. This proposal is then confirmed for the general one-dimensional case and for a system of two coupled harmonic oscillators. The use of these properties as measures for the temperature of quantum systems is mentioned.

Wigner-function-based solution schemes for electromagnetic wave beams in fluctuating media

Electromagnetic waves are described by Maxwell’s equations together with the constitutive equation of the considered medium. The latter equation in general may introduce complicated operators. As an example, for electron cyclotron (EC) waves in a hot plasma, an integral operator is present. Moreover, the wavelength and computational domain may differ by orders of magnitude making a direct numerical solution unfeasible, with the available numerical techniques. On the other hand, given the scale separation between the free-space wavelength $$\lambda _0$$ λ 0 and the scale L of the medium inhomogeneity, an asymptotic solution for a wave beam can be constructed in the limit $$\kappa = 2\pi L / \lambda _0 \rightarrow \infty$$ κ = 2 π L / λ 0 → ∞ , which is referred to as the semiclassical limit. One example is the paraxial Wentzel-Kramer-Brillouin (pWKB) approximation. However, the semiclassical limit of the wave field may be inaccurate when random short-scale fluctuations of the medium are present. A phase-space description based on the statistically averaged Wigner function may solve this problem. The Wigner function in the semiclassical limit is determined by the wave kinetic equation (WKE), derived from Maxwell’s equations. We present a paraxial expansion of the Wigner function around the central ray and derive a set of ordinary differential equations (phase-space beam-tracing equations) for the Gaussian beam width along the central ray trajectory.