non-Gaussian Wave Functionals Research Articles

Quantum nature of Wigner function for inflationary tensor perturbations

We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor perturbations. Then we argue that it is no longer an appropriate description for the probability distribution in the sense that quantum nature allows negativity around vanishing phase variables. This comes from the non-Gaussian wavefunction in the mixed state as a result of the non-linear interaction between super- and sub-horizon modes. We also show that this is related to the explicit infrared divergence in the Wigner function, in contrast to the trace of the density matrix.

Dyson–Schwinger Approach to Hamiltonian QCD

Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By means of the DSEs the various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms of the variational kernels of our trial ansatz. Equations of motion for these variational kernels are derived by minimizing the energy density and solved numerically.

Dyson-Schwinger approach to Hamiltonian quantum chromodynamics

The general method for treating non-Gaussian wave functionals in the Hamiltonian formulation of a quantum field theory, which was previously proposed and developed for Yang-Mills theory in Coulomb gauge, is generalized to full QCD. For this purpose the quark part of the QCD vacuum wave functional is expressed in the basis of coherent fermion states, which are defined in terms of Grassmann variables. Our variational Ansatz for the QCD vacuum wave functional is assumed to be given by exponentials of polynomials in the occurring fields and, furthermore, contains an explicit coupling of the quarks to the gluons. Exploiting Dyson-Schwinger equation techniques, we express the various $n$-point functions, which are required for the expectation values of observables like the Hamiltonian, in terms of the variational kernels of our trial Ansatz. Finally, the equations of motion for these variational kernels are derived by minimizing the energy density.

Variational approach to Yang–Mills theory with non-Gaussian wave functionals

A general method for treating non-Gaussian wave functionals in quantum field theory is presented and applied to the Hamiltonian approach to Yang–Mills theory in Coulomb gauge in order to include a three-gluon kernel in the exponential of the vacuum wave functional. The three-gluon and ghost–gluon vertices are calculated using the propagators found in the variational approach with a Gaussian trial wave functional as input.

Study of Concurrence and D-Concurrence on Two-Qubits Resulted in Pair Coherent States in Language of SU(2) Coherent States

Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first terms of this states, one two-qubits formed. Because of the importance of two-qubits in theory of quantum entanglement, with two different measures with the title of concurrence and D-concurrence, we have studied the amount of entanglement and discussed its details. At the end, we describe these measures for pair coherent states as a function of the amplitude of the SU(2) coherent states.

Quantitative measures of entanglement in pair-coherent states

The pair coherent states for a two-mode radiation field are known to belong to a family of states with non-Gaussian wave function. The nature of quantum entanglement between the two modes and some features of non-classicality are studied for such states. The existing criteria for inseparability are examined in the context of pair coherent states.