G. Melkonyan

Quantum chaos at finite temperature

Abstract We use the quantum action to study quantum chaos at finite temperature. We present a numerical study of a classically chaotic 2-D Hamiltonian system — harmonic oscillators with anharmonic coupling. We construct the quantum action non-perturbatively and find temperature-dependent quantum corrections in the action parameters. We compare Poincare sections of the quantum action at finite temperature with those of the classical action.

Renormalisation in quantum mechanics

We study a recently proposed quantum action depending on temperature. At zero temperature the quantum action is obtained analytically and reproduces the exact ground state energy and wave function. This is demonstrated for a number of cases with parity symmetric confining potentials. In the case of the hydrogen atom, it also reproduces exactly energy and wave function of a subset of excited state (those of lowest energy for given angular momentum l) and the quantum action is consistent with O(4) symmetry. In the case of a double-well potential, the quantum action generates the ground state of double-hump shape. In all cases we observe a coincidence (in position) of minima of the quantum potential with maxima of the wave function. The semi-classical WKB formula for the ground state wave function becomes exact after replacing the parameters of the classical action by those of quantum action.

Is quantum chaos weaker than classical chaos

Abstract We investigate chaotic behavior in a 2D Hamiltonian system—oscillators with anharmonic coupling. We compare the classical system with quantum system. Via the quantum action, we construct Poincare sections and compute Lyapunov exponents for the quantum system. We find that the quantum system is globally less chaotic than the classical system. We also observe with increasing energy the distribution of Lyapunov exponents approaching a Gaussian with a strong correlation between its mean value and energy.

Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?

We discuss the questions: How to compare quantitatively classical chaos with quantum chaos? Which one is stronger? What are the underlying physical reasons?

Comparison of classical chaos with quantum chaos

We investigate chaotic behaviour in a 2D Hamiltonian system—oscillators with anharmonic coupling. We compare the classical system with the quantum system. Via the quantum action, we construct Poincare sections and compute Lyapunov exponents for the quantum system. We find that the quantum system is globally less chaotic than the classical system. We also observe with increasing energy the distribution of Lyapunov exponents approaching a Gaussian with a strong correlation between its mean value and energy.

Test of quantum action for the inverse square potential

We compute numerically the quantum action for the inverse square potential and compare the global fit method with a new method, the flow equation. We investigate the error of fitting quantum-mechanical transition amplitudes by the quantum action. The flow equation works well in the regime of large T giving results consistent with the global fit method.

Stationary Points of Scalar Fields Coupled to Gravity

We investigate the dynamics of gravity coupled to a scalar field using a non-canonical form of the kinetic term. It is shown that its singular point represents an attractor for classical solutions and the stationary value of the field may occur distant from the minimum of the potential. In this paper properties of universes with such stationary states are considered. We reveal that such state can be responsible for modern dark energy density.

Alternative perspective on quantum tunneling and instantons

We present an alternative way to compute and interpret quantum tunneling in a one-dimensional double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been confirmed by numerical simulations giving relative errors in the order of 10{sup -5}. In contrast to the classical potential, the quantum potential has a triple well if the classical wells are deep enough. Its minima are located at the positions of extrema of the ground state wave function. The striking feature is that a single trajectory with a double instanton reproduces the tunneling amplitude. This is in contrast to the standard instanton approach, where infinitely many instantons and anti-instantons have to be taken into account. The quantum action functional is valid in the deep quantum regime in contrast to the semiclassical regime where the standard instanton approach holds. We compare both approaches via numerical simulations. While the standard instanton picture describes only the transition between potential minima of equal depth, the quantum action may give rise to instantons also for asymmetric potential minima. Such a case is illustrated by an example.