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G. Melkonyan

Publications and source records attributed to G. Melkonyan.

17 recordsLinked to original sources
arXiv2011

Fluctuation Statistics and Diffusive Properties of the 2D Triangular Lorentz Gas in the Finite-Horizon Regime

We study chaotic behavior and diffusion in the 2D periodic Lorentz gas in the finite-horizon regime. The dynamical observable which we consider is the length of single particle's trajectories, which moves in a triangular array of rigid disks. To analyze the chaoticity of this system, we construct a matrix of the length of trajectories and perform a level spacing analysis of the spectrum of this matrix. We find that a universal behavior occurs both in level spacing distribution and spectral rigidity. In order to examine diffusion in this classical system, we investigate the variance of the length of trajectories versus number of collisions to disks. In the case where there is a finite-horizon, such a variance scales linearly with number of bounces. This shows that a normal diffusion exists and a central limit theorem is maintained in this regime.

nlin.CD↗
arXiv2011

Excited States of U(1)$_{2+1}$ Lattice Gauge Theory from Monte Carlo Hamiltonian

We address an old problem in lattice gauge theory - the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. As strategy, we propose to construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution. Then we compute transition amplitudes between stochastic basis states. From a matrix of transition elements we extract energy spectra and wave functions. We apply this method to U(1)$_{2+1}$ lattice gauge theory. We test the method by computing the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian of this theory and compare them with analytical results. We observe a reasonable scaling of energies and wave functions in the variable of time. We also present first results on a small lattice for the full Hamiltonian including the magnetic term.

hep-lat↗
arXiv2007

Universality of Level Spacing Distributions in Classical Chaos

We suggest that random matrix theory applied to a classical action matrix can be used in classical physics to distinguish chaotic from non-chaotic behavior. We consider the 2-D stadium billiard system as well as the 2-D anharmonic and harmonic oscillator. By unfolding of the spectrum of such matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe Poissonian behavior in the integrable case and Wignerian behavior in the chaotic case. We present numerical evidence that the action matrix of the stadium billiard displays GOE behavior and give an explanation for it. The findings present evidence for universality of level fluctuations - known from quantum chaos - also to hold in classical physics.

nlin.CD↗
arXiv2006

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.

hep-th↗
arXiv2004

Alternative Perspective on Quantum Tunneling and Instantons

We present a new way to compute and interpret quantum tunneling in a 1-D 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 1e-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 position 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-instatons have to be taken into account. The quantum action functional is valid in the deep quantum regime in contrast to the semi-classical 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 case is illustrated by an example.

quant-ph↗
arXiv2004

Quantum chaos viewed from quantum action

We consider a mixed chaotic Hamiltonian system and compare classical with quantum chaos. As alternative to the methods of enegy level spacing statistics and trace formulas, we construct a quantum action and a quantum analogue phase space to analyse quantum chaos.

quant-ph↗
arXiv2004

Comparison of classical chaos with quantum chaos

We investigate chaotic behavior in a 2-D Hamiltonian system - oscillators with anharmonic coupling. We compare the classical system with quantum system. Via the quantum action, we construct Poincaré 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 exponts approaching a Gaussian with a strong correlation between its mean value and energy.

quant-ph↗
arXiv2003

Is Quantum Chaos Weaker Than Classical Chaos?

We investigate chaotic behavior in a 2-D Hamiltonian system - oscillators with anharmonic coupling. We compare the classical system with quantum system. Via the quantum action, we construct Poincaré 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 exponts approaching a Gaussian with a strong correlation between its mean value and energy.

quant-ph↗
arXiv2002

Test of Quantum Action for Inverse Square Potential

We present a numerical study of the quantum action previously introduced as a parametrisation of Q.M. transition amplitudes. We address the questions: Is the quantum action possibly an exact parametrisation in the whole range of transition times ($0 < T < \infty$)? Is the presence of potential terms beyond those occuring in the classical potential required? What is the error of the parametrisation estimated from the numerical fit? How about convergence and stability of the fitting method (dependence on grid points, resolution, initial conditions, internal precision etc.)? Further we compare two methods of numerical determination of the quantum action: (i) global fit of the Q.M. transition amplitudes and (ii) flow equation. As model we consider the inverse square potential, for which the Q.M. transition amplitudes are analytically known. We find that the relative error of the parametrisation starts from zero at T=0 increases to about $10^{-3}$ at $T=1/E_{gr}$ and then decreases to zero when $T \to \infty$. Second, we observe stability of the quantum action under variation of the control parameters. Finally, the flow equation method works well in the regime of large $T$ giving stable results under variation of initial data and consistent with the global fit method.

quant-ph↗
arXiv2002

Nonlinear dynamics in quantum physics- the study of quantum chaos

We use the quantum action to study the dynamics of quantum system at finite temperature. We construct the quantum action non-perturbatively and find temperature dependent action parameters. Here we apply the quantum action to study quantum chaos. We present a numerical study of a classically chaotic 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling. We compare Poincaré sections for the quantum action at finite temperature with those of classical action.

quant-ph↗
arXiv2002

Thermodynamics from Monte Carlo Hamiltonian

We construct an effective low-energy Hamiltonian from the classical action via Monte Carlo with importance sampling. We use Monte Carlo (i) to compute matrix elements of the transition amplitude and (ii) to construct stochastically a basis. The MC Hamiltonian allows to obtain energies and wave functions of low-lying states. It allows also to compute thermodynamical observables in some temperature window (starting from temperature zero). We present examples from lattice field theory (Klein-Gordon model).

hep-lat↗
arXiv2001

From Quantum Action to Quantum Chaos

We have recently suggested a quantum action, which has the form of a classical action and takes into account quantum effects via renormalized action parameters. Here we apply it to quantum chaos. We study a system in 2-D with weak anharmonic coupling ($V_{coupl} \propto x^{2}y^{2}$) being classically chaotic. We construct the quantum action at finite temperature. We compute Poincaré sections of the quantum action at that temperature and compare it with those of the classical action. We observe chaotic behavior in both cases.

quant-ph↗
arXiv2001

Quantum Chaos at Finite Temperature - a New Approach via the Quantum Action

We address the problem of quantum chaos: Is there a rigorous, physically meaningful definition of chaos in quantum physics? Can the tools of classical chaos theory, like Lyapunov exponents, Poincaré sections etc. be carried over to quantum systems? Can quantitative predictions be made? We show that the recently proposed quantum action is well suited to answer those questions. As an example we study chaotic behavior of the 2-D anharmonic oscillator and compare classical with quantum chaos. Moreover, we study quantum chaos as function of temperature (the classical system can be considered as the limit where temperature goes to infinity).

quant-ph↗
arXiv2001

Renormalisation in Quantum Mechanics

We study a recently proposed quantum action depending on temperature. We construct a renormalisation group equation describing the flow of action parameters with temperature. At zero temperature the quantum action is obtained analytically and is found free of higher time derivatives. It makes the quantum action an ideal tool to investigate quantum chaos and quantum instantons.

hep-th↗
arXiv2001

Quantum Chaos at Finite Temperature

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 Poincaré sections of the quantum action at finite temperature with those of the classical action.

quant-ph↗