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H. Kroger

Publications and source records attributed to H. Kroger.

16 recordsLinked to original sources
arXiv2009

Spectrum and Wave Functions of Excited States in Lattice Gauge Theory

We suggest a new method to compute the spectrum and wave functions of excited states. We construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution and compute transition amplitudes between stochastic basis states. From such transition matrix we extract wave functions and the energy spectrum. We apply this method to $U(1)_{2+1}$ lattice gauge theory. As a test we compute the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian and compare it with analytical results. We find excellent agreement. We observe 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↗
arXiv2005

Measure of the path integral in lattice gauge theory

We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in contrast to the calculation of ratios of amplitudes). Single amplitudes are required for computation of the partition function and the free energy. For U(1) lattice gauge theory, we present a numerical simulation of the transition amplitude comparing the path integral with the evolution in terms of the Hamiltonian, showing good agreement.

hep-lat↗
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

What does quantum chaos mean?

We discuss how the concept of the quantum action can be used to characterize quantum chaos. As an example we study quantum mechanics of the inverse square potential in order to test some questions related to quantum action. Quantum chaos is discussed for the 2-D hamiltonian system of harmonic oscillators with anharmonic coupling.

quant-ph↗
arXiv2002

Phonon deficit effect and solid state refrigerators based on superconducting tunnel junctions

Thin film devices have the advantage of being extremely compact, operate in a continuous mode, dissipate little power, and can easily be integrated in cryogenic detectors. Motivated by such possibilities, we investigate the phonon deficit effect in thin film $SIS$ (superconductor--insulator--superconductor) and $SIN$ tunnel junctions. Under certain circumstances, the phonon absorption spectra of such tunnel junctions have spectral windows of phonon absorption/emission. We propose to use phonon filters to select the phonon absorbtion windows and thus to enhance the cooling effect. Membranes attached to such tunnel junctions can be cooled in this way more effectively. We discuss a particular superlattice design of corresponding phonon filters.

cond-mat.supr-con↗
arXiv2001

Algorithm for Computing Excited States in Quantum Theory

Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in the conventional approach, it is extremely difficult to compute the excited states. Here we present a different algorithm: the Monte Carlo Hamiltonian method, designed to overcome the difficulties of the conventional approach. As a new example, application to the Klein-Gordon field theory is shown.

quant-ph↗
arXiv2001

Monte Carlo Hamiltonian: Generalization to Quantum Field Theory

Monte Carlo techniques with importance sampling have been extensively applied to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is extremely difficult to compute the excited states using the conventional Monte Carlo algorithm. Our recently developed approach: the Monte Carlo Hamiltonian method, has been designed to overcome the difficulties of the conventional approach. In this paper, we extend the method to many body systems and quantum field theory. The Klein-Gordon field theory is used as a testing ground.

hep-lat↗
arXiv2000

Hamiltonian lattice QCD at finite chemical potential

At sufficiently high temperature and density, quantum chromodynamics (QCD) is expected to undergo a phase transition from the confined phase to the quark-gluon plasma phase. In the Lagrangian lattice formulation the Monte Carlo method works well for QCD at finite temperature, however, it breaks down at finite chemical potential. We develop a Hamiltonian approach to lattice QCD at finite chemical potential and solve it in the case of free quarks and in the strong coupling limit. At zero temperature, we calculate the vacuum energy, chiral condensate, quark number density and its susceptibility, as well as mass of the pseudoscalar, vector mesons and nucleon. We find that the chiral phase transition is of first order, and the critical chemical potential is $μ_C =m_{dyn}^{(0)}$ (dynamical quark mass at $μ=0$). This is consistent with $μ_C \approx M_N^{(0)}/3$ (where $M_N^{(0)}$ is the nucleon mass at $μ=0$).

hep-lat↗
arXiv1999

Monte Carlo Hamiltonian - From Statistical Physics to Quantum Theory

Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in some areas of application to quantum theories computational progress has been slow. Here we present a recently developed approach: the Monte Carlo Hamiltonian method, designed to overcome the difficulties of the conventional approach.

cond-mat.stat-mech↗
arXiv1995

Measuring the Hausdorff Dimension of Quantum Mechanical Paths

We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving $d_{H}=2$ like the free motion. A velocity dependent action ($S \propto \int dt \mid \vec{v} \mid^α$) in the path integral (e.g. electrons moving in solids, or Brueckner's theory of nuclear matter) yields $d_{H}=\frac{α}{α- 1}$ if $α> 2$ and $d_{H}=2$ if $α\leq 2$. We discuss the relevance of fractal pathes in solid state physics and in $QFT$, in particular for the Wilson loop in $QCD$.

hep-lat↗