arXiv subjects

Bernd A. Berg

Publications and source records attributed to Bernd A. Berg.

At least 73 records · Page 4Linked to original sources

arXiv2001

Multi-overlap simulations of spin glasses

We present results of recent high-statistics Monte Carlo simulations of the Edwards-Anderson Ising spin-glass model in three and four dimensions. The study is based on a non-Boltzmann sampling technique, the multi-overlap algorithm which is specifically tailored for sampling rare-event states. We thus concentrate on those properties which are difficult to obtain with standard canonical Boltzmann sampling such as the free-energy barriers F^q_B in the probability density P_J(q) of the Parisi overlap parameter q and the behaviour of the tails of the disorder averaged density P(q) = [P_J(q)]_av.

cond-mat.dis-nn↗

arXiv2001

Zero-modes of the QED Neuberger Dirac operator

We consider $4d$ compact lattice QED in the quenched approximation. First, we briefly summarize the spectrum of the staggered Dirac operator and its connection with random matrix theory. Afterwards we present results for the low-lying eigenmodes of the Neuberger overlap-Dirac operator. In the strong coupling phase we find exact zero-modes. Subsequently we discuss possibly related topological excitations of the U(1) lattice gauge theory.

hep-lat↗

arXiv2001

About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass

Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated system. For certain probability densities this predicts the characteristic large $x$ fall-off behavior $f(x)\sim\exp (-a e^x)$, $a>0$. Using a multicanonical Monte Carlo technique, we have calculated the Parisi overlap distribution $P(q)$ for the three-dimensional Edward-Anderson Ising spin glass at and below the critical temperature, even where $P(q)$ is exponentially small. We find that a probability distribution related to extreme order statistics gives an excellent description of $P(q)$ over about 80 orders of magnitude.

cond-mat.stat-mech↗

arXiv2001

Exact Zero-Modes of the Compact QED Dirac Operator

We calculate the low-lying eigenmodes of the Neuberger overlap-Dirac operator for $4d$ compact lattice QED in the quenched approximation. In the strong coupling phase we find exact zero-modes, quite similar as in non-Abelian lattice QCD. Subsequently we make an attempt to identify responsible topological excitations of the U(1) lattice gauge theory.

hep-lat↗

arXiv2001

A Regularization of Quantum Gravity

We re-examine results of the Liouville theory and provide arguments that a {\it negative} bare cosmological constant is essential to define two-dimensional quantum gravity. From this we are naturally led to a regularization of quantum gravity within the Regge approach such that it is described by small fluctuations around equilateral triangles, whose average link length approaches zero in the continuum limit. We investigate a model based on this idea numerically and present evidence for the desired long-range correlations. Interestingly, the approach might generalize to higher dimensions. The picture of an inflated balloon, which is often used to demonstrate the properties of an expanding classical universe, seems to be valuable to understand quantum gravity as well.

hep-lat↗

arXiv2000

Clopper-Pearson Bounds from HEP Data Cuts

For the measurement of $N_s$ signals in $N$ events rigorous confidence bounds on the true signal probability $p_{\rm exact}$ were established in a classical paper by Clopper and Pearson [Biometrica 26, 404 (1934)]. Here, their bounds are generalized to the HEP situation where cuts on the data tag signals with probability $P_s$ and background data with likelihood $P_b<P_s$. The Fortran program which, on input of $P_s$, $P_b$, the number of tagged data $N^Y$ and the total number of data $N$, returns the requested confidence bounds as well as bounds on the entire cumulative signal distribution function, is available on the web. In particular, the method is of interest in connection with the statistical analysis part of the ongoing Higgs search at the LEP experiments.

hep-ex↗

arXiv2000

The transformations of non-abelian gauge fields under translations

I consider infinitesimal translations $x'^α=x^α+δx^α$ and demand that Noether's approach gives a symmetric energy-momentum tensor as it is required for gravitational sources. This argument determines the transformations of non-abelian gauge fields under infinitesimal translations to differ from the usually assumed invariance by the gauge transformation, $A'^a_γ (x') - A^a_γ(x) = \partial_γ [ δx_β A^{a β}(x)] + C^a_{bc} δx_β A^{c β}(x) A^{b}_γ(x)$ where the $C^a_{bc}$ are the structure constants of the gauge group.

hep-th↗

arXiv2000

The transformations of the electromagnetic potentials under translations

I consider infinitesimal translations $x'^α=x^α+δx^α$ and demand that Noether's approach gives a symmetric electromagnetic energy-momentum tensor as it is required for gravitational sources. This argument determines the transformations of the electromagnetic potentials under infinitesimal translations to be $A'_γ (x') = A_γ(x)+\partial_γ [δx_β A^β(x)]$, which differs from the usually assumed invariance $A'_γ (x') = A_γ(x)$, by the gauge transformation $\partial_γ [δx_β A^β(x)]$.

hep-th↗

arXiv2000

Spin glass overlap barriers in three and four dimensions

For the Edwards-Anderson Ising spin-glass model in three and four dimensions (3d and 4d) we have performed high statistics Monte Carlo calculations of those free-energy barriers $F^q_B$ which are visible in the probability density $P_J(q)$ of the Parisi overlap parameter $q$. The calculations rely on the recently introduced multi-overlap algorithm. In both dimensions, within the limits of lattice sizes investigated, these barriers are found to be non-self-averaging and the same is true for the autocorrelation times of our algorithm. Further, we present evidence that barriers hidden in $q$ dominate the canonical autocorrelation times.

cond-mat.dis-nn↗

arXiv1999

Random Matrix Theory and Dirac Spectrum at Nonzero Temperature and Density

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory on various lattice sizes. As a measure of the fluctuation properties of the eigenvalues, we study the nearest-neighbor spacing distribution, $P(s)$. We further study lattice QCD at nonzero chemical potential, $μ$, by constructing the spacing distribution of adjacent eigenvalues in the complex plane. We find that in all regions of their phase diagrams, compact lattice gauge theories have bulk spectral correlations given by random matrix theory, which is an indication for quantum chaos.

hep-lat↗

arXiv1999

Introduction to Multicanonical Monte Carlo Simulations

Monte Carlo simulation with {\it a-priori} unknown weights have attracted recent attention and progress has been made in understanding (i) the technical feasibility of such simulations and (ii) classes of systems for which such simulations lead to major improvements over conventional Monte Carlo simulations. After briefly sketching the history of multicanonical calculations and their range of application, a general introduction in the context of the statistical physics of the d-dimensional generalized Potts models is given. Multicanonical simulations yield canonical expectation values for a range of temperatures or any other parameter(s) for which appropriate weights can be constructed. We shall address in some details the question how the multicanonical weights are actually obtained. Subsequently miscellaneous topics related to the considered algorithms are reviewed. Then multicanonical studies of first order phase transitions are discussed and finally applications to complex systems such as spin glasses and proteins.

cond-mat↗

arXiv1999

U(1) staggered Dirac operator and random matrix

We investigate the spectrum of the staggered Dirac operator in 4d quenched U(1) lattice gauge theory and its relationship to random matrix theory. In the confined as well as in the Coulomb phase the nearest-neighbor spacing distribution of the unfolded eigenvalues is well described by the chiral unitary ensemble. The same is true for the distribution of the smallest eigenvalue and the microscopic spectral density in the confined phase. The physical origin of the chiral condensate in this phase deserves further study.

hep-lat↗

arXiv1998

Energy barriers of spin glasses from multi-overlap simulations

We report large-scale simulations of the three-dimensional Edwards-Anderson Ising spin glass system using the recently introduced multi-overlap Monte Carlo algorithm. In this approach the temperature is fixed and two replica are coupled through a weight factor such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for the entire $q$-range (multi-overlap) follow by reweighting. We present an analysis of the performance of the algorithm and in particular discuss results on spin glass free-energy barriers which are hard to obtain with conventional algorithms. In addition we discuss the non-trivial scaling behavior of the canonical $q$-distributions in the broken phase.

cond-mat.dis-nn↗

arXiv1998

Covariant Wave Function Reduction and Coherent Decays of Kaon Pair

The recently developed relativistically covariant formulation of wave function reduction is illustrated for Lipkin's proposal to study CP violation in the coherent decay of kaon pairs. Covariant results are obtained in agreement with an amplitude approach proposed in the literature.

hep-ph↗

arXiv1998

Relativistic Quantum Field Theory with a Physical State Vector

Evolution of a physical quantum state vector is described as governed by two distinct physical laws: Continuous, unitary time evolution and a relativistically covariant reduction process. In previous literature, it was concluded that a relativistically satisfactory version of the collapse postulate is in contradiction with physical measurements of a non-local state history. Here it is shown that such measurements are excluded when reduction is formulated as a physical process and the measurement devices are included as part of the state vector.

quant-ph↗

arXiv1998

Could Spontaneous Transitions be Spontaneous?

It is considered to re-formulate quantum theory as it appears: A theory of continuous and causal time evolution, interrupted by discontinuous and stochastic jumps. To develop the (missing) theory of jumps a heuristic-phenomenological approach is suggested. Relying on a global reduction process, a hypothesis is introduced postulating spontaneous collapse of superpositions of states which describe spontaneous absorption or emission. The collapse probability determines a mean collapse time $τ^c = b \hbar / \triangle E$, where $b$ is a dimensionless constant and $\triangle E$ is the difference in energy distribution between alternative branches. Ramsey atomic beam spectroscopy yields a lower bound on $b$ and avalanche photodiodes give an upper bound, such that $1.35\cdot 10^{11} < b < 3.8\cdot 10^{21}$. Ample opportunities for experimental improvements exist.

hep-ph↗

arXiv1998

Configuration Space for Random Walk Dynamics

Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a configuration to be sampled depends on a number of unusual quantities, which are explained in this paper. This has been overlooked in recent literature, where the method is advertised for the calculation of canonical expectation values. We illustrate these points for the $2d$ Ising model. In addition, we proof a previously conjectured equation which relates microcanonical expectation values to the spectral density.

cond-mat.stat-mech↗

arXiv1998

Quantum Theory and Spacelike Measurements

Experimentally observed violations of Bell inequalities rule out local realistic theories. Consequently, the quantum state vector becomes a strong candidate for providing an objective picture of reality. However, such an ontological view of quantum theory faces difficulties when spacelike measurements on entangled states have to be described, because time ordering of spacelike events can change under Lorentz-Poincaré transformations. In the present paper it is shown that a necessary condition for consistency is to require state vector reduction on the backward light-cone. A fresh approach to the quantum measurement problem appears feasible within such a framework.

quant-ph↗