arXiv subjects

Rudolf A. Römer

Publications and source records attributed to Rudolf A. Römer.

At least 55 records · Page 3Linked to original sources

arXiv2010

Symmetry Content and Observation of Charged Collective Excitations for Graphene in Strong Magnetic Fields

We show that graphene in a strong magnetic field with partially filled Landau levels sustains charged collective excitations, which are bound states of three-particle complexes. Some of these states are optically bright and may be detected in spectroscopy experiments, enhancing the current understanding of electron-electron interactions in graphene. The states can be classified using the geometrical symmetries - non-commutative magnetic translations and generalized rotations - in addition to the dynamical SU(4) symmetry in graphene. From the SU(4) symmetry point of view, such excitations are analogous to bound states of two quarks and one antiquark qqqbar with four flavors. We establish a flavor optical selection rule to identify the bright states for experimental studies.

cond-mat.mes-hall↗

arXiv2010

Critical parameters from generalised multifractal analysis at the Anderson transition

We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction amplitudes is sufficient to characterize the transition. In combination with finite-size scaling, this formalism permits the critical parameters to be estimated without the need for conductance or other transport measurements. Applying this method to high-precision data for wavefunction statistics obtained by exact diagonalization of the three-dimensional Anderson model, we estimate the critical exponent $ν=1.58\pm 0.03$.

cond-mat.dis-nn↗

arXiv2008

Sensitivity of protein rigidity analysis to small structural variations: a large-scale comparative analysis

Rigidity analysis using the "pebble game" can usefully be applied to protein crystal structures to obtain information on protein folding, assembly and the structure-function relationship. However, previous work using this technique has not made clear how sensitive rigidity analysis is to small structural variations. We present a comparative study in which rigidity analysis is applied to multiple structures, derived from different organisms and different conditions of crystallisation, for each of several different proteins. We find that rigidity analysis is best used as a comparative tool to highlight the effects of structural variation. Our use of multiple protein structures brings out a previously unnoticed peculiarity in the rigidity of trypsin.

q-bio.MN↗

arXiv2008

Critical parameters for the disorder-induced metal-insulator transition in FCC and BCC lattices

We use a transfer-matrix method to study the disorder-induced metal-insulator transition. We take isotropic nearest- neighbor hopping and an onsite potential with uniformly distributed disorder. Following previous work done on the simple cubic lattice, we perform numerical calculations for the body centered cubic and face centered cubic lattices, which are more common in nature. We obtain the localization length from calculated Lyapunov exponents for different system sizes. This data is analyzed using finite-size scaling to find the critical parameters. We create an energy-disorder phase diagram for both lattice types, noting that it is symmetric about the band center for the body centered cubic lattice, but not for the face centered cubic lattice. We find a critical exponent of approximately 1.5-1.6 for both lattice types for transitions occurring either at fixed energy or at fixed disorder, agreeing with results previously obtained for other systems belonging to the same orthogonal universality class. We notice an increase in critical disorder with the number of nearest neighbors, which agrees with intuition.

cond-mat.dis-nn↗

arXiv2007

Electric Transport Properties of the p53 Gene and the Effects of Point Mutations

In this work, charge transport (CT) properties of the p53 gene are numerically studied by the transfer matrix method, and using either single or double strand effective tight-binding models. A statistical analysis of the consequences of known p53 point mutations on CT features is performed. It is found that in contrast to other kind of mutation defects, cancerous mutations result in much weaker changes of CT efficiency. Given the envisioned role played by CT in the DNA-repairing mechanism, our theoretical results suggest an underlying physical explanation at the origin of carcinogenesis.

q-bio.GN↗

arXiv2007

Point Mutations Effects on Charge Transport Properties of the Tumor-Suppressor Gene p53

We report on a theoretical study of point mutations effects on charge transfer properties in the DNA sequence of the tumor-suppressor p53 gene. On the basis of effective single-strand or double-strand tight-binding models which simulate hole propagation along the DNA, a statistical analysis of charge transmission modulations associated with all possible point mutations is performed. We find that in contrast to non-cancerous mutations, mutation hotspots tend to result in significantly weaker {\em changes of transmission properties}. This suggests that charge transport could play a significant role for DNA-repairing deficiency yielding carcinogenesis.

q-bio.GN↗

arXiv2001

Percolation, Renormalization and the Quantum-Hall Transition

In this article, I give a pedagogical introduction and overview of percolation theory. Special emphasis will be put on the review of some of the most prominent of the algorithms that have been devised to study percolation numerically. At the central stage shall be the real-space renormalization group treatment of the percolation problem. As a rather novel application of this approach to percolation, I will review recent results using similar real-space renormalization ideas that have been applied to the quantum Hall transition.

cond-mat.mes-hall↗

arXiv2000

Energy-level statistics at the metal-insulator transition in anisotropic systems

We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e. weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition using energy-level statistics. The values of the critical disorder $W_c$ are consistent with results of previous studies, including the transfer-matrix method and multifractal analysis of the wave functions. $W_c$ decreases from its isotropic value with a power law as a function of anisotropy. Using high accuracy data for large system sizes we estimate the critical exponent $ν=1.45\pm0.2$. This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class. The critical level statistics which is independent of the system size at the transition changes from its isotropic form towards the Poisson statistics with increasing anisotropy.

cond-mat.dis-nn↗

arXiv1999

Critical properties of the metal-insulator transition in anisotropic systems

We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e., weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition by means of the transfer-matrix method. The values of the critical disorder $W_c$ obtained are consistent with results of previous studies, including multifractal analysis of the wave functions and energy level statistics. $W_c$ decreases from its isotropic value with a power law as a function of anisotropy. Using high accuracy data for large system sizes we estimate the critical exponent as $ν=1.62\pm0.07$. This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class.

cond-mat.dis-nn↗

arXiv1998

Energy level statistics at the metal-insulator transition in the Anderson model of localization with anisotropic hopping

Recently, a metal-insulator transition (MIT) was found in the anisotropic Anderson model of localization by transfer-matrix methods (TMM). This MIT has been also investigated by multifractal analysis (MFA) and the same critical disorders $W_c$ have been obtained within the accuracy of the data. We now employ energy level statistics (ELS) to further characterize the MIT. We find a crossover of the nearest-neighbor level spacing distribution $P(s)$ from GOE statistics at small disorder indicating metallic behavior to the Poisson distribution at large disorder characteristic for localized states. An analysis of the system size dependence of the spectral rigidity $Δ_3(L)$ confirms the values of $W_c$ from TMM and MFA.

cond-mat.dis-nn↗

arXiv1997

The Mott-Anderson transition in the disordered one-dimensional Hubbard model

We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder $Δ_c \approx U/2$. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.

cond-mat.str-el↗

arXiv1996

Multifractal analysis of the metal-insulator transition in anisotropic systems

We study the Anderson model of localization with anisotropic hopping in three dimensions for weakly coupled chains and weakly coupled planes. The eigenstates of the Hamiltonian, as computed by Lanczos diagonalization for systems of sizes up to $48^3$, show multifractal behavior at the metal-insulator transition even for strong anisotropy. The critical disorder strength $W_c$ determined from the system size dependence of the singularity spectra is in a reasonable agreement with a recent study using transfer matrix methods. But the respective spectrum at $W_c$ deviates from the ``characteristic spectrum'' determined for the isotropic system. This indicates a quantitative difference of the multifractal properties of states of the anisotropic as compared to the isotropic system. Further, we calculate the Kubo conductivity for given anisotropies by exact diagonalization. Already for small system sizes of only $12^3$ sites we observe a rapidly decreasing conductivity in the directions with reduced hopping if the coupling becomes weaker.

cond-mat↗

arXiv1995

Conservation laws in the continuum $1/r^2$ systems

We study the conservation laws of both the classical and the quantum mechanical continuum $1/r^2$ type systems. For the classical case, we introduce new integrals of motion along the recent ideas of Shastry and Sutherland (SS), supplementing the usual integrals of motion constructed much earlier by Moser. We show by explicit construction that one set of integrals can be related algebraically to the other. The difference of these two sets of integrals then gives rise to yet another complete set of integrals of motion. For the quantum case, we first need to resum the integrals proposed by Calogero, Marchioro and Ragnisco. We give a diagrammatic construction scheme for these new integrals, which are the quantum analogues of the classical traces. Again we show that there is a relationship between these new integrals and the quantum integrals of SS by explicit construction.

cond-mat↗

arXiv1995

Enhanced Charge and Spin Currents in the One-Dimensional Disordered Mesoscopic Hubbard Ring

We consider a one-dimensional mesoscopic Hubbard ring with and without disorder and compute charge and spin stiffness as a measure of the permanent currents. For finite disorder we identify critical disorder strength beyond which the charge currents in a system with repulsive interactions are {\em larger} than those for a free system. The spin currents in the disordered repulsive Hubbard model are enhanced only for small $U$, where the magnetic state of the system corresponds to a charge density wave pinned to the impurities. For large $U$, the state of the system corresponds to localized isolated spins and the spin currents are found to be suppressed. For the attractive Hubbard model we find that the charge currents are always suppressed compared to the free system at all length scales.

cond-mat↗

arXiv1994

Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse-sinh-square of the distance. This interaction contains a variable range as a parameter, and can thus interpolate between the known solutions for the nearest-neighbor chain, and the inverse-square chain. The energy, susceptibility, charge stiffness and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.

cond-mat↗

arXiv1994

Transport Properties of a One-Dimensional Two-Component Quantum Liquid with Hyperbolic Interactions

We present an investigation of the sinh-cosh (SC) interaction model with twisted boundary conditions. We argue that, when unlike particles repel, the SC model may be usefully viewed as a Heisenberg-Ising fluid with moving Heisenberg-Ising spins. We derive the Luttinger liquid relation for the stiffness and the susceptibility, both from conformal arguments, and directly from the integral equations. Finally, we investigate the opening and closing of the ground state gaps for both SC and Heisenberg-Ising models, as the interaction strength is varied.

cond-mat↗

arXiv1994

Exact Derivation of Luttinger Liquid Relation in a One-Dimensional Two-Component Quantum System with Hyperbolic Interactions

We present an exact calculation of the Luttinger liquid relation for the one-dimensional, two-component SC model in the interaction strength range $-1<s<0$ by appropriately varying the limits of the integral Bethe Ansatz equations. The result is confirmed by numerical and conformal methods. By a related study of the transport properties of the SC model, we can give an exact formula for the susceptibility. Our method is applicable to a wide range of models such as, e.g., the Heisenberg-Ising chain.

cond-mat↗

arXiv1993

Critical Exponents for the SC-Model in the Zero Sector

In this paper, we continue our investigation of a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential $s(s+1)/{\rm sinh}^{2}(r)$, while unlike particles interact with a pair potential $-s(s+1)/{\rm cosh}^{2}(r)$. For an equal number of particles of the two components, the ground state for $s>0$ corresponds to an antiferromagnet/insulator. Excitations consist of a gapless pair-hole--pair continuum, a two-particle continuum with gap and excitons with gap. For $-1<s<0$, the system has two gapless excitations --- a particle-hole continuum and a two spin-wave continuum. Using finite-size scaling methods of conformal field theory, we calculate the asymptotic expressions and critical exponents for correlation functions of these gapless excitations at zero temperature. The conformal structure is closely related to the Hubbard model with repulsive on-site interaction.

cond-mat↗