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Thorsten Emig

Publications and source records attributed to Thorsten Emig.

72 records · Page 4Linked to original sources
arXiv2003

Geometry Dependence of Casimir Forces beyond the Proximity Approximation

Casimir interactions between macroscopic objects are strongly influenced by their geometrical features as shape and orientation as well as by their material properties. The effect of geometry is commonly obtained from the proximity approximation (PA). Here we present a path integral quantization for the electromagnetic field in the presence of deformed metallic surfaces. From the resulting effective action the Casimir force between the surfaces can be calculated without the PA. For corrugated surfaces the force is obtained both perturbatively for small deformations and by a numerical approach for general deformation amplitudes. For general dielectric materials with flat surfaces a path integral based derivation of the Lifshitz theory is outlined, pointing towards a possible approach to study the combined effect of deformations and material properties.

cond-mat.stat-mech↗
arXiv2003

Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder

We study the statistics of thermodynamic quantities in two related systems with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in a random potential and the 2-dimensional random bond dimer model. The first system is examined by a replica-symmetric Bethe ansatz (RBA) while the latter is studied numerically by a polynomial algorithm which circumvents slow glassy dynamics. We establish a mapping of the two models which allows for a detailed comparison of RBA predictions and simulations. Over a wide range of disorder strength, the effective lattice stiffness and cumulants of various thermodynamic quantities in both approaches are found to agree excellently. Our comparison provides, for the first time, a detailed quantitative confirmation of the replica approach and renders the planar line lattice a unique testing ground for concepts in random systems.

cond-mat.dis-nn↗
arXiv2003

Towards a Theory of Molecular Forces between Deformed Media

A macroscopic theory for the molecular or Casimir interaction of dielectric materials with arbitrarily shaped surfaces is developed. The interaction is generated by the quantum and thermal fluctuations of the electromagnetic field which depend on the dielectric function of the materials. Using a path integral approach for the electromagnetic gauge field, we derive an effective Gaussian action which can be used to compute the force between the objects. No assumptions about the independence of the shape and material dependent contributions to the interaction are made. In the limiting case of flat surfaces our approach yields a simple and compact derivation of the Lifshitz theory for molecular forces. For ideal metals with arbitrarily deformed surfaces the effective action can be calculated explicitly. For the general case of deformed dielectric materials the applicability of perturbation theory and numerical techniques to the evaluation of the force from the effective action is discussed.

cond-mat.stat-mech↗
arXiv2002

Is there a Glass Transition in Planar Vortex Systems?

The criteria for the existence of a glass transition in a planar vortex array with quenched disorder are studied. Applying a replica Bethe ansatz, we obtain for self-avoiding vortices the exact quenched average free energy and effective stiffness which is found to be in excellent agreement with recent numerical results for the related random bond dimer model [1]. Including a repulsive vortex interaction and a finite vortex persistence length ξ, we find that for ξ\to 0 the system is at {\em all} temperatures in a glassy phase; a glass transition exists only for finite ξ. Our results indicate that planar vortex arrays in superconducting films are glassy at presumably all temperatures.

cond-mat.dis-nn↗
arXiv2002

Normal and Lateral Casimir Forces between Deformed Plates

The Casimir force between macroscopic bodies depends strongly on their shape and orientation. To study this geometry dependence in the case of two deformed metal plates, we use a path integral quantization of the electromagnetic field which properly treats the many-body nature of the interaction, going beyond the commonly used pairwise summation (PWS) of van der Waals forces. For arbitrary deformations we provide an analytical result for the deformation induced change in Casimir energy, which is exact to second order in the deformation amplitude. For the specific case of sinusoidally corrugated plates, we calculate both the normal and the lateral Casimir forces. The deformation induced change in the Casimir interaction of a flat and a corrugated plate shows an interesting crossover as a function of the ratio of the mean platedistance H to the corrugation length λ: For λ\ll H we find a slower decay \sim H^{-4}, compared to the H^{-5} behavior predicted by PWS which we show to be valid only for λ\gg H. The amplitude of the lateral force between two corrugated plates which are out of registry is shown to have a maximum at an optimal wavelength of λ\approx 2.5 H. With increasing H/λ\gtrsim 0.3 the PWS approach becomes a progressively worse description of the lateral force due to many-body effects. These results may be of relevance for the design and operation of novel microelectromechanical systems (MEMS) and other nanoscale devices.

cond-mat.stat-mech↗
arXiv2002

Casimir Forces: An Exact Approach for Periodically Deformed Objects

A novel approach for calculating Casimir forces between periodically deformed objects is developed. This approach allows, for the first time, a rigorous non-perturbative treatment of the Casimir effect for disconnected objects beyond Casimir's original two-plate configuration. The approach takes into account the collective nature of fluctuation induced forces, going beyond the commonly used pairwise summation of two-body van der Waals forces. As an application of the method, we exactly calculate the Casimir force due to scalar field fluctuations between a flat and a rectangular corrugated plate. In the latter case, the force is found to be always attractive.

cond-mat.stat-mech↗
arXiv2002

Delocalization in Coupled Luttinger Liquids with Impurities

We study effects of quenched disorder on coupled two-dimensional arrays of Luttinger liquids (LL) as a model for stripes in high-T_c compounds. In the framework of a renormalization-group analysis, we find that weak inter-LL charge-density-wave couplings are always irrelevant as opposed to the pure system. By varying either disorder strength, intra- or inter-LL interactions, the system can undergo a delocalization transition between an insulator and a novel strongly anisotropic metallic state with LL-like transport. This state is characterized by short-ranged charge-density-wave order, the superconducting order is quasi long-ranged along the stripes and short-ranged in the transversal direction.

cond-mat.dis-nn↗
arXiv2001

Probing the Strong Boundary Shape Dependence of the Casimir Force

We study the geometry dependence of the Casimir energy for deformed metal plates by a path integral quantization of the electromagnetic field. For the first time, we give a complete analytical result for the deformation induced change in Casimir energy δ\cal E in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for δ\cal E as a function of the ratio of the mean plate distance H, to the corrugation length λ: For λ\ll H we find a {\em slower} decay \sim H^{-4}, compared to the H^{-5} behavior predicted by the commonly used pairwise summation of van der Waals forces, which is valid only for λ\gg H.

cond-mat.stat-mech↗
arXiv2001

Probability Distributions of Line Lattices in Random Media from the 1D Bose Gas

The statistical properties of a two dimensional lattice of elastic lines in a random medium are studied using the Bethe ansatz. We present a novel mapping of the dilute random line lattice onto the weak coupling limit of a pure Bose gas with delta-function interactions. Using this mapping, we calculate the cumulants of the free energy in the dilute limit exactly. The relation between density and displacement correlation functions in the two models is examined and compared with existing results from renormalization group and variational ansaetze.

cond-mat.stat-mech↗
arXiv2000

Thermodynamic Fingerprints of Disorder in Flux Line Lattices and other Glassy Mesoscopic Systems

We examine probability distributions for thermodynamic quantities in finite-sized random systems close to criticality. Guided by available exact results, a general ansatz is proposed for replicated free energies, which leads to scaling forms for cumulants of various macroscopic observables. For the specific example of a planar flux line lattice in a two dimensional superconducting film near H_c1, we provide detailed results for the statistics of the magnetic flux density, susceptibility, heat capacity, and their cross-correlations.

cond-mat.dis-nn↗
arXiv1999

Exact Solutions of a Model for Granular Avalanches

We present exact solutions of the non-linear {\sc bcre} model for granular avalanches without diffusion. We assume a generic sandpile profile consisting of two regions of constant but different slope. Our solution is constructed in terms of characteristic curves from which several novel predictions for experiments on avalanches are deduced: Analytical results are given for the shock condition, shock coordinates, universal quantities at the shock, slope relaxation at large times, velocities of the active region and of the sandpile profile.

cond-mat.stat-mech↗
arXiv1999

Non-Universal Quasi-Long Range Order in the Glassy Phase of Impure Superconductors

The structural correlation functions of a weakly disordered Abrikosov lattice are calculated for the first time in a systematic RG-expansion in d=4-εdimensions. It is shown, that in the asymptotic limit the Abrikosov lattice exhibits still quasi long range translational order described by a non-universal exponent \barη_{\bf G} which depends on the ratio of the renormalized elastic constants κ=\tilde c_{66}/\tilde c_{11} of the flux line (FL) lattice. Our calculations show clearly three distinct scaling regimes corresponding to the Larkin, the manifold and the asymptotic Bragg glass regime. On a wide range of intermediate length scales the FL displacement correlation function increases as a power law with twice of the manifold roughness exponent ζ_{rm}(κ), which is also non-universal. Our results, in particular the κ-dependence of the exponents, are in variance with those of the variational treatment with replica symmetry breaking which allows in principle an experimental discrimination between the two approaches.

cond-mat.stat-mech↗
arXiv1998

Roughening Transition of Interfaces in Disordered Systems

The behavior of interfaces in the presence of both lattice pinning and random field (RF) or random bond (RB) disorder is studied using scaling arguments and functional renormalization techniques. For the first time we show that there is a continuous disorder driven roughening transition from a flat to a rough state for internal interface dimensions 2<D<4. The critical exponents are calculated in an ε-expansion. At the transition the interface shows a superuniversal logarithmic roughness for both RF and RB systems. A transition does not exist at the upper critical dimension D_c=4. The transition is expected to be observable in systems with dipolar interactions by tuning the temperature.

cond-mat.stat-mech↗
arXiv1998

Disorder Driven Roughening Transitions of Elastic Manifolds and Periodic Elastic Media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in ε=4-D. At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value p_c=6/π\sqrtε. For p<p_c the medium is always flat. Critical exponents are calculated in a double expansion in μ=p^2/p_c^2-1 and ε=4-D and fulfill the scaling relations of random field models.

cond-mat.stat-mech↗
arXiv1998

A New Disorder Driven Roughening Transition of CDW's and Flux Line Lattices

We study the competition between pinning of a charge density wave (CDW) by random distributed impurities and a periodic potential of the underlying crystal lattice. In d=3 dimensions, we find for commensurate phases of order p>p_c\approx 6/πa disorder driven continuous roughening transition from a 'flat' phase with translational long range order to a 'rough' glassy phase with quasi long range order. Critical exponents are calculated in a double expansion in μ=p^2/p_c^2-1 and ε=4-d and fulfill the scaling relations of random field models. Implications for flux line lattices in high temperature superconductors are briefly discussed.

cond-mat.stat-mech↗
arXiv1997

Propagation of an electromagnetic pulse through a waveguide with a barrier: A time domain solution within classical electrodynamics

An electromagnetic truncated Gaussian pulse propagates through a waveguide with piecewise different dielectric constants. The waveguide contains a barrier, namely a region of a lower dielectric constant compared to the neighboring regions. This set-up yields a purely imaginary wave vector in the region of the barrier ('electromagnetic tunneling'). We exactly calculate the time-dependent Green's function for a slightly simplified dispersion relation. In order to observe the plain tunneling effect we neglect the distortions caused by the wave guide in obtaining the transmitted pulse. The wave front of the pulse travels with the vacuum speed of light. Nevertheless, behind the barrier, the maximum of the transmitted pulse turns up at an earlier time than in the case without an barrier. This effect will be explained in terms of the energy flow across the barrier. The solutions obtained reproduce the shape of the pulses measured in the tunneling experiments of Enders and Nimtz [J. Phys. (France) I2, 1693 (1992); Phys. Rev. E48, 632 (1993); Phys. Rev. B47, 9605 (1993); J. Phys. (France) I3, 1089 (1993); 4, 565 (1994)].

physics.class-ph↗
arXiv1997

Charge Modulation at the Surface of High-T_c Superconductors

It is shown here that surfaces of high-temperature superconductors are covered by dipole layers. The charge density modulation is induced by the local suppression of the gap function at the surface. This effect is studied in the framework of the Ginzburg-Landau theory and crucially depends on the appropriate boundary conditions. Those are derived from Gor'kov's equations for a d-wave pairing symmetry. Within this framework the structure of the surface dipole layer is determined. The contribution of this charging to a lens-effect of superconducting films with holes, which has been studied in recent experiments, is discussed.

cond-mat.supr-con↗