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International audience; We consider the open isotropic spin-1/2 Heisenberg quantum spin chain with a finite number N of sites coupled at the ends to a dissipative environment that favors polarization of the boundary spins in different directions. We review the matrix product ansatz (MPA) that yields the exact reduced density matrix of the Heisenberg chain. We develop the matrix algebra coming from the MPA in more detail than in previous work. We hence obtain exact results for the nonequilibrium partition function, about the impact of quantum fluctuations on the targeted boundary states, and for current–magnetization correlations in the steady state. The boundary states turn out to be pure to the order o(N−2). We show that the local magnetization and the local current perpendicular to the plane spanned by the boundary polarizations exhibit long-range correlations while the local magnetization correlations with the local in-plane currents are strongly suppressed.

We consider the contribution of electron-electron interactions to the orbital magnetization of a two-dimensional electron gas, focusing on the ballistic limit in the regime of negligible Landau-level spacing. This regime can be described by combining diagrammatic perturbation theory with semiclassical techniques. At sufficiently low temperatures, the interaction-induced magnetization overwhelms the Landau and Pauli contributions. Curiously, the interaction-induced magnetization is third-order in the (renormalized) Coulomb interaction. We give a simple interpretation of this effect in terms of classical paths using a renormalization argument: a polygon must have at least three sides in order to enclose area. To leading order in the renormalized interaction, the renormalization argument gives exactly the same result as the full treatment., 11 pages including 4 ps figures; uses revtex and epsf.sty

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents omega>0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as t ~ log^{1/omega}. Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of omega, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities., 13 pages RevTeX, 10 eps-figures included

International audience; We study analytically, in one dimension, the survival probability $P_{s}(t)$ up to time $t$ of an immobile target surrounded by mutually noninteracting traps each performing a continuous-time random walk (CTRW) in continuous space. We consider a general CTRW with symmetric and continuous (but otherwise arbitrary) jump length distribution $f(\eta)$ and arbitrary waiting time distribution $\psi(\tau)$. The traps are initially distributed uniformly in space with density $\rho$. We prove an exact relation, valid for all time $t$, between $P_s(t)$ and the expected maximum $E[M(t)]$ of the trap process up to time $t$, for rather general stochastic motion $x_{\rm trap}(t)$ of each trap. When $x_{\rm trap}(t)$ represents a general CTRW with arbitrary $f(\eta)$ and $\psi(\tau)$, we are able to compute exactly the first two leading terms in the asymptotic behavior of $E[M(t)]$ for large $t$. This allows us subsequently to compute the precise asymptotic behavior, $P_s(t)\sim a\, \exp[-b\, t^{\theta}]$, for large $t$, with exact expressions for the stretching exponent $\theta$ and the constants $a$ and $b$ for arbitrary CTRW. By choosing appropriate $f(\eta)$ and $\psi(\tau)$, we recover the previously known results for diffusive and subdiffusive traps. However, our result is more general and includes, in particular, the superdiffusive traps as well as totally anomalous traps.

We address the issue why a cosmological constant (dark energy) possesses a small positive value instead of being zero. Motivated by the cosmic landscape picture, we mimic the dark energy by a scalar field with potential wells and show that other degrees of freedom interacting with it can localize this field by decoherence in one of the wells. Dark energy can then acquire a small positive value. We also show that the additional degrees of freedom enhance the tunneling rate between the wells. The consideration is performed in detail for the case of two wells and then extended to a large number of wells., Comment: 39 pages, 2 figures, final version

Made available in DSpace on 2022-04-28T23:48:52Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-05-06 In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension. © 2011 American Physical Society. Institut für Theoretische Physik Universität zu Köln, Zülpicher Straße 77 Instituto de Física Teórica Universidade Estadual Paulista Institut für Theoretische Physik Universität Stuttgart, Pfaffenwaldring 57 Institut für Theoretische Festkörperphysik RWTH Aachen, Otto-Blumenthal-Strasse 26 Institute of Theoretical Physics École Polytechnique Fédérale de Lausanne (EPFL) Condensed Matter Theory Group LOMA Université de Bordeaux i Institut für Theoretische Physik Technische Universität Dresden Instituto de Física Teórica Universidade Estadual Paulista

We calculate the Casimir interaction between a sphere and a plate, both described by the plasma model, the Drude model, or generalizations of the two models. We compare the results at both zero and finite temperatures. At asymptotically large separations we obtain analytical results for the interaction that reveal a non-universal, i.e., material dependent interaction for the plasma model. The latter result contains the asymptotic interaction for Drude metals and perfect reflectors as different but universal limiting cases. This observation is related to the screening of a static magnetic field by a London superconductor. For small separations we find corrections to the proximity force approximation (PFA) that support correlations between geometry and material properties that are not captured by the Lifshitz theory. Our results at finite temperatures reveal for Drude metals a non-monotonic temperature dependence of the Casimir free energy and a negative entropy over a sizeable range of separations., Comment: 11 pages, 5 figures

We study the mesoscopic Kondo box, consisting of a quantum spin 1/2 interacting with a chaotic electronic bath as can be realized by a magnetic impurity coupled to electrons on a quantum dot, using a mean-field approach for the Kondo interaction. Its umerical efficiency allows us to analyze the Kondo temperature, the local magnetic susceptibility, and the conductance statistics for a large number of samples with energy levels obtained by random matrix theory. We see pronounced parity effects in the average values and in the probability distributions, depending on an even and odd electronic occupation of the quantum dot, respectively. These parity effects are directly accessible in experiments., Comment: 5 pages, 3 figures

The properties of fluctuation induced interactions like van der Waals and Casimir-Lifshitz forces are of interest in a plethora of fields ranging from biophysics to nanotechnology. Here we describe a general approach to compute these interactions. It is based on a combination of methods from statistical physics and scattering theory. We showcase how it is exquisitely suited to analyze a variety of previously unexplored phenomena. Examples are given to show how the interplay of geometry and material properties helps to understand and control these forces., 21 pages, 7 figures. Contribution to QFEXT09 proceedings

We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for the corresponding exterior configuration., 4 pages, 3 figures

The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, $H$ and $\theta$, and the cylinder's parabolic radius $R$. As $H/R\to 0$, the proximity force approximation becomes exact. The opposite limit of $R/H\to 0$ corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed., Comment: 5 pages, 3 figures, uses RevTeX; v2: expanded conclusions; v3: fixed missing factor in Eq. (3) and incorrect diagram label (no changes to results); v4: fix similar factor in Eq. (16) (again no changes to results)

We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object's electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another., 12 pages, 6 figures

We study a lattice field model which qualitatively reflects the phenomenon of Anderson localization and delocalization for real symmetric band matrices. In this statistical mechanics model, the field takes values in a supermanifold based on the hyperbolic plane. Correlations in this model may be described in terms of a random walk in a highly correlated random environment. We prove that in three or more dimensions the model has a `diffusive' phase at low temperatures. Localization is expected at high temperatures. Our analysis uses estimates on non-uniformly elliptic Green's functions and a family of Ward identities coming from internal supersymmetry., Comment: 55 pages, 6 figures

We investigate the influence of quantum fluctuations and weak disorder on the vortex dynamics in a two-dimensional superconducting Berezinskii-Kosterlitz-Thouless system. The temperature below which quantum fluctuations dominate the vortex creep is determined, and the transport in this quantum regime is described. The crossover from quantum to classical regime is discussed and the quantum correction to the classical current-voltage relation is determined. It is found that weak disorder can effectively reduce the critical current as compared to that in the clean system., Comment: 4 pages, 2 figures

4 pages, 3 figures; International audience; The Casimir interaction between two objects, or between an object and a plane, depends on their relative orientations. We make these angular dependences explicit by considering prolate or oblate spheroids. The variation with orientation is calculated exactly at asymptotically large distances for the electromagnetic field, and at arbitrary separations for a scalar field. For a spheroid in front of a mirror, the leading term is orientation independent, and we find the optimal orientation from computations at higher order.

Casimir interactions are not pair-wise additive. This property leads to collective effects that we study for a pair of objects near a conducting wall. We employ a scattering approach to compute the interaction in terms of fluctuating multipoles. The wall can lead to a non-monotonic force between the objects. For two atoms with anisotropic electric and magnetic dipole polarizabilities we demonstrate that this non-monotonic effect results from a competition between two- and three body interactions. By including higher order multipoles we obtain the force between two macroscopic metallic spheres for a wide range of sphere separations and distances to the wall., 4 pages, 4 figures

The influence of randomly distributed point impurities and planar defects on order and transport in type-II superconductors and related systems is studied. It is shown that the Bragg glass phase is unstable with respect to planar efects. Even a single weak defect plane oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is a relevant perturbation in the Bragg glass. A defect that is aligned with the magnetic field restores the flux density oscillations which decay algebraically with the distance from the defect. The theory exhibits striking similarities to the physics of a Luttinger liquid with a frozen impurity. The exponent for the flux line creep in the direction perpendicular to a relevant defect is derived. We find that the flux line lattice exhibits in the presence of many randomly distributed parallel planar defects aligned to the magnetic field a new glassy phase which we call planar glass. The planar glass is characterized by diverging shear and tilt moduli, a transverse Meissner effect, resistance against shear deformations. We also obtain sample to sample fluctuations of the longitudinal magnetic susceptibility and an exponential decay of translational long range order in the direction perpendicular to the defects. The flux creep perpendicular to the defects leads to a nonlinear resistivity $\rho(J \to 0)\sim \exp[-(J_D/J)^{3/2}]$. Strong planar defects enforce arrays of dislocations that are located at the defects with a Burgers vector parallel to the defects in order to relax shear strain., Comment: 27 pages

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation., 43 pages, 10 figures

International audience; We study collective interaction effects that result from the change of free quantum electrodynamic field fluctuations by one- and two-dimensional perfect metal structures. The Casimir interactions in geometries containing plates and cylinders is explicitly computed using partial wave expansions of constrained path integrals. We generalize previously obtained results and provide a more detailed description of the technical aspects of the approach \cite{Emig06}. We find that the interactions involving cylinders have a weak logarithmic dependence on the cylinder radius, reflecting that one-dimensional perturbations are marginally relevant in 4D space-time. For geometries containing two cylinders and one or two plates, we confirm a previously found non-monotonic dependence of the interaction on the object's separations which does not follow from pair-wise summation of two-body forces. Qualitatively, this effect is explained in terms of fluctuating charges and currents and their mirror images.

We have developed an exact, general method to compute Casimir interactions between a finite number of compact objects of arbitrary shape and separation. Here, we present details of the method for a scalar field to illustrate our approach in its most simple form; the generalization to electromagnetic fields is outlined in Ref. [1]. The interaction between the objects is attributed to quantum fluctuations of source distributions on their surfaces, which we decompose in terms of multipoles. A functional integral over the effective action of multipoles gives the resulting interaction. Each object's shape and boundary conditions enter the effective action only through its scattering matrix. Their relative positions enter through universal translation matrices that depend only on field type and spatial dimension. The distinction of our method from the pairwise summation of two-body potentials is elucidated in terms of the scattering processes between three objects. To illustrate the power of the technique, we consider Robin boundary conditions $\phi -\lambda \partial_n \phi=0$, which interpolate between Dirichlet and Neumann cases as $\lambda$ is varied. We obtain the interaction between two such spheres analytically in a large separation expansion, and numerically for all separations. The cases of unequal radii and unequal $\lambda$ are studied. We find sign changes in the force as a function of separation in certain ranges of $\lambda$ and see deviations from the proximity force approximation even at short separations, most notably for Neumann boundary conditions., Comment: 27 pages, 9 figures

We study by exact diagonalization, in the lowest Landau level approximation, the Coulomb interaction problem of N = 4 and N = 6 quantum dot in the limit of zero Zeeman coupling. We find that meron excitations constitute the lowest lying states of the quantum dots. This is based on a mapping between the excitations of the dot and states of the Haldane-Shastry spin chain., 4 pages, 5 figures

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate--sphere, where it is known at large separations. The force has an unexpectedly weak decay \sim L/(H^3 \ln(H/R)) at large plate--cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures., Comment: 4 pages, 3 figures

A new approach to the Helmholtz spectrum for arbitrarily shaped boundaries and a rather general class of boundary conditions is introduced. We derive the boundary induced change of the density of states in terms of the free Green's function from which we obtain both perturbative and non-perturbative results for the Casimir interaction between deformed surfaces. As an example, we compute the lateral electrodynamic Casimir force between two corrugated surfaces over a wide parameter range. Universal behavior, fixed only by the largest wavelength component of the surface shape, is identified at large surface separations. This complements known short distance expansions which are also reproduced., 8 pages, J Phys A Special Issue QFEXT05