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H. Kleinert

Publications and source records attributed to H. Kleinert.

At least 91 records · Page 5Linked to original sources
arXiv1999

Perturbation Theory for Particle in a Box

Recently developed strong-coupling theory open up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum mechanics of a point particle in a one-dimensional box. Introducing an auxiliary harmonic mass term $m$, the ground-state energy $E^{(0)$ can be expanded perturbatively in powers of $1/md$, where $d$ is the box size. The removal of the infrared cutoff $m$ requires the resummation of the series at infinitely strong coupling. We show that strong-coupling theory yields a fast-convergent sequence of approximations to the well-known quantum-mechanical energy $E^{(0)= π^2/2d^2$.

cond-mat↗
arXiv1999

Strong-Coupling Calculation of Fluctuation Pressure of a Membrane Between Walls

We calculate analytically the proportionality constant in the pressure law of a membrane between parallel walls from the strong-coupling limit of variational perturbation theory up to third order. Extrapolating the zeroth to third approximations to infinity yields the pressure constant alpha=0.0797149. This result lies well within the error bounds of the most accurate available Monte-Carlo result 0.0798 +- 0.0003.

cond-mat↗
arXiv1999

Pressure of Membrane between Walls

For a single membrane of stiffness kappa fluctuating between two planar walls of distance d, we calculate analytically the proportionality constant in the pressure law p proportional to T^2/kappa^2 d^3, in very good agreement with results from Monte Carlo simulations.

cond-mat↗
arXiv1999

Derivative Expansion of One-Loop Effective Energy of Stiff Membranes with Tension

With help of a derivative expansion, the one-loop corrections to the energy functional of a nearly flat, stiff membrane with tension due to thermal fluctuations are calculated in the Monge parametrization. Contrary to previous studies, an arbitrary tilt of the surface is allowed to exhibit the nontrivial relations between the different, highly nonlinear terms accompanying the ultraviolet divergences. These terms are shown to have precisely the same form as those in the original energy functional, as necessary for renormalizability. Also infrared divergences arise. These, however, are shown to cancel in a nontrivial way.

cond-mat↗
arXiv1999

Universality Class of Confining Strings

A recently proposed model of confining strings has a non-local world-sheet action induced by a space-time Kalb-Ramond tensor field. Here we show that, in the large-D approximation, an infinite set of ghost- and tachyon-free truncations of the derivative expansion of this action all lead to c=1 models. Their infrared limit describes smooth strings with world-sheets of Hausdorff dimension D_H=2 and long-range orientational order, as expected for QCD strings.

hep-th↗
arXiv1999

Floppy Membranes

Floppy membranes are tensionless surfaces without extrinsic stiffness, whose fluctuations are governed by fourth-order bending elasticity. This suppresses spiky superstructures and ensures that floppy membranes remain smooth over any distance, with Hausdorff dimension D=2, in contrast to surfaces with stiffness, which are rough on the scale of some finite persistence length.

cond-mat↗
arXiv1998

Variational Perturbation Theory for Density Matrices

We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the temperature-dependent density of a particle in a double-well and of the electron in a hydrogen atom.

quant-ph↗
arXiv1998

Strings with Negative Stiffness and Hyperfine Structure

We propose a new string model by adding a higher-order gradient term to the rigid string, so that the stiffness can be positive or negative without loosing stability. In the large-D approximation, the model has three phases, one of which with a new type of generalized "antiferromagnetic" orientational correlations. We find an infrared-stable fixed point describing world-sheets with vanishing tension and Hausdorff dimension D_H=2. Crumpling is prevented by the new term which suppresses configurations with rapidly changing extrinsic curvature.

hep-th↗
arXiv1998

Real Interquark Potential Between a Heavy and a Light Quark at All Distances

We point out that in infinite spacetime dimensions, the singularity in the interquark potential at small distances disappears if the string is anchored at one end to a heavy quark, at the other end to a light quark. This suggests that if quarks are placed at the end of strings some unphysical features such as tachyon states may be absent also in in finite dimensions.

hep-th↗
arXiv1998

Two Phase Transitions in Chiral Gross-Neveu Model in $2+ ε$ Dimensions at Low N

We show that the chiral Gross-Neveu model in $2+ ε$ dimensions has for a small number $N$ of fermions two phase transitions corresponding to pair formation and pair condensation. In the first transition, fermions and antifermions acquire spontaneously a mass and are bound to pairs which behave like a Bose liquid in a chirally symmetric state. In the second transition, the Bose liquid condenses into a coherent state which breaks chiral symmetry. This suggests the possibility that in particle physics, the generation of quark masses may also happen separately from the breakdown of chiral symmetry.

hep-th↗
arXiv1998

Crossover from Weak- to Strong-Coupling Superconductivity and to Normal State with Pseudogap

For an electron gas with a $ δ$-function attraction we investigate the crossover from weak-coupling to strong-coupling superconductivity as well as normal state near the temperature $T^*$, at which the strong coupling produces a pseudogap in the energy spectrum due to the binding of electron pairs. We present curves for the behavior of the superconductive transition temperature, the gap formation temperature, the gap size and several thermodynamic quantities as functions of coupling strength and temperature, both in two and three dimensions.

cond-mat↗
arXiv1998

Simple Explicit Formulas for Gaussian Path Integrals with Time-Dependent Frequencies

Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary conditions on a line segment. This permits us to take advantage of Wronski's construction method for Green functions without knowledge of eigenvalues. Our final formula expresses the ratios of functional determinants in terms of an ordinary $2\times2$ -determinant of a constant matrix constructed from two linearly independent solutions of a the homogeneous differential equations associated with the second-order differential operators. For ratios of determinants encountered in semiclassical fluctuations around a classical solution, the result can further be expressed in terms of this classical solution. In the presence of a zero mode, our method allows for a simple universal regularization of the functional determinants. For Dirichlet's boundary condition, our result is equivalent to Gelfand-Yaglom's. Explicit formulas are given for a harmonic oscillator with an arbitrary time-dependent frequency.

quant-ph↗
arXiv1998

Smoothening Transition of Rough Surfactant Surfaces

We propose a model for surfaces in mixtures of oil, water and surfactants with strong electric dipoles. The dipole interactions give rise to a non-local interaction with negative stiffness between surface elements. We show that, for large space dimension D, this model has a phase transition from rough to smooth surfaces. Contrary to models with a simple quadratic curvature energy of positive sign, which always have a finite persistence length typical of rough surfaces, the smooth surfaces in our model exhibit long-range correlations of a generalized antiferromagnetic type. These correlations might be related to the recently observed "egg carton" superstructure of membranes.

cond-mat.soft↗
arXiv1998

Spiky Phases of Smooth Membranes. Implications for Smooth Strings

We point out a possible mechanism by which smooth surfaces can become spiky as the constant of curvature stiffness $κ$ falls below certain critical values. This happens either in a single first-order transition, or in a sequence of two Kosterlitz-Thouless-like transitions. There may also be additional phases in which the spikes form a hexagonal solid-like array or a disordered liquid-like structure. Our discussion suggests that there exist smooth strings between quarks.

cond-mat↗
arXiv1998

Novel Geometric Gauge Invariance of Autoparallels

We draw attention to a novel type of geometric gauge invariance relating the autoparallel equations of motion in different Riemann-Cartan spacetimes with each other. The novelty lies in the fact that the equations of motion are invariant even though the actions are not. As an application we use this gauge transformation to map the action of a spinless point particle in a Riemann-Cartan spacetime with a gradient torsion to a purely Riemann spacetime, in which the initial torsion appears as a nongeometric external field. By extremizing the transformed action in the usual way, we obtain the same autoparallel equations of motion as those derived in the initial spacetime with torsion via a recently-discovered variational principle.

gr-qc↗