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H. Kleinert

Publications and source records attributed to H. Kleinert.

At least 37 records · Page 2Linked to original sources
arXiv2008

Phase Diagram of Vortices in High-Tc Superconductors from Lattice Defect Model with Pinning

The theory presented is based on a simple Hamiltonian for a vortex lattice in a weak impurity background which includes linear elasticity and plasticity, the latter in the form of integer valued fields accounting for defects. Within a quadratic approximation in the impurity potential, we find a first-order Bragg-glass, vortex-glass transition line showing a reentrant behavior for superconductors with a melting line near $ H_{c2} $. Going beyond the quadratic approximation by using the variational approach of Mézard and Parisi established for random manifolds, we obtain a phase diagram containing a third-order glass transition line. The glass transition line separates the vortex glass and the vortex liquid. Furthermore, we find a unified first-order line consisting of the melting transition between the Bragg glass and the vortex liquid phase as well as a disorder induced first-order line between the Bragg glass and the vortex glass phase. The reentrant behavior of this line within the quadratic approach mentioned above vanished. We calculate the entropy and magnetic induction jumps over the first-order line.

cond-mat.supr-con↗
arXiv2007

Stiff Quantum Polymers

At ultralow temperatures, polymers exhibit quantum behavior, which is calculated here for the moments and of the end-to-end distribution in the large-stiffness regime. The result should be measurable for polymers in wide optical traps.

cond-mat.soft↗
arXiv2007

Boltzmann Distribution and Temperature of Stock Markets

The minute fluctuations of of S&P 500 and NASDAQ 100 indices display Boltzmann statistics over a wide range of positive as well as negative returns, thus allowing us to define a {\em market temperature} for either sign. With increasing time the sharp Boltzmann peak broadens into a Gaussian whose volatility $ σ$ measured in $1/ \sqrt{\rm min}$ is related to the temperature $T$ by $T= σ/ \sqrt{2}$. Plots over the years 1990--2006 show that the arrival of the 2000 crash was preceded by an increase in market temperature, suggesting that this increase can be used as a warning signal for crashes. A plot of the Dow Jones temperature over 78 years reveals a remarkable stability through many historical turmoils, interrupted only by short heat bursts near the crashes.

physics.soc-ph↗
arXiv2006

Defect induced melting of vortices in high-${\bf T_c} $ superconductors: A model based on continuum elasticity theory

We set up a melting model for vortex lattices in high-temperature superconductors based on the continuum elasticity theory. The model is Gaussian and includes defect fluctuations by means of a discrete-valued vortex gauge field. We derive the melting temperature of the lattice and predict the size of the Lindemann number. Our result agrees well with experiments for $ {\rm YBa}_2 {\rm Cu}_3 {\rm O}_{7-δ} $, and with modifications also for $ {\rm Bi}_2 {\rm Sr}_2 {\rm Ca} {\rm Cu}_2 {\rm O}_8 $ . We calculate the jumps in the entropy and the magnetic induction at the melting transition.

cond-mat.supr-con↗
arXiv2006

Gapless Hartree-Fock-Bogoliubov Approximation for Bose Gases

A dilute Bose system with Bose-Einstein condensate is considered. It is shown that the Hartree-Fock-Bogolubov approximation can be made both conserving as well as gapless. This is achieved by taking into account all physical normalization conditions, that is, the normalization condition for the condensed particles and that for the total number of particles. Two Lagrange multipliers, introduced for preserving these normalization conditions, make the consideration completely self-consistent.

cond-mat.stat-mech↗
arXiv2006

Triangular Lattice Model of 2D Defect Melting

We set up a harmonic lattice model for 2D defect melting which, in contrast to earlier simple-cubic models, lives on a triangular lattice. Integer-valued plastic defect gauge fields allow for the thermal generation of dislocations and disclinations. The model produces universal formulas for the melting temperature expressed in terms of the elastic constants, which are different from those derived for square lattices. They determine a Lindemann-like parameter for two-dimensional melting. In contrast to the square crystal which underwent a first-order melting transition, the triangular model melts in two steps. Our results are applied to the melting of Lennard-Jones and electron lattices.

cond-mat.soft↗
arXiv2005

Quantum Behavior of Deterministic Systems with Information Loss. Path Integral Approach

't Hooft's derivation of quantum from classical physics is analyzed by means of the classical path integral of Gozzi et al.. It is shown how the key element of this procedure - the loss of information constraint - can be implemented by means of Faddeev-Jackiw's treatment of constrained systems. It is argued that the emergent quantum systems are identical with systems obtained in [Phys.Rev. A 71 (2005) 052507] through Dirac-Bergmann's analysis. We illustrate our approach with two simple examples - free particle and linear harmonic oscillator. Potential Liouville anomalies are shown to be absent.

quant-ph↗
arXiv2005

Vortex Origin of Tricritical Point in Ginzburg-Landau Theory

Motivated by recent experimental progress in the critical regime of high-$T_c$ superconductors we show how the tricritical point in a superconductor can be derived from the Ginzburg-Landau theory as a consequence of vortex fluctuations. Our derivation explains why usual renormalization group arguments always produce a first-order transition, in contrast to experimental evidence and Monte Carlo simulations.

cond-mat.supr-con↗
arXiv2005

Nonperturbative Effects on T_c of Interacting Bose Gases in Power-Law Traps

The critical temperature T_c of an interacting Bose gas trapped in a general power-law potential V(x)=\sum_i U_i|x_i|^{p_i} is calculated with the help of variational perturbation theory. It is shown that the interaction-induced shift in T_c fulfills the relation (T_c-T_c^0)/T_c^0= D_1(eta)a + D'(eta)a^{2 eta}+ O(a^2) with T_c^0 the critical temperature of the trapped ideal gas, a the s-wave scattering length divided by the thermal wavelength at T_c, and eta=1/2+\sum_i 1/p_i the potential-shape parameter. The terms D_1(eta)a and D'(eta) a^{2 eta} describe the leading-order perturbative and nonperturbative contributions to the critical temperature, respectively. This result quantitatively shows how an increasingly inhomogeneous potential suppresses the influence of critical fluctuations. The appearance of the a^{2 eta} contribution is qualitatively explained in terms of the Ginzburg criterion.

cond-mat.stat-mech↗
arXiv2005

Perturbation Theory for Path Integrals of Stiff Polymers

The wormlike chain model of stiff polymers is a nonlinear $σ$-model in one spacetime dimension in which the ends are fluctuating freely. This causes important differences with respect to the presently available theory which exists only for periodic and Dirichlet boundary conditions. We modify this theory appropriately and show how to perform a systematic large-stiffness expansions for all physically interesting quantities in powers of $L/ξ$, where $L$ is the length and $ξ$ the persistence length of the polymer. This requires special procedures for regularizing highly divergent Feynman integrals which we have developed in previous work. We show that by adding to the unperturbed action a correction term ${\cal A}^{\rm corr}$, we can calculate all Feynman diagrams with Green functions satisfying Neumann boundary conditions. Our expansions yield, order by order, properly normalized end-to-end distribution function in arbitrary dimensions $d$, its even and odd moments, and the two-point correlation function.

cond-mat.soft↗
arXiv2005

Anomalous Dimension of Dirac's Gauge-Invariant Nonlocal Order Parameter in Ginzburg-Landau Field Theory

In a Ginzburg-Landau theory with $n$ fields, the anomalous dimension of the gauge-invariant nonlocal order parameter defined by the long-distance limit of Dirac's gauge-invariant two-point function is calculated. The result is exact for all $n$ to first order in $ε\equiv 4-d$, and for all $d\in (2,4)$ to first order in $1/n$, and coincides with the previously calculated gauge-dependent exponent in the Landau gauge.

cond-mat.supr-con↗
arXiv2005

Geometric model of dark energy

A cosmological model with a gravitational Lagrangian $L_g(R)\propto R+A R^n$ is set up to account for the presently observed re-acceleration of the universe. The evolution equation for the scale factor $a$ of the universe is analyzed in detail for the two parameters $n=2$ and $n=4/3$, which were preferred by previous studies of the early universe. The initial conditions are specified at a red-shift parameter $z\approx 0$. The fit to the observable data fixes the free parameter $A$. The analysis shows that the model with $n=2$ agrees better with present data. Then, if we set $w(q)=-1$ at $z=0$, corresponding to the deceleration parameter $q\approx -1/2$, we find that at $z\approx 0.5$, $w(q)$ has evolved to $w\approx -0.72$, corresponding to $q\approx 0$. At $z\approx 1$ we find $w\approx 0$ corresponding to $q\approx 1/2$. These results are compared with the flat Friedmann model with cold matter and Lambda-term (LCDM model) for the same initial conditions at $z\approx 0$. The other choice of the model with $n=4/3$ allows for big crunch. However this possibility is eliminated by the fit of $A$ to the present data.

astro-ph↗
arXiv2004

Reentrant Phenomenon in Quantum Phase Diagram of Optical Boson Lattice

We calculate the location of the quantum phase transitions of a bose gas trapped in an optical lattice as a function of effective scattering length $a_{\eff}$ and temperature $T$. Knowledge of recent high-loop results on the shift of the critical temperature at weak couplings is used to locate a {\em nose} in the phase diagram above the free Bose-Einstein critical temperature $T_c^{(0)}$, thus predicting the existence of a reentrant transition {\em above} $T_c^{(0)}$, where a condensate should form when {\em increasing} $a_{\eff}$. At zero temperature, the transition to the normal phase produces the experimentally observed Mott insulator.

cond-mat.stat-mech↗
arXiv2004

Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory

We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by re-calculating the critical exponents of O(N)-symmetric $\vp^4$ theory. From only three-loop perturbation expansions in $4- ε$ dimensions we obtain {\em analytic results for the exponents, with practically the same accuracy as those derived recently from ordinary field-theoretic variational perturbational theory to seventh order. In particular, the theory explains the best-measured exponent $\al\approx-0.0127$ of the specific heat peak in superfluid helium, found in a satellite experiment with a temperature resolution of nanoKelvin. In addition, our analytic expressions reproduce also the exactly known large-N behaviour of the exponents $ ν$ and $ γ= ν(2- η) $ with high precision.

cond-mat.stat-mech↗
arXiv2003

World Nematic Crystal Model of Gravity Explaining the Absence of Torsion

Assuming that at small distances space-time is equivalent to an elastic medium which is isotropic in space and time directions, we demonstrate that the quantum nematic liquid arising from this crystal by spontaneous proliferation of dislocations corresponds with a medium which is merely carrying curvature rigidity. This medium is at large distances indistinguishable from Einstein's spacetime of general relativity. It does not support torsion and possesses string-like curvature sources which in spacetime form world surfaces.

cond-mat.stat-mech↗
arXiv2003

End-to-End Distribution Function

We set up and solve a recursion relation for all even moments of a two-dimensional stiff polymer (Porod-Kratky wormlike chain) and determine from these moments a simple analytic expression for the end-to-end distribution at all persistence lengths.

cond-mat.soft↗
arXiv2003

End-To-End Distribution Function Function of Stiff Polymers for all Persistence Lengths

We set up recursion relations for calculating all even moments of the end-to-end distance of a Porod-Kratky wormlike chains in $D$ dimensions. From these moments we derive a simple analytic expression for the end-to-end distribution in three dimensions valid for all peristence lengths. It is in excellent agreement with Monte Carlo data for stiff chains and goes properly over into the Gaussian random-walk distributions for low stiffness.

cond-mat↗