Searcharxiv⌕ Search

arXiv subjects

Adriaan M. J. Schakel

Publications and source records attributed to Adriaan M. J. Schakel.

At least 37 records · Page 2Linked to original sources
arXiv2003

Zeta Function Regularization of Infrared Divergences in Bose-Einstein Condensation

The perturbative calculation of the effect of fluctuations in the nonzero frequency modes of a weakly interacting Bose gas on the condensation temperature is reviewed. These dynamic modes, discarded in most of the recent studies, have a temperature-induced energy gap that allows for a perturbative approach. The simple, yet powerful algorithm used to calculate the effect in a high-temperature expansion in conjunction with zeta function regularization of infrared divergences is explained in detail. The algorithm is shown to be reliable by demonstrating that it reproduces known results for a series of examples. With two-loop contributions properly included, the dynamic modes are seen not to lead to a shift in the condensation temperature, thus revising our earlier finding obtained at one loop.

cond-mat↗
arXiv2002

Gauge-invariant critical exponents for the Ginzburg-Landau model

The critical behavior of the Ginzburg-Landau model is described in a manifestly gauge-invariant manner. The gauge-invariant correlation-function exponent is computed to first order in the $4-d$ and $1/n$-expansion, and found to agree with the ordinary exponent obtained in the covariant gauge, with the parameter $α=1-d$ in the gauge-fixing term $(\partial_μA_μ)^2 /2 α$.

cond-mat↗
arXiv2002

Entangled Vortices: Onsager's geometrical picture of superfluid phase transitions

Superfluid phase transitions are discussed from a geometrical perspective as envisaged by Onsager. The approach focuses on vortex loops which close to the critical temperature form a fluctuating vortex tangle. As the transition is approached, vortex lines proliferate and thereby disorder the superfluid state, so that the system reverts to the normal state. It is shown in detail that loop proliferation can be described in exactly the same way as cluster percolation. Picturing vortex loops as worldlines of bosons, with one of the spatial coordinates interpreted as the time coordinate, a quantitative description of vortex loops can be given. Applying a rotation (to superfluids) or a magnetic field (to superconductors), which suppresses the formation of vortex loops and instead can lead to open vortex lines along the field direction, is shown to be equivalent to taking the nonrelativistic limit. The nonrelativistic theory is the one often used to study vortex lattice melting and to describe the resulting entangled vortex liquid.

cond-mat↗
arXiv2001

On the Ground State of Electron Gases at Negative Compressibility

Two- and three-dimensional electron gases with a uniform neutralizing background are studied at negative compressibility. Parametrized expressions for the dielectric function are used to access this strong-coupling regime, where the screened Coulomb potential becomes overall attractive for like charges. Closely examining these expressions reveals that the ground state with a periodic modulation of the charge density, albeit exponentially damped, replaces the homogeneous one at positive compressibility. The wavevector characterizing the new ground state depends on the density and is complex, having a positive imaginary part, as does the homogeneous ground state, and real part, as does the genuine charge density wave.

cond-mat↗
arXiv2001

Effective Free Energy of Ginzburg-Landau Model

It is argued that the presence of a nonanalytic term in the effective potential of the Ginzburg-Landau model is immaterial as far as the order of the superconductor-normal phase transition is concerned. To achieve agreement with the renormalization group, the effective potential has to be extended to include derivative terms, which provide the theory with a low momentum scale which can be varied to probe the (possible) fixed point.

cond-mat↗
arXiv2000

Superconductor-Insulator Quantum Phase Transitions

In these lectures, superconductivity in impure thin films close to the absolute zero of temperature is discussed. The behavior as function of the applied magnetic field and the amount of impurities suggests the presence of a superconductor-insulator transition at zero temperature. The theory of superconductivity in the limit where all the electrons become tightly bound in pairs is used to explain the main characteristics of the transition. In that limit, where the theory becomes equivalent to a phase-only theory, electron pairs exist on either side of the transition. The presentation is pedagogical in nature and includes exercises as a learning aid for those new to the field.

cond-mat↗
arXiv2000

Self-Duality in Superconductor-Insulator Quantum Phase Transitions

It is argued that close to a Coulomb interacting quantum critical point, the interaction between two vortices in a disordered superconducting thin film separated by a distance $r$ changes from logarithmic in the mean-field region to $1/r$ in the region dominated by quantum critical fluctuations. This gives support to the charge-vortex duality picture of the observed reflection symmetry in the current-voltage characteristics on both sides of the transition.

cond-mat↗
arXiv2000

Percolation, Bose-Einstein Condensation, and String Proliferation

The close analogy between cluster percolation and string proliferation in the context of critical phenomena is studied. Like clusters in percolation theory, closed strings, which can be either finite-temperature worldlines or topological line defects, are described by a distribution parametrized by only two exponents. On approaching the critical point, the string tension vanishes, and the loops proliferate thereby signalling the onset of Bose-Einstein condensation (in case of worldlines) or the disordering of the ordered state (in case of vortices). The ideal Bose gas with modified energy spectrum is used as a stepping stone to derive general expressions for the critical exponents in terms of the two exponents parameterizing the loop distribution near criticality.

cond-mat↗
arXiv2000

Vertical Melting of a Stack of Membranes

A stack of tensionless membranes with nonlinear curvature energy and vertical harmonic interaction is studied. At low temperatures, the system forms a lamellar phase. At a critical temperature, the stack disorders vertically in a melting-like transition.

cond-mat↗
arXiv2000

Comment on "The Transition Temperature of the Dilute Interacting Bose Gas" and on "Transition Temperature of a Uniform Bose Gas"

It is pointed out that first, contrary to the claim by Baym et al.[Phys. Rev. Lett 83, 1703 (1999)], the shift in the transition temperature of a weakly interacting Bose gas can be calculated perturbatively. And second, that the regime considered by Huang [Phys. Rev. Lett 83, 3770 (1999)] while addressing the same issue does not describe the Bose-Einstein condensed phase.

cond-mat↗
arXiv2000

Quantum Statistical Mechanics of Nonrelativistic Membranes: Crumpling Transition at Finite Temperature

The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to {\em stiffen} the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.

cond-mat↗
arXiv1999

String Picture of Bose-Einstein Condensation

A nonrelativistic Bose gas is represented as a grand-canonical ensemble of fluctuating closed spacetime strings of arbitrary shape and length. The loops are characterized by their string tension and the number of times they wind around the imaginary time axis. At the temperature where Bose-Einstein condensation sets in, the string tension, being determined by the chemical potential, vanishes, the system becomes critical, and the strings proliferate. A comparison with Feynman's description in terms of rings of cyclicly permuted bosons shows that the winding number of a loop corresponds to the number of particles contained in a ring.

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

Time-Dependent Ginzburg-Landau Theory and Duality

In the first part of this review paper, the time-dependent Ginzburg-Landau theory is derived starting from the microscopic BCS model with the help of a derivative expansion. Special attention is paid to two space dimensions, where the entire crossover from the weak-coupling BCS limit to the strong-coupling BEC limit of tightly bound fermion pairs is accessible analytically. The second part deals with the dual approach to the time-independent Ginzburg-Landau theory in three space dimensions. In this approach, the magnetic vortices of a superconductor play the central role, and the superconductor-to-normal phase transition is understood as a proliferation of these vortices.

cond-mat↗
arXiv1998

Quantum Phase Transitions in 2d Quantum Liquids

These lectures provide a pedagogical introduction to the theory of continuous quantum phase transitions. Various two-dimensional condensed matter systems, such as a superconducting film, a quantum Hall liquid, and an array of Josephson junctions, undergo such a phase transition at the absolute zero of temperature. The universality classes defined by repulsively interacting bosons with and without disorder are shown to play a central role in understanding these systems.

cond-mat↗
arXiv1998

On the Description of Quantum Vortices in Superfluid Films

The dynamics of vortices in a superfluid film at the absolute zero of temperature is studied. The quantum-mechanical, i.e., ``first-quantized'' description is compared to a recently proposed quantum-field-theoretic, i.e., ``second-quantized'' description. The theory, consisting of the nonrelativistic effective action of phonons linearly coupled to a Chern-Simons term, is used to calculate the one-loop amplitude for the elastic scattering of phonons from a vortex.

cond-mat↗
arXiv1998

Boulevard of Broken Symmetries

Effective theories of quantum liquids (superconductors and superfluids of various types) are derived starting from microscopic models at the absolute zero of temperature. Special care is taken to assure Galilei invariance. The effective theories are employed to investigate the quantum numbers carried by the topological defects present in the phases with spontaneously broken symmetries. Due to topological terms induced by quantum fluctuations, these numbers are sometimes found to be fractional. The zero-temperature effective theories are further used to study the quantum critical behavior of the liquid-to-insulator transition which these systems undergo as the applied magnetic field, the amount of impurities, or the charge carrier density varies. The classical, finite-temperature phase transitions to the normal state are discussed from the point of view of dual theories, where the defects of the original formulation become the elementary excitations. A connection with bosonization is pointed out.

cond-mat↗