A Scaling Approach to Ideal Quantum Gases
The thermodynamic properties of ideal quantum gases are derived solely from dimensional arguments, the Pauli principle and thermodynamic relations, without resorting to statistical mechanics.
physics.ed-ph↗
arXiv subjects
Thomas Nattermann
Publications and source records attributed to Thomas Nattermann.
Pinning and Sliding of Driven Elastic Systems: from Domain Walls to Charge Density Waves
The review is devoted to the theory of collective and it local pinning effects in various disordered non-linear driven systems. Although the emphasis is put on charge and spin density waves and magnetic domain walls, the theory has also applications to flux lines and lattices thereof, dislocation lines, adsorbed mono-layers and related systems. In the first part we focus on the theory of the collective pinning which includes the equilibrium properties of elastic systems with frozen-in disorder as well as the features close to the dynamic depinning transition enforced by an external driving force and at finite temperatures. Thermal fluctuations smear out this transition and allow for a creep motion of the elastic objects even at small forces. An ac-driving force also destroys the sharp transition which is replaced by a velocity hysteresis. The second part is devoted to the local pinning picture and its applications. Inclusion of plastic deformations results in a rich cross-over behavior of the force-velocity relation as well as of the frequency dependence of the dynamic response. The local pinning recovers and exploits new elements of the energy landscape such as termination points of metastable branches or irreversibility of other ones related to generation of topological defects in the course of sliding. It also gives access to the quantum creep described as a tunneling between retarded and advanced configurations.
cond-mat.stat-mech↗
Hysteresis mediated by a domain wall motion
The position of an interface (domain wall) in a medium with random pinning defects is not determined unambiguously by a current value of the driving force even in average. Based on general theory of the interface motion in a random medium we study this hysteresis, different possible shapes of domain walls and dynamical phase transitions between them. Several principal characteristics of the hysteresis, including the coercive force and the curves of dynamical phase transitions obey scaling laws and display a critical behavior in a vicinity of the mobility threshold. At finite temperature the threshold is smeared and a new range of thermally activated hysteresis appears. At a finite frequency of the driving force there exists a range of the non-adiabatic regime, in which not only the position, but also the average velocity of the domain wall displays hysteresis.
cond-mat.dis-nn↗
Influence of thermal fluctuations on quantum phase transitions in one-dimensional disordered systems: Charge density waves and Luttinger liquids
The low temperature phase diagram of 1D weakly disordered quantum systems like charge or spin density waves and Luttinger liquids is studied by a \emph{full finite temperature} renormalization group (RG) calculation. For vanishing quantum fluctuations this approach is amended by an \emph{exact} solution in the case of strong disorder and by a mapping onto the \emph{Burgers equation with noise} in the case of weak disorder, respectively. At \emph{zero} temperature we reproduce the quantum phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At \emph{finite} temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wave length of the phason excitations. The existence of a zero temperature transition is reflected in a rich cross-over phase diagram of the correlation functions. In particular we find four different scaling regions: a \emph{classical disordered}, a \emph{quantum disordered}, a \emph{quantum critical} and a \emph{thermal} region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential. Applications to related systems are discussed as well.
cond-mat.str-el↗
Flux-lattice melting in two-dimensional disordered superconductors
The flux line lattice melting transition in two-dimensional pure and disordered superconductors is studied by a Monte Carlo simulation using the lowest Landau level approximation and quasi-periodic boundary condition on a plane. The position of the melting line was determined from the diffraction pattern of the superconducting order parameter. In the clean case we confirmed the results from earlier studies which show the existence of a quasi-long range ordered vortex lattice at low temperatures. Adding frozen disorder to the system the melting transition line is shifted to slightly lower fields. The correlations of the order parameter for translational long range order of the vortex positions seem to decay slightly faster than a power law (in agreement with the theory of Carpentier and Le Doussal) although a simple power law decay cannot be excluded. The corresponding positional glass correlation function decays as a power law establishing the existence of a quasi-long range ordered positional glass formed by the vortices. The correlation function characterizing a phase coherent vortex glass decays however exponentially ruling out the possible existence of a phase coherent vortex glass phase.
cond-mat.supr-con↗
Displacement Profile of Charge Density Waves and Domain Walls at Critical Depinning
The influence of a strong surface potential on the critical depinning of an elastic system driven in a random medium is considered. If the surface potential prevents depinning completely the elastic system shows a parabolic displacement profile. Its curvature $\mathcal{C}$ exhibits at zero temperature a pronounced rhombic hysteresis curve of width $2f_c$ with the bulk depinning threshold $f_c$. The hysteresis disappears at non-zero temperatures if the driving force is changed adiabatically. If the surface depins by the applied force or thermal creep, $\mathcal{C}$ is reduced with increasing velocity. The results apply, e.g., to driven magnetic domain walls, flux-line lattices and charge-density waves.
cond-mat.stat-mech↗
Variable range hopping and quantum creep in one dimension
We study the quantum non linear response to an applied electric field $E$ of a one dimensional pinned charge density wave or Luttinger liquid in presence of disorder. From an explicit construction of low lying metastable states and of bounce instanton solutions between them, we demonstrate quantum creep $v = e^{- c/E^{1/2}}$ as well as a sharp crossover at $E=E^*$ towards a linear response form consistent with variable range hopping arguments, but dependent only on electronic degrees of freedom.
cond-mat.dis-nn↗
One-dimensional Disordered Density Waves and Superfluids: The Role of Quantum Phase Slips and Thermal Fluctuations
The low temperature phase diagram of 1D disordered quantum systems like charge or spin density waves, superfluids and related systems is considered by a full finite T renormalization group approach, presented here for the first time. At zero temperature the consideration of quantum phase slips leads to a new scenario for the unpinning (delocalization) transition. At finite T a rich cross-over diagram is found which reflects the zero temperature quantum critical behavior.
cond-mat.str-el↗
A New Criterion for Crack Formation in Disordered Materials
Crack formation is conventionally described as a nucleation phenomenon despite the fact that the temperatures necessary to overcome the nucleation barrier are far too high. In this paper we consider the possibility that cracks are created due to the presence of frozen disorder (e.g. heterogeneities or frozen dislocations). In particular we calculate the probability for the occurrence of a critical crack in a quasi two-dimensional disordered elastic system. It turns out that this probability takes the form of an Arrhenius law (as for thermal nucleation) but with the temperature T replaced by an effective disorder temperature T_eff which depends on the strength of the disorder. The extension of these results to d=3 dimensions is briefly discussed.
cond-mat.stat-mech↗
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↗
Reply to "Comment on `Roughening Transition of Interfaces in Disordered Systems'"
We reply to the recent comment cond-mat/9810097 on our original Letter `Roughening Transition of Interfaces in Disordered Systems', Phys. Rev. Lett. 81, 1469 (1998).
cond-mat.stat-mech↗
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↗
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↗
Van der Waals interaction between flux lines in High-T_c Superconductors
In anisotropic or layered superconductors thermal fluctuations as well as impurities induce a van der Waals (vdW) attraction between flux lines, as has recently been shown by Blatter and Geshkenbein in the thermal case [Phys. Rev. Lett. 77, 4958 (1996)] and by Mukherji and Nattermann in the disorder dominated case [Phys. Rev. Lett. 79, 139 (1997)]. This attraction together with the entropic or disorder induced repulsion has interesting consequences for the low field phase diagram. We present two derivations of the vdW attraction, one of which is based on an intuitive picture, the other one following from a systematic expansion of the free energy of two interacting flux lines. Both the thermal and the disorder dominated case are considered. In the thermal case in the absence of disorder, we use scaling arguments as well as a functional renormalization of the vortex-vortex interaction energy to calculate the effective Gibbs free energy on the scale of the mean flux line distance. We discuss the resulting low field phase diagram and make quantitative predictions for pure BiSCCO (Bi_2-Sr_2-CaCu_2-O_8). In the case with impurities, the Gibbs free energy is calculated on the basis of scaling arguments, allowing for a semi-quantitative discussion of the low-field, low-temperature phase diagram in the presence of impurities.
cond-mat.supr-con↗
Theory of Hysteresis Loop in Ferromagnets
We consider three mechanisms of hysteresis phenomena in alternating magnetic field: the domain wall motion in a random medium, the nucleation and the retardation of magnetization due to slow (critical) fluctuations. We construct quantitative theory for all these processes. The hysteresis is characterized by two dynamic threshold fields, by coercive field and by the so-called reversal field. Their ratios to the static threshold field is shown to be function of two dimensionless variables constituted from the frequency and amplitude of the ac field as well as from some characteristics of the magnet. The area and the shape of the hysteresis loop are found. We consider different limiting cases in which power dependencies are valid. Numerical simulations show the domain wall formation and propagation and confirm the main theoretical predictions. Theory is compared with available experimental data.
cond-mat.mtrl-sci↗
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↗
Steric repulsion and van der Waals attraction between flux lines in disordered high Tc superconductors
We show that in anisotropic or layered superconductors impurities induce a van der Waals attraction between flux lines. This attraction together with the disorder induced repulsion may change the low B - low T phase diagram significantly from that of the pure thermal case considered recently by Blatter and Geshkenbein [Phys. Rev. Lett. 77, 4958 (1996)].
cond-mat.stat-mech↗
On the Incommensurate Phase of Pure and Doped Spin-Peierls System CuGeO_3
Phases and phase transitions in pure and doped spin-Peierls system CuGeO_3 are considered on the basis of a Landau-theory. In particular we discuss the critical behaviour, the soliton width and the low temperature specific heat of the incommensurate phase. We show, that dilution leads always to the destruction of long range order in this phase, which is replaced by an algebraic decay of correlations if the disorder is weak.
cond-mat.dis-nn↗