927 research outputs found
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
Domain Walls in Helical Magnets: Elasticity and Pinning
Recently completely new types of domain walls (DWs) have been discovered in
helical magnets, consisting generically of a regular array of {\it pairs} of
magnetic vortex lines \cite{Li+12}. Only for special orientations DWs are free
of vortices. In this article we calculate their elastic and pinning properties,
using the pitch angle as a small parameter. In particular we show that
vortex free DWs exhibit long range elasticity which makes them very stiff and
suppresses their pinning by impurities. Their roughening transition temperature
is of the order of the N\'eel temperature. DWs including vortices (either by
orientation or due to step formation above their roughening transition) show
short range elasticity and strong pinning by impurities. These results apply
both to centro-symmetric as well as to non-centrosymmetric systems. The
application to chiral liquid crystals is briefly discussed
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 \epsilon=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/\pi\sqrt{\epsilon}. For p<p_c the medium is always flat. Critical
exponents are calculated in a double expansion in \mu=p^2/p_c^2-1 and
\epsilon=4-D and fulfill the scaling relations of random field models.Comment: 23 pages, 9 figure
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 exhibits at zero temperature
a pronounced rhombic hysteresis curve of width with the bulk depinning
threshold . 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, is reduced with increasing velocity. The
results apply, e.g., to driven magnetic domain walls, flux-line lattices and
charge-density waves.Comment: 4 pages, 2 figure
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
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.Comment: 19 pages EPJ style, 9 PostScript figures. Minor additions to the
first submission. Accepted for publication in EPJ
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