Density of hedgehogs just after a quench
Density of vortices and monopoles after a rapid pressure quench is predicted. Critical exponents are worked out in overdamped and underdamped limits.
cond-mat↗
arXiv subjects
Jacek Dziarmaga
Publications and source records attributed to Jacek Dziarmaga.
Density of kinks just after a quench in an underdamped system
A quench in an underdamped one dimensional $ϕ^4$ model is studied by analytical methods. The density of kinks just after the transition is proportional to the square root of the rate of the quench for slow quenches. If the quench is shorter that the relaxation time, then the density scales like the third root of the rate.
cond-mat↗
Density of kinks just after a quench in an overdamped system
A quench in an overdamped one dimensional $ϕ^4$ model is studied by analytical and numerical methods. For an infinite system or a finite system with free boundary conditions, the density of kinks after the transition is proportional to the eighth root of the rate of the quench. For a system with periodic boundary conditions, it is proportional to the fourth root of the rate. The critical exponent predicted in Zurek scenario is put in question.
cond-mat↗
Unpolarized quasielectrons and the spin polarization at filling fractions between 1/3 and 2/5
We prove that for a hard core interaction the ground state spin polarization in the low Zeeman energy limit is given by $P=2/ν-5$ for filling fractions in the range $ 1/3 \leqν\leq 2/5 $. The same result holds for a Coulomb potential except for marginally small magnetic fields. At the magnetic fields $B<20T$ unpolarized quasielectrons can manifest themselves by a characteristic peak in the I-V characteristics for tunneling between two $ν=1/3$ ferromagnets.
cond-mat↗
Dissipative Dynamics of Solitons in Planar Ferromagnets
Dynamics of magnetic bubbles in planar ferromagnets described by the Landau-Lifshitz equation with dissipation is analyzed. The pure O(3) sigma model has static multisoliton solutions, characterized by a number of parameters. The parameters describe a finite dimensional manifold. A small perturbation of energy functional with respect to the sigma model forces solitons to move. Multisoliton dynamics is effectively reduced to a flow in the parameter space.
cond-mat↗
Statistics of skyrmions and the 5/2 puzzle
1) For the hard core interaction there is some freedom left in the choice of the exact multiskyrmionic wave function's topology. The statistics of textured quasiholes, analyzed by calculation of the Berry phase, depends on this choice of topology. 2) We find a class of textured two-hole eigenstates of the Coulomb interaction. There is no definite quantum statistics but there is a definite rule of how to construct Coulomb eigenstates out of the hard core wave functions. 3) A wave function for the 5/2 state is constructed according to this rule.
cond-mat.mes-hall↗
Transition from ν=8/5 to ν=5/3 in the low Zeeman energy limit
Skyrmions in the FQHE at filling fractions above ν=1/3 are studied within the anyon model and by exact diagonalization. Relations to the composite fermion theory are pointed out. We find that unpolarized quasiparticles above ν=1/3 are stable below B\approx 0.02T. At low Zeeman energy the polarization in the range ν=8/5 ... 5/3 is found to be a linear function of the filling factor. We also reexamine the energy and wave function of skyrmions at ν=1 by a new method.
cond-mat.mes-hall↗
Skyrmions in quantum Hall systems are dynamical objects
Removed to be revised. Diagonalization for a larger cut-off M shows that the definite size effects are M-dependent. Scaling with M shows that in the thermodynamic limit the skyrmion wave-function tends to the translationally invariant hard core wave function. Finite M breaks translational invariance and at the same time it exponentially suppresses the tail of the wave-function. Details will be published.
cond-mat↗
Einstein-Infeld-Hoffman method and soliton dynamics in a parity noninvariant system
We consider slow motion of a pointlike topological defect (vortex) in the nonlinear Schrodinger equation minimally coupled to Chern-Simons gauge field and subject to external uniform magnetic field. It turns out that a formal expansion of fields in powers of defect velocity yields only the trivial static solution. To obtain a nontrivial solution one has to treat velocities and accelerations as being of the same order. We assume that acceleration is a linear form of velocity. The field equations linearized in velocity uniquely determine the linear relation. It turns out that the only nontrivial solution is the cyclotron motion of the vortex together with the whole condensate. This solution is a perturbative approximation to the center of mass motion known from the theory of magnetic translations.
hep-th↗
Statistics of skyrmions in Quantum Hall systems
We analyze statistical interactions of skyrmions in the quantum Hall system near a critical filling fraction in the framework of the Ginzburg-Landau model. The phase picked up by the wave-function during an exchange of two skyrmions close to $ν=1/(2n+1)$ is $π[S+1/2(2n+1)]$, where $S$ is the skyrmion's spin. In the same setting an exchange of two fully polarized vortices gives rise to the phase $π/(2n+1)$. Skyrmions with odd and even numbers of reversed spins have different quantum statistics. Condensation of skyrmions with an even number of reversed spins leads to filling fractions with odd denominators, while condensation of those with an odd number of reversed spins gives rise to filling fractions with even denominators.
cond-mat↗
Vortices in superconducting films - statistics and fractional quantum Hall effect
We present a new derivation of the Berry phase picked up during exchange of parallel vortices. This derivation is based on the Bogolubov - de Gennes formalism. The origin of the Magnus force is also critically reanalised. The Magnus force can be interpreted as interaction with effective magnetic field. The efective magnetic field may be even of the order $10^{6} T/Å$. We discuss a possibility of the FQHE in vortex systems. As the real magnetic field is varied to drive changes in vortex density, the vortex density will prefer to stay at some quantised values. The mere existence of the FQHE does not depend on vortex quantumstatistics although the pattern of the plateaux does. We also discuss how the density of anyonic vortices can lower the effective strengh of the Magnus force, what might be observable in measurements of Hall resitivity.
cond-mat↗
Dynamics of overlapping vortices in complex scalar fields
We investigate dynamics of overlapping vortices in the nonlinear Schrödinger equation, the nonlinear heat equation and in the equation with an intermediate Schrödinger-diffusion dynamics. Because of formal similarity on a perturbative level we discuss also the nonlinear wave equation (Goldstone model). Special solutions are found like vortex helices, double-helices and braids, breather states and vortex mouths. A pair of vortices in the Goldstone model scatters by the right angle in the head-on collision. It is found that in a dissipative system there is a characteristic lenght scale above which vortices can be entangled but below which the entanglement is unstable.
cond-mat↗
Vortices in superconducting films are anyons
We point out that nontrivial quantumstatistics of vortices in planar superfluid systems has its origin in the Schrodinger equation rather then the Chern-Simons term. Vortices in superfluid helium films are not anyons because helium films are compressible. Quantum Hall effect layers admit vortices with nontrivial statistical interactions thanks to their incompressibility. We consider type II planar superconductors described by time-dependent nonlinear Schrodinger equation. Inside of a vortex core superconductor is in the normal state. Because of that vortices in superconducting films are anyons. We consider also vortex loops in 3 dimensions but a phase factor due to linking of vortex loops' worldsheets is not a topological invariant.
cond-mat↗
Intercommutation of Z-string loops violates baryon number
We show that delinking of Z-string loops changes helicity and thus violates baryon number. The key point is that an unlinked vortex loop can not be twisted. Helicity of an eventual magnetic twist when averaged in time is zero.
hep-ph↗
More on scattering of Chern-Simons vortices
I derive a general formalism for finding kinetic terms of the effective Lagrangian for slowly moving Chern-Simons vortices. Deformations of fields linear in velocities are taken into account. From the equations they must satisfy I extract the kinetic term in the limit of coincident vortices. For vortices passing one over the other there is locally the right-angle scattering. The method is based on analysis of field equations instead of action functional so it may be useful also for nonvariational equations in nonrelativistic models of Condensed Matter Physics.
hep-th↗
Vortices and hierarchy of states in double-layer fractional Hall effect
Vortex solutions in $U(1)\times U(1)$ Chern-Simons theory coupled to a pair of hard-core bosons representing two layers of electrons are analysed. It is shown that there is such a range of parameters $(αβ<γ^{2})$ in which finite charge $(1,0)$ or $(0,1)$ vortices can not exist. Instead the minimal flux quanta are $(1,1)$ hybrids. Their statistical dominance is shown to have an influence on Haldane-Halderin hierarchy of states. The form of Coulomb potential and its influence on the range of physically acceptable states is discussed.
cond-mat↗
Only hybrid anyons can exist in broken symmetry phase of nonrelativistic $U(1)^{2}$ Chern-Simons theory
We present two examples of parity-invariant $[U(1)]^{2}$ Chern-Simons-Higgs models with spontaneously broken symmetry. The models possess topological vortex excitations. It is argued that the smallest possible flux quanta are composites of one quantum of each type $(1,1)$. These hybrid anyons will dominate the statistical properties near the ground state. We analyse their statistical interactions and find out that unlike in the case of Jackiw-Pi solitons there is short range magnetic interaction which can lead to formation of bound states of hybrid anyons. In addition to mutual interactions they possess internal structure which can lead upon quantisation to discrete spectrum of energy levels.
hep-th↗
Travelling waves in multivortex configurations
We investigate zero modes of a multivortex background which are due to the energetic degeneracy of the planar static n-vortex solution in Bogomol'nyi limit of the Abelian Higgs model parametrised by a set of 2n real parameters. The zero modes take the form of waves travelling with a speed of light independently along each of the vortices irrespectively to their mutual separations. String description of these zero modes is constructed. We also comment on the remnants of the modes a little outside of the Bogomol'nyi limit.
hep-th↗