1,865 research outputs found
Classical Time Crystals
We consider the possibility that classical dynamical systems display motion
in their lowest energy state, forming a time analogue of crystalline spatial
order. Challenges facing that idea are identified and overcome. We display
arbitrary orbits of an angular variable as lowest-energy trajectories for
nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry
provide a natural arena for formation of time crystals. We exhibit models of
that kind, including a model with traveling density waves.Comment: 5 pages, 1 figur
Lagrangian Particle Statistics in Turbulent Flows from a Simple Vortex Model
The statistics of Lagrangian particles in turbulent flows is considered in
the framework of a simple vortex model. Here, the turbulent velocity field is
represented by a temporal sequence of Burgers vortices of different
circulation, strain, and orientation. Based on suitable assumptions about the
vortices' statistical properties, the statistics of the velocity increments is
derived. In particular, the origin and nature of small-scale intermittency in
this model is investigated both numerically and analytically
Model study of the sign problem in the mean-field approximation
We argue the sign problem of the fermion determinant at finite density. It is
unavoidable not only in Monte-Carlo simulations on the lattice but in the
mean-field approximation as well. A simple model deriving from Quantum
Chromodynamics (QCD) in the double limit of large quark mass and large quark
chemical potential exemplifies how the sign problem arises in the Polyakov loop
dynamics at finite temperature and density. In the color SU(2) case our
mean-field estimate is in excellent agreement with the lattice simulation. We
combine the mean-field approximation with a simple phase reweighting technique
to circumvent the complex action encountered in the color SU(3) case. We also
investigate the mean-field free energy, from the saddle-point of which we can
estimate the expectation value of the Polyakov loop.Comment: 14 page, 18 figures, typos corrected, references added, some
clarification in sec.I
Shiba impurity bound states as a probe of topological superconductivity and Fermion parity changing quantum phase transitions
Spin-orbit coupled superconductors are potentially interesting candidates for
realizing topological and potentially non-Abelian states with Majorana
Fermions. We argue that time-reversal broken spin-orbit coupled superconductors
generically can be characterized as having sub-gap states that are bound to
localized non-magnetic impurities. Such bound states, which are referred to as
Shiba states, can be detected as sharp resonances in the tunneling spectrum of
the spin-orbit coupled superconductors. The Shiba state resonance can be tuned
using a gate-voltage or a magnetic field from being at the edge of the gap at
zero magnetic fields to crossing zero energy when the Zeeman splitting is tuned
into the topological superconducting regime. The zero-crossing signifies a
Fermion parity changing first order quantum phase transition, which is
characterized by a Pfaffian topological invariant.
These zero-crossings of the impurity level can be used to locally
characterize the topological superconducting state from tunneling experiments.Comment: 5 pages; 3 figures: minor reference update
Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate
A real-space formulation is given for the recently discussed exciton
condensate in a symmetrically biased graphene bilayer. We show that in the
continuum limit an oddly-quantized vortex in this condensate binds exactly one
zero mode per valley index of the bilayer. In the full lattice model the zero
modes are split slightly due to intervalley mixing. We support these results by
an exact numerical diagonalization of the lattice Hamiltonian. We also discuss
the effect of the zero modes on the charge content of these vortices and deduce
some of their interesting properties.Comment: (v2) A typo in Fig. 1 and a slight error in Eq. (4) corrected; all
the main results and conclusions remain unchange
SO(3) family symmetry and axions
Motivated by the idea of comprehensive unification, we study a gauged SO(3)
flavor extension of the extended Standard Model, including right-handed
neutrinos and a Peccei-Quinn symmetry with simple charge assignments. The model
accommodates the observed fermion masses and mixings and yields a
characteristic, successful relation among them. The Peccei-Quinn symmetry is an
essential ingredient.Comment: 9 pages, matches published versio
Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
We construct a Hamiltonian that singles out the chiral spin liquid on a
square lattice with periodic boundary conditions as the exact and, apart from
the two-fold topological degeneracy, unique ground state.Comment: 5 pages, no figure
Is there an attraction between spinons in the Haldane--Shastry model?
While the Bethe Ansatz solution of the Haldane--Shastry model appears to
suggest that the spinons represent a free gas of half-fermions, Bernevig,
Giuliano, and Laughlin (BGL) (cond-mat/0011069, cond-mat/0011270) have
concluded recently that there is an attractive interaction between spinons. We
argue that the dressed scattering matrix obtained with the asymptotic Bethe
Ansatz is to be interpreted as the true and physical scattering matrix of the
excitations, and hence, that the result by BGL is inconsistent with an earlier
result by Essler (cond-mat/9406081). We critically re-examine the analysis of
BGL, and conclude that there is no interaction between spinons or spinons and
holons in the Haldane--Shastry model
Energy Spectrum of Anyons in a Magnetic Field
For the many-anyon system in external magnetic field, we derive the energy
spectrum as an exact solution of the quantum eigenvalue problem with particular
topological constraints. Our results agree with the numerical spectra recently
obtained for the 3- and the 4-anyon systems.Comment: 11 pages in Plain LaTeX (plus 4 figures available on request), DFPD
92/TH/4
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