22 research outputs found
Phase Transitions in Quantum Pattern Recognition
With the help of quantum mechanics one can formulate a model of associative memory with optimal storage capacity. I generalize this model by introducing a parameter playing the role of an effective temperature. The corresponding thermodynamics provides criteria to tune the efficiency of quantum pattern recognition. I show that the associative memory undergoes a phase transition from a disordered high-temperature phase with no correlation between input and output to an ordered, low-temperature phase with minimal input-output Hamming distance
QCD-Like Behaviour of High-Temperature Confining Strings
We show that, contrary to previous string models, the high-temperature behaviour of the recently proposed confining strings reproduces exactly the correct large-N QCD result, a {\it necessary} condition for any string model of confinement
Confining Strings with Topological Term
We consider several aspects of `confining strings', recently proposed to describe the confining phase of gauge field theories. We perform the exact duality transformation that leads to the confining string action and show that it reduces to the Polyakov action in the semiclassical approximation. In 4D we introduce a `-term' and compute the low-energy effective action for the confining string in a derivative expansion. We find that the coefficient of the extrinsic curvature (stiffness) is negative, confirming previous proposals. In the absence of a -term, the effective string action is only a cut-off theory for finite values of the coupling e, whereas for generic values of , the action can be renormalized and to leading order we obtain the Nambu-Goto action plus a topological `spin' term that could stabilize the system
Confining Strings at High Temperature
We show that the high-temperature behaviour of the recently proposed
confining strings reproduces exactly the correct large-N QCD result, for a
large class of truncations of the long-range interaction between surface
elements.Comment: 8 pages, no figure
Classification of Quantum Hall Universality Classes by $\ W_{1+\infty}\ $ symmetry
We show how two-dimensional incompressible quantum fluids and their
excitations can be viewed as edge conformal field theories,
thereby providing an algebraic characterization of incompressibility. The
Kac-Radul representation theory of the algebra leads then to
a purely algebraic complete classification of hierarchical quantum Hall states,
which encompasses all measured fractions. Spin-polarized electrons in
single-layer devices can only have Abelian anyon excitations.Comment: 11 pages, RevTeX 3.0, MPI-Ph/93-75 DFTT 65/9
Infinite Symmetry in the Quantum Hall Effect
Free planar electrons in a uniform magnetic field are shown to possess the
symmetry of area-preserving diffeomorphisms (-infinity algebra).
Intuitively, this is a consequence of gauge invariance, which forces dynamics
to depend only on the flux. The infinity of generators of this symmetry act
within each Landau level, which is infinite-dimensional in the thermodynamical
limit. The incompressible ground states corresponding to completely filled
Landau levels (integer quantum Hall effect) are shown to be infinitely
symmetric, since they are annihilated by an infinite subset of generators. This
geometrical characterization of incompressibility also holds for fractional
fillings of the lowest level (simplest fractional Hall effect) in the presence
of Haldane's effective two-body interactions. Although these modify the
symmetry algebra, the corresponding incompressible ground states proposed by
Laughlin are again symmetric with respect to the modified infinite algebra.Comment: 28 page
Conformal Symmetry and Universal Properties of Quantum Hall States
The low-lying excitations of a quantum Hall state on a disk geometry are edge
excitations. Their dynamics is governed by a conformal field theory on the
cylinder defined by the disk boundary and the time variable. We give a simple
and detailed derivation of this conformal field theory for integer filling,
starting from the microscopic dynamics of -dimensional non-relativistic
electrons in Landau levels. This construction can be generalized to describe
Laughlin's fractional Hall states via chiral bosonization, thereby making
contact with the effective Chern-Simons theory approach. The conformal field
theory dictates the finite-size effects in the energy spectrum. An experimental
or numerical verification of these universal effects would provide a further
confirmation of Laughlin's theory of incompressible quantum fluids.Comment: 39 pages, 7 figures (not included, they are mailed on request),
harvmac CERN-TH 6702/9