23 research outputs found
General topological features and instanton vacuum in quantum Hall and spin liquids
We introduce the concept of super universality in quantum Hall and spin
liquids which has emerged from previous studies. It states that all the
fundamental features of the quantum Hall effect are generically displayed as
general topological features of the parameter in nonlinear sigma
models in two dimensions. To establish super universality in spin liquids we
revisit the mapping by Haldane who argued that the anti ferromagnetic
Heisenberg spin chain is effectively described by the O(3) nonlinear sigma
model with a term. By combining the path integral representation for
the dimerized spin chain with renormalization group decimation
techniques we generalise the Haldane approach to include a more complicated
theory, the fermionic rotor chain, involving four different renormalization
group parameters. We show how the renormalization group calculation technique
can be used to lay the bridge between the fermionic rotor chain and the sigma
model. As an integral and fundamental aspect of the mapping we establish the
topological significance of the dangling spin at the edge of the chain which is
in all respects identical to the massless chiral edge excitations in quantum
Hall liquids. We consider various different geometries of the spin chain and
show that for each of the different geometries correspond to a topologically
equivalent quantum Hall liquid.Comment: Title changed, Section 2 and Appendix expanded, an error in the
expression for theta correcte
Ground state fidelity and quantum phase transitions in free Fermi systems
We compute the fidelity between the ground states of general quadratic
fermionic hamiltonians and analyze its connections with quantum phase
transitions. Each of these systems is characterized by a real
matrix whose polar decomposition, into a non-negative and a unitary
, contains all the relevant ground state (GS) information. The boundaries
between different regions in the GS phase diagram are given by the points of,
possibly asymptotic, singularity of . This latter in turn implies a
critical drop of the fidelity function. We present general results as well as
their exemplification by a model of fermions on a totally connected graph.Comment: 4 pages, 2 figure
New nonlinear coherent states and some of their nonclassical properties
We construct a displacement operator type nonlinear coherent state and
examine some of its properties. In particular it is shown that this nonlinear
coherent state exhibits nonclassical properties like squeezing and
sub-Poissonian behaviour.Comment: 3 eps figures. to appear in J.Opt
The quantum state vector in phase space and Gabor's windowed Fourier transform
Representations of quantum state vectors by complex phase space amplitudes,
complementing the description of the density operator by the Wigner function,
have been defined by applying the Weyl-Wigner transform to dyadic operators,
linear in the state vector and anti-linear in a fixed `window state vector'.
Here aspects of this construction are explored, with emphasis on the connection
with Gabor's `windowed Fourier transform'. The amplitudes that arise for simple
quantum states from various choices of window are presented as illustrations.
Generalized Bargmann representations of the state vector appear as special
cases, associated with Gaussian windows. For every choice of window, amplitudes
lie in a corresponding linear subspace of square-integrable functions on phase
space. A generalized Born interpretation of amplitudes is described, with both
the Wigner function and a generalized Husimi function appearing as quantities
linear in an amplitude and anti-linear in its complex conjugate.
Schr\"odinger's time-dependent and time-independent equations are represented
on phase space amplitudes, and their solutions described in simple cases.Comment: 36 pages, 6 figures. Revised in light of referees' comments, and
further references adde
Phase properties of a new nonlinear coherent state
We study phase properties of a displacement operator type nonlinear coherent
state. In particular we evaluate the Pegg-Barnett phase distribution and
compare it with phase distributions associated with the Husimi Q function and
the Wigner function. We also study number- phase squeezing of this state.Comment: 8 eps figures. to appear in J.Opt
Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length
We study the problem of the attractive inverse square potential in quantum
mechanics with a generalized uncertainty relation. Using the momentum
representation, we show that this potential is regular in this framework. We
solve analytically the s-wave bound states equation in terms of Heun's
functions. We discuss in detail the bound states spectrum for a specific form
of the generalized uncertainty relation. The minimal length may be interpreted
as characterizing the dimension of the system.Comment: 30 pages, 3 figure
Classical phase space and statistical mechanics of identical particles
Starting from the quantum theory of identical particles, we show how to
define a classical mechanics that retains information about the quantum
statistics. We consider two examples of relevance for the quantum Hall effect:
identical particles in the lowest Landau level, and vortices in the
Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical}
statistical mechanics is shown to be a nontrivial classical limit of Haldane's
exclusion statistics.Comment: 40 pages, Late
Scalar Field Theory on Fuzzy S^4
Scalar fields are studied on fuzzy and a solution is found for the
elimination of the unwanted degrees of freedom that occur in the model. The
resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4
in the fuzzy context.Comment: 16 pages, LaTe
Winding Transitions at Finite Energy and Temperature: An O(3) Model
Winding number transitions in the two dimensional softly broken O(3)
nonlinear sigma model are studied at finite energy and temperature. New
periodic instanton solutions which dominate the semiclassical transition
amplitudes are found analytically at low energies, and numerically for all
energies up to the sphaleron scale. The Euclidean period beta of these finite
energy instantons increases with energy, contrary to the behavior found in the
abelian Higgs model or simple one dimensional systems. This results in a sharp
crossover from instanton dominated tunneling to sphaleron dominated thermal
activation at a certain critical temperature. Since this behavior is traceable
to the soft breaking of conformal invariance by the mass term in the sigma
model, semiclassical winding number transition amplitudes in the electroweak
theory in 3+1 dimensions should exhibit a similar sharp crossover. We argue
that this is indeed the case in the standard model for M_H < 4 M_W.Comment: 21 pages (14 figures), RevTeX (plus macro), uses eps