79 research outputs found
Quantum Hall Effect on the Hyperbolic Plane in the presence of disorder
We study both the continuous model and the discrete model of the integer
quantum Hall effect on the hyperbolic plane in the presence of disorder,
extending the results of an earlier paper [CHMM]. Here we model impurities,
that is we consider the effect of a random or almost periodic potential as
opposed to just periodic potentials. The Hall conductance is identified as a
geometric invariant associated to an algebra of observables, which has plateaus
at gaps in extended states of the Hamiltonian. We use the Fredholm modules
defined in [CHMM] to prove the integrality of the Hall conductance in this
case. We also prove that there are always only a finite number of gaps in
extended states of any random discrete Hamiltonian. [CHMM] A. Carey, K.
Hannabuss, V. Mathai and P. McCann, Quantum Hall Effect on the Hyperbolic
Plane, Communications in Mathematical Physics, 190 vol. 3, (1998) 629-673.Comment: LaTeX2e, 17 page
Quantum Hall Effect and Noncommutative Geometry
We study magnetic Schrodinger operators with random or almost periodic
electric potentials on the hyperbolic plane, motivated by the quantum Hall
effect in which the hyperbolic geometry provides an effective Hamiltonian. In
addition we add some refinements to earlier results. We derive an analogue of
the Connes-Kubo formula for the Hall conductance via the quantum adiabatic
theorem, identifying it as a geometric invariant associated to an algebra of
observables that turns out to be a crossed product algebra. We modify the
Fredholm modules defined in [CHMM] in order to prove the integrality of the
Hall conductance in this case.Comment: 18 pages, paper rewritte
Physical flavor neutrino states
The problem of representation for flavor states of mixed neutrinos is
discussed. By resorting to recent results, it is shown that a specific
representation exists in which a number of conceptual problems are resolved.
Phenomenological consequences of our analysis are explored.Comment: Presented at 5th International Workshop DICE2010: Space-Time-Matter -
Current Issues in Quantum Mechanics and Beyon
Mixing and oscillations of neutral particles in Quantum Field Theory
We study the mixing of neutral particles in Quantum Field Theory: neutral
boson field and Majorana field are treated in the case of mixing among two
generations. We derive the orthogonality of flavor and mass representations and
show how to consistently calculate oscillation formulas, which agree with
previous results for charged fields and exhibit corrections with respect to the
usual quantum mechanical expressions.Comment: 8 pages, revised versio
Fermion mixing in quasi-free states
Quantum field theoretic treatments of fermion oscillations are typically
restricted to calculations in Fock space. In this letter we extend the
oscillation formulae to include more general quasi-free states, and also
consider the case when the mixing is not unitary.Comment: 10 pages, Plain Te
Boundary conformal fields and Tomita--Takesaki theory
Motivated by formal similarities between the continuum limit of the Ising
model and the Unruh effect, this paper connects the notion of an Ishibashi
state in boundary conformal field theory with the Tomita--Takesaki theory for
operator algebras. A geometrical approach to the definition of Ishibashi states
is presented, and it is shownthat, when normalisable the Ishibashi states are
cyclic separating states, justifying the operator state correspondence. When
the states are not normalisable Tomita--Takesaki theory offers an alternative
approach based on left Hilbert algebras, opening the way to extensions of our
construction and the state-operator correspondence.Comment: plain Te
T-duality for principal torus bundles
In this paper we study T-duality for principal torus bundles with H-flux. We
identify a subset of fluxes which are T-dualizable, and compute both the dual
torus bundle as well as the dual H-flux. We briefly discuss the generalized
Gysin sequence behind this construction and provide examples both of non
T-dualizable and of T-dualizable H-fluxes.Comment: 9 pages, typos removed and minor corrections mad
Quantizing the damped harmonic oscillator
We consider the Fermi quantization of the classical damped harmonic
oscillator (dho). In past work on the subject, authors double the phase space
of the dho in order to close the system at each moment in time. For an
infinite-dimensional phase space, this method requires one to construct a
representation of the CAR algebra for each time. We show that unitary dilation
of the contraction semigroup governing the dynamics of the system is a logical
extension of the doubling procedure, and it allows one to avoid the
mathematical difficulties encountered with the previous method.Comment: 4 pages, no figure
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