808 research outputs found
Dynamical two electron states in a Hubbard-Davydov model
We study a model in which a Hubbard Hamiltonian is coupled to the dispersive
phonons in a classical nonlinear lattice. Our calculations are restricted to
the case where we have only two quasi-particles of opposite spins, and we
investigate the dynamics when the second quasi-particle is added to a state
corresponding to a minimal energy single quasi-particle state. Depending on the
parameter values, we find a number of interesting regimes. In many of these,
discrete breathers (DBs) play a prominent role with a localized lattice mode
coupled to the quasiparticles. Simulations with a purely harmonic lattice show
much weaker localization effects. Our results support the possibility that DBs
are important in HTSC.Comment: 14 pages, 12 fig
The vanishing of L2 harmonic one-forms on based path spaces
We prove the triviality of the first L2 cohomology class of based path spaces
of Riemannian manifolds furnished with Brownian motion measure, and the
consequent vanishing of L2 harmonic one-forms. We give explicit formulae for
closed and co-closed one-forms expressed as differentials of functions and
co-differentials of L2 two-forms, respectively; these are considered as
extended Clark-Ocone formulae. A feature of the proof is the use of the
temporal structure of path spaces to relate a rough exterior derivative
operator on one-forms to the exterior differentiation operator used to
construct the de Rham complex and the self-adjoint Laplacian on L2 one-forms.
This Laplacian is shown to have a spectral gap
Quantum Measurements, Energy Conservation and Quantum Clocks
We consider a spin chain extending from Alice to Bob with next neighbors
interactions, initially in its ground state. Assuming that Bob measures the
last spin of the chain, the energy of the spin chain has to increase, at least
on average, due to the measurement disturbance. Presumably, the energy is
provided by Bob's measurement apparatus. Assuming now that, simultaneously to
Bob's measurement, Alice measures the first spin, we show that either energy is
not conserved, - implausible - or the projection postulate doesn't apply, and
that there is signalling. An explicit measurement model shows that energy is
conserved (as expected), but that the spin chain energy increase is not
provided by the measurement apparatus(es), that the projection postulate is not
always valid - illustrating the Wigner-Araki-Yanase (WAY) theorem - and that
there is signalling, indeed. The signalling is due to the non-local interaction
Hamiltonian. This raises the question of a suitable quantum information
inspired model of such non-local Hamiltonians.Comment: 7 pages + appendices, 6 figure
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