5,235 research outputs found
Entanglement Induced Phase Transitions
Starting from the canonical ensemble over the space of pure quantum states,
we obtain an integral representation for the partition function. This is used
to calculate the magnetisation of a system of N spin-1/2 particles. The results
suggest the existence of a new type of first order phase transition that occurs
at zero temperature in the absence of spin-spin interactions. The transition
arises as a consequence of quantum entanglement. The effects of internal
interactions are analysed and the behaviour of the magnetic susceptibility for
a small number of interacting spins is determined.Comment: 4 pages, 2 figure
Must a Hamiltonian be Hermitian?
A consistent physical theory of quantum mechanics can be built on a complex
Hamiltonian that is not Hermitian but instead satisfies the physical condition
of space-time reflection symmetry (PT symmetry). Thus, there are infinitely
many new Hamiltonians that one can construct that might explain experimental
data. One would think that a quantum theory based on a non-Hermitian
Hamiltonian violates unitarity. However, if PT symmetry is not broken, it is
possible to use a previously unnoticed physical symmetry of the Hamiltonian to
construct an inner product whose associated norm is positive definite. This
construction is general and works for any PT-symmetric Hamiltonian. The
dynamics is governed by unitary time evolution. This formulation does not
conflict with the requirements of conventional quantum mechanics. There are
many possible observable and experimental consequences of extending quantum
mechanics into the complex domain, both in particle physics and in solid state
physics.Comment: Revised version to appear in American Journal of Physic
Deformations of Oka manifolds
We investigate the behaviour of the Oka property with respect to deformations
of compact complex manifolds. We show that in a family of compact complex
manifolds, the set of Oka fibres corresponds to a G-delta subset of the base.
We give a necessary and sufficient condition for the limit fibre of a sequence
of Oka fibres to be Oka in terms of a new uniform Oka property. We show that if
the fibres are tori, then the projection is an Oka map. Finally, we consider
holomorphic submersions with noncompact fibres
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