2,564 research outputs found
Parity balance of the -th dimension edges in Hamiltonian cycles of the hypercube
Let be an integer, and let . An -th dimension
edge in the -dimensional hypercube is an edge such that
differ just at their -th entries. The parity of an -th
dimension edge \edg{v_1}{v_2} is the number of 1's modulus 2 of any of its
vertex ignoring the -th entry. We prove that the number of -th dimension
edges appearing in a given Hamiltonian cycle of with parity zero
coincides with the number of edges with parity one. As an application of this
result it is introduced and explored the conjecture of the inscribed squares in
Hamiltonian cycles of the hypercube: Any Hamiltonian cycle in contains
two opposite edges in a 4-cycle. We prove this conjecture for , and
for any Hamiltonian cycle containing more than edges in the same
dimension. This bound is finally improved considering the equi-independence
number of , which is a concept introduced in this paper for bipartite
graphs
Structural change in multipartite entanglement sharing: a random matrix approach
We study the typical entanglement properties of a system comprising two
independent qubit environments interacting via a shuttling ancilla. The initial
preparation of the environments is modeled using random-matrix techniques. The
entanglement measure used in our study is then averaged over many histories of
randomly prepared environmental states. Under a Heisenberg interaction model,
the average entanglement between the ancilla and one of the environments
remains constant, regardless of the preparation of the latter and the details
of the interaction. We also show that, upon suitable kinematic and dynamical
changes in the ancilla-environment subsystems, the entanglement-sharing
structure undergoes abrupt modifications associated with a change in the
multipartite entanglement class of the overall system's state. These results
are invariant with respect to the randomized initial state of the environments.Comment: 10 pages, RevTeX4 (Minor typo's corrected. Closer to published
version
Relaxation Phenomena in a System of Two Harmonic Oscillators
We study the process by which quantum correlations are created when an
interaction Hamiltonian is repeatedly applied to a system of two harmonic
oscillators for some characteristic time interval. We show that, for the case
where the oscillator frequencies are equal, the initial Maxwell-Boltzmann
distributions of the uncoupled parts evolve to a new equilibrium
Maxwell-Boltzmann distribution through a series of transient Maxwell-Boltzmann
distributions. Further, we discuss why the equilibrium reached when the two
oscillator frequencies are unequal, is not a thermal one. All the calculations
are exact and the results are obtained through an iterative process, without
using perturbation theory.Comment: 22 pages, 6 Figures, Added contents, to appear in PR
SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases
We construct a family of rotationally invariant, local, S=1/2 Klein
Hamiltonians on various lattices that exhibit ground state manifolds spanned by
nearest-neighbor valence bond states. We show that with selected perturbations
such models can be driven into phases modeled by well understood quantum dimer
models on the corresponding lattices. Specifically, we show that the
perturbation procedure is arbitrarily well controlled by a new parameter which
is the extent of decoration of the reference lattice. This strategy leads to
Hamiltonians that exhibit i) RVB phases in two dimensions, ii) U(1) RVB
phases with a gapless ``photon'' in three dimensions, and iii) a Cantor
deconfined region in two dimensions. We also construct two models on the
pyrochlore lattice, one model exhibiting a RVB phase and the other a U(1)
RVB phase.Comment: 16 pages, 15 figures; 1 figure and some references added; some minor
typos fixe
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