337 research outputs found
Correlation Energy and Entanglement Gap in Continuous Models
Our goal is to clarify the relation between entanglement and correlation
energy in a bipartite system with infinite dimensional Hilbert space. To this
aim we consider the completely solvable Moshinsky's model of two linearly
coupled harmonic oscillators. Also for small values of the couplings the
entanglement of the ground state is nonlinearly related to the correlation
energy, involving logarithmic or algebraic corrections. Then, looking for
witness observables of the entanglement, we show how to give a physical
interpretation of the correlation energy. In particular, we have proven that
there exists a set of separable states, continuously connected with the
Hartree-Fock state, which may have a larger overlap with the exact ground
state, but also a larger energy expectation value. In this sense, the
correlation energy provides an entanglement gap, i.e. an energy scale, under
which measurements performed on the 1-particle harmonic sub-system can
discriminate the ground state from any other separated state of the system.
However, in order to verify the generality of the procedure, we have compared
the energy distribution cumulants for the 1-particle harmonic sub-system of the
Moshinsky's model with the case of a coupling with a damping Ohmic bath at 0
temperature.Comment: 26 pages, 6 figure
The symmetry structure of the heavenly equation
We show that excitations of physical interest of the heavenly equation are
generated by symmetry operators which yields two reduced equations with
different characteristics. One equation is of the Liouville type and gives rise
to gravitational instantons, including those found by Eguchi-Hanson and
Gibbons-Hawking. The second equation appears for the first time in the theory
of heavenly spaces and provides meron-like configurations endowed with a
fractional topological charge. A link is also established between the heavenly
equation and the socalled Schr{\"o}der equation, which plays a crucial role in
the bootstrap model and in the renormalization theory.Comment: LaTex, 13 page
The Prolongation Problem for the Heavenly Equation
We provide an exact regular solution of an operator system arising as the
prolongation structure associated with the heavenly equation. This solution is
expressed in terms of operator Bessel coefficients.Comment: 9 pages, Proc. SIGRAV Conference (Bari 1998
Topological Field Theory and Nonlinear -Models on Symmetric Spaces
We show that the classical non-abelian pure Chern-Simons action is related to
nonrelativistic models in (2+1)-dimensions, via reductions of the gauge
connection in Hermitian symmetric spaces. In such models the matter fields are
coupled to gauge Chern-Simons fields, which are associated with the isotropy
subgroup of the considered symmetric space. Moreover, they can be related to
certain (integrable and non-integrable) evolution systems, as the Ishimori and
the Heisenberg model. The main classical and quantum properties of these
systems are discussed in connection with the topological field theory and the
condensed matter physics.Comment: LaTeX format, 31 page
Generalized time-dependent oscillators:results from a group-theoretical approach and their application to cosmology
Some results following from the analysis of generalized time-dependent oscillators in the framework of the Lie group theory are reviewed. Their role in treating aspects concerning the loss of coherence in cosmological models is discussed
Equations of the reaction-diffusion type with a loop algebra structure
A system of equations of the reaction-diffusion type is studied in the
framework of both the direct and the inverse prolongation structure. We find
that this system allows an incomplete prolongation Lie algebra, which is used
to find the spectral problem and a whole class of nonlinear field equations
containing the original ones as a special case.Comment: 16 pages, LaTex. submitted to Inverse Problem
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