11,219 research outputs found

### Coherent pairing states for the Hubbard model

We consider the Hubbard model and its extensions on bipartite lattices. We
define a dynamical group based on the $\eta$-pairing operators introduced by
C.N.Yang, and define coherent pairing states, which are combinations of
eigenfunctions of $\eta$-operators. These states permit exact calculations of
numerous physical properties of the system, including energy, various
fluctuations and correlation functions, including pairing ODLRO to all orders.
This approach is complementary to BCS, in that these are superconducting
coherent states associated with the exact model, although they are not
eigenstates of the Hamiltonian.Comment: 5 pages, RevTe

### Coherent States from Combinatorial Sequences

We construct coherent states using sequences of combinatorial numbers such as
various binomial and trinomial numbers, and Bell and Catalan numbers. We show
that these states satisfy the condition of the resolution of unity in a natural
way. In each case the positive weight functions are given as solutions of
associated Stieltjes or Hausdorff moment problems, where the moments are the
combinatorial numbers.Comment: 4 pages, Latex; Conference 'Quantum Theory and Symmetries 2', Krakow,
Poland, July 200

### Condition for tripartite entanglement

We propose a scheme for classifying the entanglement of a tripartite pure
qubit state. This classification scheme consists of an ordered list of seven
elements. These elements are the Cayley hyper-determinant, and its six
associated $2 \times 2$ subdeterminants. In particular we show that this
classification provides a necessary and sufficient condition for separability.Comment: 8 pages, to appear in the Proceedings of "Quantum Theory and
Symmetries 7", Prague, Aug 7-13, 201

### Combinatorial coherent states via normal ordering of bosons

We construct and analyze a family of coherent states built on sequences of
integers originating from the solution of the boson normal ordering problem.
These sequences generalize the conventional combinatorial Bell numbers and are
shown to be moments of positive functions. Consequently, the resulting coherent
states automatically satisfy the resolution of unity condition. In addition
they display such non-classical fluctuation properties as super-Poissonian
statistics and squeezing.Comment: 12 pages, 7 figures. 20 references. To be published in Letters in
Mathematical Physic

### On the Structure of the Bose-Einstein Condensate Ground State

We construct a macroscopic wave function that describes the Bose-Einstein
condensate and weakly excited states, using the su(1,1) structure of the
mean-field hamiltonian, and compare this state with the experimental values of
second and third order correlation functions.Comment: 10 pages, 2 figure

### Dissipative effects in Multilevel Systems

Dissipation is sometimes regarded as an inevitable and regrettable presence in the real evolution of a quantum system. However, the effects may not always be malign, although often non-intuitive and may even be beneficial. In this note we we display some of these effects for N-level systems, where N = 2,3,4.
We start with an elementary introduction to dissipative effects on the Bloch Sphere, and its interior, the Bloch Ball, for a two-level system. We describe explicitly the hamiltonian evolution as well as the purely dissipative dynamics, in the latter case giving the t-> infinity limits of the motion. This discussion enables us to provide an intuitive feeling for the measures of control-reachable states. For the three-level case we discuss the impossibility of isolating a two-level (qubit) subsystem; this is a Bohm-Aharonov type consequence of dissipation.
We finally exemplify the four-level case by giving constraints on the decay of two-qubit entanglement

### Criteria for reachability of quantum states

We address the question of which quantum states can be inter-converted under
the action of a time-dependent Hamiltonian. In particular, we consider the
problem applied to mixed states, and investigate the difference between pure
and mixed-state controllability introduced in previous work. We provide a
complete characterization of the eigenvalue spectrum for which the state is
controllable under the action of the symplectic group. We also address the
problem of which states can be prepared if the dynamical Lie group is not
sufficiently large to allow the system to be controllable.Comment: 14 pages, IoP LaTeX, first author has moved to Cambridge university
([email protected]

### Combinatorial Physics, Normal Order and Model Feynman Graphs

The general normal ordering problem for boson strings is a combinatorial
problem. In this note we restrict ourselves to single-mode boson monomials.
This problem leads to elegant generalisations of well-known combinatorial
numbers, such as Bell and Stirling numbers. We explicitly give the generating
functions for some classes of these numbers. Finally we show that a graphical
representation of these combinatorial numbers leads to sets of model field
theories, for which the graphs may be interpreted as Feynman diagrams
corresponding to the bosons of the theory. The generating functions are the
generators of the classes of Feynman diagrams.Comment: 9 pages, 4 figures. 12 references. Presented at the Symposium
'Symmetries in Science XIII', Bregenz, Austria, 200

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