255 research outputs found
Spin network setting of topological quantum computation
The spin network simulator model represents a bridge between (generalised)
circuit schemes for standard quantum computation and approaches based on
notions from Topological Quantum Field Theories (TQFTs). The key tool is
provided by the fiber space structure underlying the model which exhibits
combinatorial properties closely related to SU(2) state sum models, widely
employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.Comment: Proc. "Foundations of Quantum Information", Camerino (Italy), 16-19
April 2004, to be published in Int. J. of Quantum Informatio
Quantum global vortex strings in a background field
We consider quantum global vortex string correlation functions, within the
Kalb-Ramond framework, in the presence of a background field-strength tensor
and investigate the conditions under which this yields a nontrivial
contribution to those correlation functions. We show that a background field
must be supplemented to the Kalb-Ramond theory, in order to correctly describe
the quantum properties of the vortex strings. The explicit form of this
background field and the associated quantum vortex string correlation function
are derived. The complete expression for the quantum vortex creation operator
is explicitly obtained. We discuss the potential applicability of our results
in the physics of superfluids and rotating Bose-Einstein condensates.Comment: To appear in Journal of Physics A: Mathematical and Genera
Bose-Einstein condensation in inhomogeneous Josephson arrays
We show that spatial Bose-Einstein condensation of non-interacting bosons
occurs in dimension d < 2 over discrete structures with inhomogeneous topology
and with no need of external confining potentials. Josephson junction arrays
provide a physical realization of this mechanism. The topological origin of the
phenomenon may open the way to the engineering of quantum devices based on
Bose-Einstein condensation. The comb array, which embodies all the relevant
features of this effect, is studied in detail.Comment: 4 pages, 5 figure
Quantum statistical properties of some new classes of intelligent states associated with special quantum systems
Based on the {\it nonlinear coherent states} method, a general and simple
algebraic formalism for the construction of \textit{`-deformed intelligent
states'} has been introduced. The structure has the potentiality to apply to
systems with a known discrete spectrum as well as the generalized coherent
states with known nonlinearity function . As some physical appearance of
the proposed formalism, a few new classes of intelligent states associated with
\textit{`center of-mass motion of a trapped ion'}, \textit{`harmonious states'}
and \textit{`hydrogen-like spectrum'} have been realized. Finally, the
nonclassicality of the obtained states has been investigated. To achieve this
purpose the quantum statistical properties using the Mandel parameter and the
squeezing of the quadratures of the radiation field corresponding to the
introduced states have been established numerically.Comment: 13page
Thermalization of a Brownian particle via coupling to low-dimensional chaos
It is shown that a paradigm of classical statistical mechanics --- the
thermalization of a Brownian particle --- has a low-dimensional, deterministic
analogue: when a heavy, slow system is coupled to fast deterministic chaos, the
resultant forces drive the slow degrees of freedom toward a state of
statistical equilibrium with the fast degrees. This illustrates how concepts
useful in statistical mechanics may apply in situations where low-dimensional
chaos exists.Comment: Revtex, 11 pages, no figures
Quantum geometry and quantum algorithms
Motivated by algorithmic problems arising in quantum field theories whose
dynamical variables are geometric in nature, we provide a quantum algorithm
that efficiently approximates the colored Jones polynomial. The construction is
based on the complete solution of Chern-Simons topological quantum field theory
and its connection to Wess-Zumino-Witten conformal field theory. The colored
Jones polynomial is expressed as the expectation value of the evolution of the
q-deformed spin-network quantum automaton. A quantum circuit is constructed
capable of simulating the automaton and hence of computing such expectation
value. The latter is efficiently approximated using a standard sampling
procedure in quantum computation.Comment: Submitted to J. Phys. A: Math-Gen, for the special issue ``The
Quantum Universe'' in honor of G. C. Ghirard
Topological origin of the phase transition in a mean-field model
We argue that the phase transition in the mean-field XY model is related to a
particular change in the topology of its configuration space. The nature of
this topological transition can be discussed on the basis of elementary Morse
theory using the potential energy per particle V as a Morse function. The value
of V where such a topological transition occurs equals the thermodynamic value
of V at the phase transition and the number of (Morse) critical points grows
very fast with the number of particles N. Furthermore, as in statistical
mechanics, also in topology the way the thermodynamic limit is taken is
crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the
text. To appear in Physical Review Letter
Topology and phase transitions: a paradigmatic evidence
We report upon the numerical computation of the Euler characteristic \chi (a
topologic invariant) of the equipotential hypersurfaces \Sigma_v of the
configuration space of the two-dimensional lattice model. The pattern
\chi(\Sigma_v) vs. v (potential energy) reveals that a major topology change in
the family {\Sigma_v}_{v\in R} is at the origin of the phase transition in the
model considered. The direct evidence given here - of the relevance of topology
for phase transitions - is obtained through a general method that can be
applied to any other model.Comment: 4 pages, 4 figure
Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model
The ground states of the two-dimensional repulsive Hubbard model are studied
within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge
properties are determined by systematic, large-scale, exact numerical
calculations, and quantified as a function of electron doping . In the
solution of the self-consistent UHF equations, multiple initial configurations
and simulated annealing are used to facilitate convergence to the global
minimum. New approaches are employed to minimize finite-size effects in order
to reach the thermodynamic limit. At low to moderate interacting strengths and
low doping, the UHF ground state is a linear spin-density wave (l-SDW), with
antiferromagnetic order and a modulating wave. The wavelength of the modulating
wave is . Corresponding charge order exists but is substantially weaker
than the spin order, hence holes are mobile. As the interaction is increased,
the l-SDW states evolves into several different phases, with the holes
eventually becoming localized. A simple pairing model is presented with
analytic calculations for low interaction strength and small doping, to help
understand the numerical results and provide a physical picture for the
properties of the SDW ground state. By comparison with recent many-body
calculations, it is shown that, for intermediate interactions, the UHF solution
provides a good description of the magnetic correlations in the true ground
state of the Hubbard model.Comment: 13 pages, 17 figure, 0 table
Spin networks, quantum automata and link invariants
The spin network simulator model represents a bridge between (generalized)
circuit schemes for standard quantum computation and approaches based on
notions from Topological Quantum Field Theories (TQFT). More precisely, when
working with purely discrete unitary gates, the simulator is naturally modelled
as families of quantum automata which in turn represent discrete versions of
topological quantum computation models. Such a quantum combinatorial scheme,
which essentially encodes SU(2) Racah--Wigner algebra and its braided
counterpart, is particularly suitable to address problems in topology and group
theory and we discuss here a finite states--quantum automaton able to accept
the language of braid group in view of applications to the problem of
estimating link polynomials in Chern--Simons field theory.Comment: LateX,19 pages; to appear in the Proc. of "Constrained Dynamics and
Quantum Gravity (QG05), Cala Gonone (Italy) September 12-16 200
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