20,465 research outputs found
Extended matter coupled to BF theory
Recently, a topological field theory of membrane-matter coupled to BF theory
in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss
various aspects of the four-dimensional theory. Firstly, we study classical
solutions leading to an interpretation of the theory in terms of strings
propagating on a flat spacetime. We also show that the general classical
solutions of the theory are in one-to-one correspondence with solutions of
Einstein's equations in the presence of distributional matter (cosmic strings).
Secondly, we quantize the theory and present, in particular, a prescription to
regularize the physical inner product of the canonical theory. We show how the
resulting transition amplitudes are dual to evaluations of Feynman diagrams
coupled to three-dimensional quantum gravity. Finally, we remove the regulator
by proving the topological invariance of the transition amplitudes.Comment: 27 pages, 7 figure
The Two-Point Function and the Effective Magnetic Field in Diluted Ising Models on the Cayley Tree
Some results on the two-point function and on the analytic structure of the
momenta of the effective fugacity at the origin for a class of diluted
ferromagnetic Ising models on the Cayley tree are presented.Comment: 22 page
Effective geometry in Astrophysics
The effective metric is introduced by means of two examples (non-linear
electromagnetism and hydrodynamics),along with applications in Astrophysics. A
sketch of the generality of the effect is also given.Comment: 9 pages, contributions for the proceedings of the First International
Workshop on Astronomy and Relativistic Astrophysics (IWARA 2003), Olinda
(Brazil
Analog black holes in flowing dielectrics
We show that a flowing dielectric medium with a linear response to an
external electric field can be used to generate an analog geometry that has
many of the formal properties of a Schwarzschild black hole for light rays, in
spite of birefringence. We also discuss the possibility of generating these
analog black holes in the laboratory.Comment: Revtex4 file, 7 pages, 4 eps figures, a few changes in presentation,
some references added, conclusions unchange
Spin Foam Diagrammatics and Topological Invariance
We provide a simple proof of the topological invariance of the Turaev-Viro
model (corresponding to simplicial 3d pure Euclidean gravity with cosmological
constant) by means of a novel diagrammatic formulation of the state sum models
for quantum BF-theories. Moreover, we prove the invariance under more general
conditions allowing the state sum to be defined on arbitrary cellular
decompositions of the underlying manifold. Invariance is governed by a set of
identities corresponding to local gluing and rearrangement of cells in the
complex. Due to the fully algebraic nature of these identities our results
extend to a vast class of quantum groups. The techniques introduced here could
be relevant for investigating the scaling properties of non-topological state
sums, being proposed as models of quantum gravity in 4d, under refinement of
the cellular decomposition.Comment: 20 pages, latex with AMS macros and eps figure
Renormalization of tensor-network states
We have discussed the tensor-network representation of classical statistical
or interacting quantum lattice models, and given a comprehensive introduction
to the numerical methods we recently proposed for studying the tensor-network
states/models in two dimensions. A second renormalization scheme is introduced
to take into account the environment contribution in the calculation of the
partition function of classical tensor network models or the expectation values
of quantum tensor network states. It improves significantly the accuracy of the
coarse grained tensor renormalization group method. In the study of the quantum
tensor-network states, we point out that the renormalization effect of the
environment can be efficiently and accurately described by the bond vector.
This, combined with the imaginary time evolution of the wavefunction, provides
an accurate projection method to determine the tensor-network wavfunction. It
reduces significantly the truncation error and enable a tensor-network state
with a large bond dimension, which is difficult to be accessed by other
methods, to be accurately determined.Comment: 18 pages 23 figures, minor changes, references adde
Artificial Neural Network to predict mean monthly total ozone in Arosa, Switzerland
Present study deals with the mean monthly total ozone time series over Arosa,
Switzerland. The study period is 1932-1971. First of all, the total ozone time
series has been identified as a complex system and then Artificial Neural
Networks models in the form of Multilayer Perceptron with back propagation
learning have been developed. The models are Single-hidden-layer and
Two-hidden-layer Perceptrons with sigmoid activation function. After sequential
learning with learning rate 0.9 the peak total ozone period (February-May)
concentrations of mean monthly total ozone have been predicted by the two
neural net models. After training and validation, both of the models are found
skillful. But, Two-hidden-layer Perceptron is found to be more adroit in
predicting the mean monthly total ozone concentrations over the aforesaid
period.Comment: 22 pages, 14 figure
Decoherence and relaxation in the interacting quantum dot system
In this paper we study the low temperature kinetics of the electrons in the
system composed of a quantum dot connected to two leads by solving the equation
of motion. The decoherence and the relaxation of the system caused by the gate
voltage noise and electron-phonon scattering are investigated. In order to take
account of the strong correlation of the electrons in this system, the
quasi-exact wave functions are calculated using an improved matrix product
states algorithm. This algorithm enables us to calculate the wave functions of
the ground state and the low lying excited states with satisfied accuracy and
thus enables us to study the kinetics of the system more effectively. It is
found that although both of these two mechanisms are proportional to the
electron number operator in the dot, the kinetics are quite different. The
noise induced decoherence is much more effective than the energy relaxation,
while the energy relaxation and decoherence time are of the same order for the
electron-phonon scattering. Moreover, the noise induced decoherence increases
with the lowering of the dot level, but the relaxation and decoherence due to
the electron-phonon scattering decrease.Comment: Minor revision. Add journal referenc
Robust control of decoherence in realistic one-qubit quantum gates
We present an open loop (bang-bang) scheme to control decoherence in a
generic one-qubit quantum gate and implement it in a realistic simulation. The
system is consistently described within the spin-boson model, with interactions
accounting for both adiabatic and thermal decoherence. The external control is
included from the beginning in the Hamiltonian as an independent interaction
term. After tracing out the environment modes, reduced equations are obtained
for the two-level system in which the effects of both decoherence and external
control appear explicitly. The controls are determined exactly from the
condition to eliminate decoherence, i.e. to restore unitarity. Numerical
simulations show excellent performance and robustness of the proposed control
scheme.Comment: 21 pages, 8 figures, VIth International Conference on Quantum
Communication, Measurement and Computing (Boston, 2002
Exact results on the dynamics of multi-component Bose-Einstein condensate
We study the time-evolution of the two dimensional multi-component
Bose-Einstein condensate in an external harmonic trap with arbitrary
time-dependent frequency. We show analytically that the time-evolution of the
total mean-square radius of the wave-packet is determined in terms of the same
solvable equation as in the case of a single-component condensate. The dynamics
of the total mean-square radius is also the same for the rotating as well as
the non-rotating multi-component condensate. We determine the criteria for the
collapse of the condensate at a finite time. Generalizing our previous work on
a single-component condensate, we show explosion-implosion duality in the
multi-component condensate.Comment: Two-column 6 pages, RevTeX, no figures(v1); Added an important
reference, version to appear in Physical Review A (v2
- …