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Register a new userSolitons and entanglement in the double sine-Gordon model
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Added by
Norton G. de Almeida Dr.
Publication date
2014
fields
Physics
and research's language is
English
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The bipartite ground state entanglement in a finite linear harmonic chain of particles is numerically investigated. The particles are subjected to an external on-site periodic potential belonging to a family parametrized by the unit interval encompassing the sine-Gordon potential at both ends of the interval. Strong correspondences between the soliton entanglement entropy and the kink energy distribution profile as functions of the sub-chain length are found.
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We analyze the diffusive motion of kink solitons governed by the thermal sine-Gordon equation. We analytically calculate the correlation function of the position of the kink center as well as the diffusion coefficient, both up to second-order in temperature. We find that the kink behavior is very similar to that obtained in the overdamped limit: There is a quadratic dependence on temperature in the diffusion coefficient that comes from the interaction among the kink and phonons, and the average value of the wave function increases with $sqrt{t}$ due to the variance of the centers of individual realizations and not due to kink distortions. These analytical results are fully confirmed by numerical simulations.
We consider the canonical symplectic form for sine-Gordon evaluated explicitly on the solitons of the model. The integral over space in the form, which arises because the canonical argument uses the Lagrangian density, is done explicitly in terms of functions arising in the group doublecrossproduct formulation of the inverse scattering procedure, and we are left with a simple expression given by two boundary terms. The expression is then evaluated explicitly in terms of the changes in the positions and momenta of the solitons, and we find agreement with a result of Babelon and Bernard who have evaluated the form using a different argument, where it is diagonal in terms of `in or `out co-ordinates. Using the result, we also investigate the higher conserved charges within the inverse scattering framework, check that they Poisson commute and evaluate them on the soliton solutions.
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field theories such as sine-Gordon field theory can be employed to describe a qubit. Primary logical gates are from twist, pump, glue, and shuffle operations that can be realized in principle by tuning parameters of the systems. Our scheme demonstrates the power of 1D quantum systems for robust quantum computing.
In this work, we evaluate the Shannon-like entropic measure of spatially-localized functions for a five-dimensional braneworld generated by a double sine-Gordon (DSG) potential. The differential configurational entropy (DCE) has been shown in several recent works to be a configurational informational measure (CIM) that selects critical points and brings out phase transitions in confined energy models with arbitrary parameters. We select the DSG scenario because it presents an energy-degenerate spatially localized profile where the solutions to the scalar field demonstrate critical behavior that is only a result of geometrical effects. As we will show, the DCE evaluation provides a method for predicting the existence of a transition between the phases of the domain wall solutions. Moreover, the entropic measure reveals information about the model that is capable of describing the phase sector where we obtain resonance modes on the massive spectra of the graviton. The graviton resonance lifetimes are related to the existence of scales on which 4D gravity is recovered. Thus, we correlate the critical points defined by the {CIMs} with the existence of resonances and their lifetimes. To extend our research regarding this system, we calculate the corrections to Newtons Law coming from the graviton modes.
Extending our previous construction in the sine-Gordon model, we show how to introduce two kinds of fermionic screening operators, in close analogy with conformal field theory with c<1.
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