81 research outputs found
Mean-field expansion and meson effects in chiral condensate of analytically regularized Nambu -- Jona-Lasinio model
Scalar meson contributions in chiral quark condensate are calculated for
analytically regularized Nambu -- Jona-Lasinio model in framework of mean-field
expansion in bilocal-source formalism. Sigma-meson contribution for physical
values of parameters is found to be small. Pion contribution is found to be
significant and should be taken into account at the choice of the parameter
values.Comment: 12 pages, Plain LaTex, no figures, final versio
High density quark matter in the NJL model with dimensional vs. cut-off regularization
We investigate color superconducting phase at high density in the extended
Nambu--Jona-Lasinio model for the two flavor quarks. Because of the
non-renormalizability of the model, physical observables may depend on the
regularization procedure, that is why we apply two types of regularization, the
cut-off and the dimensional one to evaluate the phase structure, the equation
of state and the relationship between the mass and the radius of a dense star.
To obtain the phase structure we evaluate the minimum of the effective
potential at finite temperature and chemical potential. The stress tensor is
calculated to derive the equation of state. Solving the
Tolman-Oppenheimer-Volkoff equation, we show the relationship between the mass
and the radius of a dense star. The dependence on the regularization is found
not to be small for these phenomena in the color superconducting phase.Comment: 10 pages, 11 figures; a few points corrected and references adde
Quantum state transfer in spin chains with q-deformed interaction terms
We study the time evolution of a single spin excitation state in certain
linear spin chains, as a model for quantum communication. Some years ago it was
discovered that when the spin chain data (the nearest neighbour interaction
strengths and the magnetic field strengths) are related to the Jacobi matrix
entries of Krawtchouk polynomials or dual Hahn polynomials, so-called perfect
state transfer takes place. The extension of these ideas to other types of
discrete orthogonal polynomials did not lead to new models with perfect state
transfer, but did allow more insight in the general computation of the
correlation function. In the present paper, we extend the study to discrete
orthogonal polynomials of q-hypergeometric type. A remarkable result is a new
analytic model where perfect state transfer is achieved: this is when the spin
chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. The
other cases studied here (affine q-Krawtchouk polynomials, quantum q-Krawtchouk
polynomials, dual q-Krawtchouk polynomials, q-Hahn polynomials, dual q-Hahn
polynomials and q-Racah polynomials) do not give rise to models with perfect
state transfer. However, the computation of the correlation function itself is
quite interesting, leading to advanced q-series manipulations
Quantum communication and state transfer in spin chains
We investigate the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. We consider first the simplest possible spin chain, where the spin chain data (the nearest neighbour interaction strengths and the magnetic field strengths) are constant throughout the chain. The time evolution of a single spin state is determined, and this time evolution is illustrated by means of an animation. Some years ago it was discovered that when the spin chain data are of a special form so-called perfect state transfer takes place. These special spin chain data can be linked to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials. We discuss here the case related to Krawtchouk polynomials, and illustrate the possibility of perfect state transfer by an animation showing the time evolution of the spin chain from an initial single spin state. Very recently, these ideas were extended to discrete orthogonal polynomials of q-hypergeometric type. Here, a remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. This case is discussed here, and again illustrated by means of an animation
On Quantization of Time-Dependent Systems with Constraints
The Dirac method of canonical quantization of theories with second class
constraints has to be modified if the constraints depend on time explicitly. A
solution of the problem was given by Gitman and Tyutin. In the present work we
propose an independent way to derive the rules of quantization for these
systems, starting from physical equivalent theory with trivial
non-stationarity.Comment: 4 page
Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator
The SU(1,1) coherent states for a relativistic model of the linear singular
oscillator are considered. The corresponding partition function is evaluated.
The path integral for the transition amplitude between SU(1,1) coherent states
is given. Classical equations of the motion in the generalized curved phase
space are obtained. It is shown that the use of quasiclassical Bohr-Sommerfeld
quantization rule yields the exact expression for the energy spectrum.Comment: 14 pages, 2 figures, Uses RevTeX4 styl
Two regularizations - two different models of Nambu-Jona-Lasinio
Two variants of the Nambu--Jona-Lasinio model -- the model with 4-dimensional
cutoff and the model with dimensionally-analytical regularization -- are
systematically compared. It is shown that they are, in essence, two different
models of light-quark interaction. In the mean-field approximation the
distinction becomes apparent in a behavior of scalar amplitude near the
threshold. For 4-dimensional cutoff the pole term can be extracted, which
corresponds to sigma-meson. For dimensionally-analytical regularization the
singularity of the scalar amplitude is not pole, and this singularity is quite
disappeared at some value of the regularization parameter.
Still more essential distinction of these models exists in the
next-to-leading order of mean-field expansion. The calculations of meson
contributions in the quark chiral condensate and in the dynamical quark mass
demonstrate, that these contributions though their relatively smallness can
destabilize the Nambu--Jona-Lasinio model with 4-dimensional cutoff. On the
contrary, the Nambu--Jona-Lasinio model with dimensionally-analytical
regularization is stabilized with the next-to-leading order, i.e. the value of
the regularization parameter shifts to the stability region, where these
contributions decrease.Comment: 14 pages; Journal version; parameter fixing procedure is modifie
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