A Parafermionic Generalization of the Jaynes Cummings Model

We introduce a parafermionic version of the Jaynes Cummings Hamiltonian, by coupling $k$ Fock parafermions (nilpotent of order $F$) to a 1D harmonic oscillator, representing the interaction with a single mode of the electromagnetic field. We argue that for $k=1$ and $F\leq 3$ there is no difference between Fock parafermions and quantum spins $s=\frac{F-1}{2}$. We also derive a semiclassical approximation of the canonical partition function of the model by assuming $\hbar$ to be small in the regime of large enough total number of excitations $n$, where the dimension of the Hilbert space of the problem becomes constant as a function of $n$. We observe in this case an interesting behaviour of the average of the bosonic number operator showing a single crossover between regimes with different integer values of this observable. These features persist when we generalize the parafermionic Hamiltonian by deforming the bosonic oscillator with a generic function $\Phi(x)$; the $q-$deformed bosonic oscillator corresponds to a specific choice of the deformation function $\Phi$. In this particular case, we observe at most $k(F-1)$ crossovers in the behavior of the mean bosonic number operator, suggesting a phenomenology of superradiance similar to the $k-$atoms Jaynes Cummings model.Comment: to appear on J.Phys.

Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

We consider critical dense polymers ${\cal L}(1,2)$. We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including the indecomposable structure of the transfer matrix. Integrals of motion are defined directly on the lattice in terms of the Temperley Lieb Algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained thus providing a reason for their introduction.Comment: 53 pages, version accepted for publishing on JSTA

A fully-discrete entropy conserving/stable discretization for inviscid unsteady flows

The aim of this work is to contribute to the development of a high-order accurate discretization that is entropy conserving and entropy stable both in space and in time. To do this, the general framework is based on a high-order accurate discontinuous Galerkin (dG) method in space with entropy working variables, several entropy conservative and stable numerical fluxes and an entropy conserving modified Crank-Nicolson method. We present the first results, obtained with the discretizations here proposed, for two bi-dimensional unsteady viscous test-case: the Taylor-Green vortex and the double shear layer

On the Integrable Structure of the Ising Model

Starting from the lattice $A_3$ realization of the Ising model defined on a strip with integrable boundary conditions, the exact spectrum (including excited states) of all the local integrals of motion is derived in the continuum limit by means of TBA techniques. It is also possible to follow the massive flow of this spectrum between the UV $c=1/2$ conformal fixed point and the massive IR theory. The UV expression of the eigenstates of such integrals of motion in terms of Virasoro modes is found to have only rational coefficients and their fermionic representation turns out to be simply related to the quantum numbers describing the spectrum.Comment: 18 pages, no figure

Neurochemical Correlates of Brain Atrophy in Fibromyalgia Syndrome: A Magnetic Resonance Spectroscopy and Cortical Thickness Study.

(1) Background: Recently, a series of clinical neuroimaging studies on fibromyalgia (FM) have shown a reduction in cortical volume and abnormally high glutamate (Glu) and glutamate + glutamine (Glx) levels in regions associated with pain modulation. However, it remains unclear whether the volumetric decreases and increased Glu levels in FM are related each other. We hypothesized that higher Glu levels are related to decreases in cortical thickness (CT) and volume in FM patients. (2) Methods: Twelve females with FM and 12 matched healthy controls participated in a session of combined 3.0 Tesla structural magnetic resonance imaging (MRI) and single-voxel MR spectroscopy focused on the thalami and ventrolateral prefrontal cortices (VLPFC). The thickness of the cortical and subcortical gray matter structures and the Glu/Cr and Glx/Cr ratios were estimated. Statistics included an independent t-test and Spearman's test. (3) Results: The Glu/Cr ratio of the left VLPFC was negatively related to the CT of the left inferior frontal gyrus (pars opercularis (p = 0.01; r = -0.75) and triangularis (p = 0.01; r = -0.70)). Moreover, the Glx/Cr ratio of the left VLPFC was negatively related to the CT of the left middle anterior cingulate gyrus (p = 0.003; r = -0.81). Significantly lower CTs in FM were detected in subparts of the cingulate gyrus on both sides and in the right inferior occipital gyrus (p < 0.001). (4) Conclusions: Our findings are in line with previous observations that high glutamate levels can be related, in a concentration-dependent manner, to the morphological atrophy described in FM patients