Quantum phase transition in the Frenkel-Kontorova chain: from pinned instanton glass to sliding phonon gas

We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime when the classical model is located in the pinned phase characterized by the gaped phonon excitations and devil's staircase. By extensive quantum Monte Carlo simulations we show that for the effective Planck constant $\hbar$ smaller than the critical value $\hbar_c$ the quantum chain is in the pinned instanton glass phase. In this phase the elementary excitations have two branches: phonons, separated from zero energy by a finite gap, and instantons which have an exponentially small excitation energy. At $\hbar=\hbar_c$ the quantum phase transition takes place and for $\hbar>\hbar_c$ the pinned instanton glass is transformed into the sliding phonon gas with gapless phonon excitations. This transition is accompanied by the divergence of the spatial correlation length and appearence of sliding modes at $\hbar>\hbar_c$.Comment: revtex 16 pages, 18 figure

Change in left ventricular geometry during antihypertensive treatment in children with primary hypertension

The pattern of the left ventricle (LV) has important significance in adults with hypertension. The aim of the present study was to analyze changes and determinants of LV geometry after 1 year of antihypertensive treatment in children with primary hypertension (PH) in relation to metabolic abnormalities and anthropometrical parameters. In 86 children (14.1 ± 2.4 years) with newly diagnosed PH, LV geometry and biochemical parameters before and after 12 months of standard antihypertensive therapy were assessed. At baseline, normal LV geometry (NG) was found in 42 (48.9%), concentric remodeling (CR) in 4 (4.6%), concentric hypertrophy (CH) in 8 (9.3%), and eccentric hypertrophy (EH) in 32 (37.2%) patients. The prevalence of NG in patients with severe hypertension was significantly lower than in patients with ambulatory hypertension. There were no differences in dipping status in relation to LV geometry. Patients with CH and EH were more viscerally obese than patients with NG. Patients with CH had higher diastolic blood pressure in comparison with EH patients (p < 0.05). The main predictor of relative wall thickness (RWT) was the triglycerides to high density lipoprotein cholesterol (TG/HDL) ratio (R2 = 0.319, β = 0.246, p = 0.004). Patients received 12 months of antihypertensive treatment, either lifestyle modification only (n = 37) or lifestyle modification plus antihypertensive medications (n = 49) if severe ambulatory hypertension or target organ damage were present. After 12 months of treatment the prevalence of EH (37.2% vs 18.6%, p = 0.003) decreased but prevalence of CH did not change. Patients in whom RWT decreased also decreased waist circumference and TG/HDL; the main predictor of RWT decrease was a decrease of the TG/HDL ratio (β = 0.496, R2 = 0.329, p = 0.002). In adolescents with PH, LV geometry is related to central obesity and insulin resistance. Decrease of abdominal obesity and insulin resistance are the most important predictors of normalization of LV geometry, however CH has lower potential to normalize LV geometry