We investigate the behavior of an N -component quantum rotor coupled to a bosonic dissipative bath having a sub-Ohmic spectral density J(ω) ∝ ω s with s < 1. With increasing dissipation strength, this system undergoes a quantum phase transition from a delocalized phase to a localized phase. We determine the exact critical behavior of this transition in the large-N limit. For 1 > s > 1/2, we find nontrivial critical behavior corresponding to an interacting renormalization group fixed point while we find mean-field behavior for s < 1/2. The results agree with those of the corresponding long-range interacting classical model. The quantum-to-classical mapping is therefore valid for the sub-Ohmic rotor model.
The current in a simple electric circuit consisting of a resistor and a power supply is studied under the assumption that the current starts from zero and reaches its maximum value. It suggests that an evolution process of a current occurs approximating the circuit temporarily to an R-L circuit. The current equation is solved analytically using Mittag-Leffler function. The equation was also solved numerically. Results supported the assumed behavior of current to evolve from zero to its saturation value.MSC 2010 : Primary 26A33: Secondary 30B10, 33B15, 44A10, 47N70, 94C05
We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the lowtemperature thermodynamic behavior in both phases, which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.
Absorbance of normally incident electromagnetic wave on a cold, weakly collisional, and inhomogeneous magnetoplasma slab is investigated. The plasma density is Budden-like sinusoidal profile, where the inhomogeniety is treated as a multilayered system of homogeneous sub-cells within the transfer matrix technique. For incident wave frequencies much above the ion cyclotron frequency, only right hand circularly polarized waves are relevant for wave propagation parallel to a static magnetic field. Calculations are performed in normalized parameters, that make the results suitable for many applications including atmospheric and laboratory plasmas. The presence of the dc-magnetic field leads to the formation of two absorption bands explained by plasma collisional dissipation and electron cyclotron resonance in the low frequency branch of the $R$-wave below the electron cyclotron frequency. The transmittance shows the emergence of the low frequency electron cyclotron wave, which becomes a Whistler mode at very low frequency. More detailed discussion on the effect of plasma collisionality, inhomogeneity, and dc-magnetic field on the propagation characteristics is given at the relevant place within the body of the manuscript.
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