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Register a new userThermal and electrical properties of a solid through Fibonacci oscillators
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We investigate the thermodynamics of a crystalline solid applying q-deformed algebra of Fibonacci oscillators through the generalized Fibonacci sequence of two real and independent deformation parameters q1 and q2. We based part of our study on both Einstein and Debye models, exploring primarily (q1,q2)-deformed thermal and electric conductivities as a function of Debye specific heat. The results revealed that q-deformation acts as a factor of disorder or impurity, modifying the characteristics of a crystalline structure. Specially, one may find the possibility of adjusting the Fibonacci oscillators to describe the change of thermal and electrical conductivities of a given element as one inserts impurities. Each parameter can be associated to different types of deformations such as disorders and impurities.
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We compute the ($q_1,q_2$)-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the ($q_1, q_2$)-extension of Jackson derivative. The deformed energy spectrum is also found in terms of these parameters. We conclude that the deformation is more effective in higher excited states. We conjecture that this achievement may find applications in the inclusion of disorder and impurity in quantum systems. The ordinary quantum mechanics is easily recovered as $q_1 = 1$ and $q_2to1$ or vice versa.
In this paper we report a theoretical model based on Green functions, Floquet theory and averaging techniques up to second order that describes the dynamics of parametrically-driven oscillators with added thermal noise. Quantitative estimates for heating and quadrature thermal noise squeezing near and below the transition line of the first parametric instability zone of the oscillator are given. Furthermore, we give an intuitive explanation as to why heating and thermal squeezing occur. For small amplitudes of the parametric pump the Floquet multipliers are complex conjugate of each other with a constant magnitude. As the pump amplitude is increased past a threshold value in the stable zone near the first parametric instability, the two Floquet multipliers become real and have different magnitudes. This creates two different effective dissipation rates (one smaller and the other larger than the real dissipation rate) along the stable manifolds of the first-return Poincare map. We also show that the statistical average of the input power due to thermal noise is constant and independent of the pump amplitude and frequency. The combination of these effects cause most of heating and thermal squeezing. Very good agreement between analytical and numerical estimates of the thermal fluctuations is achieved.
More than half a century ago Penrose asked: are the superfluid and solid state of matter mutually exclusive or do there exist supersolid materials where the atoms form a regular lattice and simultaneously flow without friction? Recent experiments provide evidence that supersolid behavior indeed exists in Helium-4 -- the most quantum material known in Nature. In this paper we show that large local strain in the vicinity of crystalline defects is the origin of supersolidity in Helium-4. Although ideal crystals of Helium-4 are not supersolid, the gap for vacancy creation closes when applying a moderate stress. While a homogeneous system simply becomes unstable at this point, the stressed core of crystalline defects (dislocations and grain boundaries) undergoes a radical transformation and can become superfluid.
Dislocations are shown to be smooth at zero temperature because of the effective Coulomb-type interaction between kinks. Crossover to finite temperature rougnehing is suggested to be a mechanism responsible for the softening of he4 shear modulus recently observed by Day and Beamish (Nature, {bf 450}, 853 (2007)). We discuss also that strong suppresion of superfuidity along the dislocation core by thermal kinks can lead to locking in of the mechanical and superfluid responses.
We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial (identity) channel, similar to the quantum Heisenberg model favoring pairs of spins to form spin singlets. We present an introduction to the theory of anyons and discuss in detail how basis sets and matrix representations of the interaction terms can be obtained, using non-Abelian Fibonacci anyons as example. Besides discussing the golden chain, a one-dimensional system of anyons with nearest neighbor interactions, we also present the derivation of more complicated interaction terms, such as three-anyon interactions in the spirit of the Majumdar-Ghosh spin chain, longer range interactions and two-leg ladders. We also discuss generalizations to anyons with general non-Abelian su(2)_k statistics. The k to infinity limit of the latter yields ordinary SU(2) spin chains.
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