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Author: HARET CODRATIAN ROSU

Inhomogeneous barotropic FRW cosmologies with constant-shifted conformal hubble parameters

HARET CODRATIAN ROSU (2013)

"It is known that the barotropic FRW system of differential equations for zero cosmological constant can be reduced to simple harmonic oscillator (HO) differential equations in the conformal time variable. This is due to the fact that the Hubble rate parameter in conformal time is the solution of a simple Riccati equation of constant coefficients. In previous works, we have used this mathematical result to set the barotropic HO equations in the nonrelativistic supersymmetric approach by factorizing them. If a constant additive parameter, denoted by S, is added to the common Riccati solution of these supersymmetric partner cosmologies one obtains inhomogeneous barotropic cosmologies with periodic singularities in their spatial curvature indices that are counterparts of the non-shifted supersymmetric partners. The zero-mode solutions of these cyclic singular cosmologies are reviewed here as a function of real and imaginary shift parameter. We also notice the modulated zero modes obtained by using the general Riccati solution and comment on their cosmological application."

Article

Barotropic FRW cosmologies Cosmological zero-modes Shifted Riccati procedure Factorization CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA

Shifted one-parameter supersymmetric family of quartic asymmetric double-well potentials

HARET CODRATIAN ROSU (2014)

"Extending our previous work (Rosu, Mancas, Chen, Ann.Phys. 343 (2014) 87-102), we define supersymmetric partner potentials through a particular Riccati solution of the form F(x) = (x − c)2 − 1, where c is a real shift parameter, and work out the quartic double-well family of oneparameter isospectral potentials obtained by using the corresponding general Riccati solution. For these parametric double well potentials, we study how the localization properties of the two wells depend on the parameter of the potentials for various values of the shifting parameter. We also consider the supersymmetric parametric family of the first double-well potential in the Razavy chain of double well potentials corresponding to F(x) = 1/2 sinh 2x−2 (1+p2) sinh 2x/(1+p2) cosh 2x+1 , both unshifted and shifted, to test and compare the localization properties."

Article

Shifted quartic double well Razavy potential Zero mode Localization Riccati solution Darboux deformation. CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA

An amplitude-phase (Ermakov–Lewis) approach for the Jackiw–Pi model of bilayer graphene

HARET CODRATIAN ROSU (2009)

"In the context of bilayer graphene we use the simple gauge model of Jackiw and Pi to construct its numerical solutions in powers of the bias poten-tial V according to a general scheme due to Kravchenko. Next, using this numerical solutions, we develop the Ermakov-Lewis approach for the same model. This leads us to numerical calculations of the Lewis-Riesenfeld phases that could be of forthcoming experimental interest for bilayer graphene. We also present a generalization of the Ioﬀe-Korsch nonlinear Darboux transformation."

Article

Condensed matter: electrical, magnetic and optical Surfaces, interfaces and thin films Nanoscale science and low-D systems CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA

Barotropic FRW cosmologies with Chiellini damping in comoving time

HARET CODRATIAN ROSU (2015)

"For non-zero cosmological constant Λ, we show that the barotropic FRW cosmologies as worked out in the comoving time lead in the radiation-dominated case to scale factors of identical form as for the Chiellini dissipative scale factors in conformal time obtained recently by us in Phys. Lett. A 379 (2015) 882-887. This is due to the Ermakov equation which is obtained in this case. For zero cosmological constant, several textbook solutions are provided as particular cases of Λ = 0."

Article

Barotropicfluid FRW cosmology Cosmological constant CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA

A note on Verhulst's logistic equation and related logistic maps

HARET CODRATIAN ROSU (2010)

"We consider the Verhulst logistic equation and a couple of forms of the corresponding logistic maps. For the case of the logistic equation we show that using the general Riccati solution only changes the initial conditions of the equation. Next, we consider two forms of corresponding logistic maps reporting the following "

Article

Computational physics Environmental and Earth science Statistical physics and nonlinear systems CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA

Newton’s laws of motion in the form of a Riccati equation

HARET CODRATIAN ROSU (2002)

"We discuss two applications of a Riccati equation to Newton’s laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=krε. For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems."

Article

One-parameter isospectral special functions

HARET CODRATIAN ROSU (2003)

"Using a combination of the ladder operators of Pina [1] and the Pammetric operators of Mielnik [2] we introduce second order linear differential equations whose eigenfunctions are isospectral to the special functions of the mathematical physics and illustrate the method with several key examples."

"Usando una combinación de los operadores de escalera de Piña [1] y de los operadores parametricos de Mielnik [2] introducimos operadores lineales de segundo orden con eigenfunciones que son formas isoespectrales de las funciones especiales de la física matemática y presentamos algunos ejemplos básicos."

Article

Supersymmetry Riccati equation Liouville operators Supersimetría Ecuación de Riccati Operadores de Liouville CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA

Transform of Riccati equation of constant coefficients through fractional procedure

HARET CODRATIAN ROSU (2003)

"We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term expressed as a power of the independent variable which is of the same order as the order of the applied fractional derivative. We provide the solutions of the modified equation and employ the results for the case of the cosmological Riccati equation of FRW barotropic cosmologies that has been recently introduced by Faraoni."

Article

FOKKER-PLANCK EQUATION ANOMALOUS DIFFUSION COSMOLOGICAL FLUIDS DYNAMICS CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA

Mutually unbiased phase states, phase uncertainties, and Gauss sums

HARET CODRATIAN ROSU (2005)

"Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1/d√, with d the dimension of the finite Hilbert space, are becoming more and more studied for applications such as quantum tomography and cryptography, and in relation to entangled states and to the Heisenberg-Weil group of quantum optics. Complete sets of MUBs of cardinality d+1 have been derived for prime power dimensions d=pm using the tools of abstract algebra. Presumably, for non prime dimensions the cardinality is much less. Here we reinterpret MUBs as quantum phase states, i.e. as eigenvectors of Hermitian phase operators generalizing those introduced by Pegg and Barnett in 1989. We relate MUB states to additive characters of Galois fields (in odd characteristic p) and to Galois rings (in characteristic 2). Quantum Fourier transforms of the components in vectors of the bases define a more general class of MUBs with multiplicative characters and additive ones altogether. We investigate the complementary properties of the above phase operator with respect to the number operator. We also study the phase probability distribution and variance for general pure quantum electromagnetic states and find them to be related to the Gauss sums, which are sums over all elements of the field (or of the ring) of the product of multiplicative and additive characters. Finally, we relate the concepts of mutual unbiasedness and maximal entanglement. This allows to use well studied algebraic concepts as efficient tools in the study of entanglement and its information aspects."

Article

Adsorption of molecular gases on porous materials in the SAFT-VR approximation

HARET CODRATIAN ROSU (2010)

"A simple molecular thermodynamic approach is applied to the study of the adsorption of gases of chain molecules on solid surfaces. We use a model based on the Statistical Associating Fluid Theory for Variable Range (SAFT-VR) potentials [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, A. N. Burgess, J. Chem. Phys. 106 (1997) 4168] that we extend by including a quasi-two-dimensional approximation to describe the adsorption properties of this type of real gases [A. Mart´ınez, M. Castro, C. McCabe, A. Gil-Villegas, J. Chem. Phys. 126 (2007) 074707]. The model is applied to ethane, ethylene, propane, and carbon dioxide adsorbed on activated carbon and silica gel, which are porous media of signiﬁcant industrial interest. We show that the adsorption isotherms obtained by means of the present SAFT-VR modeling are in fair agreement with the experimental results provided in the literature."

Article

Adsorption Statistical associating ﬂuid Helmholtz free energy Porous material CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA