Modern Physics Letters B

We consider the time evolution of a two level system (a two level atom or a qubit) and show that it is characterized by a local (in time) gauge invariant evolution equation. The covariant derivative operator is constructed and related to the free energy. We show that the gauge invariant characterization of the time evolution of the two level system is analogous to the birefringence phenomenon in optics. The relation with Berry-like and Anandan–Aharonov phase is pointed out. Finally, we discuss entropy, environment effects and the distance in projective Hilbert space between two level states in their evolution.

A detailed study of the effect caused by the partial substitution of Er by Ce on fluctuation conductivity of the Er_1-xCe_xBa₂Cu₃O_7-δ; 0 ≤ x ≤ 0.10; is presented. The combined experimental results of structural and electrical measurements indicate that Ce substitutes Er for x ≤ 0.10 with no significant structural distortions. However, there is suppression of the superconducting state with zero-resistance state at temperatures ≥ 86.3 K. The results were analyzed in terms of the temperature derivative of the resistivity and the logarithmic temperature derivative of the conductivity to identify power-law divergences of the conductivity. The data revealed the occurrence of a two-stage intragranular-intergranular transition. Above the critical temperature, the Gaussian and critical regimes were observed. Also, from the critical exponents analysis, we observed a splitting of the pairing transition for Ce-doped samples, suggesting the occurrence of a phase separation. On approaching the zero resistance state, our results showed a power-law behavior that corresponds to a phase transition from a paracoherent to a coherent state of the granular array and which does not depend on Ce doping.

Under investigation in this paper is a generalized variable-coefficient Korteweg–de Vries (vcKdV) model with external-force and perturbed/dissipative terms, which can describe various real dynamical processes of physics from atmosphere blocking and gravity waves, blood vessels, Bose–Einstein condensates, rods and positons and so on. With the aid of symbolic computation, a generalized Miura transformation is proposed to relate the solutions of the vcKdV equation to those of a variable-coefficient modified Korteweg–de Vries equation. Then by using such a Miura transformation and the Galilean invariant transformation, the existence of infinite conservation laws are proved under the Painlevé integrable condition. These results may be valuable for the new discoveries in dynamical systems described by integrable vcKdV models and the theoretical study of the relationships among infinite conservation laws, the integrability of the nonlinear evolution equation and inverse scattering transform.

The scattering properties of one-dimensional potential with gain are studied by using a Schrödinger-like equation. The corresponding Hamiltonian is non-Hermitian with a real energy spectrum. The amplification-absorption duality previously observed is interpreted in terms of the transmission and reflection phases. For a rectangular barrier, the transmission phase oscillates with the barrier width as for passive systems, but the oscillations period is significantly reduced in the absorption region. In this region the reflection phase vanishes and the multiple scattering and interferences dominate. The gain effect is also investigated for double barrier structures as well as superlattices with active potentials. It is found that resonant tunneling energy and the mini-band width are not influenced by the gain, but the transmission is enhanced for small values of the potential imaginary part. For large values, the resonant transmission significantly decreases and the mini-bands disappear.

We use the Kondo lattice model to investigate the possibility of ferromagnetism and half-metallicity in local moment systems. Using the spectral density approach and making use of the fact that the spontaneous magnetization of local moment and the itinerant electron polarization are coupled, we derive an expression for the paramagnetic susceptibility. The magnetic ordering temperature is determined from the singularities of the susceptibility. The magnetic phase diagram is constructed in T - n (band filling) plane. It is found that ferromagnetism is possible only for small values of n. It is also found that the temperature drives the transition of the system from half-metal to metal.

The optical polaron confined to quantum well with tunable dimensions is investigated within the framework of a variational technique intending to give a unified characterization of problem for all the coupling strengths. The ground state energy and the number of phonons around the electron are studied as a function of the degree of confinement of the quantum well to interpolate between all possible confinement geometries. A comparison is made with the pure strong-coupling and the pure weak-coupling theories and a good agreement is obtained.