International Journal of Modern Physics B

Hans Bethe's doctoral research was primarily in solid-state physics. During the late 1920's and early 1930's he played a major role in developing the new quantum theory of solids. Though nuclear physics became his main interest in the mid 1930's, he continued to write papers in solid-state physics into the late 1940's, and remained interested in the subject all his life.

An alternative wavefunction to the description of the dynamic localization of a charged particle moving on a one-dimensional lattice under the influence of a periodic time dependent electric field is written down. For this purpose the method of characteristics such as applied by Dunlap and Kenkre [Phys. Rev. B34, 3625 (1986)] has been modified by using a different integration variable. Handling this wavefunction one is faced with the selection of admissible time values. This results in a conditionally exactly solvable problem, now by accounting specifically for the implementation of a time discretization working in conjunction with a related dynamic localization condition. In addition, one resorts to the strong field limit, which amounts to replace, to leading order, the large order zeros of the Bessel function J₀(z), used before in connection with the cosinusoidal modulation, by integral multiples of π. Here z stands for the ratio between the field amplitude and the frequency. The modulation function of the electric field vanishes on the nodal points of the time grid, which stands for an effective field-free behavior. This opens the way to propose quickly tractable dynamic localization conditions for arbitrary periodic modulations. We have also found that the present time discretization approach produces the minimization of the mean square displacement characterizing the usual exact wavefunction. Other realizations and comparisons have also been presented.

This paper presents an active control method for controlling general uncertain chaotic systems with parameters perturbation. And a sufficient condition is drawn for the stability of the controlled chaotic systems and is applied to guiding the design of the controllers. Finally, numerical results are used to show the robustness and effectiveness of the proposed control strategy.

Squeezing of the electromagnetic field is a purely quantum mechanical phenomenon and this quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. It has generated a great deal of interest in view of the possibility of reducing the noise of an optical signal below the vacuum limit i.e. zero-point oscillations. In this paper the concept of nth-order amplitude squeezing is introduced in the fundamental mode in four- and six-wave mixing processes as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. It established the coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing upto n=3 are studied. Dependence of squeezing on photon number is also established. The conditions for obtaining maximum and minimum squeezing are obtained. The method of present investigation can be applied to any higher-order non-linear optical processes and the technique can also be extended for studying squeezing in any N-photon process in general. Further, nth-order squeezing of radiation in N-photon process can also be investigated. The results obtained may help in selecting a suitable process to generate optimum squeezing in the radiation field.

We present a numerical study of the influence of junction-geometries and disorder on quantum-mechanical transmission by considering the presence of an impurity in a wide-narrow-wide (W-N-W) quantum-wire junction. The device is modeled as an electron waveguide of finite cross section. Transmission and reflection probabilities as well as conductance are computed by using model expansions of the wave function together with a waveguide-matching technique. The calculations show that the transmission of the two-dimensional electron gas through the W-N-W geometry is highly sensitive to geometries of junction and can be suppressed by the presence of a repulsive or attractive impurity potential. Furthermore, the depression effect becomes more visible if the absolute value of potential strength becomes bigger.

By using unitary transformation and representation theory of quantum mechanics, we obtain two forms of density matrix respectively in (x₁, p₂) and (x₁, x₂) representations for an electron, with an anisotropic effective mass, confined in quantum dots under a uniform magnetic field (UMF). We find that both forms of density matrix can play an implemental role in the thermodynamical calculation. But, in order to calculate thermal average of angular momentum in z direction for this system, the density matrix in (x₁, p₂) representations is a more convenient form. When the confinement to electron in quantum dots disappears, we encounter a divergence problem of thermal average for some physical quantities. However, in the calculation of the thermal average of Hamiltonian, these divergent quantities cancelled each other out. And we eventually obtain a reasonable result.

The conductance anomaly behavior for superconductor-semiconductor-superconductor junctions is investigated. We propose a potential profile at the interface which depends on the intrinsic parameters of the junctions, e.g. carrier concentration. The tunneling probability is derived by the WKB method and the corresponding conductance is expressed in terms of the tunneling probability through Landauer–Buttiker formula. The results show a zero-bias anomaly (ZBA) for the dependence of conductance on bias voltage. Also, the oscillatory behavior of the conductance with the magnetic field, due to the chaotic behavior of the junction.

In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator

For the case α=1,β=1 and mass m real, we find the eigenfunctions and eigenvalues of energy, the coherent states, the time evolution of the operators in the Heisenberg picture and the uncertainty relations. In this case the operator ℋ is Hermitian and PT-symmetric. Also for the case m complex α=1,β=1, the operator ℋ is non-Hermitian and no more PT symmetric, but CPT symmetric with real discrete positive spectrum and the CPT symmetry is preserved. In the general case α,β,m complex, for the non-Hermitian operator ℋ, we obtain complex spectrum and for the special values of the complex parameters α,β the spectrum is real discrete and positive and the CPT symmetry is preserved. The general problem of deformed oscillator for non hermitian operators can be applied to the Solid State Physics.

Electron clusters, X-rays and nanosecond radio-frequency pulses are produced by 100 mW continuous-wave laser illuminating ferroelectric crystal of LiNbO₃. A long-living stable electron droplet with the size of about 100μm has freely moved with the velocity ~0.5 cm/s in the air near the surface of the crystal experiencing the Earth gravitational field. The microscopic model of cluster stability, which is based on submicroscopic mechanics developed in the real physical space, is suggested. The role of a restraining force plays the inerton field, a substructure of the particles' matter waves, which a solitary one can elastically withstand the Coulomb repulsion of electrons. It is shown that electrons in the droplet are heavy electrons whose mass exceeds the rest mass of free electron at least 1 million of times. Application for X-ray imaging and lithography is discussed.