Related papers: General Properties of Two-dimensional Conformal Tr…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
A powerful technique is introduced for simulating mechanical and electromechanical properties of one-dimensional nanostructures under arbitrary combinations of bending, twisting, and stretching. The technique is based on a novel control of…
Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often…
We develop a theory of nonlinear response to an electric field of a two-dimensional electron gas (2DEG) placed in a classically strong magnetic field. The latter leads to a non-linear current-voltage characteristic at a relatively weak…
We study non-linear phenomena in double barrier heterostructures. Systems in 3D under the effect of an external magnetic field along the current and 1D systems are analyzed. Non-linearities are reflected in the I-V characteristic curve as…
This article reviews the static and dynamic properties of spontaneous superstructures formed by electrons. Representations of such electronic crystals are charge density waves and spin density waves in inorganic as well as organic low…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
The technique of transformation optics (TO) is an elegant method for the design of electromagnetic media with tailored optical properties. In this paper, we focus on the formal structure of TO theory. By using a complete covariant…
We show that the the cyclotron resonance in a two-dimensional electron gas has non-trivial properties if the correlation length of the disorder is larger than the de Broglie wavelength: (a) the lineshape assumes three different forms in…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
A study of the $\lambda$- and $N$-atomic configurations under dipolar interaction with $2$ modes of electromagnetic radiation is presented. The corresponding quantum phase diagrams are obtained by means of a variational procedure. Both…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
Geometrical properties of two-dimensional mixtures near the jamming transition point are numerically investigated using harmonic particles under mechanical training. The configurations generated by the quasi-static compression and…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
Two-dimensional electron systems with fascinating properties exist in multilayers of standard semiconductors, on helium surfaces, and in oxides. Compared to the two-dimensional (2D) electron gases of semiconductors, the 2D electron systems…
The conductance of a disordered finite-size electron system is calculated by reducing the initial dynamic problem of arbitrary dimensionality to strictly one-dimensional problems for one-particle mode propagators. The metallic ground state…
The electronic properties of two-dimensional materials and their heterostructures can be dramatically altered by varying the relative angle between the layers. This makes it theoretically possible to realize a new class of twistable…
We present a model which provides a plausible explanation of the effect of zero-resistance and zero-conductance states in two-dimensional electron systems subjected to a magnetic field and irradiated with microwaves observed in a number of…
We consider a pair of artificial atoms with different ground state energies. By means of finite element calculations we predict that the ground state energies can be tuned into resonance if the artificial atoms are placed into a flexible…
The conductance of disordered nano-wires at T=0 is calculated in one-particle approximation by reducing the original multi-dimensional problem for an open bounded system to a set of exactly one-dimensional non-Hermitian problems for mode…