Related papers: Solitons in a one-dimensional Wigner crystal
Strongly interacting solitons confined to an optical resonator would offer unique capabilities for experiments in communication, computation, and sensing with light. Here we report on the discovery of soliton crystals in monolithic Kerr…
We investigate the low density limit of the Homogeneous Electron system, often called the {\it Strictly Correlated} regime. We begin with a systematic presentation of the expansion around infinite $r_S$, based on the first quantized…
The stabilization of one-dimensional solitons by a nonlinear lattice against the critical collapse in the focusing quintic medium is a challenging issue. We demonstrate that this purpose can be achieved by combining a…
Coupled semiconductor quantum dots form artificial molecules where relevant energy scales controlling the interacting ground state can be easily tuned. By applying an external magnetic field it is possible to drive the system from a weak to…
Wigner crystallization in mesoscopic quantum dots containing only few ($N < 50$) electrons exhibits a number of interesting peculiarities: (i) there exist two distinct crystal phases, and (ii) the phase boundary sensitively depends on the…
We numerically generate, and then study the basic properties of dark soliton-like excitations in a dipolar gas confined in a quasi one dimensional trap. These excitations, although very similar to dark solitons in a gas with contact…
The Wigner time delay of slow particles in the process of their elastic scattering by complex targets formed by several zero-range potentials is investigated. It is shown that at asymptotically large distances from the target, the…
We report the numerical realization and demonstration of robustness of certain 2-component structures in Bose-Einstein Condensates in 2 and 3 spatial dimensions with non-trivial topological charge in one of the components. In particular, we…
We demonstrate that unrestricted Hartree-Fock theory applied to electrons in a uniform potential has stable Wigner crystal solutions for $r_s \geq 1.44$ in two dimensions and $r_s \geq 4.5$ in three dimensions. The correlation energies of…
Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal…
We consider the formation and stability of the vibronic polaron arising in a degenerate or nearly degenerate electronic system coupled to an appropriate vibrational mode. We define the electron-phonon coupling as a mixing of the electronic…
Excitons in low-dimensional materials behave mathematically as confined hydrogen atoms. An appealing unified description of confinement in quantum wells or wires, etc., is found by restricting space to a fractional dimension 1 < D <= 3…
The energy band structure of excitons is studied in periodic potentials produced by the short-range interaction between the exciton and electrons of Wigner or Moir\'{e} lattices. Treating the exciton as a point-like dipole that interacts…
The crystalline or liquid character of the downward cusp states in N-electron parabolic quantum dots (QD's) at high magnetic fields is investigated using conditional probability distributions obtained from exact diagonalization. These…
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities and numerically find…
Quantum and classical integrable systems share common mathematical structures, and the phenomena appearing in them are interrelated. Solitons, which universally appear in classical integrable systems, also appear in quantum integrable…
The influence of long-range Coulomb interactions on the properties of one-dimensional (1D) strongly correlated electron systems in vicinity of the metal-insulator phase transition is considered. It is shown that unscreened repulsive Coulomb…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
Peierls distortion and quantum solitons are two hallmarks of 1-dimensional condensed-matter systems. Here we propose a quantum model for a one-dimensional system of non-linearly interacting electrons and phonons, where the phonons are…
The dynamics of quasicrystals is characterized by the existence of phason excitations in addition to the usual phonon modes. In order to investigate their interplay on an elementary level we resort to various one-dimensional model systems.…