Related papers: Experimental evidence of variable-order behavior o…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
It is known that the gradient method can be viewed as a dynamic system where various iterative schemes can be designed as a part of the closed loop system with desirable properties. In this paper, the finite-time and fixed-time convergence…
The origin of the non commutativity of the limits $t \to \infty$ and $N \to \infty$ in the dynamics of first order transitions is investigated. In the large-N model, i.e. $N \to \infty$ taken first, the low temperature phase is…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
The hunt for exotic quantum phase transitions described by emergent fractionalized degrees of freedom coupled to gauge fields requires a precise determination of the fixed point structure from the field theoretical side, and an extreme…
We consider a fractionally damped oscillator, where the damping term is expressed by the Caputo fractional derivative of order $\beta\in (0,1).$ The impulse response of this oscillator can be expressed in terms of the bivariate…
We study dense mixtures of passive and active self-aligning disks with isotropic or anisotropic mobility. We find that the passive fraction controls an order-disorder transition that is continuous in the isotropic case and discontinuous in…
In this brief review, we introduce a new spin ladder system called skewed spin ladders and discuss the exotic quantum phases of this system. The spin ladders studied are the 5/7, 3/4 and 3/5 systems corresponding to alternately fused 5 and…
The liquid-to-ordered phase transition in a bilayer system of fermions is studied within the context of a recently proposed density-functional theory [Phys. Rev. A {\bf 92}, 023614 (2015)]. In each two-dimensional layer, the fermions…
The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fr\"ohlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum…
The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between…
We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a "crystalline" configuration to that of a disordered state that can be characterized as a soliton "gas". As…
An exactly soluble one-dimensional model of electrons interacting with order parameter fluctations associated with short-range order is considered. The energy and momentum dependence of the electronic self energy and spectral function are…
We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ Basing on the finite-difference Gr\"{u}nwald-Letnikov…
The subject of fractional calculus has witnessed rapid development over past few decades. In particular the area of fractional differential equations has received considerable attention. Several theoretical results have been obtained and…
We investigate, through the density-matrix renormalization group and the Lanczos technique, the possibility of a two-leg Kondo ladder present an incommensurate orbital order. Our results indicate a staggered short-range orbital order at…
One-dimensional metals, such as quantum wires or carbon nanotubes, can carry charge in arbitrary units, smaller or larger than a single electron charge. However, according to Luttinger theory, which describes the low-energy excitations of…
We investigate the effect of a dynamical collective mode coupled with quasiparticles at specific wavevectors only. This coupling describes the incipient tendency to order and produces shadow spectral features at high energies, while leaving…
In complex electronic materials, coupling between electrons and the atomic lattice gives rise to remarkable phenomena, including colossal magnetoresistance and metal-insulator transitions. Charge-ordered phases are a prototypical…
We consider an off-lattice liquid crystal pair potential in strictly two dimensions. The potential is purely repulsive and short-ranged. Nevertheless, by means of a single parameter in the potential, the system is shown to undergo a…