Related papers: Dynamics of the Fermion-Rotor System
The Jordan-Wigner transformation is known as a powerful tool in condensed matter theory, especially in the theory of low-dimensional quantum spin systems. The aim of this chapter is to review the application of the Jordan-Wigner…
We propose a new low-energy theory for itinerant fermions near a ferromagnetic quantum critical point. We show that the full low-energy model includes, in addition to conventional interaction via spin fluctuations, another type of…
It is generally believed that the 1+1D model for a single chiral fermion does not exist by itself alone on lattice. The obstruction to such a lattice realization is the failure to reproduce the quantum anomalies of a chiral fermion in…
We review the intriguing many-body physics resulting out of the interplay of a single, local impurity and the two-particle interaction in a one-dimensional Fermi system. Even if the underlying homogeneous correlated system is taken to be…
We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using such variables as the object location, the surface concentration of active molecules and the hydrodynamic surface…
The behavior of coupled harmonic oscillators in systems with specified boundary conditions is typically characterized by resonances whose frequency spectra represent harmonics according to properties of the individual oscillators, the…
The quantum three-rotor problem concerns the dynamics of 3 equally massive particles moving on a circle subject to pairwise attractive cosine potentials and can model coupled Josephson junctions. Classically, it displays order-chaos-order…
Quantized vortices carry the angular momentum in rotating superfluids, and are key to the phenomenon of quantum turbulence. Advances in ultra-cold atom technology enable quantum turbulence to be studied in regimes with both experimental and…
We revisit the problem of dynamical response in spin-charge separated one dimensional quantum fluids. In the framework of Luttinger liquid theory, the dynamical response is formulated in terms of noninteracting bosonic collective…
Fermionic Molecular Dynamics (FMD) models a system of fermions by means of many-body states which are composed of antisymmetrized products of single-particle states. These consist of one or several Gaussians localized in coordinate and…
The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide…
We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions ($d=2,3$). We show that in both cases nontrivial topology is manifested by the presence of the $(d-2)$-dimensional edge…
We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasi-energy which is…
The static and dynamics properties of finite-size lattice quantum spin models which spontaneously break a continuous $U(1)$ symmetry in the thermodynamic limit are of central importance for a wide variety of physical systems, from condensed…
We review the theory of interacting Fermi systems whose low-energy physics is governed by forward scattering, i.e. scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids…
We present a numerical analysis of spin-$\frac{1}{2}$ fermions in a one-dimensional harmonic potential in the presence of a magnetic point-like impurity at the center of the trap. The model represents a few-body analogue of a magnetic…
The scattering of Dirac fermions in the background fields of topological solitons of the $(2+1)$-dimensional $\mathbb{CP}^{N-1}$ model is studied using analytical and numerical methods. It is shown that the exact solutions for fermionic…
We analyze the out-of-time-order correlation functions of a solvable model of a large number, $N$, of $M$-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. We focus on the growth of…
The quantum rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a $d$-dimensional model in the spherical approximation confined to a general…
Currently, there is much interest in discovering analytically tractable (3+1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of…