Related papers: Localised and nonlocalised structures in nonlinear…
We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites…
This work establishes the algebraic structure of the Kohn-Sham equations to be solved in a density formulation of electron and phonon dynamics, including the superconducting order parameter. A Bogoliubov transform is required to diagonalize…
It is shown that the mean-field description of a boson-fermion mixture with a dominating fermionic component, loaded in a one-dimensional optical lattice, is reduced to the nonlinear Schr\"{o}dinger equation with a periodic potential and…
We apply a recently proposed path-integral approach to non-local bosonization to a Thirring-like system modeling non-relativistic massless particles interacting with localized fermionic impurities. We consider forward scattering processes…
A system of nonlocal electron-transport equations for small perturbations in a magnetized plasma is derived using the systematic closure procedure of V. Yu. Bychenkov et al., Phys. Rev. Lett. 75, 4405 (1995). Solution to the linearized…
Several families of nonlinear field equations are known to possess space- localized singularity-free solutions which describe fields with finite Hermitian norms. This paper studies the interaction of such fields with given electromagnetic…
We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing.…
Contrary to the common wisdom, local bosonizations of fermionic systems exist in higher dimensions. Interestingly, resulting bosonic variables must satisfy local constraints of a gauge type. They effectively replace long distance exchange…
A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear…
We present the spin-wave theory of the excitation spectrum and quench dynamics of the non-Hermitian transverse-field Ising model. The complex excitation spectrum is obtained for a generic hypercubic lattice using the linear approximation of…
While condensed matter systems host both Fermionic and Bosonic quasi-particles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations…
This work deals with fermions in the background of distinct localized structures in the two-dimensional spacetime. Although the structures have similar topological character, which is responsible for the appearance of fractionally charged…
We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization. We…
We present a bosonization procedure which replaces fermions with generalized spin variables subject to local constraints. It requires that the number of Majorana modes per lattice site matches the coordination number modulo two. If this…
A general form of a many-body Hamiltonian is considered, which includes an interacting fermionic sub-system coupled to non-interacting extended fermionic and bosonic systems. We show that the exact dynamics of the extended bosonic system…
When high-frequency sound waves travel through media with anomalous diffusion, such as biological tissues, their motion can be described by nonlinear wave equations of fractional higher order. These can be understood as nonlocal…
A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
We address ourselves to a class of systems composed of two coupled subsystems without any intra-subsystem interaction: itinerant Fermions and localized Bosons on a lattice. Switching on an interaction between the two subsystems leads to…
We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. At non-half-fillings, a superfluid-supersolid transition occurs at intermediate boson-phonon couplings, while at…