Related papers: Form factor approach to dynamical correlation func…
This article presents factor copula approaches to model temporal dependency of non-Gaussian (continuous/discrete) longitudinal data. Factor copula models are canonical vine copulas which explain the underlying dependence structure of a…
The q-model is a random walk model used to describe the flow of stress in a stationary granular medium. Here we derive the exact horizontal and vertical correlation functions for the q-model in two dimensions. We show that close to a…
The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is…
Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with…
Linear response theory and Green's functions provide a universal framework for understanding dynamical correlations in strongly correlated open quantum systems. While the theoretical foundation for non-Hermitian linear response has been…
The one-dimensional hard rod model describes impenetrable bosons with finite diameter, extending the Lieb-Liniger model to systems with excluded volume interactions. Here, we investigate the thermodynamics of quantum HRs using Yang-Yang…
The Calogero-Sutherland model represents a paradigmatic example of an integrable quantum system with applications ranging from cold atoms to random matrix theory. Combining sum rules with the Monte Carlo technique, we introduce a stochastic…
We present a quantum theory for the dynamic structure factors in non-equilibrium, correlated, two-component systems such as plasmas or warm dense matter. Using this general framework, we derive expressions for effective local field…
We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schr\"odinger equation. We examine how the fractional derivative order $\alpha$ influences non-classical…
It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…
In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are…
We study a simple model of a quantum Hall system with the electrons confined to a linear, narrow channel. The system is mapped to a 1D system which in the low-energy approximation has the form of a Luttinger liquid with different…
We derive an analytic expression for the zero temperature Fourier transform of the density-density correlation function of a multicomponent Luttinger liquid with different velocities. By employing Schwinger identity and a generalized…
We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ The description of the singularities of dynamic response functions near an edge $\epsilon(k)$ is…
We apply the recently developed thermal form factor expansion method to evaluate the real-time longitudinal spin-spin correlation functions of the spin-$\frac{1}{2}$ XXZ chain in the antiferromagnetically ordered regime at temperature…
For various one-dimensional quantum liquids in the framework of the Luttinger model (bosonization) we establish the relations between the coefficients before the power-law asymptotics of the correlators (prefactors) and the formfactors of…
Driven critical dynamics in quantum phase transitions holds significant theoretical importance, and also practical applications in fast-developing quantum devices. While scaling corrections have been shown to play important roles in fully…
Coupled nonlinear Schr\"odinger equations model various physical phenomena, such as wave propagation in nonlinear optics, multi-component Bose-Einstein condensates, and shallow water waves. Despite their extensive applications, analytical…
The spinless fermion model with hard core repulsive potential extended on a few lattice sites is considered.The Luttinger liquid behaviour is studied for the different values of a hard core radius. A critical exponent of the one particle…
We have developed a method for complementing an arbitrary classical dynamical system to a quantum system using the Lorenz and R\"ossler systems as examples. The Schr\"odinger equation for the corresponding quantum statistical ensemble is…