Related papers: Method of difference-differential equations for so…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
A quasi-one-dimensional Bose-Einstein condensate loaded into a quasi-periodic potential created by two sub-lattices of comparable amplitudes and incommensurate periods is considered. Although the conventional tight-binding approximation is…
We propose discrete TBA equations for models with discrete spectrum. We illustrate our construction on the Calogero-Moser model and determine the discrete 2-body TBA function which yields the exact N-body Calogero-Moser thermodynamics. We…
We study the interplay of quantum statistics, strong interactions and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain…
In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme…
We study a relativistic scalar field model for self-bound Bose-Einstein condensates (BECs) by analyzing a nonlinear Klein-Gordon equation with cubic and logarithmic interactions. This framework captures essential features of quantum…
Irrotational ow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrodinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by…
We study the symmetry reduction of nonlinear partial differential equations which are used for describing diffusion processes in nonhomogeneous medium. We find ansatzes reducing partial differential equations to systems of ordinary…
The coordinate Bethe Ansatz solution of the log-gamma polymer is extended to boundary conditions with one fixed end and the other attached to one half of a one-dimensional lattice. The large-time limit is studied using a saddle-point…
Measuring the full distribution of individual particles is of fundamental importance to characterize many-body quantum systems through correlation functions at any order. Here we demonstrate the possibility to reconstruct the momentum-space…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe…
The equation of motion for the two-fermion two-time correlation function in the pairing channel is considered at finite temperature. Within the Matsubara formalism, the Dyson-type Bethe-Salpeter equation (Dyson-BSE) with the…
A gauge-invariant Wigner quantum mechanical theory is obtained by applying the Weyl-Stratonovich transform to the von Neumann equation for the density matrix. The transform reduces to the Weyl transform in the electrostatic limit, when the…
Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present. In this work, we rigorously address this issue and put forth an exact representation of…
Finite-difference Lattice Boltzmann (LB) models are proposed for simulating gas flows in devices with microscale geometries. The models employ the roots of half-range Gauss-Hermite polynomials as discrete velocities. Unlike the standard LB…
For the one-dimensional repulsive Bose gas (Lieb-Liniger model), we study a special class of highly-excited states obtained by giving a finite momentum to subgroups of particles. These states, which correspond to `splitting' the ground…
We study the out of equilibrium steady state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low…
The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the…